From 79b18eed68a394b9139745c98624da893247b97d Mon Sep 17 00:00:00 2001
From: "github-actions[bot]" <github-actions[bot]@users.noreply.github.com>
Date: Sat, 19 Oct 2024 09:48:32 +0000
Subject: [PATCH] deploy:
 ShangjinTang/docusaurus@3653c62ac98c439af56e43cd4a18809aebeac944

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e}},D.stopWordFilter=D.generateStopWordFilter(["a","able","about","across","after","all","almost","also","am","among","an","and","any","are","as","at","be","because","been","but","by","can","cannot","could","dear","did","do","does","either","else","ever","every","for","from","get","got","had","has","have","he","her","hers","him","his","how","however","i","if","in","into","is","it","its","just","least","let","like","likely","may","me","might","most","must","my","neither","no","nor","not","of","off","often","on","only","or","other","our","own","rather","said","say","says","she","should","since","so","some","than","that","the","their","them","then","there","these","they","this","tis","to","too","twas","us","wants","was","we","were","what","when","where","which","while","who","whom","why","will","with","would","yet","you","your"]),D.Pipeline.registerFunction(D.stopWordFilter,"stopWordFilter"),D.trimmer=function(e){return e.update((function(e){return e.replace(/^\W+/,"").replace(/\W+$/,"")}))},D.Pipeline.registerFunction(D.trimmer,"trimmer"),D.TokenSet=function(){this.final=!1,this.edges={},this.id=D.TokenSet._nextId,D.TokenSet._nextId+=1},D.TokenSet._nextId=1,D.TokenSet.fromArray=function(e){for(var t=new D.TokenSet.Builder,n=0,r=e.length;n<r;n++)t.insert(e[n]);return t.finish(),t.root},D.TokenSet.fromClause=function(e){return"editDistance"in e?D.TokenSet.fromFuzzyString(e.term,e.editDistance):D.TokenSet.fromString(e.term)},D.TokenSet.fromFuzzyString=function(e,t){for(var n=new D.TokenSet,r=[{node:n,editsRemaining:t,str:e}];r.length;){var a=r.pop();if(a.str.length>0){var o,i=a.str.charAt(0);i in a.node.edges?o=a.node.edges[i]:(o=new D.TokenSet,a.node.edges[i]=o),1==a.str.length&&(o.final=!0),r.push({node:o,editsRemaining:a.editsRemaining,str:a.str.slice(1)})}if(0!=a.editsRemaining){if("*"in a.node.edges)var s=a.node.edges["*"];else{s=new D.TokenSet;a.node.edges["*"]=s}if(0==a.str.length&&(s.final=!0),r.push({node:s,editsRemaining:a.editsRemaining-1,str:a.str}),a.str.length>1&&r.push({node:a.node,editsRemaining:a.editsRemaining-1,str:a.str.slice(1)}),1==a.str.length&&(a.node.final=!0),a.str.length>=1){if("*"in a.node.edges)var l=a.node.edges["*"];else{l=new D.TokenSet;a.node.edges["*"]=l}1==a.str.length&&(l.final=!0),r.push({node:l,editsRemaining:a.editsRemaining-1,str:a.str.slice(1)})}if(a.str.length>1){var c,u=a.str.charAt(0),d=a.str.charAt(1);d in a.node.edges?c=a.node.edges[d]:(c=new D.TokenSet,a.node.edges[d]=c),1==a.str.length&&(c.final=!0),r.push({node:c,editsRemaining:a.editsRemaining-1,str:u+a.str.slice(2)})}}}return n},D.TokenSet.fromString=function(e){for(var t=new D.TokenSet,n=t,r=0,a=e.length;r<a;r++){var o=e[r],i=r==a-1;if("*"==o)t.edges[o]=t,t.final=i;else{var s=new D.TokenSet;s.final=i,t.edges[o]=s,t=s}}return n},D.TokenSet.prototype.toArray=function(){for(var e=[],t=[{prefix:"",node:this}];t.length;){var n=t.pop(),r=Object.keys(n.node.edges),a=r.length;n.node.final&&(n.prefix.charAt(0),e.push(n.prefix));for(var o=0;o<a;o++){var i=r[o];t.push({prefix:n.prefix.concat(i),node:n.node.edges[i]})}}return e},D.TokenSet.prototype.toString=function(){if(this._str)return this._str;for(var e=this.final?"1":"0",t=Object.keys(this.edges).sort(),n=t.length,r=0;r<n;r++){var a=t[r];e=e+a+this.edges[a].id}return e},D.TokenSet.prototype.intersect=function(e){for(var t=new D.TokenSet,n=void 0,r=[{qNode:e,output:t,node:this}];r.length;){n=r.pop();for(var a=Object.keys(n.qNode.edges),o=a.length,i=Object.keys(n.node.edges),s=i.length,l=0;l<o;l++)for(var c=a[l],u=0;u<s;u++){var d=i[u];if(d==c||"*"==c){var p=n.node.edges[d],f=n.qNode.edges[c],m=p.final&&f.final,h=void 0;d in n.output.edges?(h=n.output.edges[d]).final=h.final||m:((h=new D.TokenSet).final=m,n.output.edges[d]=h),r.push({qNode:f,output:h,node:p})}}}return t},D.TokenSet.Builder=function(){this.previousWord="",this.root=new D.TokenSet,this.uncheckedNodes=[],this.minimizedNodes={}},D.TokenSet.Builder.prototype.insert=function(e){var t,n=0;if(e<this.previousWord)throw new Error("Out of order word insertion");for(var r=0;r<e.length&&r<this.previousWord.length&&e[r]==this.previousWord[r];r++)n++;this.minimize(n),t=0==this.uncheckedNodes.length?this.root:this.uncheckedNodes[this.uncheckedNodes.length-1].child;for(r=n;r<e.length;r++){var a=new D.TokenSet,o=e[r];t.edges[o]=a,this.uncheckedNodes.push({parent:t,char:o,child:a}),t=a}t.final=!0,this.previousWord=e},D.TokenSet.Builder.prototype.finish=function(){this.minimize(0)},D.TokenSet.Builder.prototype.minimize=function(e){for(var t=this.uncheckedNodes.length-1;t>=e;t--){var n=this.uncheckedNodes[t],r=n.child.toString();r in this.minimizedNodes?n.parent.edges[n.char]=this.minimizedNodes[r]:(n.child._str=r,this.minimizedNodes[r]=n.child),this.uncheckedNodes.pop()}},D.Index=function(e){this.invertedIndex=e.invertedIndex,this.fieldVectors=e.fieldVectors,this.tokenSet=e.tokenSet,this.fields=e.fields,this.pipeline=e.pipeline},D.Index.prototype.search=function(e){return this.query((function(t){new D.QueryParser(e,t).parse()}))},D.Index.prototype.query=function(e){for(var t=new D.Query(this.fields),n=Object.create(null),r=Object.create(null),a=Object.create(null),o=Object.create(null),i=Object.create(null),s=0;s<this.fields.length;s++)r[this.fields[s]]=new D.Vector;e.call(t,t);for(s=0;s<t.clauses.length;s++){var l=t.clauses[s],c=null,u=D.Set.empty;c=l.usePipeline?this.pipeline.runString(l.term,{fields:l.fields}):[l.term];for(var d=0;d<c.length;d++){var p=c[d];l.term=p;var f=D.TokenSet.fromClause(l),m=this.tokenSet.intersect(f).toArray();if(0===m.length&&l.presence===D.Query.presence.REQUIRED){for(var h=0;h<l.fields.length;h++){o[O=l.fields[h]]=D.Set.empty}break}for(var g=0;g<m.length;g++){var b=m[g],y=this.invertedIndex[b],v=y._index;for(h=0;h<l.fields.length;h++){var _=y[O=l.fields[h]],x=Object.keys(_),S=b+"/"+O,E=new D.Set(x);if(l.presence==D.Query.presence.REQUIRED&&(u=u.union(E),void 0===o[O]&&(o[O]=D.Set.complete)),l.presence!=D.Query.presence.PROHIBITED){if(r[O].upsert(v,l.boost,(function(e,t){return e+t})),!a[S]){for(var w=0;w<x.length;w++){var k,T=x[w],A=new D.FieldRef(T,O),C=_[T];void 0===(k=n[A])?n[A]=new D.MatchData(b,O,C):k.add(b,O,C)}a[S]=!0}}else void 0===i[O]&&(i[O]=D.Set.empty),i[O]=i[O].union(E)}}}if(l.presence===D.Query.presence.REQUIRED)for(h=0;h<l.fields.length;h++){o[O=l.fields[h]]=o[O].intersect(u)}}var I=D.Set.complete,R=D.Set.empty;for(s=0;s<this.fields.length;s++){var O;o[O=this.fields[s]]&&(I=I.intersect(o[O])),i[O]&&(R=R.union(i[O]))}var N=Object.keys(n),L=[],P=Object.create(null);if(t.isNegated()){N=Object.keys(this.fieldVectors);for(s=0;s<N.length;s++){A=N[s];var F=D.FieldRef.fromString(A);n[A]=new D.MatchData}}for(s=0;s<N.length;s++){var j=(F=D.FieldRef.fromString(N[s])).docRef;if(I.contains(j)&&!R.contains(j)){var M,U=this.fieldVectors[F],B=r[F.fieldName].similarity(U);if(void 0!==(M=P[j]))M.score+=B,M.matchData.combine(n[F]);else{var z={ref:j,score:B,matchData:n[F]};P[j]=z,L.push(z)}}}return L.sort((function(e,t){return t.score-e.score}))},D.Index.prototype.toJSON=function(){var e=Object.keys(this.invertedIndex).sort().map((function(e){return[e,this.invertedIndex[e]]}),this),t=Object.keys(this.fieldVectors).map((function(e){return[e,this.fieldVectors[e].toJSON()]}),this);return{version:D.version,fields:this.fields,fieldVectors:t,invertedIndex:e,pipeline:this.pipeline.toJSON()}},D.Index.load=function(e){var t={},n={},r=e.fieldVectors,a=Object.create(null),o=e.invertedIndex,i=new D.TokenSet.Builder,s=D.Pipeline.load(e.pipeline);e.version!=D.version&&D.utils.warn("Version mismatch when loading serialised index. Current version of lunr '"+D.version+"' does not match serialized index '"+e.version+"'");for(var l=0;l<r.length;l++){var c=(d=r[l])[0],u=d[1];n[c]=new D.Vector(u)}for(l=0;l<o.length;l++){var d,p=(d=o[l])[0],f=d[1];i.insert(p),a[p]=f}return i.finish(),t.fields=e.fields,t.fieldVectors=n,t.invertedIndex=a,t.tokenSet=i.root,t.pipeline=s,new D.Index(t)},D.Builder=function(){this._ref="id",this._fields=Object.create(null),this._documents=Object.create(null),this.invertedIndex=Object.create(null),this.fieldTermFrequencies={},this.fieldLengths={},this.tokenizer=D.tokenizer,this.pipeline=new D.Pipeline,this.searchPipeline=new D.Pipeline,this.documentCount=0,this._b=.75,this._k1=1.2,this.termIndex=0,this.metadataWhitelist=[]},D.Builder.prototype.ref=function(e){this._ref=e},D.Builder.prototype.field=function(e,t){if(/\//.test(e))throw new RangeError("Field '"+e+"' contains illegal character '/'");this._fields[e]=t||{}},D.Builder.prototype.b=function(e){this._b=e<0?0:e>1?1:e},D.Builder.prototype.k1=function(e){this._k1=e},D.Builder.prototype.add=function(e,t){var n=e[this._ref],r=Object.keys(this._fields);this._documents[n]=t||{},this.documentCount+=1;for(var a=0;a<r.length;a++){var o=r[a],i=this._fields[o].extractor,s=i?i(e):e[o],l=this.tokenizer(s,{fields:[o]}),c=this.pipeline.run(l),u=new D.FieldRef(n,o),d=Object.create(null);this.fieldTermFrequencies[u]=d,this.fieldLengths[u]=0,this.fieldLengths[u]+=c.length;for(var p=0;p<c.length;p++){var f=c[p];if(null==d[f]&&(d[f]=0),d[f]+=1,null==this.invertedIndex[f]){var m=Object.create(null);m._index=this.termIndex,this.termIndex+=1;for(var h=0;h<r.length;h++)m[r[h]]=Object.create(null);this.invertedIndex[f]=m}null==this.invertedIndex[f][o][n]&&(this.invertedIndex[f][o][n]=Object.create(null));for(var g=0;g<this.metadataWhitelist.length;g++){var b=this.metadataWhitelist[g],y=f.metadata[b];null==this.invertedIndex[f][o][n][b]&&(this.invertedIndex[f][o][n][b]=[]),this.invertedIndex[f][o][n][b].push(y)}}}},D.Builder.prototype.calculateAverageFieldLengths=function(){for(var e=Object.keys(this.fieldLengths),t=e.length,n={},r={},a=0;a<t;a++){var o=D.FieldRef.fromString(e[a]),i=o.fieldName;r[i]||(r[i]=0),r[i]+=1,n[i]||(n[i]=0),n[i]+=this.fieldLengths[o]}var s=Object.keys(this._fields);for(a=0;a<s.length;a++){var l=s[a];n[l]=n[l]/r[l]}this.averageFieldLength=n},D.Builder.prototype.createFieldVectors=function(){for(var e={},t=Object.keys(this.fieldTermFrequencies),n=t.length,r=Object.create(null),a=0;a<n;a++){for(var o=D.FieldRef.fromString(t[a]),i=o.fieldName,s=this.fieldLengths[o],l=new D.Vector,c=this.fieldTermFrequencies[o],u=Object.keys(c),d=u.length,p=this._fields[i].boost||1,f=this._documents[o.docRef].boost||1,m=0;m<d;m++){var h,g,b,y=u[m],v=c[y],_=this.invertedIndex[y]._index;void 0===r[y]?(h=D.idf(this.invertedIndex[y],this.documentCount),r[y]=h):h=r[y],g=h*((this._k1+1)*v)/(this._k1*(1-this._b+this._b*(s/this.averageFieldLength[i]))+v),g*=p,g*=f,b=Math.round(1e3*g)/1e3,l.insert(_,b)}e[o]=l}this.fieldVectors=e},D.Builder.prototype.createTokenSet=function(){this.tokenSet=D.TokenSet.fromArray(Object.keys(this.invertedIndex).sort())},D.Builder.prototype.build=function(){return this.calculateAverageFieldLengths(),this.createFieldVectors(),this.createTokenSet(),new D.Index({invertedIndex:this.invertedIndex,fieldVectors:this.fieldVectors,tokenSet:this.tokenSet,fields:Object.keys(this._fields),pipeline:this.searchPipeline})},D.Builder.prototype.use=function(e){var t=Array.prototype.slice.call(arguments,1);t.unshift(this),e.apply(this,t)},D.MatchData=function(e,t,n){for(var r=Object.create(null),a=Object.keys(n||{}),o=0;o<a.length;o++){var i=a[o];r[i]=n[i].slice()}this.metadata=Object.create(null),void 0!==e&&(this.metadata[e]=Object.create(null),this.metadata[e][t]=r)},D.MatchData.prototype.combine=function(e){for(var t=Object.keys(e.metadata),n=0;n<t.length;n++){var r=t[n],a=Object.keys(e.metadata[r]);null==this.metadata[r]&&(this.metadata[r]=Object.create(null));for(var o=0;o<a.length;o++){var i=a[o],s=Object.keys(e.metadata[r][i]);null==this.metadata[r][i]&&(this.metadata[r][i]=Object.create(null));for(var l=0;l<s.length;l++){var c=s[l];null==this.metadata[r][i][c]?this.metadata[r][i][c]=e.metadata[r][i][c]:this.metadata[r][i][c]=this.metadata[r][i][c].concat(e.metadata[r][i][c])}}}},D.MatchData.prototype.add=function(e,t,n){if(!(e in this.metadata))return this.metadata[e]=Object.create(null),void(this.metadata[e][t]=n);if(t in this.metadata[e])for(var r=Object.keys(n),a=0;a<r.length;a++){var o=r[a];o in this.metadata[e][t]?this.metadata[e][t][o]=this.metadata[e][t][o].concat(n[o]):this.metadata[e][t][o]=n[o]}else this.metadata[e][t]=n},D.Query=function(e){this.clauses=[],this.allFields=e},D.Query.wildcard=new String("*"),D.Query.wildcard.NONE=0,D.Query.wildcard.LEADING=1,D.Query.wildcard.TRAILING=2,D.Query.presence={OPTIONAL:1,REQUIRED:2,PROHIBITED:3},D.Query.prototype.clause=function(e){return"fields"in e||(e.fields=this.allFields),"boost"in e||(e.boost=1),"usePipeline"in e||(e.usePipeline=!0),"wildcard"in e||(e.wildcard=D.Query.wildcard.NONE),e.wildcard&D.Query.wildcard.LEADING&&e.term.charAt(0)!=D.Query.wildcard&&(e.term="*"+e.term),e.wildcard&D.Query.wildcard.TRAILING&&e.term.slice(-1)!=D.Query.wildcard&&(e.term=e.term+"*"),"presence"in e||(e.presence=D.Query.presence.OPTIONAL),this.clauses.push(e),this},D.Query.prototype.isNegated=function(){for(var e=0;e<this.clauses.length;e++)if(this.clauses[e].presence!=D.Query.presence.PROHIBITED)return!1;return!0},D.Query.prototype.term=function(e,t){if(Array.isArray(e))return e.forEach((function(e){this.term(e,D.utils.clone(t))}),this),this;var n=t||{};return n.term=e.toString(),this.clause(n),this},D.QueryParseError=function(e,t,n){this.name="QueryParseError",this.message=e,this.start=t,this.end=n},D.QueryParseError.prototype=new Error,D.QueryLexer=function(e){this.lexemes=[],this.str=e,this.length=e.length,this.pos=0,this.start=0,this.escapeCharPositions=[]},D.QueryLexer.prototype.run=function(){for(var e=D.QueryLexer.lexText;e;)e=e(this)},D.QueryLexer.prototype.sliceString=function(){for(var e=[],t=this.start,n=this.pos,r=0;r<this.escapeCharPositions.length;r++)n=this.escapeCharPositions[r],e.push(this.str.slice(t,n)),t=n+1;return e.push(this.str.slice(t,this.pos)),this.escapeCharPositions.length=0,e.join("")},D.QueryLexer.prototype.emit=function(e){this.lexemes.push({type:e,str:this.sliceString(),start:this.start,end:this.pos}),this.start=this.pos},D.QueryLexer.prototype.escapeCharacter=function(){this.escapeCharPositions.push(this.pos-1),this.pos+=1},D.QueryLexer.prototype.next=function(){if(this.pos>=this.length)return D.QueryLexer.EOS;var e=this.str.charAt(this.pos);return this.pos+=1,e},D.QueryLexer.prototype.width=function(){return this.pos-this.start},D.QueryLexer.prototype.ignore=function(){this.start==this.pos&&(this.pos+=1),this.start=this.pos},D.QueryLexer.prototype.backup=function(){this.pos-=1},D.QueryLexer.prototype.acceptDigitRun=function(){var e,t;do{t=(e=this.next()).charCodeAt(0)}while(t>47&&t<58);e!=D.QueryLexer.EOS&&this.backup()},D.QueryLexer.prototype.more=function(){return this.pos<this.length},D.QueryLexer.EOS="EOS",D.QueryLexer.FIELD="FIELD",D.QueryLexer.TERM="TERM",D.QueryLexer.EDIT_DISTANCE="EDIT_DISTANCE",D.QueryLexer.BOOST="BOOST",D.QueryLexer.PRESENCE="PRESENCE",D.QueryLexer.lexField=function(e){return e.backup(),e.emit(D.QueryLexer.FIELD),e.ignore(),D.QueryLexer.lexText},D.QueryLexer.lexTerm=function(e){if(e.width()>1&&(e.backup(),e.emit(D.QueryLexer.TERM)),e.ignore(),e.more())return D.QueryLexer.lexText},D.QueryLexer.lexEditDistance=function(e){return e.ignore(),e.acceptDigitRun(),e.emit(D.QueryLexer.EDIT_DISTANCE),D.QueryLexer.lexText},D.QueryLexer.lexBoost=function(e){return e.ignore(),e.acceptDigitRun(),e.emit(D.QueryLexer.BOOST),D.QueryLexer.lexText},D.QueryLexer.lexEOS=function(e){e.width()>0&&e.emit(D.QueryLexer.TERM)},D.QueryLexer.termSeparator=D.tokenizer.separator,D.QueryLexer.lexText=function(e){for(;;){var t=e.next();if(t==D.QueryLexer.EOS)return D.QueryLexer.lexEOS;if(92!=t.charCodeAt(0)){if(":"==t)return D.QueryLexer.lexField;if("~"==t)return e.backup(),e.width()>0&&e.emit(D.QueryLexer.TERM),D.QueryLexer.lexEditDistance;if("^"==t)return e.backup(),e.width()>0&&e.emit(D.QueryLexer.TERM),D.QueryLexer.lexBoost;if("+"==t&&1===e.width())return e.emit(D.QueryLexer.PRESENCE),D.QueryLexer.lexText;if("-"==t&&1===e.width())return e.emit(D.QueryLexer.PRESENCE),D.QueryLexer.lexText;if(t.match(D.QueryLexer.termSeparator))return D.QueryLexer.lexTerm}else e.escapeCharacter()}},D.QueryParser=function(e,t){this.lexer=new D.QueryLexer(e),this.query=t,this.currentClause={},this.lexemeIdx=0},D.QueryParser.prototype.parse=function(){this.lexer.run(),this.lexemes=this.lexer.lexemes;for(var e=D.QueryParser.parseClause;e;)e=e(this);return this.query},D.QueryParser.prototype.peekLexeme=function(){return this.lexemes[this.lexemeIdx]},D.QueryParser.prototype.consumeLexeme=function(){var e=this.peekLexeme();return this.lexemeIdx+=1,e},D.QueryParser.prototype.nextClause=function(){var e=this.currentClause;this.query.clause(e),this.currentClause={}},D.QueryParser.parseClause=function(e){var t=e.peekLexeme();if(null!=t)switch(t.type){case D.QueryLexer.PRESENCE:return D.QueryParser.parsePresence;case D.QueryLexer.FIELD:return D.QueryParser.parseField;case D.QueryLexer.TERM:return D.QueryParser.parseTerm;default:var n="expected either a field or a term, found "+t.type;throw t.str.length>=1&&(n+=" with value '"+t.str+"'"),new D.QueryParseError(n,t.start,t.end)}},D.QueryParser.parsePresence=function(e){var t=e.consumeLexeme();if(null!=t){switch(t.str){case"-":e.currentClause.presence=D.Query.presence.PROHIBITED;break;case"+":e.currentClause.presence=D.Query.presence.REQUIRED;break;default:var n="unrecognised presence operator'"+t.str+"'";throw new D.QueryParseError(n,t.start,t.end)}var r=e.peekLexeme();if(null==r){n="expecting term or field, found nothing";throw new D.QueryParseError(n,t.start,t.end)}switch(r.type){case D.QueryLexer.FIELD:return D.QueryParser.parseField;case D.QueryLexer.TERM:return D.QueryParser.parseTerm;default:n="expecting term or field, found '"+r.type+"'";throw new D.QueryParseError(n,r.start,r.end)}}},D.QueryParser.parseField=function(e){var t=e.consumeLexeme();if(null!=t){if(-1==e.query.allFields.indexOf(t.str)){var n=e.query.allFields.map((function(e){return"'"+e+"'"})).join(", "),r="unrecognised field '"+t.str+"', possible fields: "+n;throw new D.QueryParseError(r,t.start,t.end)}e.currentClause.fields=[t.str];var a=e.peekLexeme();if(null==a){r="expecting term, found nothing";throw new D.QueryParseError(r,t.start,t.end)}if(a.type===D.QueryLexer.TERM)return D.QueryParser.parseTerm;r="expecting term, found '"+a.type+"'";throw new D.QueryParseError(r,a.start,a.end)}},D.QueryParser.parseTerm=function(e){var t=e.consumeLexeme();if(null!=t){e.currentClause.term=t.str.toLowerCase(),-1!=t.str.indexOf("*")&&(e.currentClause.usePipeline=!1);var n=e.peekLexeme();if(null!=n)switch(n.type){case D.QueryLexer.TERM:return e.nextClause(),D.QueryParser.parseTerm;case D.QueryLexer.FIELD:return e.nextClause(),D.QueryParser.parseField;case D.QueryLexer.EDIT_DISTANCE:return D.QueryParser.parseEditDistance;case D.QueryLexer.BOOST:return D.QueryParser.parseBoost;case D.QueryLexer.PRESENCE:return e.nextClause(),D.QueryParser.parsePresence;default:var r="Unexpected lexeme type '"+n.type+"'";throw new D.QueryParseError(r,n.start,n.end)}else e.nextClause()}},D.QueryParser.parseEditDistance=function(e){var t=e.consumeLexeme();if(null!=t){var n=parseInt(t.str,10);if(isNaN(n)){var r="edit distance must be numeric";throw new D.QueryParseError(r,t.start,t.end)}e.currentClause.editDistance=n;var a=e.peekLexeme();if(null!=a)switch(a.type){case D.QueryLexer.TERM:return e.nextClause(),D.QueryParser.parseTerm;case D.QueryLexer.FIELD:return e.nextClause(),D.QueryParser.parseField;case D.QueryLexer.EDIT_DISTANCE:return D.QueryParser.parseEditDistance;case D.QueryLexer.BOOST:return D.QueryParser.parseBoost;case D.QueryLexer.PRESENCE:return e.nextClause(),D.QueryParser.parsePresence;default:r="Unexpected lexeme type '"+a.type+"'";throw new D.QueryParseError(r,a.start,a.end)}else e.nextClause()}},D.QueryParser.parseBoost=function(e){var t=e.consumeLexeme();if(null!=t){var n=parseInt(t.str,10);if(isNaN(n)){var r="boost must be numeric";throw new D.QueryParseError(r,t.start,t.end)}e.currentClause.boost=n;var a=e.peekLexeme();if(null!=a)switch(a.type){case D.QueryLexer.TERM:return e.nextClause(),D.QueryParser.parseTerm;case 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e.languages.kotlin["class-name"];var t={"interpolation-punctuation":{pattern:/^\$\{?|\}$/,alias:"punctuation"},expression:{pattern:/[\s\S]+/,inside:e.languages.kotlin}};e.languages.insertBefore("kotlin","string",{"string-literal":[{pattern:/"""(?:[^$]|\$(?:(?!\{)|\{[^{}]*\}))*?"""/,alias:"multiline",inside:{interpolation:{pattern:/\$(?:[a-z_]\w*|\{[^{}]*\})/i,inside:t},string:/[\s\S]+/}},{pattern:/"(?:[^"\\\r\n$]|\\.|\$(?:(?!\{)|\{[^{}]*\}))*"/,alias:"singleline",inside:{interpolation:{pattern:/((?:^|[^\\])(?:\\{2})*)\$(?:[a-z_]\w*|\{[^{}]*\})/i,lookbehind:!0,inside:t},string:/[\s\S]+/}}],char:{pattern:/'(?:[^'\\\r\n]|\\(?:.|u[a-fA-F0-9]{0,4}))'/,greedy:!0}}),delete e.languages.kotlin.string,e.languages.insertBefore("kotlin","keyword",{annotation:{pattern:/\B@(?:\w+:)?(?:[A-Z]\w*|\[[^\]]+\])/,alias:"builtin"}}),e.languages.insertBefore("kotlin","function",{label:{pattern:/\b\w+@|@\w+\b/,alias:"symbol"}}),e.languages.kt=e.languages.kotlin,e.languages.kts=e.languages.kotlin}(A),A.languages.c=A.languages.extend("clike",{comment:{pattern:/\/\/(?:[^\r\n\\]|\\(?:\r\n?|\n|(?![\r\n])))*|\/\*[\s\S]*?(?:\*\/|$)/,greedy:!0},string:{pattern:/"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"/,greedy:!0},"class-name":{pattern:/(\b(?:enum|struct)\s+(?:__attribute__\s*\(\([\s\S]*?\)\)\s*)?)\w+|\b[a-z]\w*_t\b/,lookbehind:!0},keyword:/\b(?:_Alignas|_Alignof|_Atomic|_Bool|_Complex|_Generic|_Imaginary|_Noreturn|_Static_assert|_Thread_local|__attribute__|asm|auto|break|case|char|const|continue|default|do|double|else|enum|extern|float|for|goto|if|inline|int|long|register|return|short|signed|sizeof|static|struct|switch|typedef|typeof|union|unsigned|void|volatile|while)\b/,function:/\b[a-z_]\w*(?=\s*\()/i,number:/(?:\b0x(?:[\da-f]+(?:\.[\da-f]*)?|\.[\da-f]+)(?:p[+-]?\d+)?|(?:\b\d+(?:\.\d*)?|\B\.\d+)(?:e[+-]?\d+)?)[ful]{0,4}/i,operator:/>>=?|<<=?|->|([-+&|:])\1|[?:~]|[-+*/%&|^!=<>]=?/}),A.languages.insertBefore("c","string",{char:{pattern:/'(?:\\(?:\r\n|[\s\S])|[^'\\\r\n]){0,32}'/,greedy:!0}}),A.languages.insertBefore("c","string",{macro:{pattern:/(^[\t 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t=/\/\*(?:[^*/]|\*(?!\/)|\/(?!\*)|<self>)*\*\//.source,n=0;n<2;n++)t=t.replace(/<self>/g,(function(){return 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A.languages.go["class-name"],function(e){var t=/\b(?:alignas|alignof|asm|auto|bool|break|case|catch|char|char16_t|char32_t|char8_t|class|co_await|co_return|co_yield|compl|concept|const|const_cast|consteval|constexpr|constinit|continue|decltype|default|delete|do|double|dynamic_cast|else|enum|explicit|export|extern|final|float|for|friend|goto|if|import|inline|int|int16_t|int32_t|int64_t|int8_t|long|module|mutable|namespace|new|noexcept|nullptr|operator|override|private|protected|public|register|reinterpret_cast|requires|return|short|signed|sizeof|static|static_assert|static_cast|struct|switch|template|this|thread_local|throw|try|typedef|typeid|typename|uint16_t|uint32_t|uint64_t|uint8_t|union|unsigned|using|virtual|void|volatile|wchar_t|while)\b/,n=/\b(?!<keyword>)\w+(?:\s*\.\s*\w+)*\b/.source.replace(/<keyword>/g,(function(){return t.source}));e.languages.cpp=e.languages.extend("c",{"class-name":[{pattern:RegExp(/(\b(?:class|concept|enum|struct|typename)\s+)(?!<keyword>)\w+/.source.replace(/<keyword>/g,(function(){return t.source}))),lookbehind:!0},/\b[A-Z]\w*(?=\s*::\s*\w+\s*\()/,/\b[A-Z_]\w*(?=\s*::\s*~\w+\s*\()/i,/\b\w+(?=\s*<(?:[^<>]|<(?:[^<>]|<[^<>]*>)*>)*>\s*::\s*\w+\s*\()/],keyword:t,number:{pattern:/(?:\b0b[01']+|\b0x(?:[\da-f']+(?:\.[\da-f']*)?|\.[\da-f']+)(?:p[+-]?[\d']+)?|(?:\b[\d']+(?:\.[\d']*)?|\B\.[\d']+)(?:e[+-]?[\d']+)?)[ful]{0,4}/i,greedy:!0},operator:/>>=?|<<=?|->|--|\+\+|&&|\|\||[?:~]|<=>|[-+*/%&|^!=<>]=?|\b(?:and|and_eq|bitand|bitor|not|not_eq|or|or_eq|xor|xor_eq)\b/,boolean:/\b(?:false|true)\b/}),e.languages.insertBefore("cpp","string",{module:{pattern:RegExp(/(\b(?:import|module)\s+)/.source+"(?:"+/"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"|<[^<>\r\n]*>/.source+"|"+/<mod-name>(?:\s*:\s*<mod-name>)?|:\s*<mod-name>/.source.replace(/<mod-name>/g,(function(){return n}))+")"),lookbehind:!0,greedy:!0,inside:{string:/^[<"][\s\S]+/,operator:/:/,punctuation:/\./}},"raw-string":{pattern:/R"([^()\\ 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e}},D.stopWordFilter=D.generateStopWordFilter(["a","able","about","across","after","all","almost","also","am","among","an","and","any","are","as","at","be","because","been","but","by","can","cannot","could","dear","did","do","does","either","else","ever","every","for","from","get","got","had","has","have","he","her","hers","him","his","how","however","i","if","in","into","is","it","its","just","least","let","like","likely","may","me","might","most","must","my","neither","no","nor","not","of","off","often","on","only","or","other","our","own","rather","said","say","says","she","should","since","so","some","than","that","the","their","them","then","there","these","they","this","tis","to","too","twas","us","wants","was","we","were","what","when","where","which","while","who","whom","why","will","with","would","yet","you","your"]),D.Pipeline.registerFunction(D.stopWordFilter,"stopWordFilter"),D.trimmer=function(e){return e.update((function(e){return e.replace(/^\W+/,"").replace(/\W+$/,"")}))},D.Pipeline.registerFunction(D.trimmer,"trimmer"),D.TokenSet=function(){this.final=!1,this.edges={},this.id=D.TokenSet._nextId,D.TokenSet._nextId+=1},D.TokenSet._nextId=1,D.TokenSet.fromArray=function(e){for(var t=new D.TokenSet.Builder,n=0,r=e.length;n<r;n++)t.insert(e[n]);return t.finish(),t.root},D.TokenSet.fromClause=function(e){return"editDistance"in e?D.TokenSet.fromFuzzyString(e.term,e.editDistance):D.TokenSet.fromString(e.term)},D.TokenSet.fromFuzzyString=function(e,t){for(var n=new D.TokenSet,r=[{node:n,editsRemaining:t,str:e}];r.length;){var a=r.pop();if(a.str.length>0){var o,i=a.str.charAt(0);i in a.node.edges?o=a.node.edges[i]:(o=new D.TokenSet,a.node.edges[i]=o),1==a.str.length&&(o.final=!0),r.push({node:o,editsRemaining:a.editsRemaining,str:a.str.slice(1)})}if(0!=a.editsRemaining){if("*"in a.node.edges)var s=a.node.edges["*"];else{s=new D.TokenSet;a.node.edges["*"]=s}if(0==a.str.length&&(s.final=!0),r.push({node:s,editsRemaining:a.editsRemaining-1,str:a.str}),a.str.length>1&&r.push({node:a.node,editsRemaining:a.editsRemaining-1,str:a.str.slice(1)}),1==a.str.length&&(a.node.final=!0),a.str.length>=1){if("*"in a.node.edges)var l=a.node.edges["*"];else{l=new D.TokenSet;a.node.edges["*"]=l}1==a.str.length&&(l.final=!0),r.push({node:l,editsRemaining:a.editsRemaining-1,str:a.str.slice(1)})}if(a.str.length>1){var c,u=a.str.charAt(0),d=a.str.charAt(1);d in a.node.edges?c=a.node.edges[d]:(c=new D.TokenSet,a.node.edges[d]=c),1==a.str.length&&(c.final=!0),r.push({node:c,editsRemaining:a.editsRemaining-1,str:u+a.str.slice(2)})}}}return n},D.TokenSet.fromString=function(e){for(var t=new D.TokenSet,n=t,r=0,a=e.length;r<a;r++){var o=e[r],i=r==a-1;if("*"==o)t.edges[o]=t,t.final=i;else{var s=new D.TokenSet;s.final=i,t.edges[o]=s,t=s}}return n},D.TokenSet.prototype.toArray=function(){for(var e=[],t=[{prefix:"",node:this}];t.length;){var n=t.pop(),r=Object.keys(n.node.edges),a=r.length;n.node.final&&(n.prefix.charAt(0),e.push(n.prefix));for(var o=0;o<a;o++){var i=r[o];t.push({prefix:n.prefix.concat(i),node:n.node.edges[i]})}}return e},D.TokenSet.prototype.toString=function(){if(this._str)return this._str;for(var e=this.final?"1":"0",t=Object.keys(this.edges).sort(),n=t.length,r=0;r<n;r++){var a=t[r];e=e+a+this.edges[a].id}return e},D.TokenSet.prototype.intersect=function(e){for(var t=new D.TokenSet,n=void 0,r=[{qNode:e,output:t,node:this}];r.length;){n=r.pop();for(var a=Object.keys(n.qNode.edges),o=a.length,i=Object.keys(n.node.edges),s=i.length,l=0;l<o;l++)for(var c=a[l],u=0;u<s;u++){var d=i[u];if(d==c||"*"==c){var p=n.node.edges[d],f=n.qNode.edges[c],m=p.final&&f.final,h=void 0;d in n.output.edges?(h=n.output.edges[d]).final=h.final||m:((h=new D.TokenSet).final=m,n.output.edges[d]=h),r.push({qNode:f,output:h,node:p})}}}return t},D.TokenSet.Builder=function(){this.previousWord="",this.root=new D.TokenSet,this.uncheckedNodes=[],this.minimizedNodes={}},D.TokenSet.Builder.prototype.insert=function(e){var t,n=0;if(e<this.previousWord)throw new Error("Out of order word insertion");for(var r=0;r<e.length&&r<this.previousWord.length&&e[r]==this.previousWord[r];r++)n++;this.minimize(n),t=0==this.uncheckedNodes.length?this.root:this.uncheckedNodes[this.uncheckedNodes.length-1].child;for(r=n;r<e.length;r++){var a=new D.TokenSet,o=e[r];t.edges[o]=a,this.uncheckedNodes.push({parent:t,char:o,child:a}),t=a}t.final=!0,this.previousWord=e},D.TokenSet.Builder.prototype.finish=function(){this.minimize(0)},D.TokenSet.Builder.prototype.minimize=function(e){for(var t=this.uncheckedNodes.length-1;t>=e;t--){var n=this.uncheckedNodes[t],r=n.child.toString();r in this.minimizedNodes?n.parent.edges[n.char]=this.minimizedNodes[r]:(n.child._str=r,this.minimizedNodes[r]=n.child),this.uncheckedNodes.pop()}},D.Index=function(e){this.invertedIndex=e.invertedIndex,this.fieldVectors=e.fieldVectors,this.tokenSet=e.tokenSet,this.fields=e.fields,this.pipeline=e.pipeline},D.Index.prototype.search=function(e){return this.query((function(t){new D.QueryParser(e,t).parse()}))},D.Index.prototype.query=function(e){for(var t=new D.Query(this.fields),n=Object.create(null),r=Object.create(null),a=Object.create(null),o=Object.create(null),i=Object.create(null),s=0;s<this.fields.length;s++)r[this.fields[s]]=new D.Vector;e.call(t,t);for(s=0;s<t.clauses.length;s++){var l=t.clauses[s],c=null,u=D.Set.empty;c=l.usePipeline?this.pipeline.runString(l.term,{fields:l.fields}):[l.term];for(var d=0;d<c.length;d++){var p=c[d];l.term=p;var f=D.TokenSet.fromClause(l),m=this.tokenSet.intersect(f).toArray();if(0===m.length&&l.presence===D.Query.presence.REQUIRED){for(var h=0;h<l.fields.length;h++){o[O=l.fields[h]]=D.Set.empty}break}for(var g=0;g<m.length;g++){var b=m[g],y=this.invertedIndex[b],v=y._index;for(h=0;h<l.fields.length;h++){var _=y[O=l.fields[h]],x=Object.keys(_),S=b+"/"+O,E=new D.Set(x);if(l.presence==D.Query.presence.REQUIRED&&(u=u.union(E),void 0===o[O]&&(o[O]=D.Set.complete)),l.presence!=D.Query.presence.PROHIBITED){if(r[O].upsert(v,l.boost,(function(e,t){return e+t})),!a[S]){for(var w=0;w<x.length;w++){var k,T=x[w],A=new D.FieldRef(T,O),C=_[T];void 0===(k=n[A])?n[A]=new D.MatchData(b,O,C):k.add(b,O,C)}a[S]=!0}}else void 0===i[O]&&(i[O]=D.Set.empty),i[O]=i[O].union(E)}}}if(l.presence===D.Query.presence.REQUIRED)for(h=0;h<l.fields.length;h++){o[O=l.fields[h]]=o[O].intersect(u)}}var I=D.Set.complete,R=D.Set.empty;for(s=0;s<this.fields.length;s++){var O;o[O=this.fields[s]]&&(I=I.intersect(o[O])),i[O]&&(R=R.union(i[O]))}var N=Object.keys(n),L=[],P=Object.create(null);if(t.isNegated()){N=Object.keys(this.fieldVectors);for(s=0;s<N.length;s++){A=N[s];var F=D.FieldRef.fromString(A);n[A]=new D.MatchData}}for(s=0;s<N.length;s++){var j=(F=D.FieldRef.fromString(N[s])).docRef;if(I.contains(j)&&!R.contains(j)){var M,U=this.fieldVectors[F],B=r[F.fieldName].similarity(U);if(void 0!==(M=P[j]))M.score+=B,M.matchData.combine(n[F]);else{var z={ref:j,score:B,matchData:n[F]};P[j]=z,L.push(z)}}}return L.sort((function(e,t){return t.score-e.score}))},D.Index.prototype.toJSON=function(){var e=Object.keys(this.invertedIndex).sort().map((function(e){return[e,this.invertedIndex[e]]}),this),t=Object.keys(this.fieldVectors).map((function(e){return[e,this.fieldVectors[e].toJSON()]}),this);return{version:D.version,fields:this.fields,fieldVectors:t,invertedIndex:e,pipeline:this.pipeline.toJSON()}},D.Index.load=function(e){var t={},n={},r=e.fieldVectors,a=Object.create(null),o=e.invertedIndex,i=new D.TokenSet.Builder,s=D.Pipeline.load(e.pipeline);e.version!=D.version&&D.utils.warn("Version mismatch when loading serialised index. Current version of lunr '"+D.version+"' does not match serialized index '"+e.version+"'");for(var l=0;l<r.length;l++){var c=(d=r[l])[0],u=d[1];n[c]=new D.Vector(u)}for(l=0;l<o.length;l++){var d,p=(d=o[l])[0],f=d[1];i.insert(p),a[p]=f}return i.finish(),t.fields=e.fields,t.fieldVectors=n,t.invertedIndex=a,t.tokenSet=i.root,t.pipeline=s,new D.Index(t)},D.Builder=function(){this._ref="id",this._fields=Object.create(null),this._documents=Object.create(null),this.invertedIndex=Object.create(null),this.fieldTermFrequencies={},this.fieldLengths={},this.tokenizer=D.tokenizer,this.pipeline=new D.Pipeline,this.searchPipeline=new D.Pipeline,this.documentCount=0,this._b=.75,this._k1=1.2,this.termIndex=0,this.metadataWhitelist=[]},D.Builder.prototype.ref=function(e){this._ref=e},D.Builder.prototype.field=function(e,t){if(/\//.test(e))throw new RangeError("Field '"+e+"' contains illegal character '/'");this._fields[e]=t||{}},D.Builder.prototype.b=function(e){this._b=e<0?0:e>1?1:e},D.Builder.prototype.k1=function(e){this._k1=e},D.Builder.prototype.add=function(e,t){var n=e[this._ref],r=Object.keys(this._fields);this._documents[n]=t||{},this.documentCount+=1;for(var a=0;a<r.length;a++){var o=r[a],i=this._fields[o].extractor,s=i?i(e):e[o],l=this.tokenizer(s,{fields:[o]}),c=this.pipeline.run(l),u=new D.FieldRef(n,o),d=Object.create(null);this.fieldTermFrequencies[u]=d,this.fieldLengths[u]=0,this.fieldLengths[u]+=c.length;for(var p=0;p<c.length;p++){var f=c[p];if(null==d[f]&&(d[f]=0),d[f]+=1,null==this.invertedIndex[f]){var m=Object.create(null);m._index=this.termIndex,this.termIndex+=1;for(var h=0;h<r.length;h++)m[r[h]]=Object.create(null);this.invertedIndex[f]=m}null==this.invertedIndex[f][o][n]&&(this.invertedIndex[f][o][n]=Object.create(null));for(var g=0;g<this.metadataWhitelist.length;g++){var b=this.metadataWhitelist[g],y=f.metadata[b];null==this.invertedIndex[f][o][n][b]&&(this.invertedIndex[f][o][n][b]=[]),this.invertedIndex[f][o][n][b].push(y)}}}},D.Builder.prototype.calculateAverageFieldLengths=function(){for(var e=Object.keys(this.fieldLengths),t=e.length,n={},r={},a=0;a<t;a++){var o=D.FieldRef.fromString(e[a]),i=o.fieldName;r[i]||(r[i]=0),r[i]+=1,n[i]||(n[i]=0),n[i]+=this.fieldLengths[o]}var s=Object.keys(this._fields);for(a=0;a<s.length;a++){var l=s[a];n[l]=n[l]/r[l]}this.averageFieldLength=n},D.Builder.prototype.createFieldVectors=function(){for(var e={},t=Object.keys(this.fieldTermFrequencies),n=t.length,r=Object.create(null),a=0;a<n;a++){for(var o=D.FieldRef.fromString(t[a]),i=o.fieldName,s=this.fieldLengths[o],l=new D.Vector,c=this.fieldTermFrequencies[o],u=Object.keys(c),d=u.length,p=this._fields[i].boost||1,f=this._documents[o.docRef].boost||1,m=0;m<d;m++){var h,g,b,y=u[m],v=c[y],_=this.invertedIndex[y]._index;void 0===r[y]?(h=D.idf(this.invertedIndex[y],this.documentCount),r[y]=h):h=r[y],g=h*((this._k1+1)*v)/(this._k1*(1-this._b+this._b*(s/this.averageFieldLength[i]))+v),g*=p,g*=f,b=Math.round(1e3*g)/1e3,l.insert(_,b)}e[o]=l}this.fieldVectors=e},D.Builder.prototype.createTokenSet=function(){this.tokenSet=D.TokenSet.fromArray(Object.keys(this.invertedIndex).sort())},D.Builder.prototype.build=function(){return this.calculateAverageFieldLengths(),this.createFieldVectors(),this.createTokenSet(),new D.Index({invertedIndex:this.invertedIndex,fieldVectors:this.fieldVectors,tokenSet:this.tokenSet,fields:Object.keys(this._fields),pipeline:this.searchPipeline})},D.Builder.prototype.use=function(e){var t=Array.prototype.slice.call(arguments,1);t.unshift(this),e.apply(this,t)},D.MatchData=function(e,t,n){for(var r=Object.create(null),a=Object.keys(n||{}),o=0;o<a.length;o++){var i=a[o];r[i]=n[i].slice()}this.metadata=Object.create(null),void 0!==e&&(this.metadata[e]=Object.create(null),this.metadata[e][t]=r)},D.MatchData.prototype.combine=function(e){for(var t=Object.keys(e.metadata),n=0;n<t.length;n++){var r=t[n],a=Object.keys(e.metadata[r]);null==this.metadata[r]&&(this.metadata[r]=Object.create(null));for(var o=0;o<a.length;o++){var i=a[o],s=Object.keys(e.metadata[r][i]);null==this.metadata[r][i]&&(this.metadata[r][i]=Object.create(null));for(var l=0;l<s.length;l++){var c=s[l];null==this.metadata[r][i][c]?this.metadata[r][i][c]=e.metadata[r][i][c]:this.metadata[r][i][c]=this.metadata[r][i][c].concat(e.metadata[r][i][c])}}}},D.MatchData.prototype.add=function(e,t,n){if(!(e in this.metadata))return this.metadata[e]=Object.create(null),void(this.metadata[e][t]=n);if(t in this.metadata[e])for(var r=Object.keys(n),a=0;a<r.length;a++){var o=r[a];o in this.metadata[e][t]?this.metadata[e][t][o]=this.metadata[e][t][o].concat(n[o]):this.metadata[e][t][o]=n[o]}else this.metadata[e][t]=n},D.Query=function(e){this.clauses=[],this.allFields=e},D.Query.wildcard=new String("*"),D.Query.wildcard.NONE=0,D.Query.wildcard.LEADING=1,D.Query.wildcard.TRAILING=2,D.Query.presence={OPTIONAL:1,REQUIRED:2,PROHIBITED:3},D.Query.prototype.clause=function(e){return"fields"in e||(e.fields=this.allFields),"boost"in e||(e.boost=1),"usePipeline"in e||(e.usePipeline=!0),"wildcard"in e||(e.wildcard=D.Query.wildcard.NONE),e.wildcard&D.Query.wildcard.LEADING&&e.term.charAt(0)!=D.Query.wildcard&&(e.term="*"+e.term),e.wildcard&D.Query.wildcard.TRAILING&&e.term.slice(-1)!=D.Query.wildcard&&(e.term=e.term+"*"),"presence"in e||(e.presence=D.Query.presence.OPTIONAL),this.clauses.push(e),this},D.Query.prototype.isNegated=function(){for(var e=0;e<this.clauses.length;e++)if(this.clauses[e].presence!=D.Query.presence.PROHIBITED)return!1;return!0},D.Query.prototype.term=function(e,t){if(Array.isArray(e))return e.forEach((function(e){this.term(e,D.utils.clone(t))}),this),this;var n=t||{};return n.term=e.toString(),this.clause(n),this},D.QueryParseError=function(e,t,n){this.name="QueryParseError",this.message=e,this.start=t,this.end=n},D.QueryParseError.prototype=new Error,D.QueryLexer=function(e){this.lexemes=[],this.str=e,this.length=e.length,this.pos=0,this.start=0,this.escapeCharPositions=[]},D.QueryLexer.prototype.run=function(){for(var e=D.QueryLexer.lexText;e;)e=e(this)},D.QueryLexer.prototype.sliceString=function(){for(var e=[],t=this.start,n=this.pos,r=0;r<this.escapeCharPositions.length;r++)n=this.escapeCharPositions[r],e.push(this.str.slice(t,n)),t=n+1;return e.push(this.str.slice(t,this.pos)),this.escapeCharPositions.length=0,e.join("")},D.QueryLexer.prototype.emit=function(e){this.lexemes.push({type:e,str:this.sliceString(),start:this.start,end:this.pos}),this.start=this.pos},D.QueryLexer.prototype.escapeCharacter=function(){this.escapeCharPositions.push(this.pos-1),this.pos+=1},D.QueryLexer.prototype.next=function(){if(this.pos>=this.length)return D.QueryLexer.EOS;var e=this.str.charAt(this.pos);return this.pos+=1,e},D.QueryLexer.prototype.width=function(){return this.pos-this.start},D.QueryLexer.prototype.ignore=function(){this.start==this.pos&&(this.pos+=1),this.start=this.pos},D.QueryLexer.prototype.backup=function(){this.pos-=1},D.QueryLexer.prototype.acceptDigitRun=function(){var e,t;do{t=(e=this.next()).charCodeAt(0)}while(t>47&&t<58);e!=D.QueryLexer.EOS&&this.backup()},D.QueryLexer.prototype.more=function(){return this.pos<this.length},D.QueryLexer.EOS="EOS",D.QueryLexer.FIELD="FIELD",D.QueryLexer.TERM="TERM",D.QueryLexer.EDIT_DISTANCE="EDIT_DISTANCE",D.QueryLexer.BOOST="BOOST",D.QueryLexer.PRESENCE="PRESENCE",D.QueryLexer.lexField=function(e){return e.backup(),e.emit(D.QueryLexer.FIELD),e.ignore(),D.QueryLexer.lexText},D.QueryLexer.lexTerm=function(e){if(e.width()>1&&(e.backup(),e.emit(D.QueryLexer.TERM)),e.ignore(),e.more())return D.QueryLexer.lexText},D.QueryLexer.lexEditDistance=function(e){return e.ignore(),e.acceptDigitRun(),e.emit(D.QueryLexer.EDIT_DISTANCE),D.QueryLexer.lexText},D.QueryLexer.lexBoost=function(e){return e.ignore(),e.acceptDigitRun(),e.emit(D.QueryLexer.BOOST),D.QueryLexer.lexText},D.QueryLexer.lexEOS=function(e){e.width()>0&&e.emit(D.QueryLexer.TERM)},D.QueryLexer.termSeparator=D.tokenizer.separator,D.QueryLexer.lexText=function(e){for(;;){var t=e.next();if(t==D.QueryLexer.EOS)return D.QueryLexer.lexEOS;if(92!=t.charCodeAt(0)){if(":"==t)return D.QueryLexer.lexField;if("~"==t)return e.backup(),e.width()>0&&e.emit(D.QueryLexer.TERM),D.QueryLexer.lexEditDistance;if("^"==t)return e.backup(),e.width()>0&&e.emit(D.QueryLexer.TERM),D.QueryLexer.lexBoost;if("+"==t&&1===e.width())return e.emit(D.QueryLexer.PRESENCE),D.QueryLexer.lexText;if("-"==t&&1===e.width())return e.emit(D.QueryLexer.PRESENCE),D.QueryLexer.lexText;if(t.match(D.QueryLexer.termSeparator))return D.QueryLexer.lexTerm}else e.escapeCharacter()}},D.QueryParser=function(e,t){this.lexer=new D.QueryLexer(e),this.query=t,this.currentClause={},this.lexemeIdx=0},D.QueryParser.prototype.parse=function(){this.lexer.run(),this.lexemes=this.lexer.lexemes;for(var e=D.QueryParser.parseClause;e;)e=e(this);return this.query},D.QueryParser.prototype.peekLexeme=function(){return this.lexemes[this.lexemeIdx]},D.QueryParser.prototype.consumeLexeme=function(){var e=this.peekLexeme();return this.lexemeIdx+=1,e},D.QueryParser.prototype.nextClause=function(){var e=this.currentClause;this.query.clause(e),this.currentClause={}},D.QueryParser.parseClause=function(e){var t=e.peekLexeme();if(null!=t)switch(t.type){case D.QueryLexer.PRESENCE:return D.QueryParser.parsePresence;case D.QueryLexer.FIELD:return D.QueryParser.parseField;case D.QueryLexer.TERM:return D.QueryParser.parseTerm;default:var n="expected either a field or a term, found "+t.type;throw t.str.length>=1&&(n+=" with value '"+t.str+"'"),new D.QueryParseError(n,t.start,t.end)}},D.QueryParser.parsePresence=function(e){var t=e.consumeLexeme();if(null!=t){switch(t.str){case"-":e.currentClause.presence=D.Query.presence.PROHIBITED;break;case"+":e.currentClause.presence=D.Query.presence.REQUIRED;break;default:var n="unrecognised presence operator'"+t.str+"'";throw new D.QueryParseError(n,t.start,t.end)}var r=e.peekLexeme();if(null==r){n="expecting term or field, found nothing";throw new D.QueryParseError(n,t.start,t.end)}switch(r.type){case D.QueryLexer.FIELD:return D.QueryParser.parseField;case D.QueryLexer.TERM:return D.QueryParser.parseTerm;default:n="expecting term or field, found '"+r.type+"'";throw new D.QueryParseError(n,r.start,r.end)}}},D.QueryParser.parseField=function(e){var t=e.consumeLexeme();if(null!=t){if(-1==e.query.allFields.indexOf(t.str)){var n=e.query.allFields.map((function(e){return"'"+e+"'"})).join(", "),r="unrecognised field '"+t.str+"', possible fields: "+n;throw new D.QueryParseError(r,t.start,t.end)}e.currentClause.fields=[t.str];var a=e.peekLexeme();if(null==a){r="expecting term, found nothing";throw new D.QueryParseError(r,t.start,t.end)}if(a.type===D.QueryLexer.TERM)return D.QueryParser.parseTerm;r="expecting term, found '"+a.type+"'";throw new D.QueryParseError(r,a.start,a.end)}},D.QueryParser.parseTerm=function(e){var t=e.consumeLexeme();if(null!=t){e.currentClause.term=t.str.toLowerCase(),-1!=t.str.indexOf("*")&&(e.currentClause.usePipeline=!1);var n=e.peekLexeme();if(null!=n)switch(n.type){case D.QueryLexer.TERM:return e.nextClause(),D.QueryParser.parseTerm;case D.QueryLexer.FIELD:return e.nextClause(),D.QueryParser.parseField;case D.QueryLexer.EDIT_DISTANCE:return D.QueryParser.parseEditDistance;case D.QueryLexer.BOOST:return D.QueryParser.parseBoost;case D.QueryLexer.PRESENCE:return e.nextClause(),D.QueryParser.parsePresence;default:var r="Unexpected lexeme type '"+n.type+"'";throw new D.QueryParseError(r,n.start,n.end)}else e.nextClause()}},D.QueryParser.parseEditDistance=function(e){var t=e.consumeLexeme();if(null!=t){var n=parseInt(t.str,10);if(isNaN(n)){var r="edit distance must be numeric";throw new D.QueryParseError(r,t.start,t.end)}e.currentClause.editDistance=n;var a=e.peekLexeme();if(null!=a)switch(a.type){case D.QueryLexer.TERM:return e.nextClause(),D.QueryParser.parseTerm;case D.QueryLexer.FIELD:return e.nextClause(),D.QueryParser.parseField;case D.QueryLexer.EDIT_DISTANCE:return D.QueryParser.parseEditDistance;case D.QueryLexer.BOOST:return D.QueryParser.parseBoost;case D.QueryLexer.PRESENCE:return e.nextClause(),D.QueryParser.parsePresence;default:r="Unexpected lexeme type '"+a.type+"'";throw new D.QueryParseError(r,a.start,a.end)}else e.nextClause()}},D.QueryParser.parseBoost=function(e){var t=e.consumeLexeme();if(null!=t){var n=parseInt(t.str,10);if(isNaN(n)){var r="boost must be numeric";throw new D.QueryParseError(r,t.start,t.end)}e.currentClause.boost=n;var a=e.peekLexeme();if(null!=a)switch(a.type){case D.QueryLexer.TERM:return e.nextClause(),D.QueryParser.parseTerm;case 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e.languages.kotlin["class-name"];var t={"interpolation-punctuation":{pattern:/^\$\{?|\}$/,alias:"punctuation"},expression:{pattern:/[\s\S]+/,inside:e.languages.kotlin}};e.languages.insertBefore("kotlin","string",{"string-literal":[{pattern:/"""(?:[^$]|\$(?:(?!\{)|\{[^{}]*\}))*?"""/,alias:"multiline",inside:{interpolation:{pattern:/\$(?:[a-z_]\w*|\{[^{}]*\})/i,inside:t},string:/[\s\S]+/}},{pattern:/"(?:[^"\\\r\n$]|\\.|\$(?:(?!\{)|\{[^{}]*\}))*"/,alias:"singleline",inside:{interpolation:{pattern:/((?:^|[^\\])(?:\\{2})*)\$(?:[a-z_]\w*|\{[^{}]*\})/i,lookbehind:!0,inside:t},string:/[\s\S]+/}}],char:{pattern:/'(?:[^'\\\r\n]|\\(?:.|u[a-fA-F0-9]{0,4}))'/,greedy:!0}}),delete e.languages.kotlin.string,e.languages.insertBefore("kotlin","keyword",{annotation:{pattern:/\B@(?:\w+:)?(?:[A-Z]\w*|\[[^\]]+\])/,alias:"builtin"}}),e.languages.insertBefore("kotlin","function",{label:{pattern:/\b\w+@|@\w+\b/,alias:"symbol"}}),e.languages.kt=e.languages.kotlin,e.languages.kts=e.languages.kotlin}(A),A.languages.c=A.languages.extend("clike",{comment:{pattern:/\/\/(?:[^\r\n\\]|\\(?:\r\n?|\n|(?![\r\n])))*|\/\*[\s\S]*?(?:\*\/|$)/,greedy:!0},string:{pattern:/"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"/,greedy:!0},"class-name":{pattern:/(\b(?:enum|struct)\s+(?:__attribute__\s*\(\([\s\S]*?\)\)\s*)?)\w+|\b[a-z]\w*_t\b/,lookbehind:!0},keyword:/\b(?:_Alignas|_Alignof|_Atomic|_Bool|_Complex|_Generic|_Imaginary|_Noreturn|_Static_assert|_Thread_local|__attribute__|asm|auto|break|case|char|const|continue|default|do|double|else|enum|extern|float|for|goto|if|inline|int|long|register|return|short|signed|sizeof|static|struct|switch|typedef|typeof|union|unsigned|void|volatile|while)\b/,function:/\b[a-z_]\w*(?=\s*\()/i,number:/(?:\b0x(?:[\da-f]+(?:\.[\da-f]*)?|\.[\da-f]+)(?:p[+-]?\d+)?|(?:\b\d+(?:\.\d*)?|\B\.\d+)(?:e[+-]?\d+)?)[ful]{0,4}/i,operator:/>>=?|<<=?|->|([-+&|:])\1|[?:~]|[-+*/%&|^!=<>]=?/}),A.languages.insertBefore("c","string",{char:{pattern:/'(?:\\(?:\r\n|[\s\S])|[^'\\\r\n]){0,32}'/,greedy:!0}}),A.languages.insertBefore("c","string",{macro:{pattern:/(^[\t 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t=/\/\*(?:[^*/]|\*(?!\/)|\/(?!\*)|<self>)*\*\//.source,n=0;n<2;n++)t=t.replace(/<self>/g,(function(){return 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A.languages.go["class-name"],function(e){var t=/\b(?:alignas|alignof|asm|auto|bool|break|case|catch|char|char16_t|char32_t|char8_t|class|co_await|co_return|co_yield|compl|concept|const|const_cast|consteval|constexpr|constinit|continue|decltype|default|delete|do|double|dynamic_cast|else|enum|explicit|export|extern|final|float|for|friend|goto|if|import|inline|int|int16_t|int32_t|int64_t|int8_t|long|module|mutable|namespace|new|noexcept|nullptr|operator|override|private|protected|public|register|reinterpret_cast|requires|return|short|signed|sizeof|static|static_assert|static_cast|struct|switch|template|this|thread_local|throw|try|typedef|typeid|typename|uint16_t|uint32_t|uint64_t|uint8_t|union|unsigned|using|virtual|void|volatile|wchar_t|while)\b/,n=/\b(?!<keyword>)\w+(?:\s*\.\s*\w+)*\b/.source.replace(/<keyword>/g,(function(){return t.source}));e.languages.cpp=e.languages.extend("c",{"class-name":[{pattern:RegExp(/(\b(?:class|concept|enum|struct|typename)\s+)(?!<keyword>)\w+/.source.replace(/<keyword>/g,(function(){return t.source}))),lookbehind:!0},/\b[A-Z]\w*(?=\s*::\s*\w+\s*\()/,/\b[A-Z_]\w*(?=\s*::\s*~\w+\s*\()/i,/\b\w+(?=\s*<(?:[^<>]|<(?:[^<>]|<[^<>]*>)*>)*>\s*::\s*\w+\s*\()/],keyword:t,number:{pattern:/(?:\b0b[01']+|\b0x(?:[\da-f']+(?:\.[\da-f']*)?|\.[\da-f']+)(?:p[+-]?[\d']+)?|(?:\b[\d']+(?:\.[\d']*)?|\B\.[\d']+)(?:e[+-]?[\d']+)?)[ful]{0,4}/i,greedy:!0},operator:/>>=?|<<=?|->|--|\+\+|&&|\|\||[?:~]|<=>|[-+*/%&|^!=<>]=?|\b(?:and|and_eq|bitand|bitor|not|not_eq|or|or_eq|xor|xor_eq)\b/,boolean:/\b(?:false|true)\b/}),e.languages.insertBefore("cpp","string",{module:{pattern:RegExp(/(\b(?:import|module)\s+)/.source+"(?:"+/"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"|<[^<>\r\n]*>/.source+"|"+/<mod-name>(?:\s*:\s*<mod-name>)?|:\s*<mod-name>/.source.replace(/<mod-name>/g,(function(){return n}))+")"),lookbehind:!0,greedy:!0,inside:{string:/^[<"][\s\S]+/,operator:/:/,punctuation:/\./}},"raw-string":{pattern:/R"([^()\\ 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diff --git a/blog/atom.xml b/blog/atom.xml
index c39092ce6..25e45b8ef 100644
--- a/blog/atom.xml
+++ b/blog/atom.xml
@@ -1,20 +1,20 @@
 <?xml version="1.0" encoding="utf-8"?>
 <feed xmlns="http://www.w3.org/2005/Atom">
-    <id>https://www.szdev.com/blog</id>
+    <id>https://ShangjinTang.github.io/blog</id>
     <title>Sol 的空间 Blog</title>
     <updated>2024-10-18T00:00:00.000Z</updated>
     <generator>https://github.com/jpmonette/feed</generator>
-    <link rel="alternate" href="https://www.szdev.com/blog"/>
+    <link rel="alternate" href="https://ShangjinTang.github.io/blog"/>
     <subtitle>Sol 的空间 Blog</subtitle>
-    <icon>https://www.szdev.com/img/favicon_sol.ico</icon>
+    <icon>https://ShangjinTang.github.io/img/favicon_sol.ico</icon>
     <entry>
         <title type="html"><![CDATA[支持嵌入 YouTube 和 Bilibili 视频]]></title>
-        <id>https://www.szdev.com/blog/mdx/support-video-link</id>
-        <link href="https://www.szdev.com/blog/mdx/support-video-link"/>
+        <id>https://ShangjinTang.github.io/blog/mdx/support-video-link</id>
+        <link href="https://ShangjinTang.github.io/blog/mdx/support-video-link"/>
         <updated>2024-10-18T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。]]></summary>
         <content type="html"><![CDATA[<p>基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参数说明">参数说明<a href="https://www.szdev.com/blog/mdx/support-video-link#%E5%8F%82%E6%95%B0%E8%AF%B4%E6%98%8E" class="hash-link" aria-label="参数说明的直接链接" title="参数说明的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参数说明">参数说明<a href="https://shangjintang.github.io/blog/mdx/support-video-link#%E5%8F%82%E6%95%B0%E8%AF%B4%E6%98%8E" class="hash-link" aria-label="参数说明的直接链接" title="参数说明的直接链接">​</a></h2>
 <p>React 组件： <code>YouTube</code> / <code>Bilibili</code></p>
 <p>组件参数：</p>
 <ul>
@@ -26,11 +26,11 @@
 </li>
 <li><code>title</code>: 可选。位置在视频上方；左对齐。</li>
 </ul>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="示例">示例<a href="https://www.szdev.com/blog/mdx/support-video-link#%E7%A4%BA%E4%BE%8B" class="hash-link" aria-label="示例的直接链接" title="示例的直接链接">​</a></h2>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="youtube-嵌入">YouTube 嵌入<a href="https://www.szdev.com/blog/mdx/support-video-link#youtube-%E5%B5%8C%E5%85%A5" class="hash-link" aria-label="YouTube 嵌入的直接链接" title="YouTube 嵌入的直接链接">​</a></h3>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="示例">示例<a href="https://shangjintang.github.io/blog/mdx/support-video-link#%E7%A4%BA%E4%BE%8B" class="hash-link" aria-label="示例的直接链接" title="示例的直接链接">​</a></h2>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="youtube-嵌入">YouTube 嵌入<a href="https://shangjintang.github.io/blog/mdx/support-video-link#youtube-%E5%B5%8C%E5%85%A5" class="hash-link" aria-label="YouTube 嵌入的直接链接" title="YouTube 嵌入的直接链接">​</a></h3>
 <div class="language-jsx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-jsx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token tag punctuation" style="color:#393A34">&lt;</span><span class="token tag class-name" style="color:#00009f">YouTube</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">id</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag attr-value" style="color:#e3116c">sEQf5lcnj_o</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">title</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag attr-value" style="color:#e3116c">Animenz - Unravel [Piano Ver.]</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag" style="color:#00009f"> </span><span class="token tag punctuation" style="color:#393A34">/&gt;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <div class="video-wrap"><p class="video-title">Animenz - Unravel [Piano Ver.]</p><div class="video-container"><div style="position:relative;padding:30% 45%"><iframe style="position:absolute;width:100%;height:100%;left:0;top:0" src="https://www.youtube.com/embed/sEQf5lcnj_o?autoplay=0&amp;enablejsapi=1" allowfullscreen="" sandbox="allow-top-navigation allow-same-origin allow-forms allow-scripts" frameborder="0"></iframe></div><p></p></div></div>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="bilibili-嵌入">Bilibili 嵌入<a href="https://www.szdev.com/blog/mdx/support-video-link#bilibili-%E5%B5%8C%E5%85%A5" class="hash-link" aria-label="Bilibili 嵌入的直接链接" title="Bilibili 嵌入的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="bilibili-嵌入">Bilibili 嵌入<a href="https://shangjintang.github.io/blog/mdx/support-video-link#bilibili-%E5%B5%8C%E5%85%A5" class="hash-link" aria-label="Bilibili 嵌入的直接链接" title="Bilibili 嵌入的直接链接">​</a></h3>
 <div class="language-jsx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-jsx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token tag punctuation" style="color:#393A34">&lt;</span><span class="token tag class-name" style="color:#00009f">Bilibili</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">id</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag attr-value" style="color:#e3116c">BV1bi4y1675m</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">title</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag attr-value" style="color:#e3116c">Animenz - Unravel [钢琴版]</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag" style="color:#00009f"> </span><span class="token tag punctuation" style="color:#393A34">/&gt;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <div class="video-wrap"><p class="video-title">Animenz - Unravel [钢琴版]</p><div class="video-container"><div style="position:relative;padding:30% 45%"><iframe style="position:absolute;width:100%;height:100%;left:0;top:0" src="https://player.bilibili.com/player.html?cid=&amp;bvid=BV1px411A7ir&amp;aid=&amp;page=1&amp;as_wide=0&amp;high_quality=1&amp;danmaku=1&amp;autoplay=0" allowfullscreen="" frameborder="0" sandbox="allow-top-navigation allow-same-origin allow-forms allow-scripts" scrolling="no"></iframe></div><p></p></div></div>]]></content>
         <author>
@@ -44,8 +44,8 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[更改默认字体]]></title>
-        <id>https://www.szdev.com/blog/site/change-default-fonts</id>
-        <link href="https://www.szdev.com/blog/site/change-default-fonts"/>
+        <id>https://ShangjinTang.github.io/blog/site/change-default-fonts</id>
+        <link href="https://ShangjinTang.github.io/blog/site/change-default-fonts"/>
         <updated>2024-10-17T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[本站默认字体现已更改为 LxgwWenKai Screen.]]></summary>
         <content type="html"><![CDATA[<p>本站默认字体现已更改为 <a href="https://github.com/lxgw/LxgwWenKai-Screen" target="_blank" rel="noopener noreferrer">LxgwWenKai Screen</a>.</p>]]></content>
@@ -58,8 +58,8 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[统一中文排版]]></title>
-        <id>https://www.szdev.com/blog/tools/cli/autocorrect</id>
-        <link href="https://www.szdev.com/blog/tools/cli/autocorrect"/>
+        <id>https://ShangjinTang.github.io/blog/tools/cli/autocorrect</id>
+        <link href="https://ShangjinTang.github.io/blog/tools/cli/autocorrect"/>
         <updated>2024-10-16T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[本站使用 autocorrect 对中文内容进行统一排版和修正。]]></summary>
         <content type="html"><![CDATA[<p>本站使用 <a href="https://github.com/huacnlee/autocorrect" target="_blank" rel="noopener noreferrer">autocorrect</a> 对中文内容进行统一排版和修正。</p>]]></content>
@@ -70,8 +70,8 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[模板元编程：斐波那契数列]]></title>
-        <id>https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming</id>
-        <link href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming"/>
+        <id>https://ShangjinTang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming</id>
+        <link href="https://ShangjinTang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming"/>
         <updated>2024-02-20T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[在编程中，斐波那契数列是一个经典的数学问题。通常情况下，我们可以使用传统递归函数来计算斐波那契数列。但是运行时计算递归会造成比较长的耗时。]]></summary>
         <content type="html"><![CDATA[<p>在编程中，斐波那契数列是一个经典的数学问题。通常情况下，我们可以使用传统递归函数来计算斐波那契数列。但是运行时计算递归会造成比较长的耗时。</p>
@@ -82,11 +82,11 @@
 <li>从 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">1</span></span></span></span> 开始： <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mn>5</mn><mo separator="true">,</mo><mn>8</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">1,1,2,3,5,8,...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">5</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">8</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">...</span></span></span></span></li>
 </ul>
 <p>我们假设从 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">0</span></span></span></span> 开始，即 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mtext>，</mtext><mi>f</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mtext>，</mtext><mi>f</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mtext>，</mtext><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex"> f(0) = 0，f(1) = 1，f(2) = 1，...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord">0</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">0</span><span class="mord cjk_fallback">，</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord">...</span></span></span></span>。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="传统递归">传统递归<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E4%BC%A0%E7%BB%9F%E9%80%92%E5%BD%92" class="hash-link" aria-label="传统递归的直接链接" title="传统递归的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="传统递归">传统递归<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E4%BC%A0%E7%BB%9F%E9%80%92%E5%BD%92" class="hash-link" aria-label="传统递归的直接链接" title="传统递归的直接链接">​</a></h2>
 <div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">/**</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * @file fibonacci_recursive.cpp</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * @brief calculate fibonacci value recursively</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">calc_fibonacci</span><span class="token punctuation" style="color:#393A34">(</span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> i</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">i </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">||</span><span class="token plain"> i </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> i</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">calc_fibonacci</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">i </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">calc_fibonacci</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">i </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">calc_fibonacci</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">42</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">'\n'</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">&gt; g++ -O0 -g a.out fibonacci_recursive.cpp -o prog_fibonacci_recursive</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&gt; ./prog_fibonacci_recursive</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">267914296</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&gt; hyperfine "./prog_fibonacci_recursive"</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Benchmark 1: ./prog_fibonacci_recursive</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Time (mean ± σ):      1.657 s ±  0.015 s    [User: 1.652 s, System: 0.002 s]</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Range (min … max):    1.647 s …  1.696 s    10 runs</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="模板元编程实现">模板元编程实现<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E6%A8%A1%E6%9D%BF%E5%85%83%E7%BC%96%E7%A8%8B%E5%AE%9E%E7%8E%B0" class="hash-link" aria-label="模板元编程实现的直接链接" title="模板元编程实现的直接链接">​</a></h2>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c11">C++11<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c11" class="hash-link" aria-label="C++11的直接链接" title="C++11的直接链接">​</a></h3>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="模板元编程实现">模板元编程实现<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E6%A8%A1%E6%9D%BF%E5%85%83%E7%BC%96%E7%A8%8B%E5%AE%9E%E7%8E%B0" class="hash-link" aria-label="模板元编程实现的直接链接" title="模板元编程实现的直接链接">​</a></h2>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c11">C++11<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c11" class="hash-link" aria-label="C++11的直接链接" title="C++11的直接链接">​</a></h3>
 <p>首先，我们定义一个模板类 <code>fibonacci</code>，它具有一个静态成员变量 <code>value</code>，用于存储斐波那契数列的值。该模板类使用递归定义，根据给定的大小计算斐波那契数列值。</p>
 <div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>使用 <code>fibonacci&lt;42&gt;::value</code> 则可以得到对应的结果。这个语法类似于传统的递归，但是会在编译期进行求值。</p>
@@ -94,7 +94,7 @@
 <p>这里使用了编译期求值的关键字 <code>constexpr</code>，因此需要 C++11 版本及以上。</p>
 <div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">&gt; g++ -O0 -g -std=c++11 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&gt; ./prog_fibonacci_tmp</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">267914296</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&gt; hyperfine "./prog_fibonacci_tmp"</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Benchmark 1: ./prog_fibonacci_tmp</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Time (mean ± σ):       0.8 ms ±   0.1 ms    [User: 0.9 ms, System: 0.2 ms]</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Range (min … max):     0.6 ms …   1.5 ms    1605 runs</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p><strong>在计算第 42 个斐波那契数的时候，运行时间仅需 ~0.8ms，相当于传统递归方法 ~1.6s 的 1/2000。</strong></p>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c14">C++14<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c14" class="hash-link" aria-label="C++14的直接链接" title="C++14的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c14">C++14<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c14" class="hash-link" aria-label="C++14的直接链接" title="C++14的直接链接">​</a></h3>
 <p>在 C++17 中，通常使用 <code>_v</code> 结尾当作 <code>value</code> 类型 (参见这篇 <a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n3854.htm" target="_blank" rel="noopener noreferrer">proposal</a>)，比如：</p>
 <div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">T</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">bool</span><span class="token plain"> is_integral_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> is_integral</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">T</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>类似的，我们可以定义一个模板变量 <code>fibonacci_v</code>，用于方便地获取斐波那契数列的值。</p>
@@ -102,12 +102,12 @@
 <p>注意，这种 <code>_v</code> 的实现并不需要 C++17 的编译器；C++14 的编译器即可以满足需求。</p>
 <p>编译：</p>
 <div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">&gt; g++ -O0 -g -std=c++14 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c20">C++20<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c20" class="hash-link" aria-label="C++20的直接链接" title="C++20的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c20">C++20<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c20" class="hash-link" aria-label="C++20的直接链接" title="C++20的直接链接">​</a></h3>
 <p>C++20 中，我们可以使用 <code>concept</code> / <code>requires</code>，合并两个偏特化模板。</p>
 <div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">template &lt;int size&gt;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">concept FibonacciBaseCase = (size == 0) || (size == 1);</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">template &lt;int size&gt;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">requires FibonacciBaseCase&lt;size&gt;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">struct fibonacci&lt;size&gt; {</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">public:</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    static constexpr unsigned int value = size;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">};</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>编译：</p>
 <div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">&gt; g++ -O0 -g -std=c++20 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="完整代码">完整代码<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E5%AE%8C%E6%95%B4%E4%BB%A3%E7%A0%81" class="hash-link" aria-label="完整代码的直接链接" title="完整代码的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="完整代码">完整代码<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E5%AE%8C%E6%95%B4%E4%BB%A3%E7%A0%81" class="hash-link" aria-label="完整代码的直接链接" title="完整代码的直接链接">​</a></h2>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">c++11</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">c++14</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">c++20</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">'\n'</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">auto</span><span class="token plain"> fibonacci_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic">// std::cout &lt;&lt; fibonacci&lt;42&gt;::value &lt;&lt; '\n';</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci_v</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">'\n'</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// template &lt;&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// struct fibonacci&lt;0&gt; {</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// public:</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">//     static constexpr unsigned int value = 0;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// };</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// template &lt;&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// struct fibonacci&lt;1&gt; {</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// public:</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">//     static constexpr unsigned int value = 1;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// };</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">concept</span><span class="token plain"> </span><span class="token class-name">FibonacciBaseCase</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">||</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">requires</span><span class="token plain"> FibonacciBaseCase</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> size</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">auto</span><span class="token plain"> fibonacci_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci_v</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">'\n'</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <p>通过使用模板元编程技术，我们可以在编译时计算斐波那契数列，避免了递归函数的重复计算，在一些需要高效计算斐波那契数列的场景下，这种方法可以提供更好的性能。</p>
 <p>希望这篇博客能帮助你理解如何使用模板元编程实现斐波那契数列的编译期计算，并对此有所启发。</p>]]></content>
@@ -120,19 +120,19 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[Ubuntu 22.04 更新 C++ 编译器]]></title>
-        <id>https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204</id>
-        <link href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204"/>
+        <id>https://ShangjinTang.github.io/blog/cpp/update-compiler-on-ubuntu2204</id>
+        <link href="https://ShangjinTang.github.io/blog/cpp/update-compiler-on-ubuntu2204"/>
         <updated>2024-01-31T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[Ubuntu 22.04 默认使用 g++-11 和 clang++-14 作为默认的 g++ 和 clang++。]]></summary>
         <content type="html"><![CDATA[<p>Ubuntu 22.04 默认使用 <code>g++-11</code> 和 <code>clang++-14</code> 作为默认的 <code>g++</code> 和 <code>clang++</code>。</p>
 <p>本文说明如何升级 C++ 编译器并设置默认版本，从而使用最新的 C++ 语言特性。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-c++-compiler">安装最新版本的 C++ 编译器<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#install-latest-c++-compiler" class="hash-link" aria-label="安装最新版本的 C++ 编译器的直接链接" title="安装最新版本的 C++ 编译器的直接链接">​</a></h2>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-g++">安装最新的 g++<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#install-latest-g++" class="hash-link" aria-label="安装最新的 g++的直接链接" title="安装最新的 g++的直接链接">​</a></h3>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-c++-compiler">安装最新版本的 C++ 编译器<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#install-latest-c++-compiler" class="hash-link" aria-label="安装最新版本的 C++ 编译器的直接链接" title="安装最新版本的 C++ 编译器的直接链接">​</a></h2>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-g++">安装最新的 g++<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#install-latest-g++" class="hash-link" aria-label="安装最新的 g++的直接链接" title="安装最新的 g++的直接链接">​</a></h3>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">apt</span><span class="token plain"> update</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> add-apt-repository ppa:ubuntu-toolchain-r/test</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">apt</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">install</span><span class="token plain"> gcc-12 g++-12 </span><span class="token parameter variable" style="color:#36acaa">-y</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">apt</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">install</span><span class="token plain"> gcc-13 g++-13 </span><span class="token parameter variable" style="color:#36acaa">-y</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-clang++">安装最新的 clang++<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#install-latest-clang++" class="hash-link" aria-label="安装最新的 clang++的直接链接" title="安装最新的 clang++的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-clang++">安装最新的 clang++<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#install-latest-clang++" class="hash-link" aria-label="安装最新的 clang++的直接链接" title="安装最新的 clang++的直接链接">​</a></h3>
 <p>参见 <a href="https://apt.llvm.org/" target="_blank" rel="noopener noreferrer">LLVM Debian/Ubuntu Packages</a> 中的安装指南：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">wget</span><span class="token plain"> https://apt.llvm.org/llvm.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">chmod</span><span class="token plain"> +x llvm.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># sudo ./llvm.sh &lt;version number&gt; all</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># or</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># sudo ./llvm.sh all</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> ./llvm.sh </span><span class="token number" style="color:#36acaa">18</span><span class="token plain"> all</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-default-version">切换编译器的默认版本<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#change-default-version" class="hash-link" aria-label="切换编译器的默认版本的直接链接" title="切换编译器的默认版本的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-default-version">切换编译器的默认版本<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#change-default-version" class="hash-link" aria-label="切换编译器的默认版本的直接链接" title="切换编译器的默认版本的直接链接">​</a></h2>
 <p>上述命令执行之后，我们会发现，<code>g++</code> 仍然是 <code>g++11</code>，<code>clang++</code> 仍然是 <code>clang++-14</code>。</p>
 <p>这里介绍一下 <code>update-alternatives</code>，由于管理 Ubuntu 上软件版本的切换，使其多版本共存。语法：</p>
 <p>注册可选的软件版本：</p>
@@ -140,7 +140,7 @@
 <p>切换默认的软件版本：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--config</span><span class="token plain"> name</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <div class="theme-admonition theme-admonition-warning admonition_xJq3 alert alert--warning"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>注意</div><div class="admonitionContent_BuS1"><p>切换编译器软件包可能有风险，建议只在个人计算机上使用。</p></div></div>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-g++-default-version">切换 g++ 的默认版本<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#change-g++-default-version" class="hash-link" aria-label="切换 g++ 的默认版本的直接链接" title="切换 g++ 的默认版本的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-g++-default-version">切换 g++ 的默认版本<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#change-g++-default-version" class="hash-link" aria-label="切换 g++ 的默认版本的直接链接" title="切换 g++ 的默认版本的直接链接">​</a></h3>
 <p>注册 <code>gcc</code> / <code>g++</code> 版本：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--install</span><span class="token plain"> /usr/bin/gcc gcc /usr/bin/gcc-11 </span><span class="token number" style="color:#36acaa">11</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--slave</span><span class="token plain"> /usr/bin/g++ g++ /usr/bin/g++-11</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--install</span><span class="token plain"> /usr/bin/gcc gcc /usr/bin/gcc-12 </span><span class="token number" style="color:#36acaa">12</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--slave</span><span class="token plain"> /usr/bin/g++ g++ /usr/bin/g++-12</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--install</span><span class="token plain"> /usr/bin/gcc gcc /usr/bin/gcc-13 </span><span class="token number" style="color:#36acaa">13</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--slave</span><span class="token plain"> /usr/bin/g++ g++ /usr/bin/g++-13</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>选择默认 <code>gcc</code> / <code>g++</code> 版本：</p>
@@ -148,7 +148,7 @@
 <p>会弹出以下选项：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">There are </span><span class="token number" style="color:#36acaa">3</span><span class="token plain"> choices </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> the alternative gcc </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">providing /usr/bin/gcc</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">.</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Selection    Path             Priority   Status</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">------------------------------------------------------------</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">* </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">            /usr/bin/gcc-13   </span><span class="token number" style="color:#36acaa">13</span><span class="token plain">        auto mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">            /usr/bin/gcc-11   </span><span class="token number" style="color:#36acaa">11</span><span class="token plain">        manual mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token number" style="color:#36acaa">2</span><span class="token plain">            /usr/bin/gcc-12   </span><span class="token number" style="color:#36acaa">12</span><span class="token plain">        manual mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token number" style="color:#36acaa">3</span><span class="token plain">            /usr/bin/gcc-13   </span><span class="token number" style="color:#36acaa">13</span><span class="token plain">        manual mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Press </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">enter</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> to keep the current choice</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">*</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">, or </span><span class="token builtin class-name">type</span><span class="token plain"> selection number:</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>输入序号即可。</p>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-clang++-default-version">切换 clang++ 的默认版本<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#change-clang++-default-version" class="hash-link" aria-label="切换 clang++ 的默认版本的直接链接" title="切换 clang++ 的默认版本的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-clang++-default-version">切换 clang++ 的默认版本<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#change-clang++-default-version" class="hash-link" aria-label="切换 clang++ 的默认版本的直接链接" title="切换 clang++ 的默认版本的直接链接">​</a></h3>
 <p><code>clang</code> / <code>clang++</code> 是 LLVM 工具链的一部分，更新的时候，建议把 llvm 所有工具一起更新。</p>
 <p>这里使用以下脚本 <code>update-alternatives-clang.sh</code> 进行批量注册：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token shebang important">#!/usr/bin/env bash</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Colors</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">RESET</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable" style="color:#36acaa">tput sgr0</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">RED</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable" style="color:#36acaa">tput setaf </span><span class="token variable number" style="color:#36acaa">1</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">GREEN</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable" style="color:#36acaa">tput setaf </span><span class="token variable number" style="color:#36acaa">2</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">BOLD</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable" style="color:#36acaa">tput bold</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Get available versions from /lib/llvm-*</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># You can also use specific versions, e.g. VERSIONS=("14" "17" "18"), but not recommend</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">VERSIONS</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> </span><span class="token for-or-select variable" style="color:#36acaa">dir</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> /lib/llvm-*</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">do</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-d</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$dir</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">version</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable function" style="color:#d73a49">basename</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable string" style="color:#e3116c">"</span><span class="token variable string variable" style="color:#36acaa">$dir</span><span class="token variable string" style="color:#e3116c">"</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable operator" style="color:#393A34">|</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable function" style="color:#d73a49">cut</span><span class="token variable" style="color:#36acaa"> -d</span><span class="token variable string" style="color:#e3116c">'-'</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable parameter variable" style="color:#36acaa">-f2</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">VERSIONS</span><span class="token operator" style="color:#393A34">+=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$version</span><span class="token string" style="color:#e3116c">"</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">done</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Loop through versions</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> </span><span class="token for-or-select variable" style="color:#36acaa">VERSION</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${VERSIONS</span><span class="token string variable punctuation" style="color:#393A34">[</span><span class="token string variable" style="color:#36acaa">@</span><span class="token string variable punctuation" style="color:#393A34">]</span><span class="token string variable" style="color:#36acaa">}</span><span class="token string" style="color:#e3116c">"</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">do</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic"># Check if /lib/llvm-${VERSION} directory exists</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-d</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"/lib/llvm-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Scan paths and generate string</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">alternative_string</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">""</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">alternative_cmds</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> </span><span class="token for-or-select variable" style="color:#36acaa">cmd</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"/lib/llvm-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">/bin/"</span><span class="token plain">*</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">do</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-x</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$cmd</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&amp;&amp;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$(</span><span class="token string variable function" style="color:#d73a49">basename</span><span class="token string variable" style="color:#36acaa"> </span><span class="token string variable string" style="color:#e3116c">"</span><span class="token string variable string variable" style="color:#36acaa">$cmd</span><span class="token string variable string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">)</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">!=</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"clang"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token assign-left variable" style="color:#36acaa">base_cmd</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable function" style="color:#d73a49">basename</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable string" style="color:#e3116c">"</span><span class="token variable string variable" style="color:#36acaa">$cmd</span><span class="token variable string" style="color:#e3116c">"</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token assign-left variable" style="color:#36acaa">symlink</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">"/usr/bin/</span><span class="token string variable" style="color:#36acaa">${base_cmd}</span><span class="token string" style="color:#e3116c">-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-x</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${symlink}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    </span><span class="token assign-left variable" style="color:#36acaa">alternative_cmds</span><span class="token operator" style="color:#393A34">+=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable function" style="color:#d73a49">basename</span><span class="token variable" style="color:#36acaa"> $</span><span class="token variable punctuation" style="color:#393A34">{</span><span class="token variable" style="color:#36acaa">symlink</span><span class="token variable punctuation" style="color:#393A34">}</span><span class="token variable" style="color:#36acaa">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    </span><span class="token assign-left variable" style="color:#36acaa">alternative_string</span><span class="token operator" style="color:#393A34">+=</span><span class="token string" style="color:#e3116c">"--slave /usr/bin/</span><span class="token string variable" style="color:#36acaa">${base_cmd}</span><span class="token string" style="color:#e3116c"> </span><span class="token string variable" style="color:#36acaa">${base_cmd}</span><span class="token string" style="color:#e3116c"> </span><span class="token string variable" style="color:#36acaa">${symlink}</span><span class="token string" style="color:#e3116c"> "</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">done</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Remove specific alternative configuration</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--remove</span><span class="token plain"> clang </span><span class="token string" style="color:#e3116c">"/usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> /dev/null</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Install alternatives</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">install_command</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">"sudo update-alternatives \</span><br></span><span class="token-line" style="color:#393A34"><span class="token string" style="color:#e3116c">        --quiet \</span><br></span><span class="token-line" style="color:#393A34"><span class="token string" style="color:#e3116c">        --install /usr/bin/clang clang /usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c"> </span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c"> \</span><br></span><span class="token-line" style="color:#393A34"><span class="token string" style="color:#e3116c">        </span><span class="token string variable" style="color:#36acaa">${alternative_string}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Print the concatenated string</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${BOLD}</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">[Adding alternative /usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c"> ...]</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"Master command: clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"Slave commands: </span><span class="token string variable" style="color:#36acaa">${alternative_cmds</span><span class="token string variable punctuation" style="color:#393A34">[</span><span class="token string variable" style="color:#36acaa">*</span><span class="token string variable punctuation" style="color:#393A34">]</span><span class="token string variable" style="color:#36acaa">}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">eval</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$install_command</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Check eval command's return value</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">$?</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-eq</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${BOLD}</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">[Adding alternative /usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">: succeeded]</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">else</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${BOLD}</span><span class="token string variable" style="color:#36acaa">${RED}</span><span class="token string" style="color:#e3116c">[Adding alternative /usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">: failed]</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">""</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">else</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Remove specific alternative configuration if /lib/llvm-${VERSION} directory does not exist</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--remove</span><span class="token plain"> clang </span><span class="token string" style="color:#e3116c">"/usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&amp;&gt;</span><span class="token plain"> /dev/null</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">done</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">clang_path</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable function" style="color:#d73a49">sudo</span><span class="token variable" style="color:#36acaa"> update-alternatives --get-selections </span><span class="token variable operator" style="color:#393A34">|</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable function" style="color:#d73a49">grep</span><span class="token variable" style="color:#36acaa"> ^clang </span><span class="token variable operator" style="color:#393A34">|</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable function" style="color:#d73a49">awk</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable string" style="color:#e3116c">'{print $NF}'</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"======================================================================"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">clang alternative is set to: </span><span class="token string variable" style="color:#36acaa">${clang_path}</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"======================================================================"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># print helps</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">""</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"Info:"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">num_versions</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">${</span><span class="token variable operator" style="color:#393A34">#</span><span class="token variable" style="color:#36acaa">VERSIONS</span><span class="token variable punctuation" style="color:#393A34">[</span><span class="token variable" style="color:#36acaa">@</span><span class="token variable punctuation" style="color:#393A34">]</span><span class="token variable" style="color:#36acaa">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> num_versions </span><span class="token parameter variable" style="color:#36acaa">-gt</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"  use '</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">sudo update-alternatives --config clang</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">' to change default clang alternative"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"  use '</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">sudo update-alternatives --remove clang /usr/bin/clang-*</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">' to delete a clang alternative"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"  use '</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">sudo update-alternatives --remove-all clang</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">' to delete all clang alternatives"</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
@@ -171,8 +171,8 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[停止国际化支持]]></title>
-        <id>https://www.szdev.com/blog/site/remove-i18n-support</id>
-        <link href="https://www.szdev.com/blog/site/remove-i18n-support"/>
+        <id>https://ShangjinTang.github.io/blog/site/remove-i18n-support</id>
+        <link href="https://ShangjinTang.github.io/blog/site/remove-i18n-support"/>
         <updated>2024-01-30T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[删除所有的文章的国际化支持。之前所有文章均有双语版本，后续所有文章只会有单个语言版本。]]></summary>
         <content type="html"><![CDATA[<p>删除所有的文章的国际化支持。之前所有文章均有双语版本，后续所有文章只会有单个语言版本。</p>
@@ -201,8 +201,8 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[支持 Font Awesome]]></title>
-        <id>https://www.szdev.com/blog/mdx/support-fontawesome</id>
-        <link href="https://www.szdev.com/blog/mdx/support-fontawesome"/>
+        <id>https://ShangjinTang.github.io/blog/mdx/support-fontawesome</id>
+        <link href="https://ShangjinTang.github.io/blog/mdx/support-fontawesome"/>
         <updated>2023-12-13T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[现在可以在 mdx 中使用 Font Awesome 图标。]]></summary>
         <content type="html"><![CDATA[<p>现在可以在 mdx 中使用 <a href="https://fontawesome.com/search" target="_blank" rel="noopener noreferrer">Font Awesome 图标</a>。</p>
@@ -230,8 +230,8 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[使用 Leaflet 绘制地图]]></title>
-        <id>https://www.szdev.com/blog/mdx/interactive-map-with-leaflet</id>
-        <link href="https://www.szdev.com/blog/mdx/interactive-map-with-leaflet"/>
+        <id>https://ShangjinTang.github.io/blog/mdx/interactive-map-with-leaflet</id>
+        <link href="https://ShangjinTang.github.io/blog/mdx/interactive-map-with-leaflet"/>
         <updated>2023-11-29T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[Leaflet 是地理信息系统（GIS）中流行的开源 JavaScript 库。]]></summary>
         <content type="html"><![CDATA[<p><a href="https://leafletjs.com/" target="_blank" rel="noopener noreferrer"><strong>Leaflet</strong></a> 是地理信息系统（GIS）中流行的开源 JavaScript 库。</p>
@@ -249,16 +249,16 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[支持 Mermaid 图表]]></title>
-        <id>https://www.szdev.com/blog/mdx/support-mermaid-diagrams</id>
-        <link href="https://www.szdev.com/blog/mdx/support-mermaid-diagrams"/>
+        <id>https://ShangjinTang.github.io/blog/mdx/support-mermaid-diagrams</id>
+        <link href="https://ShangjinTang.github.io/blog/mdx/support-mermaid-diagrams"/>
         <updated>2023-11-27T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[Mermaid 是一个绘制图表的工具。]]></summary>
         <content type="html"><![CDATA[<p>Mermaid 是一个绘制图表的工具。</p>
 <p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="序列图">序列图<a href="https://www.szdev.com/blog/mdx/support-mermaid-diagrams#%E5%BA%8F%E5%88%97%E5%9B%BE" class="hash-link" aria-label="序列图的直接链接" title="序列图的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="序列图">序列图<a href="https://shangjintang.github.io/blog/mdx/support-mermaid-diagrams#%E5%BA%8F%E5%88%97%E5%9B%BE" class="hash-link" aria-label="序列图的直接链接" title="序列图的直接链接">​</a></h2>
 <div class="language-md codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockTitle_Ktv7">Example Mermaid sequence diagram</div><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-md codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token code punctuation" style="color:#393A34">```</span><span class="token code code-language">mermaid</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code code-block language-mermaid">graph TD;</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    A--&gt;B;</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    A--&gt;C;</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    B--&gt;D;</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C--&gt;D;</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code punctuation" style="color:#393A34">```</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <!-- -->
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="流程图">流程图<a href="https://www.szdev.com/blog/mdx/support-mermaid-diagrams#%E6%B5%81%E7%A8%8B%E5%9B%BE" class="hash-link" aria-label="流程图的直接链接" title="流程图的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="流程图">流程图<a href="https://shangjintang.github.io/blog/mdx/support-mermaid-diagrams#%E6%B5%81%E7%A8%8B%E5%9B%BE" class="hash-link" aria-label="流程图的直接链接" title="流程图的直接链接">​</a></h2>
 <div class="language-md codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockTitle_Ktv7">Example Mermaid flowchart</div><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-md codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token code punctuation" style="color:#393A34">```</span><span class="token code code-language">mermaid</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code code-block language-mermaid">flowchart TD</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    A[Christmas] --&gt;|Get money| B(Go shopping)</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    B --&gt; C{Let me think}</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|One| D[Laptop]</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|Two| E[iPhone]</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|Three| F[fa:fa-car Car]</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code punctuation" style="color:#393A34">```</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 ]]></content>
         <author>
@@ -272,8 +272,8 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[支持全局 Tabs 和 TabItem]]></title>
-        <id>https://www.szdev.com/blog/mdx/support-global-tabs-tabitem</id>
-        <link href="https://www.szdev.com/blog/mdx/support-global-tabs-tabitem"/>
+        <id>https://ShangjinTang.github.io/blog/mdx/support-global-tabs-tabitem</id>
+        <link href="https://ShangjinTang.github.io/blog/mdx/support-global-tabs-tabitem"/>
         <updated>2023-11-26T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[Docusaurus 提供了 ` 和 ` 组件，可以通过 MDX 在 Markdown 中使用该组件。]]></summary>
         <content type="html"><![CDATA[<p>Docusaurus 提供了 <code>&lt;Tabs&gt;</code> 和 <code>&lt;TabItem&gt;</code> 组件，可以通过 MDX 在 Markdown 中使用该组件。</p>
@@ -300,18 +300,18 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[支持 LaTeX 数学公式]]></title>
-        <id>https://www.szdev.com/blog/mdx/support-math-latex</id>
-        <link href="https://www.szdev.com/blog/mdx/support-math-latex"/>
+        <id>https://ShangjinTang.github.io/blog/mdx/support-math-latex</id>
+        <link href="https://ShangjinTang.github.io/blog/mdx/support-math-latex"/>
         <updated>2023-11-24T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[数学公式可以使用 KaTeX 渲染，目前本站已经支持。]]></summary>
         <content type="html"><![CDATA[<p>数学公式可以使用 <a href="https://katex.org/" target="_blank" rel="noopener noreferrer">KaTeX</a> 渲染，目前本站已经支持。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="usage">用法<a href="https://www.szdev.com/blog/mdx/support-math-latex#usage" class="hash-link" aria-label="用法的直接链接" title="用法的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="usage">用法<a href="https://shangjintang.github.io/blog/mdx/support-math-latex#usage" class="hash-link" aria-label="用法的直接链接" title="用法的直接链接">​</a></h2>
 <p>请阅读 <a href="https://katex.org/" target="_blank" rel="noopener noreferrer">KaTeX</a> 文档了解更多详细信息。</p>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="inline">行内公式<a href="https://www.szdev.com/blog/mdx/support-math-latex#inline" class="hash-link" aria-label="行内公式的直接链接" title="行内公式的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="inline">行内公式<a href="https://shangjintang.github.io/blog/mdx/support-math-latex#inline" class="hash-link" aria-label="行内公式的直接链接" title="行内公式的直接链接">​</a></h3>
 <p>对于行内数学公式，将 LaTeX 包裹在 <code>$</code> 之间：</p>
 <div class="language-latex codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-latex codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">假设 </span><span class="token equation string" style="color:#e3116c">$f</span><span class="token equation string equation-command regex" style="color:#36acaa">\colon</span><span class="token equation string" style="color:#e3116c">[a,b]</span><span class="token equation string equation-command regex" style="color:#36acaa">\to</span><span class="token equation string equation-command regex" style="color:#36acaa">\R</span><span class="token equation string" style="color:#e3116c">$</span><span class="token plain"> 是黎曼可积的，定义 </span><span class="token equation string" style="color:#e3116c">$F</span><span class="token equation string equation-command regex" style="color:#36acaa">\colon</span><span class="token equation string" style="color:#e3116c">[a,b]</span><span class="token equation string equation-command regex" style="color:#36acaa">\to</span><span class="token equation string equation-command regex" style="color:#36acaa">\R</span><span class="token equation string" style="color:#e3116c">$</span><span class="token plain"> 为 </span><span class="token equation string" style="color:#e3116c">$F(x)=</span><span class="token equation string equation-command regex" style="color:#36acaa">\int</span><span class="token equation string" style="color:#e3116c">_{a}^{x} f(t)</span><span class="token equation string equation-command regex" style="color:#36acaa">\,</span><span class="token equation string" style="color:#e3116c">dt$</span><span class="token plain">。那么， </span><span class="token equation string" style="color:#e3116c">$F$</span><span class="token plain"> 是连续的；并且 </span><span class="token equation string" style="color:#e3116c">$x$</span><span class="token plain"> 在 </span><span class="token equation string" style="color:#e3116c">$f$</span><span class="token plain"> 在 </span><span class="token equation string" style="color:#e3116c">$x$</span><span class="token plain"> 处连续；</span><span class="token equation string" style="color:#e3116c">$F$</span><span class="token plain"> 在 </span><span class="token equation string" style="color:#e3116c">$x$</span><span class="token plain"> 处可微，且 </span><span class="token equation string" style="color:#e3116c">$F'(x)=f(x)$</span><span class="token plain">。</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>假设 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mspace></mspace><mspace width="0.1111em"></mspace><mo lspace="0em" rspace="0.17em"></mo><mtext> ⁣</mtext><mo lspace="0em" rspace="0em">:</mo><mspace width="0.3333em"></mspace><mo stretchy="false">[</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">]</mo><mo>→</mo><mi mathvariant="double-struck">R</mi></mrow><annotation encoding="application/x-tex">f\colon[a,b]\to\R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mspace nobreak"></span><span class="mspace" style="margin-right:0.1111em"></span><span class="mpunct"></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mrel">:</span></span><span class="mspace" style="margin-right:0.3333em"></span><span class="mopen">[</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">b</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6889em"></span><span class="mord mathbb">R</span></span></span></span> 是黎曼可积的，定义 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mspace></mspace><mspace width="0.1111em"></mspace><mo lspace="0em" rspace="0.17em"></mo><mtext> ⁣</mtext><mo lspace="0em" rspace="0em">:</mo><mspace width="0.3333em"></mspace><mo stretchy="false">[</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">]</mo><mo>→</mo><mi mathvariant="double-struck">R</mi></mrow><annotation encoding="application/x-tex">F\colon[a,b]\to\R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.13889em">F</span><span class="mspace nobreak"></span><span class="mspace" style="margin-right:0.1111em"></span><span class="mpunct"></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mrel">:</span></span><span class="mspace" style="margin-right:0.3333em"></span><span class="mopen">[</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">b</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6889em"></span><span class="mord mathbb">R</span></span></span></span> 为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mi>a</mi><mi>x</mi></msubsup><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">F(x)=\int_{a}^{x} f(t)\,dt</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.13889em">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2151em;vertical-align:-0.3558em"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span></span></span></span>。那么， <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi></mrow><annotation encoding="application/x-tex">F</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.13889em">F</span></span></span></span> 是连续的；并且 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> 在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span></span></span></span> 在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> 处连续；<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi></mrow><annotation encoding="application/x-tex">F</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.13889em">F</span></span></span></span> 在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> 处可微，且 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>F</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F'(x)=f(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em">F</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span>。</p>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="blocks">公式块<a href="https://www.szdev.com/blog/mdx/support-math-latex#blocks" class="hash-link" aria-label="公式块的直接链接" title="公式块的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="blocks">公式块<a href="https://shangjintang.github.io/blog/mdx/support-math-latex#blocks" class="hash-link" aria-label="公式块的直接链接" title="公式块的直接链接">​</a></h3>
 <p>对于公式块，使用换行符和 <code>$$</code> 隔开：</p>
 <div class="language-latex codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-latex codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">$$</span><br></span><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">I = </span><span class="token equation string equation-command regex" style="color:#36acaa">\int</span><span class="token equation string" style="color:#e3116c">_0^{2</span><span class="token equation string equation-command regex" style="color:#36acaa">\pi</span><span class="token equation string" style="color:#e3116c">} </span><span class="token equation string equation-command regex" style="color:#36acaa">\sin</span><span class="token equation string" style="color:#e3116c">(x)</span><span class="token equation string equation-command regex" style="color:#36acaa">\,</span><span class="token equation string" style="color:#e3116c">dx</span><br></span><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">$$</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>I</mi><mo>=</mo><msubsup><mo>∫</mo><mn>0</mn><mrow><mn>2</mn><mi>π</mi></mrow></msubsup><mi>sin</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">I = \int_0^{2\pi} \sin(x)\,dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.476em;vertical-align:-0.9119em"></span><span class="mop"><span class="mop op-symbol large-op" style="margin-right:0.44445em;position:relative;top:-0.0011em">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.564em"><span style="top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.8129em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">π</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9119em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop">sin</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span></span>]]></content>
@@ -326,14 +326,14 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[React 支持]]></title>
-        <id>https://www.szdev.com/blog/mdx/react-support</id>
-        <link href="https://www.szdev.com/blog/mdx/react-support"/>
+        <id>https://ShangjinTang.github.io/blog/mdx/react-support</id>
+        <link href="https://ShangjinTang.github.io/blog/mdx/react-support"/>
         <updated>2023-11-23T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[博客文章支持 Docusaurus Markdown 功能，例如 MDX。]]></summary>
         <content type="html"><![CDATA[<p>博客文章支持 <a href="https://docusaurus.io/docs/markdown-features" target="_blank" rel="noopener noreferrer">Docusaurus Markdown 功能</a>，例如 <a href="https://mdxjs.com/" target="_blank" rel="noopener noreferrer">MDX</a>。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="interactive">交互式<a href="https://www.szdev.com/blog/mdx/react-support#interactive" class="hash-link" aria-label="交互式的直接链接" title="交互式的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="interactive">交互式<a href="https://shangjintang.github.io/blog/mdx/react-support#interactive" class="hash-link" aria-label="交互式的直接链接" title="交互式的直接链接">​</a></h2>
 <div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>提示</div><div class="admonitionContent_BuS1"><p>使用 React 的强大功能来创建交互式博客文章。</p><div class="language-js codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-js codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">button onClick</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">{</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=&gt;</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">alert</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">'按钮被点击了!'</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">}</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain">点击这里！</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">button</span><span class="token operator" style="color:#393A34">&gt;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><button>点击这里！</button></div></div>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="diagram">图表式<a href="https://www.szdev.com/blog/mdx/react-support#diagram" class="hash-link" aria-label="图表式的直接链接" title="图表式的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="diagram">图表式<a href="https://shangjintang.github.io/blog/mdx/react-support#diagram" class="hash-link" aria-label="图表式的直接链接" title="图表式的直接链接">​</a></h2>
 <div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>提示</div><div class="admonitionContent_BuS1"><p>使用 React 的强大功能来创建图表。</p><div class="language-mdx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-mdx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">import {Chart} from './_asset/snowfall.js';</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">export const year = 2013;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"># 去年降雪</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">{year} 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&lt;Chart year={year} color="#fcb32c" /&gt;;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h1>去年降雪</h1><p>2013<!-- --> 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。</p><div class="snowfall"><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(6 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(4.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(1.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(1.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(3.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(7 * 0.5 * (1em + 1ex))"></div></div></div></div>]]></content>
         <author>
             <name>Sol</name>
@@ -344,8 +344,8 @@
     </entry>
     <entry>
         <title type="html"><![CDATA[欢迎]]></title>
-        <id>https://www.szdev.com/blog/welcome</id>
-        <link href="https://www.szdev.com/blog/welcome"/>
+        <id>https://ShangjinTang.github.io/blog/welcome</id>
+        <link href="https://ShangjinTang.github.io/blog/welcome"/>
         <updated>2019-05-28T00:00:00.000Z</updated>
         <summary type="html"><![CDATA[Docusaurus 博客功能由 blog 插件提供支持。]]></summary>
         <content type="html"><![CDATA[<p><a href="https://docusaurus.io/docs/blog" target="_blank" rel="noopener noreferrer">Docusaurus 博客功能</a>由 <a href="https://docusaurus.io/docs/api/plugins/@docusaurus/plugin-content-blog" target="_blank" rel="noopener noreferrer">blog 插件</a>提供支持。</p>
@@ -358,7 +358,7 @@
 <li><code>2019-05-30-welcome/index.md</code></li>
 </ul>
 <p>写博客时，可以方便地在同级文件夹内引用图像：</p>
-<p><img decoding="async" loading="lazy" alt="Docusaurus 毛绒玩具" src="https://www.szdev.com/assets/images/docusaurus-plushie-banner-a60f7593abca1e3eef26a9afa244e4fb.jpeg" width="1500" height="500" class="img_ev3q"></p>
+<p><img decoding="async" loading="lazy" alt="Docusaurus 毛绒玩具" src="https://shangjintang.github.io/assets/images/docusaurus-plushie-banner-a60f7593abca1e3eef26a9afa244e4fb.jpeg" width="1500" height="500" class="img_ev3q"></p>
 <p>博客也支持标签！</p>
 <p><strong>如果不需要博客</strong>：删除此目录，并在 Docusaurus 配置中使用 <code>blog: false</code> 即可。</p>]]></content>
         <author>
diff --git a/blog/authors/index.html b/blog/authors/index.html
index 108f97f3b..609cf1d32 100644
--- a/blog/authors/index.html
+++ b/blog/authors/index.html
@@ -3,12 +3,12 @@
 <head>
 <meta charset="UTF-8">
 <meta name="generator" content="Docusaurus v3.5.2">
-<title data-rh="true">Authors | Sol 的空间</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:image" content="https://www.szdev.com/img/docusaurus-social-card.jpg"><meta data-rh="true" name="twitter:image" content="https://www.szdev.com/img/docusaurus-social-card.jpg"><meta data-rh="true" property="og:url" content="https://www.szdev.com/blog/authors"><meta data-rh="true" property="og:locale" content="zh_CN"><meta data-rh="true" name="docusaurus_locale" content="zh-CN"><meta data-rh="true" name="docsearch:language" content="zh-CN"><meta data-rh="true" property="og:title" content="Authors | Sol 的空间"><meta data-rh="true" name="docusaurus_tag" content="blog_authors_list"><meta data-rh="true" name="docsearch:docusaurus_tag" content="blog_authors_list"><link data-rh="true" rel="icon" href="/img/favicon_sol.ico"><link data-rh="true" rel="canonical" href="https://www.szdev.com/blog/authors"><link data-rh="true" rel="alternate" href="https://www.szdev.com/blog/authors" hreflang="zh-CN"><link data-rh="true" rel="alternate" href="https://www.szdev.com/blog/authors" hreflang="x-default"><link rel="alternate" type="application/rss+xml" href="/blog/rss.xml" title="Sol 的空间 RSS Feed">
+<title data-rh="true">Authors | Sol 的空间</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:image" content="https://ShangjinTang.github.io/img/docusaurus-social-card.jpg"><meta data-rh="true" name="twitter:image" content="https://ShangjinTang.github.io/img/docusaurus-social-card.jpg"><meta data-rh="true" property="og:url" content="https://ShangjinTang.github.io/blog/authors"><meta data-rh="true" property="og:locale" content="zh_CN"><meta data-rh="true" name="docusaurus_locale" content="zh-CN"><meta data-rh="true" name="docsearch:language" content="zh-CN"><meta data-rh="true" property="og:title" content="Authors | Sol 的空间"><meta data-rh="true" name="docusaurus_tag" content="blog_authors_list"><meta data-rh="true" name="docsearch:docusaurus_tag" content="blog_authors_list"><link data-rh="true" rel="icon" href="/img/favicon_sol.ico"><link data-rh="true" rel="canonical" href="https://ShangjinTang.github.io/blog/authors"><link data-rh="true" rel="alternate" href="https://ShangjinTang.github.io/blog/authors" hreflang="zh-CN"><link data-rh="true" rel="alternate" href="https://ShangjinTang.github.io/blog/authors" hreflang="x-default"><link rel="alternate" type="application/rss+xml" href="/blog/rss.xml" title="Sol 的空间 RSS Feed">
 <link rel="alternate" type="application/atom+xml" href="/blog/atom.xml" title="Sol 的空间 Atom Feed"><link rel="stylesheet" href="/assets/css/styles.abfd45f8.css">
 <script src="/assets/js/runtime~main.8ec2c78b.js" defer="defer"></script>
-<script src="/assets/js/main.e6ab80d7.js" defer="defer"></script>
+<script src="/assets/js/main.9d499883.js" defer="defer"></script>
 </head>
 <body class="navigation-with-keyboard">
-<script>!function(){function t(t){document.documentElement.setAttribute("data-theme",t)}var e=function(){try{return new URLSearchParams(window.location.search).get("docusaurus-theme")}catch(t){}}()||function(){try{return window.localStorage.getItem("theme")}catch(t){}}();t(null!==e?e:"light")}(),function(){try{const n=new URLSearchParams(window.location.search).entries();for(var[t,e]of n)if(t.startsWith("docusaurus-data-")){var a=t.replace("docusaurus-data-","data-");document.documentElement.setAttribute(a,e)}}catch(t){}}()</script><div id="__docusaurus"><div role="region" aria-label="跳到主要内容"><a class="skipToContent_fXgn" href="#__docusaurus_skipToContent_fallback">跳到主要内容</a></div><nav aria-label="主导航" class="navbar navbar--fixed-top navbarHideable_m1mJ"><div class="navbar__inner"><div class="navbar__items"><button aria-label="切换导航栏" aria-expanded="false" class="navbar__toggle clean-btn" type="button"><svg width="30" height="30" viewBox="0 0 30 30" aria-hidden="true"><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></button><a class="navbar__brand" href="/"><div class="navbar__logo"><img src="/img/logo_sol.jpg" alt="Site Logo" class="themedComponent_mlkZ themedComponent--light_NVdE"><img src="/img/logo_sol.jpg" alt="Site Logo" class="themedComponent_mlkZ themedComponent--dark_xIcU"></div><b class="navbar__title text--truncate">主页</b></a><a class="navbar__item navbar__link" href="/docs/machine-learning/intro">机器学习</a><a class="navbar__item navbar__link" href="/docs/modern-cpp/intro">现代 C++</a><a class="navbar__item navbar__link" href="/docs/modern-linux/intro">现代 Linux</a><a class="navbar__item navbar__link" href="/docs/design-patterns/intro">设计模式</a><a class="navbar__item navbar__link" href="/docs/android-framework/intro">Android 框架</a></div><div class="navbar__items navbar__items--right"><a aria-current="page" class="navbar__item navbar__link navbar__link--active" href="/blog">博客</a><div class="navbarSearchContainer_Bca1"><div class="navbar__search searchBarContainer_NW3z" dir="ltr"><input placeholder="搜索" aria-label="Search" class="navbar__search-input"><div class="loadingRing_RJI3 searchBarLoadingRing_YnHq"><div></div><div></div><div></div><div></div></div></div></div><div class="toggle_vylO colorModeToggle_DEke"><button class="clean-btn toggleButton_gllP toggleButtonDisabled_aARS" type="button" disabled="" title="切换浅色/暗黑模式（当前为浅色模式）" aria-label="切换浅色/暗黑模式（当前为浅色模式）" aria-live="polite"><svg viewBox="0 0 24 24" width="24" height="24" class="lightToggleIcon_pyhR"><path fill="currentColor" d="M12,9c1.65,0,3,1.35,3,3s-1.35,3-3,3s-3-1.35-3-3S10.35,9,12,9 M12,7c-2.76,0-5,2.24-5,5s2.24,5,5,5s5-2.24,5-5 S14.76,7,12,7L12,7z M2,13l2,0c0.55,0,1-0.45,1-1s-0.45-1-1-1l-2,0c-0.55,0-1,0.45-1,1S1.45,13,2,13z M20,13l2,0c0.55,0,1-0.45,1-1 s-0.45-1-1-1l-2,0c-0.55,0-1,0.45-1,1S19.45,13,20,13z M11,2v2c0,0.55,0.45,1,1,1s1-0.45,1-1V2c0-0.55-0.45-1-1-1S11,1.45,11,2z M11,20v2c0,0.55,0.45,1,1,1s1-0.45,1-1v-2c0-0.55-0.45-1-1-1C11.45,19,11,19.45,11,20z M5.99,4.58c-0.39-0.39-1.03-0.39-1.41,0 c-0.39,0.39-0.39,1.03,0,1.41l1.06,1.06c0.39,0.39,1.03,0.39,1.41,0s0.39-1.03,0-1.41L5.99,4.58z M18.36,16.95 c-0.39-0.39-1.03-0.39-1.41,0c-0.39,0.39-0.39,1.03,0,1.41l1.06,1.06c0.39,0.39,1.03,0.39,1.41,0c0.39-0.39,0.39-1.03,0-1.41 L18.36,16.95z M19.42,5.99c0.39-0.39,0.39-1.03,0-1.41c-0.39-0.39-1.03-0.39-1.41,0l-1.06,1.06c-0.39,0.39-0.39,1.03,0,1.41 s1.03,0.39,1.41,0L19.42,5.99z M7.05,18.36c0.39-0.39,0.39-1.03,0-1.41c-0.39-0.39-1.03-0.39-1.41,0l-1.06,1.06 c-0.39,0.39-0.39,1.03,0,1.41s1.03,0.39,1.41,0L7.05,18.36z"></path></svg><svg viewBox="0 0 24 24" width="24" height="24" class="darkToggleIcon_wfgR"><path fill="currentColor" d="M9.37,5.51C9.19,6.15,9.1,6.82,9.1,7.5c0,4.08,3.32,7.4,7.4,7.4c0.68,0,1.35-0.09,1.99-0.27C17.45,17.19,14.93,19,12,19 c-3.86,0-7-3.14-7-7C5,9.07,6.81,6.55,9.37,5.51z M12,3c-4.97,0-9,4.03-9,9s4.03,9,9,9s9-4.03,9-9c0-0.46-0.04-0.92-0.1-1.36 c-0.98,1.37-2.58,2.26-4.4,2.26c-2.98,0-5.4-2.42-5.4-5.4c0-1.81,0.89-3.42,2.26-4.4C12.92,3.04,12.46,3,12,3L12,3z"></path></svg></button></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div></nav><div id="__docusaurus_skipToContent_fallback" class="main-wrapper mainWrapper_z2l0"><div class="container margin-vert--lg"><div class="row"><aside class="col col--3"><nav class="sidebar_re4s thin-scrollbar" aria-label="最近博文导航"><div class="sidebarItemTitle_pO2u margin-bottom--md">所有文章</div><div role="group"><h3 class="yearGroupHeading_rMGB">2024</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-video-link">支持嵌入 YouTube 和 Bilibili 视频</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/site/change-default-fonts">更改默认字体</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/tools/cli/autocorrect">统一中文排版</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/cpp/calculate-fibonnaci-with-template-meta-programming">模板元编程：斐波那契数列</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/cpp/update-compiler-on-ubuntu2204">Ubuntu 22.04 更新 C++ 编译器</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/site/remove-i18n-support">停止国际化支持</a></li></ul></div><div role="group"><h3 class="yearGroupHeading_rMGB">2023</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-fontawesome">支持 Font Awesome</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/interactive-map-with-leaflet">使用 Leaflet 绘制地图</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-mermaid-diagrams">支持 Mermaid 图表</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-math-latex">支持 LaTeX 数学公式</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/react-support">React 支持</a></li></ul></div><div role="group"><h3 class="yearGroupHeading_rMGB">2019</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/welcome">欢迎</a></li></ul></div></nav></aside><main class="col col--7"><h1>Authors</h1><section class="margin-vert--lg"><ul><li class="authorListItem_n3yI"><div class="avatar margin-bottom--sm author-as-h2_gXvM"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><h2 class="authorName_yefp">Sol</h2></a><span class="authorBlogPostCount_iiJ5">13</span></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" 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2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>在编程中，斐波那契数列是一个经典的数学问题。通常情况下，我们可以使用传统递归函数来计算斐波那契数列。但是运行时计算递归会造成比较长的耗时。</p>
@@ -45,6 +45,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c20">C++20<a href="#c20
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="完整代码">完整代码<a href="#完整代码" class="hash-link" aria-label="完整代码的直接链接" title="完整代码的直接链接">​</a></h2>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">c++11</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">c++14</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">c++20</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">&#x27;\n&#x27;</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">auto</span><span class="token plain"> fibonacci_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic">// std::cout &lt;&lt; fibonacci&lt;42&gt;::value &lt;&lt; &#x27;\n&#x27;;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci_v</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">&#x27;\n&#x27;</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// template &lt;&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// struct fibonacci&lt;0&gt; {</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// public:</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">//     static constexpr unsigned int value = 0;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// };</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// template &lt;&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// struct fibonacci&lt;1&gt; {</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// public:</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">//     static constexpr unsigned int value = 1;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// };</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">concept</span><span class="token plain"> </span><span class="token class-name">FibonacciBaseCase</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">||</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">requires</span><span class="token plain"> FibonacciBaseCase</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> size</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">auto</span><span class="token plain"> fibonacci_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci_v</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">&#x27;\n&#x27;</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <p>通过使用模板元编程技术，我们可以在编译时计算斐波那契数列，避免了递归函数的重复计算，在一些需要高效计算斐波那契数列的场景下，这种方法可以提供更好的性能。</p>
-<p>希望这篇博客能帮助你理解如何使用模板元编程实现斐波那契数列的编译期计算，并对此有所启发。</p></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/cpp">cpp</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/template-meta-programming">template-meta-programming</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/tools/cli/autocorrect"><div class="pagination-nav__sublabel">较新一篇</div><div class="pagination-nav__label">统一中文排版</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/blog/cpp/update-compiler-on-ubuntu2204"><div class="pagination-nav__sublabel">较旧一篇</div><div class="pagination-nav__label">Ubuntu 22.04 更新 C++ 编译器</div></a></nav></main><div class="col col--2"><div class="tableOfContents_bqdL thin-scrollbar"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#传统递归" class="table-of-contents__link toc-highlight">传统递归</a></li><li><a href="#模板元编程实现" class="table-of-contents__link toc-highlight">模板元编程实现</a><ul><li><a href="#c11" class="table-of-contents__link toc-highlight">C++11</a></li><li><a href="#c14" class="table-of-contents__link toc-highlight">C++14</a></li><li><a href="#c20" class="table-of-contents__link toc-highlight">C++20</a></li></ul></li><li><a href="#完整代码" class="table-of-contents__link toc-highlight">完整代码</a></li></ul></div></div></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>希望这篇博客能帮助你理解如何使用模板元编程实现斐波那契数列的编译期计算，并对此有所启发。</p></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/cpp">cpp</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/template-meta-programming">template-meta-programming</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/tools/cli/autocorrect"><div class="pagination-nav__sublabel">较新一篇</div><div class="pagination-nav__label">统一中文排版</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/blog/cpp/update-compiler-on-ubuntu2204"><div class="pagination-nav__sublabel">较旧一篇</div><div class="pagination-nav__label">Ubuntu 22.04 更新 C++ 编译器</div></a></nav></main><div class="col col--2"><div class="tableOfContents_bqdL thin-scrollbar"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#传统递归" class="table-of-contents__link toc-highlight">传统递归</a></li><li><a href="#模板元编程实现" class="table-of-contents__link toc-highlight">模板元编程实现</a><ul><li><a href="#c11" class="table-of-contents__link toc-highlight">C++11</a></li><li><a href="#c14" class="table-of-contents__link toc-highlight">C++14</a></li><li><a href="#c20" class="table-of-contents__link toc-highlight">C++20</a></li></ul></li><li><a href="#完整代码" class="table-of-contents__link toc-highlight">完整代码</a></li></ul></div></div></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>Ubuntu 22.04 默认使用 <code>g++-11</code> 和 <code>clang++-14</code> 作为默认的 <code>g++</code> 和 <code>clang++</code>。</p>
@@ -44,6 +44,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-clang++-default-
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--config</span><span class="token plain"> clang</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>会弹出以下选项：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">There are </span><span class="token number" style="color:#36acaa">2</span><span class="token plain"> choices </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> the alternative clang </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">providing /usr/bin/clang</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">.</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Selection    Path               Priority   Status</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">------------------------------------------------------------</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">* </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">            /usr/bin/clang-18   </span><span class="token number" style="color:#36acaa">18</span><span class="token plain">        auto mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">            /usr/bin/clang-14   </span><span class="token number" style="color:#36acaa">14</span><span class="token plain">        manual mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token number" style="color:#36acaa">2</span><span class="token plain">            /usr/bin/clang-18   </span><span class="token number" style="color:#36acaa">18</span><span class="token plain">        manual mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Press </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">enter</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> to keep the current choice</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">*</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">, or </span><span class="token builtin class-name">type</span><span class="token plain"> selection number:</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>本站使用 <a href="https://github.com/huacnlee/autocorrect" target="_blank" rel="noopener noreferrer">autocorrect</a> 对中文内容进行统一排版和修正。</p></div><footer class="row docusaurus-mt-lg"><div class="col text--right"><a aria-label="阅读 统一中文排版 的全文" href="/blog/tools/cli/autocorrect"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/cpp/calculate-fibonnaci-with-template-meta-programming">模板元编程：斐波那契数列</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2024-02-20T00:00:00.000Z">2024年2月20日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>在编程中，斐波那契数列是一个经典的数学问题。通常情况下，我们可以使用传统递归函数来计算斐波那契数列。但是运行时计算递归会造成比较长的耗时。</p>
@@ -14,6 +14,6 @@
 <p>本文说明如何升级 C++ 编译器并设置默认版本，从而使用最新的 C++ 语言特性。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/cpp">cpp</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/ubuntu-2204">ubuntu2204</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/clang">clang</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/gcc">gcc</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 Ubuntu 22.04 更新 C++ 编译器 的全文" href="/blog/cpp/update-compiler-on-ubuntu2204"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/site/remove-i18n-support">停止国际化支持</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2024-01-30T00:00:00.000Z">2024年1月30日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 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13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>删除所有的文章的国际化支持。之前所有文章均有双语版本，后续所有文章只会有单个语言版本。</p></div><footer class="row docusaurus-mt-lg"><div class="col text--right"><a aria-label="阅读 停止国际化支持 的全文" href="/blog/site/remove-i18n-support"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-fontawesome">支持 Font Awesome</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-12-13T00:00:00.000Z">2023年12月13日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>现在可以在 mdx 中使用 <a href="https://fontawesome.com/search" target="_blank" rel="noopener noreferrer">Font Awesome 图标</a>。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/font-awesome">font-awesome</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/icon">icon</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Font Awesome 的全文" href="/blog/mdx/support-fontawesome"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/interactive-map-with-leaflet">使用 Leaflet 绘制地图</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-29T00:00:00.000Z">2023年11月29日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p><a href="https://leafletjs.com/" target="_blank" rel="noopener noreferrer"><strong>Leaflet</strong></a> 是地理信息系统（GIS）中流行的开源 JavaScript 库。</p>
 <p>本文在 MDX 中使用 <strong>Leaflet</strong> 绘制交互式地图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/map">map</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/leaflet">leaflet</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 使用 Leaflet 绘制地图 的全文" href="/blog/mdx/interactive-map-with-leaflet"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-mermaid-diagrams">支持 Mermaid 图表</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-27T00:00:00.000Z">2023年11月27日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Mermaid 是一个绘制图表的工具。</p>
 <p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mermaid">mermaid</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/diagram">diagram</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/flowchart">flowchart</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Mermaid 图表 的全文" href="/blog/mdx/support-mermaid-diagrams"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-26T00:00:00.000Z">2023年11月26日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Docusaurus 提供了 <code>&lt;Tabs&gt;</code> 和 <code>&lt;TabItem&gt;</code> 组件，可以通过 MDX 在 Markdown 中使用该组件。</p>
-<p>我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持全局 Tabs 和 TabItem 的全文" href="/blog/mdx/support-global-tabs-tabitem"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"><a class="pagination-nav__link pagination-nav__link--next" href="/blog/page/2"><div class="pagination-nav__label">较旧的博文</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持全局 Tabs 和 TabItem 的全文" href="/blog/mdx/support-global-tabs-tabitem"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"><a class="pagination-nav__link pagination-nav__link--next" href="/blog/page/2"><div class="pagination-nav__label">较旧的博文</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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diff --git a/blog/mdx/interactive-map-with-leaflet/index.html b/blog/mdx/interactive-map-with-leaflet/index.html
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class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p><a href="https://leafletjs.com/" target="_blank" rel="noopener noreferrer"><strong>Leaflet</strong></a> 是地理信息系统（GIS）中流行的开源 JavaScript 库。</p>
 <p>本文在 MDX 中使用 <strong>Leaflet</strong> 绘制交互式地图。</p>
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35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>博客文章支持 <a href="https://docusaurus.io/docs/markdown-features" target="_blank" rel="noopener noreferrer">Docusaurus Markdown 功能</a>，例如 <a href="https://mdxjs.com/" target="_blank" rel="noopener noreferrer">MDX</a>。</p>
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="interactive">交互式<a href="#interactive" class="hash-link" aria-label="交互式的直接链接" title="交互式的直接链接">​</a></h2>
 <div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>提示</div><div class="admonitionContent_BuS1"><p>使用 React 的强大功能来创建交互式博客文章。</p><div class="language-js codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-js codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">button onClick</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">{</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=&gt;</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">alert</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&#x27;按钮被点击了!&#x27;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">}</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain">点击这里！</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">button</span><span class="token operator" style="color:#393A34">&gt;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><button>点击这里！</button></div></div>
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="diagram">图表式<a href="#diagram" class="hash-link" aria-label="图表式的直接链接" title="图表式的直接链接">​</a></h2>
-<div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>提示</div><div class="admonitionContent_BuS1"><p>使用 React 的强大功能来创建图表。</p><div class="language-mdx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-mdx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">import {Chart} from &#x27;./_asset/snowfall.js&#x27;;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">export const year = 2013;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"># 去年降雪</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">{year} 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&lt;Chart year={year} color=&quot;#fcb32c&quot; /&gt;;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h1>去年降雪</h1><p>2013<!-- --> 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。</p><div class="snowfall"><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(6 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(4.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(1.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(1.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(3.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(7 * 0.5 * (1em + 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+<div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>提示</div><div class="admonitionContent_BuS1"><p>使用 React 的强大功能来创建图表。</p><div class="language-mdx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-mdx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">import {Chart} from &#x27;./_asset/snowfall.js&#x27;;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">export const year = 2013;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"># 去年降雪</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">{year} 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&lt;Chart year={year} color=&quot;#fcb32c&quot; /&gt;;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h1>去年降雪</h1><p>2013<!-- --> 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。</p><div class="snowfall"><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(6 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(4.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(1.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(1.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(3.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(7 * 0.5 * (1em + 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c-0.98,1.37-2.58,2.26-4.4,2.26c-2.98,0-5.4-2.42-5.4-5.4c0-1.81,0.89-3.42,2.26-4.4C12.92,3.04,12.46,3,12,3L12,3z"></path></svg></button></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div></nav><div id="__docusaurus_skipToContent_fallback" class="main-wrapper mainWrapper_z2l0"><div class="container margin-vert--lg"><div class="row"><aside class="col col--3"><nav class="sidebar_re4s thin-scrollbar" aria-label="最近博文导航"><div class="sidebarItemTitle_pO2u margin-bottom--md">所有文章</div><div role="group"><h3 class="yearGroupHeading_rMGB">2024</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-video-link">支持嵌入 YouTube 和 Bilibili 视频</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/site/change-default-fonts">更改默认字体</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/tools/cli/autocorrect">统一中文排版</a></li><li 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class="sidebarItemLink_mo7H" href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-math-latex">支持 LaTeX 数学公式</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/react-support">React 支持</a></li></ul></div><div role="group"><h3 class="yearGroupHeading_rMGB">2019</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/welcome">欢迎</a></li></ul></div></nav></aside><main class="col col--7"><article><header><h1 class="title_f1Hy">支持 Font Awesome</h1><div class="container_mt6G margin-vert--md"><time datetime="2023-12-13T00:00:00.000Z">2023年12月13日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>现在可以在 mdx 中使用 <a href="https://fontawesome.com/search" target="_blank" rel="noopener noreferrer">Font Awesome 图标</a>。</p>
@@ -23,6 +23,6 @@
 <li><code>xl</code>: 1.5em (24px)</li>
 <li><code>2xl</code>: 2em (32px)</li>
 <li><code>1x</code> ~ <code>10x</code>: 1em ~ 10em</li>
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+</ul></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/font-awesome">font-awesome</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/icon">icon</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/site/remove-i18n-support"><div class="pagination-nav__sublabel">较新一篇</div><div class="pagination-nav__label">停止国际化支持</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/blog/mdx/interactive-map-with-leaflet"><div class="pagination-nav__sublabel">较旧一篇</div><div class="pagination-nav__label">使用 Leaflet 绘制地图</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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diff --git a/blog/mdx/support-global-tabs-tabitem/index.html b/blog/mdx/support-global-tabs-tabitem/index.html
index 45bf634cc..bb9c269b0 100644
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c-0.98,1.37-2.58,2.26-4.4,2.26c-2.98,0-5.4-2.42-5.4-5.4c0-1.81,0.89-3.42,2.26-4.4C12.92,3.04,12.46,3,12,3L12,3z"></path></svg></button></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div></nav><div id="__docusaurus_skipToContent_fallback" class="main-wrapper mainWrapper_z2l0"><div class="container margin-vert--lg"><div class="row"><aside class="col col--3"><nav class="sidebar_re4s thin-scrollbar" aria-label="最近博文导航"><div class="sidebarItemTitle_pO2u margin-bottom--md">所有文章</div><div role="group"><h3 class="yearGroupHeading_rMGB">2024</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-video-link">支持嵌入 YouTube 和 Bilibili 视频</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/site/change-default-fonts">更改默认字体</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/tools/cli/autocorrect">统一中文排版</a></li><li 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sidebarItemLinkActive_I1ZP" href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-math-latex">支持 LaTeX 数学公式</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/react-support">React 支持</a></li></ul></div><div role="group"><h3 class="yearGroupHeading_rMGB">2019</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/welcome">欢迎</a></li></ul></div></nav></aside><main class="col col--7"><article><header><h1 class="title_f1Hy">支持全局 Tabs 和 TabItem</h1><div class="container_mt6G margin-vert--md"><time datetime="2023-11-26T00:00:00.000Z">2023年11月26日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>Docusaurus 提供了 <code>&lt;Tabs&gt;</code> 和 <code>&lt;TabItem&gt;</code> 组件，可以通过 MDX 在 Markdown 中使用该组件。</p>
@@ -22,6 +22,6 @@
   <tabitem value="banana" label="Banana">
     This is a banana 🍌
   </tabitem>
-</tabs></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/mdx/support-mermaid-diagrams"><div class="pagination-nav__sublabel">较新一篇</div><div class="pagination-nav__label">支持 Mermaid 图表</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/blog/mdx/support-math-latex"><div class="pagination-nav__sublabel">较旧一篇</div><div class="pagination-nav__label">支持 LaTeX 数学公式</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+</tabs></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/mdx/support-mermaid-diagrams"><div class="pagination-nav__sublabel">较新一篇</div><div class="pagination-nav__label">支持 Mermaid 图表</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/blog/mdx/support-math-latex"><div class="pagination-nav__sublabel">较旧一篇</div><div class="pagination-nav__label">支持 LaTeX 数学公式</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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diff --git a/blog/mdx/support-math-latex/index.html b/blog/mdx/support-math-latex/index.html
index 9befc5480..e7ec85a96 100644
--- a/blog/mdx/support-math-latex/index.html
+++ b/blog/mdx/support-math-latex/index.html
@@ -3,10 +3,10 @@
 <head>
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class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 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35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>数学公式可以使用 <a href="https://katex.org" target="_blank" rel="noopener noreferrer">KaTeX</a> 渲染，目前本站已经支持。</p>
@@ -19,6 +19,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="inline">行内公式<a
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="blocks">公式块<a href="#blocks" class="hash-link" aria-label="公式块的直接链接" title="公式块的直接链接">​</a></h3>
 <p>对于公式块，使用换行符和 <code>$$</code> 隔开：</p>
 <div class="language-latex codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-latex codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">$$</span><br></span><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">I = </span><span class="token equation string equation-command regex" style="color:#36acaa">\int</span><span class="token equation string" style="color:#e3116c">_0^{2</span><span class="token equation string equation-command regex" style="color:#36acaa">\pi</span><span class="token equation string" style="color:#e3116c">} </span><span class="token equation string equation-command regex" style="color:#36acaa">\sin</span><span class="token equation string" style="color:#e3116c">(x)</span><span class="token equation string equation-command regex" style="color:#36acaa">\,</span><span class="token equation string" style="color:#e3116c">dx</span><br></span><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">$$</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>I</mi><mo>=</mo><msubsup><mo>∫</mo><mn>0</mn><mrow><mn>2</mn><mi>π</mi></mrow></msubsup><mi>sin</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">I = \int_0^{2\pi} \sin(x)\,dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.476em;vertical-align:-0.9119em"></span><span class="mop"><span class="mop op-symbol large-op" style="margin-right:0.44445em;position:relative;top:-0.0011em">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.564em"><span style="top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.8129em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">π</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9119em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop">sin</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span></span></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/math">math</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/latex">latex</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/katex">katex</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/mdx/support-global-tabs-tabitem"><div 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+<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>I</mi><mo>=</mo><msubsup><mo>∫</mo><mn>0</mn><mrow><mn>2</mn><mi>π</mi></mrow></msubsup><mi>sin</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">I = \int_0^{2\pi} \sin(x)\,dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.476em;vertical-align:-0.9119em"></span><span class="mop"><span class="mop op-symbol large-op" style="margin-right:0.44445em;position:relative;top:-0.0011em">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.564em"><span style="top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.8129em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">π</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9119em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop">sin</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span></span></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/math">math</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/latex">latex</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/katex">katex</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/mdx/support-global-tabs-tabitem"><div 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2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>Mermaid 是一个绘制图表的工具。</p>
@@ -16,6 +16,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="序列图">序列图<a
 <!-- -->
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="流程图">流程图<a href="#流程图" class="hash-link" aria-label="流程图的直接链接" title="流程图的直接链接">​</a></h2>
 <div class="language-md codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockTitle_Ktv7">Example Mermaid flowchart</div><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-md codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token code punctuation" style="color:#393A34">```</span><span class="token code code-language">mermaid</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code code-block language-mermaid">flowchart TD</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    A[Christmas] --&gt;|Get money| B(Go shopping)</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    B --&gt; C{Let me think}</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|One| D[Laptop]</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|Two| E[iPhone]</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|Three| F[fa:fa-car Car]</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code punctuation" style="color:#393A34">```</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 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35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。</p>
@@ -28,6 +28,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="youtube-嵌入">YouTube
 <div class="video-wrap"><p class="video-title">Animenz - Unravel [Piano Ver.]</p><div class="video-container"><div style="position:relative;padding:30% 45%"><iframe style="position:absolute;width:100%;height:100%;left:0;top:0" src="https://www.youtube.com/embed/sEQf5lcnj_o?autoplay=0&amp;enablejsapi=1" allowfullscreen="" sandbox="allow-top-navigation allow-same-origin allow-forms allow-scripts" frameborder="0"></iframe></div><p></p></div></div>
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="bilibili-嵌入">Bilibili 嵌入<a href="#bilibili-嵌入" class="hash-link" aria-label="Bilibili 嵌入的直接链接" title="Bilibili 嵌入的直接链接">​</a></h3>
 <div class="language-jsx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-jsx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token tag punctuation" style="color:#393A34">&lt;</span><span class="token tag class-name" style="color:#00009f">Bilibili</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">id</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">&quot;</span><span class="token tag attr-value" style="color:#e3116c">BV1bi4y1675m</span><span class="token tag attr-value punctuation" style="color:#393A34">&quot;</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">title</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">&quot;</span><span class="token tag attr-value" style="color:#e3116c">Animenz - Unravel [钢琴版]</span><span class="token tag attr-value punctuation" style="color:#393A34">&quot;</span><span class="token tag" style="color:#00009f"> </span><span class="token tag punctuation" style="color:#393A34">/&gt;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<div class="video-wrap"><p class="video-title">Animenz - Unravel [钢琴版]</p><div class="video-container"><div style="position:relative;padding:30% 45%"><iframe style="position:absolute;width:100%;height:100%;left:0;top:0" src="https://player.bilibili.com/player.html?cid=&amp;bvid=BV1px411A7ir&amp;aid=&amp;page=1&amp;as_wide=0&amp;high_quality=1&amp;danmaku=1&amp;autoplay=0" allowfullscreen="" frameborder="0" sandbox="allow-top-navigation allow-same-origin allow-forms allow-scripts" scrolling="no"></iframe></div><p></p></div></div></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/youtube">youtube</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/bilibili">bilibili</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/video">video</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--next" href="/blog/site/change-default-fonts"><div class="pagination-nav__sublabel">较旧一篇</div><div class="pagination-nav__label">更改默认字体</div></a></nav></main><div class="col col--2"><div class="tableOfContents_bqdL thin-scrollbar"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#参数说明" class="table-of-contents__link toc-highlight">参数说明</a></li><li><a href="#示例" class="table-of-contents__link toc-highlight">示例</a><ul><li><a href="#youtube-嵌入" class="table-of-contents__link toc-highlight">YouTube 嵌入</a></li><li><a href="#bilibili-嵌入" class="table-of-contents__link toc-highlight">Bilibili 嵌入</a></li></ul></li></ul></div></div></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 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35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p><a href="https://docusaurus.io/docs/blog" target="_blank" rel="noopener noreferrer">Docusaurus 博客功能</a>由 <a href="https://docusaurus.io/docs/api/plugins/@docusaurus/plugin-content-blog" target="_blank" rel="noopener noreferrer">blog 插件</a>提供支持。</p>
-<p>使用 <code>&lt;!--</code> <code>truncate</code> <code>--&gt;</code> 注释来限制博客预览。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/docusaurus">docusaurus</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 欢迎 的全文" href="/blog/welcome"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog"><div class="pagination-nav__label">较新的博文</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>使用 <code>&lt;!--</code> <code>truncate</code> <code>--&gt;</code> 注释来限制博客预览。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/docusaurus">docusaurus</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 欢迎 的全文" href="/blog/welcome"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog"><div class="pagination-nav__label">较新的博文</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
 </body>
 </html>
\ No newline at end of file
diff --git a/blog/rss.xml b/blog/rss.xml
index fdcb9fdea..55fe02dbb 100644
--- a/blog/rss.xml
+++ b/blog/rss.xml
@@ -2,7 +2,7 @@
 <rss version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/">
     <channel>
         <title>Sol 的空间 Blog</title>
-        <link>https://www.szdev.com/blog</link>
+        <link>https://ShangjinTang.github.io/blog</link>
         <description>Sol 的空间 Blog</description>
         <lastBuildDate>Fri, 18 Oct 2024 00:00:00 GMT</lastBuildDate>
         <docs>https://validator.w3.org/feed/docs/rss2.html</docs>
@@ -10,12 +10,12 @@
         <language>zh-CN</language>
         <item>
             <title><![CDATA[支持嵌入 YouTube 和 Bilibili 视频]]></title>
-            <link>https://www.szdev.com/blog/mdx/support-video-link</link>
-            <guid>https://www.szdev.com/blog/mdx/support-video-link</guid>
+            <link>https://ShangjinTang.github.io/blog/mdx/support-video-link</link>
+            <guid>https://ShangjinTang.github.io/blog/mdx/support-video-link</guid>
             <pubDate>Fri, 18 Oct 2024 00:00:00 GMT</pubDate>
             <description><![CDATA[基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。]]></description>
             <content:encoded><![CDATA[<p>基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参数说明">参数说明<a href="https://www.szdev.com/blog/mdx/support-video-link#%E5%8F%82%E6%95%B0%E8%AF%B4%E6%98%8E" class="hash-link" aria-label="参数说明的直接链接" title="参数说明的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参数说明">参数说明<a href="https://shangjintang.github.io/blog/mdx/support-video-link#%E5%8F%82%E6%95%B0%E8%AF%B4%E6%98%8E" class="hash-link" aria-label="参数说明的直接链接" title="参数说明的直接链接">​</a></h2>
 <p>React 组件： <code>YouTube</code> / <code>Bilibili</code></p>
 <p>组件参数：</p>
 <ul>
@@ -27,11 +27,11 @@
 </li>
 <li><code>title</code>: 可选。位置在视频上方；左对齐。</li>
 </ul>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="示例">示例<a href="https://www.szdev.com/blog/mdx/support-video-link#%E7%A4%BA%E4%BE%8B" class="hash-link" aria-label="示例的直接链接" title="示例的直接链接">​</a></h2>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="youtube-嵌入">YouTube 嵌入<a href="https://www.szdev.com/blog/mdx/support-video-link#youtube-%E5%B5%8C%E5%85%A5" class="hash-link" aria-label="YouTube 嵌入的直接链接" title="YouTube 嵌入的直接链接">​</a></h3>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="示例">示例<a href="https://shangjintang.github.io/blog/mdx/support-video-link#%E7%A4%BA%E4%BE%8B" class="hash-link" aria-label="示例的直接链接" title="示例的直接链接">​</a></h2>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="youtube-嵌入">YouTube 嵌入<a href="https://shangjintang.github.io/blog/mdx/support-video-link#youtube-%E5%B5%8C%E5%85%A5" class="hash-link" aria-label="YouTube 嵌入的直接链接" title="YouTube 嵌入的直接链接">​</a></h3>
 <div class="language-jsx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-jsx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token tag punctuation" style="color:#393A34">&lt;</span><span class="token tag class-name" style="color:#00009f">YouTube</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">id</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag attr-value" style="color:#e3116c">sEQf5lcnj_o</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">title</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag attr-value" style="color:#e3116c">Animenz - Unravel [Piano Ver.]</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag" style="color:#00009f"> </span><span class="token tag punctuation" style="color:#393A34">/&gt;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <div class="video-wrap"><p class="video-title">Animenz - Unravel [Piano Ver.]</p><div class="video-container"><div style="position:relative;padding:30% 45%"><iframe style="position:absolute;width:100%;height:100%;left:0;top:0" src="https://www.youtube.com/embed/sEQf5lcnj_o?autoplay=0&amp;enablejsapi=1" allowfullscreen="" sandbox="allow-top-navigation allow-same-origin allow-forms allow-scripts" frameborder="0"></iframe></div><p></p></div></div>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="bilibili-嵌入">Bilibili 嵌入<a href="https://www.szdev.com/blog/mdx/support-video-link#bilibili-%E5%B5%8C%E5%85%A5" class="hash-link" aria-label="Bilibili 嵌入的直接链接" title="Bilibili 嵌入的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="bilibili-嵌入">Bilibili 嵌入<a href="https://shangjintang.github.io/blog/mdx/support-video-link#bilibili-%E5%B5%8C%E5%85%A5" class="hash-link" aria-label="Bilibili 嵌入的直接链接" title="Bilibili 嵌入的直接链接">​</a></h3>
 <div class="language-jsx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-jsx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token tag punctuation" style="color:#393A34">&lt;</span><span class="token tag class-name" style="color:#00009f">Bilibili</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">id</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag attr-value" style="color:#e3116c">BV1bi4y1675m</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag" style="color:#00009f"> </span><span class="token tag attr-name" style="color:#00a4db">title</span><span class="token tag attr-value punctuation attr-equals" style="color:#393A34">=</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag attr-value" style="color:#e3116c">Animenz - Unravel [钢琴版]</span><span class="token tag attr-value punctuation" style="color:#393A34">"</span><span class="token tag" style="color:#00009f"> </span><span class="token tag punctuation" style="color:#393A34">/&gt;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <div class="video-wrap"><p class="video-title">Animenz - Unravel [钢琴版]</p><div class="video-container"><div style="position:relative;padding:30% 45%"><iframe style="position:absolute;width:100%;height:100%;left:0;top:0" src="https://player.bilibili.com/player.html?cid=&amp;bvid=BV1px411A7ir&amp;aid=&amp;page=1&amp;as_wide=0&amp;high_quality=1&amp;danmaku=1&amp;autoplay=0" allowfullscreen="" frameborder="0" sandbox="allow-top-navigation allow-same-origin allow-forms allow-scripts" scrolling="no"></iframe></div><p></p></div></div>]]></content:encoded>
             <author>shangjin.tang@gmail.com (Sol)</author>
@@ -42,8 +42,8 @@
         </item>
         <item>
             <title><![CDATA[更改默认字体]]></title>
-            <link>https://www.szdev.com/blog/site/change-default-fonts</link>
-            <guid>https://www.szdev.com/blog/site/change-default-fonts</guid>
+            <link>https://ShangjinTang.github.io/blog/site/change-default-fonts</link>
+            <guid>https://ShangjinTang.github.io/blog/site/change-default-fonts</guid>
             <pubDate>Thu, 17 Oct 2024 00:00:00 GMT</pubDate>
             <description><![CDATA[本站默认字体现已更改为 LxgwWenKai Screen.]]></description>
             <content:encoded><![CDATA[<p>本站默认字体现已更改为 <a href="https://github.com/lxgw/LxgwWenKai-Screen" target="_blank" rel="noopener noreferrer">LxgwWenKai Screen</a>.</p>]]></content:encoded>
@@ -53,8 +53,8 @@
         </item>
         <item>
             <title><![CDATA[统一中文排版]]></title>
-            <link>https://www.szdev.com/blog/tools/cli/autocorrect</link>
-            <guid>https://www.szdev.com/blog/tools/cli/autocorrect</guid>
+            <link>https://ShangjinTang.github.io/blog/tools/cli/autocorrect</link>
+            <guid>https://ShangjinTang.github.io/blog/tools/cli/autocorrect</guid>
             <pubDate>Wed, 16 Oct 2024 00:00:00 GMT</pubDate>
             <description><![CDATA[本站使用 autocorrect 对中文内容进行统一排版和修正。]]></description>
             <content:encoded><![CDATA[<p>本站使用 <a href="https://github.com/huacnlee/autocorrect" target="_blank" rel="noopener noreferrer">autocorrect</a> 对中文内容进行统一排版和修正。</p>]]></content:encoded>
@@ -62,8 +62,8 @@
         </item>
         <item>
             <title><![CDATA[模板元编程：斐波那契数列]]></title>
-            <link>https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming</link>
-            <guid>https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming</guid>
+            <link>https://ShangjinTang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming</link>
+            <guid>https://ShangjinTang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming</guid>
             <pubDate>Tue, 20 Feb 2024 00:00:00 GMT</pubDate>
             <description><![CDATA[在编程中，斐波那契数列是一个经典的数学问题。通常情况下，我们可以使用传统递归函数来计算斐波那契数列。但是运行时计算递归会造成比较长的耗时。]]></description>
             <content:encoded><![CDATA[<p>在编程中，斐波那契数列是一个经典的数学问题。通常情况下，我们可以使用传统递归函数来计算斐波那契数列。但是运行时计算递归会造成比较长的耗时。</p>
@@ -74,11 +74,11 @@
 <li>从 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">1</span></span></span></span> 开始： <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mn>5</mn><mo separator="true">,</mo><mn>8</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">1,1,2,3,5,8,...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">5</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">8</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">...</span></span></span></span></li>
 </ul>
 <p>我们假设从 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">0</span></span></span></span> 开始，即 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mtext>，</mtext><mi>f</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mtext>，</mtext><mi>f</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mtext>，</mtext><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex"> f(0) = 0，f(1) = 1，f(2) = 1，...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord">0</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">0</span><span class="mord cjk_fallback">，</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord">1</span><span class="mord cjk_fallback">，</span><span class="mord">...</span></span></span></span>。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="传统递归">传统递归<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E4%BC%A0%E7%BB%9F%E9%80%92%E5%BD%92" class="hash-link" aria-label="传统递归的直接链接" title="传统递归的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="传统递归">传统递归<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E4%BC%A0%E7%BB%9F%E9%80%92%E5%BD%92" class="hash-link" aria-label="传统递归的直接链接" title="传统递归的直接链接">​</a></h2>
 <div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">/**</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * @file fibonacci_recursive.cpp</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * @brief calculate fibonacci value recursively</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">calc_fibonacci</span><span class="token punctuation" style="color:#393A34">(</span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> i</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">i </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">||</span><span class="token plain"> i </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> i</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">calc_fibonacci</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">i </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">calc_fibonacci</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">i </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">calc_fibonacci</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">42</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">'\n'</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">&gt; g++ -O0 -g a.out fibonacci_recursive.cpp -o prog_fibonacci_recursive</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&gt; ./prog_fibonacci_recursive</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">267914296</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&gt; hyperfine "./prog_fibonacci_recursive"</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Benchmark 1: ./prog_fibonacci_recursive</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Time (mean ± σ):      1.657 s ±  0.015 s    [User: 1.652 s, System: 0.002 s]</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Range (min … max):    1.647 s …  1.696 s    10 runs</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="模板元编程实现">模板元编程实现<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E6%A8%A1%E6%9D%BF%E5%85%83%E7%BC%96%E7%A8%8B%E5%AE%9E%E7%8E%B0" class="hash-link" aria-label="模板元编程实现的直接链接" title="模板元编程实现的直接链接">​</a></h2>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c11">C++11<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c11" class="hash-link" aria-label="C++11的直接链接" title="C++11的直接链接">​</a></h3>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="模板元编程实现">模板元编程实现<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E6%A8%A1%E6%9D%BF%E5%85%83%E7%BC%96%E7%A8%8B%E5%AE%9E%E7%8E%B0" class="hash-link" aria-label="模板元编程实现的直接链接" title="模板元编程实现的直接链接">​</a></h2>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c11">C++11<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c11" class="hash-link" aria-label="C++11的直接链接" title="C++11的直接链接">​</a></h3>
 <p>首先，我们定义一个模板类 <code>fibonacci</code>，它具有一个静态成员变量 <code>value</code>，用于存储斐波那契数列的值。该模板类使用递归定义，根据给定的大小计算斐波那契数列值。</p>
 <div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>使用 <code>fibonacci&lt;42&gt;::value</code> 则可以得到对应的结果。这个语法类似于传统的递归，但是会在编译期进行求值。</p>
@@ -86,7 +86,7 @@
 <p>这里使用了编译期求值的关键字 <code>constexpr</code>，因此需要 C++11 版本及以上。</p>
 <div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">&gt; g++ -O0 -g -std=c++11 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&gt; ./prog_fibonacci_tmp</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">267914296</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&gt; hyperfine "./prog_fibonacci_tmp"</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Benchmark 1: ./prog_fibonacci_tmp</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Time (mean ± σ):       0.8 ms ±   0.1 ms    [User: 0.9 ms, System: 0.2 ms]</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Range (min … max):     0.6 ms …   1.5 ms    1605 runs</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p><strong>在计算第 42 个斐波那契数的时候，运行时间仅需 ~0.8ms，相当于传统递归方法 ~1.6s 的 1/2000。</strong></p>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c14">C++14<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c14" class="hash-link" aria-label="C++14的直接链接" title="C++14的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c14">C++14<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c14" class="hash-link" aria-label="C++14的直接链接" title="C++14的直接链接">​</a></h3>
 <p>在 C++17 中，通常使用 <code>_v</code> 结尾当作 <code>value</code> 类型 (参见这篇 <a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n3854.htm" target="_blank" rel="noopener noreferrer">proposal</a>)，比如：</p>
 <div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">T</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">bool</span><span class="token plain"> is_integral_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> is_integral</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">T</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>类似的，我们可以定义一个模板变量 <code>fibonacci_v</code>，用于方便地获取斐波那契数列的值。</p>
@@ -94,12 +94,12 @@
 <p>注意，这种 <code>_v</code> 的实现并不需要 C++17 的编译器；C++14 的编译器即可以满足需求。</p>
 <p>编译：</p>
 <div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">&gt; g++ -O0 -g -std=c++14 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c20">C++20<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c20" class="hash-link" aria-label="C++20的直接链接" title="C++20的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="c20">C++20<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#c20" class="hash-link" aria-label="C++20的直接链接" title="C++20的直接链接">​</a></h3>
 <p>C++20 中，我们可以使用 <code>concept</code> / <code>requires</code>，合并两个偏特化模板。</p>
 <div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">template &lt;int size&gt;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">concept FibonacciBaseCase = (size == 0) || (size == 1);</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">template &lt;int size&gt;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">requires FibonacciBaseCase&lt;size&gt;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">struct fibonacci&lt;size&gt; {</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">public:</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    static constexpr unsigned int value = size;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">};</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>编译：</p>
 <div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">&gt; g++ -O0 -g -std=c++20 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="完整代码">完整代码<a href="https://www.szdev.com/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E5%AE%8C%E6%95%B4%E4%BB%A3%E7%A0%81" class="hash-link" aria-label="完整代码的直接链接" title="完整代码的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="完整代码">完整代码<a href="https://shangjintang.github.io/blog/cpp/calculate-fibonnaci-with-template-meta-programming#%E5%AE%8C%E6%95%B4%E4%BB%A3%E7%A0%81" class="hash-link" aria-label="完整代码的直接链接" title="完整代码的直接链接">​</a></h2>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">c++11</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">c++14</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">c++20</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">'\n'</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">auto</span><span class="token plain"> fibonacci_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic">// std::cout &lt;&lt; fibonacci&lt;42&gt;::value &lt;&lt; '\n';</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci_v</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">'\n'</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token macro property directive-hash" style="color:#36acaa">#</span><span class="token macro property directive keyword" style="color:#00009f">include</span><span class="token macro property" style="color:#36acaa"> </span><span class="token macro property string" style="color:#e3116c">&lt;iostream&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// template &lt;&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// struct fibonacci&lt;0&gt; {</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// public:</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">//     static constexpr unsigned int value = 0;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// };</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// template &lt;&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// struct fibonacci&lt;1&gt; {</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// public:</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">//     static constexpr unsigned int value = 1;</span><span class="token plain"></span><br></span><span class="token-line code-block-delete-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic">// };</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">concept</span><span class="token plain"> </span><span class="token class-name">FibonacciBaseCase</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">||</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">size </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">requires</span><span class="token plain"> FibonacciBaseCase</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">struct</span><span class="token plain"> </span><span class="token class-name">fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">static</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">unsigned</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> value </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> size</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line code-block-add-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">template</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">constexpr</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">auto</span><span class="token plain"> fibonacci_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> fibonacci</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">size</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">value</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">int</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    std</span><span class="token double-colon punctuation" style="color:#393A34">::</span><span class="token plain">cout </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> fibonacci_v</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token number" style="color:#36acaa">42</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;</span><span class="token plain"> </span><span class="token char">'\n'</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <p>通过使用模板元编程技术，我们可以在编译时计算斐波那契数列，避免了递归函数的重复计算，在一些需要高效计算斐波那契数列的场景下，这种方法可以提供更好的性能。</p>
 <p>希望这篇博客能帮助你理解如何使用模板元编程实现斐波那契数列的编译期计算，并对此有所启发。</p>]]></content:encoded>
@@ -109,19 +109,19 @@
         </item>
         <item>
             <title><![CDATA[Ubuntu 22.04 更新 C++ 编译器]]></title>
-            <link>https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204</link>
-            <guid>https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204</guid>
+            <link>https://ShangjinTang.github.io/blog/cpp/update-compiler-on-ubuntu2204</link>
+            <guid>https://ShangjinTang.github.io/blog/cpp/update-compiler-on-ubuntu2204</guid>
             <pubDate>Wed, 31 Jan 2024 00:00:00 GMT</pubDate>
             <description><![CDATA[Ubuntu 22.04 默认使用 g++-11 和 clang++-14 作为默认的 g++ 和 clang++。]]></description>
             <content:encoded><![CDATA[<p>Ubuntu 22.04 默认使用 <code>g++-11</code> 和 <code>clang++-14</code> 作为默认的 <code>g++</code> 和 <code>clang++</code>。</p>
 <p>本文说明如何升级 C++ 编译器并设置默认版本，从而使用最新的 C++ 语言特性。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-c++-compiler">安装最新版本的 C++ 编译器<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#install-latest-c++-compiler" class="hash-link" aria-label="安装最新版本的 C++ 编译器的直接链接" title="安装最新版本的 C++ 编译器的直接链接">​</a></h2>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-g++">安装最新的 g++<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#install-latest-g++" class="hash-link" aria-label="安装最新的 g++的直接链接" title="安装最新的 g++的直接链接">​</a></h3>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-c++-compiler">安装最新版本的 C++ 编译器<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#install-latest-c++-compiler" class="hash-link" aria-label="安装最新版本的 C++ 编译器的直接链接" title="安装最新版本的 C++ 编译器的直接链接">​</a></h2>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-g++">安装最新的 g++<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#install-latest-g++" class="hash-link" aria-label="安装最新的 g++的直接链接" title="安装最新的 g++的直接链接">​</a></h3>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">apt</span><span class="token plain"> update</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> add-apt-repository ppa:ubuntu-toolchain-r/test</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">apt</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">install</span><span class="token plain"> gcc-12 g++-12 </span><span class="token parameter variable" style="color:#36acaa">-y</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">apt</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">install</span><span class="token plain"> gcc-13 g++-13 </span><span class="token parameter variable" style="color:#36acaa">-y</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-clang++">安装最新的 clang++<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#install-latest-clang++" class="hash-link" aria-label="安装最新的 clang++的直接链接" title="安装最新的 clang++的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="install-latest-clang++">安装最新的 clang++<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#install-latest-clang++" class="hash-link" aria-label="安装最新的 clang++的直接链接" title="安装最新的 clang++的直接链接">​</a></h3>
 <p>参见 <a href="https://apt.llvm.org/" target="_blank" rel="noopener noreferrer">LLVM Debian/Ubuntu Packages</a> 中的安装指南：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">wget</span><span class="token plain"> https://apt.llvm.org/llvm.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">chmod</span><span class="token plain"> +x llvm.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># sudo ./llvm.sh &lt;version number&gt; all</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># or</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># sudo ./llvm.sh all</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> ./llvm.sh </span><span class="token number" style="color:#36acaa">18</span><span class="token plain"> all</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-default-version">切换编译器的默认版本<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#change-default-version" class="hash-link" aria-label="切换编译器的默认版本的直接链接" title="切换编译器的默认版本的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-default-version">切换编译器的默认版本<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#change-default-version" class="hash-link" aria-label="切换编译器的默认版本的直接链接" title="切换编译器的默认版本的直接链接">​</a></h2>
 <p>上述命令执行之后，我们会发现，<code>g++</code> 仍然是 <code>g++11</code>，<code>clang++</code> 仍然是 <code>clang++-14</code>。</p>
 <p>这里介绍一下 <code>update-alternatives</code>，由于管理 Ubuntu 上软件版本的切换，使其多版本共存。语法：</p>
 <p>注册可选的软件版本：</p>
@@ -129,7 +129,7 @@
 <p>切换默认的软件版本：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--config</span><span class="token plain"> name</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <div class="theme-admonition theme-admonition-warning admonition_xJq3 alert alert--warning"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>注意</div><div class="admonitionContent_BuS1"><p>切换编译器软件包可能有风险，建议只在个人计算机上使用。</p></div></div>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-g++-default-version">切换 g++ 的默认版本<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#change-g++-default-version" class="hash-link" aria-label="切换 g++ 的默认版本的直接链接" title="切换 g++ 的默认版本的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-g++-default-version">切换 g++ 的默认版本<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#change-g++-default-version" class="hash-link" aria-label="切换 g++ 的默认版本的直接链接" title="切换 g++ 的默认版本的直接链接">​</a></h3>
 <p>注册 <code>gcc</code> / <code>g++</code> 版本：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--install</span><span class="token plain"> /usr/bin/gcc gcc /usr/bin/gcc-11 </span><span class="token number" style="color:#36acaa">11</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--slave</span><span class="token plain"> /usr/bin/g++ g++ /usr/bin/g++-11</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--install</span><span class="token plain"> /usr/bin/gcc gcc /usr/bin/gcc-12 </span><span class="token number" style="color:#36acaa">12</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--slave</span><span class="token plain"> /usr/bin/g++ g++ /usr/bin/g++-12</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--install</span><span class="token plain"> /usr/bin/gcc gcc /usr/bin/gcc-13 </span><span class="token number" style="color:#36acaa">13</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--slave</span><span class="token plain"> /usr/bin/g++ g++ /usr/bin/g++-13</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>选择默认 <code>gcc</code> / <code>g++</code> 版本：</p>
@@ -137,7 +137,7 @@
 <p>会弹出以下选项：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">There are </span><span class="token number" style="color:#36acaa">3</span><span class="token plain"> choices </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> the alternative gcc </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">providing /usr/bin/gcc</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">.</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  Selection    Path             Priority   Status</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">------------------------------------------------------------</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">* </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">            /usr/bin/gcc-13   </span><span class="token number" style="color:#36acaa">13</span><span class="token plain">        auto mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">            /usr/bin/gcc-11   </span><span class="token number" style="color:#36acaa">11</span><span class="token plain">        manual mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token number" style="color:#36acaa">2</span><span class="token plain">            /usr/bin/gcc-12   </span><span class="token number" style="color:#36acaa">12</span><span class="token plain">        manual mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token number" style="color:#36acaa">3</span><span class="token plain">            /usr/bin/gcc-13   </span><span class="token number" style="color:#36acaa">13</span><span class="token plain">        manual mode</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Press </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">enter</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> to keep the current choice</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">*</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">, or </span><span class="token builtin class-name">type</span><span class="token plain"> selection number:</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>输入序号即可。</p>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-clang++-default-version">切换 clang++ 的默认版本<a href="https://www.szdev.com/blog/cpp/update-compiler-on-ubuntu2204#change-clang++-default-version" class="hash-link" aria-label="切换 clang++ 的默认版本的直接链接" title="切换 clang++ 的默认版本的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="change-clang++-default-version">切换 clang++ 的默认版本<a href="https://shangjintang.github.io/blog/cpp/update-compiler-on-ubuntu2204#change-clang++-default-version" class="hash-link" aria-label="切换 clang++ 的默认版本的直接链接" title="切换 clang++ 的默认版本的直接链接">​</a></h3>
 <p><code>clang</code> / <code>clang++</code> 是 LLVM 工具链的一部分，更新的时候，建议把 llvm 所有工具一起更新。</p>
 <p>这里使用以下脚本 <code>update-alternatives-clang.sh</code> 进行批量注册：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token shebang important">#!/usr/bin/env bash</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Colors</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">RESET</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable" style="color:#36acaa">tput sgr0</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">RED</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable" style="color:#36acaa">tput setaf </span><span class="token variable number" style="color:#36acaa">1</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">GREEN</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable" style="color:#36acaa">tput setaf </span><span class="token variable number" style="color:#36acaa">2</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">BOLD</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable" style="color:#36acaa">tput bold</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Get available versions from /lib/llvm-*</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># You can also use specific versions, e.g. VERSIONS=("14" "17" "18"), but not recommend</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">VERSIONS</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> </span><span class="token for-or-select variable" style="color:#36acaa">dir</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> /lib/llvm-*</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">do</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-d</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$dir</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">version</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable function" style="color:#d73a49">basename</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable string" style="color:#e3116c">"</span><span class="token variable string variable" style="color:#36acaa">$dir</span><span class="token variable string" style="color:#e3116c">"</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable operator" style="color:#393A34">|</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable function" style="color:#d73a49">cut</span><span class="token variable" style="color:#36acaa"> -d</span><span class="token variable string" style="color:#e3116c">'-'</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable parameter variable" style="color:#36acaa">-f2</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">VERSIONS</span><span class="token operator" style="color:#393A34">+=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$version</span><span class="token string" style="color:#e3116c">"</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">done</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Loop through versions</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> </span><span class="token for-or-select variable" style="color:#36acaa">VERSION</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${VERSIONS</span><span class="token string variable punctuation" style="color:#393A34">[</span><span class="token string variable" style="color:#36acaa">@</span><span class="token string variable punctuation" style="color:#393A34">]</span><span class="token string variable" style="color:#36acaa">}</span><span class="token string" style="color:#e3116c">"</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">do</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic"># Check if /lib/llvm-${VERSION} directory exists</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-d</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"/lib/llvm-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Scan paths and generate string</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">alternative_string</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">""</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">alternative_cmds</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> </span><span class="token for-or-select variable" style="color:#36acaa">cmd</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"/lib/llvm-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">/bin/"</span><span class="token plain">*</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">do</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-x</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$cmd</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&amp;&amp;</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$(</span><span class="token string variable function" style="color:#d73a49">basename</span><span class="token string variable" style="color:#36acaa"> </span><span class="token string variable string" style="color:#e3116c">"</span><span class="token string variable string variable" style="color:#36acaa">$cmd</span><span class="token string variable string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">)</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">!=</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"clang"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token assign-left variable" style="color:#36acaa">base_cmd</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable function" style="color:#d73a49">basename</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable string" style="color:#e3116c">"</span><span class="token variable string variable" style="color:#36acaa">$cmd</span><span class="token variable string" style="color:#e3116c">"</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token assign-left variable" style="color:#36acaa">symlink</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">"/usr/bin/</span><span class="token string variable" style="color:#36acaa">${base_cmd}</span><span class="token string" style="color:#e3116c">-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-x</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${symlink}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    </span><span class="token assign-left variable" style="color:#36acaa">alternative_cmds</span><span class="token operator" style="color:#393A34">+=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable function" style="color:#d73a49">basename</span><span class="token variable" style="color:#36acaa"> $</span><span class="token variable punctuation" style="color:#393A34">{</span><span class="token variable" style="color:#36acaa">symlink</span><span class="token variable punctuation" style="color:#393A34">}</span><span class="token variable" style="color:#36acaa">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    </span><span class="token assign-left variable" style="color:#36acaa">alternative_string</span><span class="token operator" style="color:#393A34">+=</span><span class="token string" style="color:#e3116c">"--slave /usr/bin/</span><span class="token string variable" style="color:#36acaa">${base_cmd}</span><span class="token string" style="color:#e3116c"> </span><span class="token string variable" style="color:#36acaa">${base_cmd}</span><span class="token string" style="color:#e3116c"> </span><span class="token string variable" style="color:#36acaa">${symlink}</span><span class="token string" style="color:#e3116c"> "</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">done</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Remove specific alternative configuration</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--remove</span><span class="token plain"> clang </span><span class="token string" style="color:#e3116c">"/usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> /dev/null</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Install alternatives</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token assign-left variable" style="color:#36acaa">install_command</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">"sudo update-alternatives \</span><br></span><span class="token-line" style="color:#393A34"><span class="token string" style="color:#e3116c">        --quiet \</span><br></span><span class="token-line" style="color:#393A34"><span class="token string" style="color:#e3116c">        --install /usr/bin/clang clang /usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c"> </span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c"> \</span><br></span><span class="token-line" style="color:#393A34"><span class="token string" style="color:#e3116c">        </span><span class="token string variable" style="color:#36acaa">${alternative_string}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Print the concatenated string</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${BOLD}</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">[Adding alternative /usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c"> ...]</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"Master command: clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"Slave commands: </span><span class="token string variable" style="color:#36acaa">${alternative_cmds</span><span class="token string variable punctuation" style="color:#393A34">[</span><span class="token string variable" style="color:#36acaa">*</span><span class="token string variable punctuation" style="color:#393A34">]</span><span class="token string variable" style="color:#36acaa">}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">eval</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">$install_command</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Check eval command's return value</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">$?</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-eq</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${BOLD}</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">[Adding alternative /usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">: succeeded]</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">else</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${BOLD}</span><span class="token string variable" style="color:#36acaa">${RED}</span><span class="token string" style="color:#e3116c">[Adding alternative /usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">: failed]</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">""</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">else</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Remove specific alternative configuration if /lib/llvm-${VERSION} directory does not exist</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token function" style="color:#d73a49">sudo</span><span class="token plain"> update-alternatives </span><span class="token parameter variable" style="color:#36acaa">--remove</span><span class="token plain"> clang </span><span class="token string" style="color:#e3116c">"/usr/bin/clang-</span><span class="token string variable" style="color:#36acaa">${VERSION}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&amp;&gt;</span><span class="token plain"> /dev/null</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">done</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">clang_path</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">$(</span><span class="token variable function" style="color:#d73a49">sudo</span><span class="token variable" style="color:#36acaa"> update-alternatives --get-selections </span><span class="token variable operator" style="color:#393A34">|</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable function" style="color:#d73a49">grep</span><span class="token variable" style="color:#36acaa"> ^clang </span><span class="token variable operator" style="color:#393A34">|</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable function" style="color:#d73a49">awk</span><span class="token variable" style="color:#36acaa"> </span><span class="token variable string" style="color:#e3116c">'{print $NF}'</span><span class="token variable" style="color:#36acaa">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"======================================================================"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">clang alternative is set to: </span><span class="token string variable" style="color:#36acaa">${clang_path}</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"======================================================================"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># print helps</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">""</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"Info:"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">num_versions</span><span class="token operator" style="color:#393A34">=</span><span class="token variable" style="color:#36acaa">${</span><span class="token variable operator" style="color:#393A34">#</span><span class="token variable" style="color:#36acaa">VERSIONS</span><span class="token variable punctuation" style="color:#393A34">[</span><span class="token variable" style="color:#36acaa">@</span><span class="token variable punctuation" style="color:#393A34">]</span><span class="token variable" style="color:#36acaa">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> num_versions </span><span class="token parameter variable" style="color:#36acaa">-gt</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">then</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"  use '</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">sudo update-alternatives --config clang</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">' to change default clang alternative"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">fi</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"  use '</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">sudo update-alternatives --remove clang /usr/bin/clang-*</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">' to delete a clang alternative"</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">"  use '</span><span class="token string variable" style="color:#36acaa">${GREEN}</span><span class="token string" style="color:#e3116c">sudo update-alternatives --remove-all clang</span><span class="token string variable" style="color:#36acaa">${RESET}</span><span class="token string" style="color:#e3116c">' to delete all clang alternatives"</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
@@ -157,8 +157,8 @@
         </item>
         <item>
             <title><![CDATA[停止国际化支持]]></title>
-            <link>https://www.szdev.com/blog/site/remove-i18n-support</link>
-            <guid>https://www.szdev.com/blog/site/remove-i18n-support</guid>
+            <link>https://ShangjinTang.github.io/blog/site/remove-i18n-support</link>
+            <guid>https://ShangjinTang.github.io/blog/site/remove-i18n-support</guid>
             <pubDate>Tue, 30 Jan 2024 00:00:00 GMT</pubDate>
             <description><![CDATA[删除所有的文章的国际化支持。之前所有文章均有双语版本，后续所有文章只会有单个语言版本。]]></description>
             <content:encoded><![CDATA[<p>删除所有的文章的国际化支持。之前所有文章均有双语版本，后续所有文章只会有单个语言版本。</p>
@@ -184,8 +184,8 @@
         </item>
         <item>
             <title><![CDATA[支持 Font Awesome]]></title>
-            <link>https://www.szdev.com/blog/mdx/support-fontawesome</link>
-            <guid>https://www.szdev.com/blog/mdx/support-fontawesome</guid>
+            <link>https://ShangjinTang.github.io/blog/mdx/support-fontawesome</link>
+            <guid>https://ShangjinTang.github.io/blog/mdx/support-fontawesome</guid>
             <pubDate>Wed, 13 Dec 2023 00:00:00 GMT</pubDate>
             <description><![CDATA[现在可以在 mdx 中使用 Font Awesome 图标。]]></description>
             <content:encoded><![CDATA[<p>现在可以在 mdx 中使用 <a href="https://fontawesome.com/search" target="_blank" rel="noopener noreferrer">Font Awesome 图标</a>。</p>
@@ -210,8 +210,8 @@
         </item>
         <item>
             <title><![CDATA[使用 Leaflet 绘制地图]]></title>
-            <link>https://www.szdev.com/blog/mdx/interactive-map-with-leaflet</link>
-            <guid>https://www.szdev.com/blog/mdx/interactive-map-with-leaflet</guid>
+            <link>https://ShangjinTang.github.io/blog/mdx/interactive-map-with-leaflet</link>
+            <guid>https://ShangjinTang.github.io/blog/mdx/interactive-map-with-leaflet</guid>
             <pubDate>Wed, 29 Nov 2023 00:00:00 GMT</pubDate>
             <description><![CDATA[Leaflet 是地理信息系统（GIS）中流行的开源 JavaScript 库。]]></description>
             <content:encoded><![CDATA[<p><a href="https://leafletjs.com/" target="_blank" rel="noopener noreferrer"><strong>Leaflet</strong></a> 是地理信息系统（GIS）中流行的开源 JavaScript 库。</p>
@@ -226,16 +226,16 @@
         </item>
         <item>
             <title><![CDATA[支持 Mermaid 图表]]></title>
-            <link>https://www.szdev.com/blog/mdx/support-mermaid-diagrams</link>
-            <guid>https://www.szdev.com/blog/mdx/support-mermaid-diagrams</guid>
+            <link>https://ShangjinTang.github.io/blog/mdx/support-mermaid-diagrams</link>
+            <guid>https://ShangjinTang.github.io/blog/mdx/support-mermaid-diagrams</guid>
             <pubDate>Mon, 27 Nov 2023 00:00:00 GMT</pubDate>
             <description><![CDATA[Mermaid 是一个绘制图表的工具。]]></description>
             <content:encoded><![CDATA[<p>Mermaid 是一个绘制图表的工具。</p>
 <p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="序列图">序列图<a href="https://www.szdev.com/blog/mdx/support-mermaid-diagrams#%E5%BA%8F%E5%88%97%E5%9B%BE" class="hash-link" aria-label="序列图的直接链接" title="序列图的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="序列图">序列图<a href="https://shangjintang.github.io/blog/mdx/support-mermaid-diagrams#%E5%BA%8F%E5%88%97%E5%9B%BE" class="hash-link" aria-label="序列图的直接链接" title="序列图的直接链接">​</a></h2>
 <div class="language-md codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockTitle_Ktv7">Example Mermaid sequence diagram</div><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-md codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token code punctuation" style="color:#393A34">```</span><span class="token code code-language">mermaid</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code code-block language-mermaid">graph TD;</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    A--&gt;B;</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    A--&gt;C;</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    B--&gt;D;</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C--&gt;D;</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code punctuation" style="color:#393A34">```</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <!-- -->
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="流程图">流程图<a href="https://www.szdev.com/blog/mdx/support-mermaid-diagrams#%E6%B5%81%E7%A8%8B%E5%9B%BE" class="hash-link" aria-label="流程图的直接链接" title="流程图的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="流程图">流程图<a href="https://shangjintang.github.io/blog/mdx/support-mermaid-diagrams#%E6%B5%81%E7%A8%8B%E5%9B%BE" class="hash-link" aria-label="流程图的直接链接" title="流程图的直接链接">​</a></h2>
 <div class="language-md codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockTitle_Ktv7">Example Mermaid flowchart</div><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-md codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token code punctuation" style="color:#393A34">```</span><span class="token code code-language">mermaid</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code code-block language-mermaid">flowchart TD</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    A[Christmas] --&gt;|Get money| B(Go shopping)</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    B --&gt; C{Let me think}</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|One| D[Laptop]</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|Two| E[iPhone]</span><br></span><span class="token-line" style="color:#393A34"><span class="token code code-block language-mermaid">    C --&gt;|Three| F[fa:fa-car Car]</span><span class="token code"></span><br></span><span class="token-line" style="color:#393A34"><span class="token code"></span><span class="token code punctuation" style="color:#393A34">```</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 ]]></content:encoded>
             <author>shangjin.tang@gmail.com (Sol)</author>
@@ -246,8 +246,8 @@
         </item>
         <item>
             <title><![CDATA[支持全局 Tabs 和 TabItem]]></title>
-            <link>https://www.szdev.com/blog/mdx/support-global-tabs-tabitem</link>
-            <guid>https://www.szdev.com/blog/mdx/support-global-tabs-tabitem</guid>
+            <link>https://ShangjinTang.github.io/blog/mdx/support-global-tabs-tabitem</link>
+            <guid>https://ShangjinTang.github.io/blog/mdx/support-global-tabs-tabitem</guid>
             <pubDate>Sun, 26 Nov 2023 00:00:00 GMT</pubDate>
             <description><![CDATA[Docusaurus 提供了 ` 和 ` 组件，可以通过 MDX 在 Markdown 中使用该组件。]]></description>
             <content:encoded><![CDATA[<p>Docusaurus 提供了 <code>&lt;Tabs&gt;</code> 和 <code>&lt;TabItem&gt;</code> 组件，可以通过 MDX 在 Markdown 中使用该组件。</p>
@@ -271,18 +271,18 @@
         </item>
         <item>
             <title><![CDATA[支持 LaTeX 数学公式]]></title>
-            <link>https://www.szdev.com/blog/mdx/support-math-latex</link>
-            <guid>https://www.szdev.com/blog/mdx/support-math-latex</guid>
+            <link>https://ShangjinTang.github.io/blog/mdx/support-math-latex</link>
+            <guid>https://ShangjinTang.github.io/blog/mdx/support-math-latex</guid>
             <pubDate>Fri, 24 Nov 2023 00:00:00 GMT</pubDate>
             <description><![CDATA[数学公式可以使用 KaTeX 渲染，目前本站已经支持。]]></description>
             <content:encoded><![CDATA[<p>数学公式可以使用 <a href="https://katex.org/" target="_blank" rel="noopener noreferrer">KaTeX</a> 渲染，目前本站已经支持。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="usage">用法<a href="https://www.szdev.com/blog/mdx/support-math-latex#usage" class="hash-link" aria-label="用法的直接链接" title="用法的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="usage">用法<a href="https://shangjintang.github.io/blog/mdx/support-math-latex#usage" class="hash-link" aria-label="用法的直接链接" title="用法的直接链接">​</a></h2>
 <p>请阅读 <a href="https://katex.org/" target="_blank" rel="noopener noreferrer">KaTeX</a> 文档了解更多详细信息。</p>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="inline">行内公式<a href="https://www.szdev.com/blog/mdx/support-math-latex#inline" class="hash-link" aria-label="行内公式的直接链接" title="行内公式的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="inline">行内公式<a href="https://shangjintang.github.io/blog/mdx/support-math-latex#inline" class="hash-link" aria-label="行内公式的直接链接" title="行内公式的直接链接">​</a></h3>
 <p>对于行内数学公式，将 LaTeX 包裹在 <code>$</code> 之间：</p>
 <div class="language-latex codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-latex codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">假设 </span><span class="token equation string" style="color:#e3116c">$f</span><span class="token equation string equation-command regex" style="color:#36acaa">\colon</span><span class="token equation string" style="color:#e3116c">[a,b]</span><span class="token equation string equation-command regex" style="color:#36acaa">\to</span><span class="token equation string equation-command regex" style="color:#36acaa">\R</span><span class="token equation string" style="color:#e3116c">$</span><span class="token plain"> 是黎曼可积的，定义 </span><span class="token equation string" style="color:#e3116c">$F</span><span class="token equation string equation-command regex" style="color:#36acaa">\colon</span><span class="token equation string" style="color:#e3116c">[a,b]</span><span class="token equation string equation-command regex" style="color:#36acaa">\to</span><span class="token equation string equation-command regex" style="color:#36acaa">\R</span><span class="token equation string" style="color:#e3116c">$</span><span class="token plain"> 为 </span><span class="token equation string" style="color:#e3116c">$F(x)=</span><span class="token equation string equation-command regex" style="color:#36acaa">\int</span><span class="token equation string" style="color:#e3116c">_{a}^{x} f(t)</span><span class="token equation string equation-command regex" style="color:#36acaa">\,</span><span class="token equation string" style="color:#e3116c">dt$</span><span class="token plain">。那么， </span><span class="token equation string" style="color:#e3116c">$F$</span><span class="token plain"> 是连续的；并且 </span><span class="token equation string" style="color:#e3116c">$x$</span><span class="token plain"> 在 </span><span class="token equation string" style="color:#e3116c">$f$</span><span class="token plain"> 在 </span><span class="token equation string" style="color:#e3116c">$x$</span><span class="token plain"> 处连续；</span><span class="token equation string" style="color:#e3116c">$F$</span><span class="token plain"> 在 </span><span class="token equation string" style="color:#e3116c">$x$</span><span class="token plain"> 处可微，且 </span><span class="token equation string" style="color:#e3116c">$F'(x)=f(x)$</span><span class="token plain">。</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>假设 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mspace></mspace><mspace width="0.1111em"></mspace><mo lspace="0em" rspace="0.17em"></mo><mtext> ⁣</mtext><mo lspace="0em" rspace="0em">:</mo><mspace width="0.3333em"></mspace><mo stretchy="false">[</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">]</mo><mo>→</mo><mi mathvariant="double-struck">R</mi></mrow><annotation encoding="application/x-tex">f\colon[a,b]\to\R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mspace nobreak"></span><span class="mspace" style="margin-right:0.1111em"></span><span class="mpunct"></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mrel">:</span></span><span class="mspace" style="margin-right:0.3333em"></span><span class="mopen">[</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">b</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6889em"></span><span class="mord mathbb">R</span></span></span></span> 是黎曼可积的，定义 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mspace></mspace><mspace width="0.1111em"></mspace><mo lspace="0em" rspace="0.17em"></mo><mtext> ⁣</mtext><mo lspace="0em" rspace="0em">:</mo><mspace width="0.3333em"></mspace><mo stretchy="false">[</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">]</mo><mo>→</mo><mi mathvariant="double-struck">R</mi></mrow><annotation encoding="application/x-tex">F\colon[a,b]\to\R</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.13889em">F</span><span class="mspace nobreak"></span><span class="mspace" style="margin-right:0.1111em"></span><span class="mpunct"></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mrel">:</span></span><span class="mspace" style="margin-right:0.3333em"></span><span class="mopen">[</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">b</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6889em"></span><span class="mord mathbb">R</span></span></span></span> 为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mi>a</mi><mi>x</mi></msubsup><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">F(x)=\int_{a}^{x} f(t)\,dt</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.13889em">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2151em;vertical-align:-0.3558em"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span></span></span></span>。那么， <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi></mrow><annotation encoding="application/x-tex">F</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.13889em">F</span></span></span></span> 是连续的；并且 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> 在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span></span></span></span> 在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> 处连续；<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi></mrow><annotation encoding="application/x-tex">F</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.13889em">F</span></span></span></span> 在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> 处可微，且 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>F</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F'(x)=f(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em">F</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span>。</p>
-<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="blocks">公式块<a href="https://www.szdev.com/blog/mdx/support-math-latex#blocks" class="hash-link" aria-label="公式块的直接链接" title="公式块的直接链接">​</a></h3>
+<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="blocks">公式块<a href="https://shangjintang.github.io/blog/mdx/support-math-latex#blocks" class="hash-link" aria-label="公式块的直接链接" title="公式块的直接链接">​</a></h3>
 <p>对于公式块，使用换行符和 <code>$$</code> 隔开：</p>
 <div class="language-latex codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-latex codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">$$</span><br></span><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">I = </span><span class="token equation string equation-command regex" style="color:#36acaa">\int</span><span class="token equation string" style="color:#e3116c">_0^{2</span><span class="token equation string equation-command regex" style="color:#36acaa">\pi</span><span class="token equation string" style="color:#e3116c">} </span><span class="token equation string equation-command regex" style="color:#36acaa">\sin</span><span class="token equation string" style="color:#e3116c">(x)</span><span class="token equation string equation-command regex" style="color:#36acaa">\,</span><span class="token equation string" style="color:#e3116c">dx</span><br></span><span class="token-line" style="color:#393A34"><span class="token equation string" style="color:#e3116c">$$</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>I</mi><mo>=</mo><msubsup><mo>∫</mo><mn>0</mn><mrow><mn>2</mn><mi>π</mi></mrow></msubsup><mi>sin</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">I = \int_0^{2\pi} \sin(x)\,dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.476em;vertical-align:-0.9119em"></span><span class="mop"><span class="mop op-symbol large-op" style="margin-right:0.44445em;position:relative;top:-0.0011em">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.564em"><span style="top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.8129em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">π</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9119em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop">sin</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span></span>]]></content:encoded>
@@ -294,14 +294,14 @@
         </item>
         <item>
             <title><![CDATA[React 支持]]></title>
-            <link>https://www.szdev.com/blog/mdx/react-support</link>
-            <guid>https://www.szdev.com/blog/mdx/react-support</guid>
+            <link>https://ShangjinTang.github.io/blog/mdx/react-support</link>
+            <guid>https://ShangjinTang.github.io/blog/mdx/react-support</guid>
             <pubDate>Thu, 23 Nov 2023 00:00:00 GMT</pubDate>
             <description><![CDATA[博客文章支持 Docusaurus Markdown 功能，例如 MDX。]]></description>
             <content:encoded><![CDATA[<p>博客文章支持 <a href="https://docusaurus.io/docs/markdown-features" target="_blank" rel="noopener noreferrer">Docusaurus Markdown 功能</a>，例如 <a href="https://mdxjs.com/" target="_blank" rel="noopener noreferrer">MDX</a>。</p>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="interactive">交互式<a href="https://www.szdev.com/blog/mdx/react-support#interactive" class="hash-link" aria-label="交互式的直接链接" title="交互式的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="interactive">交互式<a href="https://shangjintang.github.io/blog/mdx/react-support#interactive" class="hash-link" aria-label="交互式的直接链接" title="交互式的直接链接">​</a></h2>
 <div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>提示</div><div class="admonitionContent_BuS1"><p>使用 React 的强大功能来创建交互式博客文章。</p><div class="language-js codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-js codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">button onClick</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">{</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=&gt;</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">alert</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">'按钮被点击了!'</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">}</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain">点击这里！</span><span class="token operator" style="color:#393A34">&lt;</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">button</span><span class="token operator" style="color:#393A34">&gt;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><button>点击这里！</button></div></div>
-<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="diagram">图表式<a href="https://www.szdev.com/blog/mdx/react-support#diagram" class="hash-link" aria-label="图表式的直接链接" title="图表式的直接链接">​</a></h2>
+<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="diagram">图表式<a href="https://shangjintang.github.io/blog/mdx/react-support#diagram" class="hash-link" aria-label="图表式的直接链接" title="图表式的直接链接">​</a></h2>
 <div class="theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>提示</div><div class="admonitionContent_BuS1"><p>使用 React 的强大功能来创建图表。</p><div class="language-mdx codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-mdx codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">import {Chart} from './_asset/snowfall.js';</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">export const year = 2013;</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"># 去年降雪</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">{year} 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">&lt;Chart year={year} color="#fcb32c" /&gt;;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h1>去年降雪</h1><p>2013<!-- --> 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。</p><div class="snowfall"><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(6 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(4.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(1.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(1.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(2.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(3.5 * 0.5 * (1em + 1ex))"></div><div class="snowfall-bar" style="background-color:#fcb32c;height:calc(7 * 0.5 * (1em + 1ex))"></div></div></div></div>]]></content:encoded>
             <author>shangjin.tang@gmail.com (Sol)</author>
             <category>mdx</category>
@@ -309,8 +309,8 @@
         </item>
         <item>
             <title><![CDATA[欢迎]]></title>
-            <link>https://www.szdev.com/blog/welcome</link>
-            <guid>https://www.szdev.com/blog/welcome</guid>
+            <link>https://ShangjinTang.github.io/blog/welcome</link>
+            <guid>https://ShangjinTang.github.io/blog/welcome</guid>
             <pubDate>Tue, 28 May 2019 00:00:00 GMT</pubDate>
             <description><![CDATA[Docusaurus 博客功能由 blog 插件提供支持。]]></description>
             <content:encoded><![CDATA[<p><a href="https://docusaurus.io/docs/blog" target="_blank" rel="noopener noreferrer">Docusaurus 博客功能</a>由 <a href="https://docusaurus.io/docs/api/plugins/@docusaurus/plugin-content-blog" target="_blank" rel="noopener noreferrer">blog 插件</a>提供支持。</p>
@@ -323,7 +323,7 @@
 <li><code>2019-05-30-welcome/index.md</code></li>
 </ul>
 <p>写博客时，可以方便地在同级文件夹内引用图像：</p>
-<p><img decoding="async" loading="lazy" alt="Docusaurus 毛绒玩具" src="https://www.szdev.com/assets/images/docusaurus-plushie-banner-a60f7593abca1e3eef26a9afa244e4fb.jpeg" width="1500" height="500" class="img_ev3q"></p>
+<p><img decoding="async" loading="lazy" alt="Docusaurus 毛绒玩具" src="https://shangjintang.github.io/assets/images/docusaurus-plushie-banner-a60f7593abca1e3eef26a9afa244e4fb.jpeg" width="1500" height="500" class="img_ev3q"></p>
 <p>博客也支持标签！</p>
 <p><strong>如果不需要博客</strong>：删除此目录，并在 Docusaurus 配置中使用 <code>blog: false</code> 即可。</p>]]></content:encoded>
             <author>shangjin.tang@gmail.com (Sol)</author>
diff --git a/blog/site/change-default-fonts/index.html b/blog/site/change-default-fonts/index.html
index cdea2b3a8..3a1dc99d5 100644
--- a/blog/site/change-default-fonts/index.html
+++ b/blog/site/change-default-fonts/index.html
@@ -3,12 +3,12 @@
 <head>
 <meta charset="UTF-8">
 <meta name="generator" content="Docusaurus v3.5.2">
-<title data-rh="true">更改默认字体 | Sol 的空间</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:image" content="https://www.szdev.com/img/docusaurus-social-card.jpg"><meta data-rh="true" name="twitter:image" content="https://www.szdev.com/img/docusaurus-social-card.jpg"><meta data-rh="true" property="og:url" content="https://www.szdev.com/blog/site/change-default-fonts"><meta data-rh="true" property="og:locale" content="zh_CN"><meta data-rh="true" name="docusaurus_locale" content="zh-CN"><meta data-rh="true" name="docusaurus_tag" content="default"><meta data-rh="true" name="docsearch:language" content="zh-CN"><meta data-rh="true" name="docsearch:docusaurus_tag" content="default"><meta data-rh="true" property="og:title" content="更改默认字体 | Sol 的空间"><meta data-rh="true" name="description" content="本站默认字体现已更改为 LxgwWenKai Screen."><meta data-rh="true" property="og:description" content="本站默认字体现已更改为 LxgwWenKai Screen."><meta data-rh="true" property="og:type" content="article"><meta data-rh="true" property="article:published_time" content="2024-10-17T00:00:00.000Z"><meta data-rh="true" property="article:tag" content="site,font"><link data-rh="true" rel="icon" href="/img/favicon_sol.ico"><link data-rh="true" rel="canonical" href="https://www.szdev.com/blog/site/change-default-fonts"><link data-rh="true" rel="alternate" href="https://www.szdev.com/blog/site/change-default-fonts" hreflang="zh-CN"><link data-rh="true" rel="alternate" href="https://www.szdev.com/blog/site/change-default-fonts" hreflang="x-default"><script data-rh="true" type="application/ld+json">{"@context":"https://schema.org","@type":"BlogPosting","@id":"https://www.szdev.com/blog/site/change-default-fonts","mainEntityOfPage":"https://www.szdev.com/blog/site/change-default-fonts","url":"https://www.szdev.com/blog/site/change-default-fonts","headline":"更改默认字体","name":"更改默认字体","description":"本站默认字体现已更改为 LxgwWenKai Screen.","datePublished":"2024-10-17T00:00:00.000Z","author":{"@type":"Person","name":"Sol","description":"千里之行，始于足下。","email":"shangjin.tang@gmail.com","image":"https://github.com/ShangjinTang.png"},"keywords":[],"isPartOf":{"@type":"Blog","@id":"https://www.szdev.com/blog","name":"Sol 的博客"}}</script><link rel="alternate" type="application/rss+xml" href="/blog/rss.xml" title="Sol 的空间 RSS Feed">
+<title data-rh="true">更改默认字体 | Sol 的空间</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:image" content="https://ShangjinTang.github.io/img/docusaurus-social-card.jpg"><meta data-rh="true" name="twitter:image" content="https://ShangjinTang.github.io/img/docusaurus-social-card.jpg"><meta data-rh="true" property="og:url" content="https://ShangjinTang.github.io/blog/site/change-default-fonts"><meta data-rh="true" property="og:locale" content="zh_CN"><meta data-rh="true" name="docusaurus_locale" content="zh-CN"><meta data-rh="true" name="docusaurus_tag" content="default"><meta data-rh="true" name="docsearch:language" content="zh-CN"><meta data-rh="true" name="docsearch:docusaurus_tag" content="default"><meta data-rh="true" property="og:title" content="更改默认字体 | Sol 的空间"><meta data-rh="true" name="description" content="本站默认字体现已更改为 LxgwWenKai Screen."><meta data-rh="true" property="og:description" content="本站默认字体现已更改为 LxgwWenKai Screen."><meta data-rh="true" property="og:type" content="article"><meta data-rh="true" property="article:published_time" content="2024-10-17T00:00:00.000Z"><meta data-rh="true" property="article:tag" content="site,font"><link data-rh="true" rel="icon" href="/img/favicon_sol.ico"><link data-rh="true" rel="canonical" href="https://ShangjinTang.github.io/blog/site/change-default-fonts"><link data-rh="true" rel="alternate" href="https://ShangjinTang.github.io/blog/site/change-default-fonts" hreflang="zh-CN"><link data-rh="true" rel="alternate" href="https://ShangjinTang.github.io/blog/site/change-default-fonts" hreflang="x-default"><script data-rh="true" type="application/ld+json">{"@context":"https://schema.org","@type":"BlogPosting","@id":"https://ShangjinTang.github.io/blog/site/change-default-fonts","mainEntityOfPage":"https://ShangjinTang.github.io/blog/site/change-default-fonts","url":"https://ShangjinTang.github.io/blog/site/change-default-fonts","headline":"更改默认字体","name":"更改默认字体","description":"本站默认字体现已更改为 LxgwWenKai Screen.","datePublished":"2024-10-17T00:00:00.000Z","author":{"@type":"Person","name":"Sol","description":"千里之行，始于足下。","email":"shangjin.tang@gmail.com","image":"https://github.com/ShangjinTang.png"},"keywords":[],"isPartOf":{"@type":"Blog","@id":"https://ShangjinTang.github.io/blog","name":"Sol 的博客"}}</script><link rel="alternate" type="application/rss+xml" href="/blog/rss.xml" title="Sol 的空间 RSS Feed">
 <link rel="alternate" type="application/atom+xml" href="/blog/atom.xml" title="Sol 的空间 Atom Feed"><link rel="stylesheet" href="/assets/css/styles.abfd45f8.css">
 <script src="/assets/js/runtime~main.8ec2c78b.js" defer="defer"></script>
-<script src="/assets/js/main.e6ab80d7.js" defer="defer"></script>
+<script src="/assets/js/main.9d499883.js" defer="defer"></script>
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class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 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2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p>删除所有的文章的国际化支持。之前所有文章均有双语版本，后续所有文章只会有单个语言版本。</p>
@@ -27,6 +27,6 @@
 <li>
 <p>翻译不是一劳永逸的事情，每次更新某个语言的文章的时候，需要更新同时两种语言。</p>
 </li>
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authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 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1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Ubuntu 22.04 默认使用 <code>g++-11</code> 和 <code>clang++-14</code> 作为默认的 <code>g++</code> 和 <code>clang++</code>。</p>
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+<p>本文说明如何升级 C++ 编译器并设置默认版本，从而使用最新的 C++ 语言特性。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/cpp">cpp</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/ubuntu-2204">ubuntu2204</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/clang">clang</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/gcc">gcc</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 Ubuntu 22.04 更新 C++ 编译器 的全文" href="/blog/cpp/update-compiler-on-ubuntu2204"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 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10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>在编程中，斐波那契数列是一个经典的数学问题。通常情况下，我们可以使用传统递归函数来计算斐波那契数列。但是运行时计算递归会造成比较长的耗时。</p>
 <p>模板元编程可以解决这个问题，在编译时计算斐波那契数列，从而提高执行效率。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/cpp">cpp</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/template-meta-programming">template-meta-programming</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 模板元编程：斐波那契数列 的全文" href="/blog/cpp/calculate-fibonnaci-with-template-meta-programming"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/cpp/update-compiler-on-ubuntu2204">Ubuntu 22.04 更新 C++ 编译器</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2024-01-31T00:00:00.000Z">2024年1月31日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Ubuntu 22.04 默认使用 <code>g++-11</code> 和 <code>clang++-14</code> 作为默认的 <code>g++</code> 和 <code>clang++</code>。</p>
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class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Mermaid 是一个绘制图表的工具。</p>
-<p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mermaid">mermaid</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/diagram">diagram</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/flowchart">flowchart</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Mermaid 图表 的全文" href="/blog/mdx/support-mermaid-diagrams"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mermaid">mermaid</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/diagram">diagram</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/flowchart">flowchart</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Mermaid 图表 的全文" href="/blog/mdx/support-mermaid-diagrams"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Mermaid 是一个绘制图表的工具。</p>
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+<p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mermaid">mermaid</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/diagram">diagram</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/flowchart">flowchart</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Mermaid 图表 的全文" href="/blog/mdx/support-mermaid-diagrams"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 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10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>现在可以在 mdx 中使用 <a href="https://fontawesome.com/search" target="_blank" rel="noopener noreferrer">Font Awesome 图标</a>。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/font-awesome">font-awesome</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" 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href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-math-latex">支持 LaTeX 数学公式</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/react-support">React 支持</a></li></ul></div><div role="group"><h3 class="yearGroupHeading_rMGB">2019</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/welcome">欢迎</a></li></ul></div></nav></aside><main class="col col--7"><header class="margin-bottom--xl"><h1>1 篇博文 含有标签「font-awesome」</h1><a href="/blog/tags">查看所有标签</a></header><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-fontawesome">支持 Font Awesome</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-12-13T00:00:00.000Z">2023年12月13日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 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href="/blog/tags/icon">icon</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Font Awesome 的全文" href="/blog/mdx/support-fontawesome"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li 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class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 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class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 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href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-math-latex">支持 LaTeX 数学公式</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/react-support">React 支持</a></li></ul></div><div role="group"><h3 class="yearGroupHeading_rMGB">2019</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/welcome">欢迎</a></li></ul></div></nav></aside><main class="col col--7"><header class="margin-bottom--xl"><h1>1 篇博文 含有标签「latex」</h1><a href="/blog/tags">查看所有标签</a></header><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-math-latex">支持 LaTeX 数学公式</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-24T00:00:00.000Z">2023年11月24日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 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authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 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10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p><a href="https://leafletjs.com/" target="_blank" rel="noopener noreferrer"><strong>Leaflet</strong></a> 是地理信息系统（GIS）中流行的开源 JavaScript 库。</p>
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+<p>本文在 MDX 中使用 <strong>Leaflet</strong> 绘制交互式地图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/map">map</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/leaflet">leaflet</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 使用 Leaflet 绘制地图 的全文" href="/blog/mdx/interactive-map-with-leaflet"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p><a href="https://leafletjs.com/" target="_blank" rel="noopener noreferrer"><strong>Leaflet</strong></a> 是地理信息系统（GIS）中流行的开源 JavaScript 库。</p>
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10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/youtube">youtube</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/bilibili">bilibili</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/video">video</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持嵌入 YouTube 和 Bilibili 视频 的全文" href="/blog/mdx/support-video-link"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-fontawesome">支持 Font Awesome</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-12-13T00:00:00.000Z">2023年12月13日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>现在可以在 mdx 中使用 <a href="https://fontawesome.com/search" target="_blank" rel="noopener noreferrer">Font Awesome 图标</a>。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/font-awesome">font-awesome</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/icon">icon</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Font Awesome 的全文" href="/blog/mdx/support-fontawesome"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/interactive-map-with-leaflet">使用 Leaflet 绘制地图</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-29T00:00:00.000Z">2023年11月29日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p><a href="https://leafletjs.com/" target="_blank" rel="noopener noreferrer"><strong>Leaflet</strong></a> 是地理信息系统（GIS）中流行的开源 JavaScript 库。</p>
 <p>本文在 MDX 中使用 <strong>Leaflet</strong> 绘制交互式地图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/map">map</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/leaflet">leaflet</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 使用 Leaflet 绘制地图 的全文" href="/blog/mdx/interactive-map-with-leaflet"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-mermaid-diagrams">支持 Mermaid 图表</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-27T00:00:00.000Z">2023年11月27日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Mermaid 是一个绘制图表的工具。</p>
 <p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mermaid">mermaid</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/diagram">diagram</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/flowchart">flowchart</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Mermaid 图表 的全文" href="/blog/mdx/support-mermaid-diagrams"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-26T00:00:00.000Z">2023年11月26日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Docusaurus 提供了 <code>&lt;Tabs&gt;</code> 和 <code>&lt;TabItem&gt;</code> 组件，可以通过 MDX 在 Markdown 中使用该组件。</p>
-<p>我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持全局 Tabs 和 TabItem 的全文" href="/blog/mdx/support-global-tabs-tabitem"><b>阅读更多</b></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-math-latex">支持 LaTeX 数学公式</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-24T00:00:00.000Z">2023年11月24日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>数学公式可以使用 <a href="https://katex.org" target="_blank" rel="noopener noreferrer">KaTeX</a> 渲染，目前本站已经支持。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/math">math</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/latex">latex</a></li><li 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21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>数学公式可以使用 <a href="https://katex.org" target="_blank" rel="noopener noreferrer">KaTeX</a> 渲染，目前本站已经支持。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/math">math</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/latex">latex</a></li><li 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class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 476.152H1200L714.137 519.284h.026ZM569.165 687.828l-47.468-67.894-377.686-540.24h162.604l304.797 435.991 47.468 67.894 396.2 566.721H892.476L569.165 687.854v-.026Z"></path></svg></a><a href="https://github.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="GitHub"><svg viewBox="0 0 256 250" width="1em" height="1em" class="authorSocialLink_owbf githubSvg_Uu4N" xmlns="http://www.w3.org/2000/svg" style="--dark:#000;--light:#fff" preserveAspectRatio="xMidYMid"><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Mermaid 是一个绘制图表的工具。</p>
-<p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mermaid">mermaid</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/diagram">diagram</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/flowchart">flowchart</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Mermaid 图表 的全文" href="/blog/mdx/support-mermaid-diagrams"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>请参阅 <a href="https://mermaid.js.org/ecosystem/tutorials.html" target="_blank" rel="noopener noreferrer">Mermaid 教程</a> 并使用 <a href="https://mermaid.live/" target="_blank" rel="noopener noreferrer">Mermaid 实时编辑</a> 来进行绘图。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mermaid">mermaid</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/diagram">diagram</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/flowchart">flowchart</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持 Mermaid 图表 的全文" href="/blog/mdx/support-mermaid-diagrams"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Docusaurus 提供了 <code>&lt;Tabs&gt;</code> 和 <code>&lt;TabItem&gt;</code> 组件，可以通过 MDX 在 Markdown 中使用该组件。</p>
-<p>我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持全局 Tabs 和 TabItem 的全文" href="/blog/mdx/support-global-tabs-tabitem"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持全局 Tabs 和 TabItem 的全文" href="/blog/mdx/support-global-tabs-tabitem"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/cpp/calculate-fibonnaci-with-template-meta-programming">模板元编程：斐波那契数列</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/cpp/update-compiler-on-ubuntu2204">Ubuntu 22.04 更新 C++ 编译器</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/site/remove-i18n-support">停止国际化支持</a></li></ul></div><div role="group"><h3 class="yearGroupHeading_rMGB">2023</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-fontawesome">支持 Font Awesome</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/interactive-map-with-leaflet">使用 Leaflet 绘制地图</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-mermaid-diagrams">支持 Mermaid 图表</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/support-math-latex">支持 LaTeX 数学公式</a></li><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/mdx/react-support">React 支持</a></li></ul></div><div role="group"><h3 class="yearGroupHeading_rMGB">2019</h3><ul class="sidebarItemList_Yudw clean-list"><li class="sidebarItem__DBe"><a class="sidebarItemLink_mo7H" href="/blog/welcome">欢迎</a></li></ul></div></nav></aside><main class="col col--7"><header class="margin-bottom--xl"><h1>1 篇博文 含有标签「tabs」</h1><a href="/blog/tags">查看所有标签</a></header><article class="margin-bottom--xl"><header><h2 class="title_f1Hy"><a href="/blog/mdx/support-global-tabs-tabitem">支持全局 Tabs 和 TabItem</a></h2><div class="container_mt6G margin-vert--md"><time datetime="2023-11-26T00:00:00.000Z">2023年11月26日</time></div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 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-<p>我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持全局 Tabs 和 TabItem 的全文" href="/blog/mdx/support-global-tabs-tabitem"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabs">tabs</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/tabitem">tabitem</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 支持全局 Tabs 和 TabItem 的全文" href="/blog/mdx/support-global-tabs-tabitem"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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diff --git a/blog/tags/template-meta-programming/index.html b/blog/tags/template-meta-programming/index.html
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@@ -3,13 +3,13 @@
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 <meta charset="UTF-8">
 <meta name="generator" content="Docusaurus v3.5.2">
-<title data-rh="true">1 篇博文 含有标签「template-meta-programming」 | Sol 的空间</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:image" content="https://www.szdev.com/img/docusaurus-social-card.jpg"><meta data-rh="true" name="twitter:image" content="https://www.szdev.com/img/docusaurus-social-card.jpg"><meta data-rh="true" property="og:url" content="https://www.szdev.com/blog/tags/template-meta-programming"><meta data-rh="true" property="og:locale" content="zh_CN"><meta data-rh="true" name="docusaurus_locale" content="zh-CN"><meta data-rh="true" name="docsearch:language" content="zh-CN"><meta data-rh="true" property="og:title" content="1 篇博文 含有标签「template-meta-programming」 | Sol 的空间"><meta data-rh="true" name="docusaurus_tag" content="blog_tags_posts"><meta data-rh="true" name="docsearch:docusaurus_tag" content="blog_tags_posts"><link data-rh="true" rel="icon" href="/img/favicon_sol.ico"><link data-rh="true" rel="canonical" href="https://www.szdev.com/blog/tags/template-meta-programming"><link data-rh="true" rel="alternate" href="https://www.szdev.com/blog/tags/template-meta-programming" hreflang="zh-CN"><link data-rh="true" rel="alternate" href="https://www.szdev.com/blog/tags/template-meta-programming" hreflang="x-default"><link rel="alternate" type="application/rss+xml" href="/blog/rss.xml" title="Sol 的空间 RSS Feed">
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row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 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2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>在编程中，斐波那契数列是一个经典的数学问题。通常情况下，我们可以使用传统递归函数来计算斐波那契数列。但是运行时计算递归会造成比较长的耗时。</p>
-<p>模板元编程可以解决这个问题，在编译时计算斐波那契数列，从而提高执行效率。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/cpp">cpp</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/template-meta-programming">template-meta-programming</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 模板元编程：斐波那契数列 的全文" href="/blog/cpp/calculate-fibonnaci-with-template-meta-programming"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>模板元编程可以解决这个问题，在编译时计算斐波那契数列，从而提高执行效率。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/cpp">cpp</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/template-meta-programming">template-meta-programming</a></li></ul></div><div class="col text--right col--3"><a aria-label="阅读 模板元编程：斐波那契数列 的全文" href="/blog/cpp/calculate-fibonnaci-with-template-meta-programming"><b>阅读更多</b></a></div></footer></article><nav class="pagination-nav" aria-label="博文列表分页导航"></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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authorCol_Hf19"><div class="avatar margin-bottom--sm"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer" class="avatar__photo-link"><img class="avatar__photo authorImage_XqGP" src="https://github.com/ShangjinTang.png" alt="Sol"></a><div class="avatar__intro authorDetails_lV9A"><div class="avatar__name"><a href="mailto:shangjin.tang@gmail.com" target="_blank" rel="noopener noreferrer"><span class="authorName_yefp">Sol</span></a></div><small class="authorTitle_nd0D" title="千里之行，始于足下。">千里之行，始于足下。</small><div class="authorSocials_rSDt"><a href="https://x.com/ShangjinTang" target="_blank" rel="noopener noreferrer" class="authorSocialLink_owbf" title="X"><svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" fill="none" viewBox="0 0 1200 1227" class="authorSocialLink_owbf xSvg_y3PF" style="--dark:#000;--light:#fff"><path d="M714.163 519.284 1160.89 0h-105.86L667.137 450.887 357.328 0H0l468.492 681.821L0 1226.37h105.866l409.625-476.152 327.181 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10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>Ubuntu 22.04 默认使用 <code>g++-11</code> 和 <code>clang++-14</code> 作为默认的 <code>g++</code> 和 <code>clang++</code>。</p>
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1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div class="markdown"><p>基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。</p></div><footer class="row docusaurus-mt-lg"><div class="col col--9"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/mdx">mdx</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/youtube">youtube</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/bilibili">bilibili</a></li><li class="tag_QGVx"><a class="tag_zVej 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35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"></path></svg></a></div></div></div></div></div></header><div id="__blog-post-container" class="markdown"><p><a href="https://docusaurus.io/docs/blog" target="_blank" rel="noopener noreferrer">Docusaurus 博客功能</a>由 <a href="https://docusaurus.io/docs/api/plugins/@docusaurus/plugin-content-blog" target="_blank" rel="noopener noreferrer">blog 插件</a>提供支持。</p>
@@ -21,6 +21,6 @@
 <p>写博客时，可以方便地在同级文件夹内引用图像：</p>
 <p><img decoding="async" loading="lazy" alt="Docusaurus 毛绒玩具" src="/assets/images/docusaurus-plushie-banner-a60f7593abca1e3eef26a9afa244e4fb.jpeg" width="1500" height="500" class="img_ev3q"></p>
 <p>博客也支持标签！</p>
-<p><strong>如果不需要博客</strong>：删除此目录，并在 Docusaurus 配置中使用 <code>blog: false</code> 即可。</p></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/docusaurus">docusaurus</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/mdx/react-support"><div class="pagination-nav__sublabel">较新一篇</div><div class="pagination-nav__label">React 支持</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p><strong>如果不需要博客</strong>：删除此目录，并在 Docusaurus 配置中使用 <code>blog: false</code> 即可。</p></div><footer class="docusaurus-mt-lg"><div class="row margin-top--sm theme-blog-footer-edit-meta-row"><div class="col"><b>标签：</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/blog/tags/docusaurus">docusaurus</a></li></ul></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="博文分页导航"><a class="pagination-nav__link pagination-nav__link--prev" href="/blog/mdx/react-support"><div class="pagination-nav__sublabel">较新一篇</div><div class="pagination-nav__label">React 支持</div></a></nav></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -3,10 +3,10 @@
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padding-bottom--lg"><div class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><nav class="theme-doc-breadcrumbs breadcrumbsContainer_Z_bl" aria-label="页面路径"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="主页面" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">Handler</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">创建一个 Looper 线程</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>创建一个 Looper 线程</h1></header>
@@ -31,6 +31,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="方法二创建一个-h
 <p>新建 <code>MyHandlerThread.kt</code>：</p>
 <div class="language-kotlin codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-kotlin codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">package</span><span class="token plain"> com</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">example</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">myapplication</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> android</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">os</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Handler</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> android</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">os</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">HandlerThread</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> android</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">os</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Looper</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> android</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">os</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Message</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> android</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">util</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Log</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">public</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">MyHandlerThread</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">name</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"> String</span><span class="token operator" style="color:#393A34">?</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">:</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">HandlerThread</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">name</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">lateinit</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">var</span><span class="token plain"> handler</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"> Handler</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">override</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">fun</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">onLooperPrepared</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">super</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">onLooperPrepared</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        handler </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">object</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">:</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">Handler</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Looper</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">myLooper</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token operator" style="color:#393A34">!!</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token keyword" style="color:#00009f">override</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">fun</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">handleMessage</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">msg</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"> Message</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                Log</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">d</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    TAG</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    </span><span class="token string-literal singleline string" style="color:#e3116c">&quot;Received message </span><span class="token string-literal singleline interpolation interpolation-punctuation punctuation" style="color:#393A34">${</span><span class="token string-literal singleline interpolation expression">msg</span><span class="token string-literal singleline interpolation expression punctuation" style="color:#393A34">.</span><span class="token string-literal singleline interpolation expression">what</span><span class="token string-literal singleline interpolation interpolation-punctuation punctuation" style="color:#393A34">}</span><span class="token string-literal singleline string" style="color:#e3116c"> at thread id </span><span class="token string-literal singleline interpolation interpolation-punctuation punctuation" style="color:#393A34">${</span><span class="token string-literal singleline interpolation expression"></span><br></span><span class="token-line" style="color:#393A34"><span class="token string-literal singleline interpolation expression">                        </span><span class="token string-literal singleline interpolation expression function" style="color:#d73a49">currentThread</span><span class="token string-literal singleline interpolation expression punctuation" style="color:#393A34">(</span><span class="token string-literal singleline interpolation expression punctuation" style="color:#393A34">)</span><span class="token string-literal singleline interpolation expression punctuation" style="color:#393A34">.</span><span class="token string-literal singleline interpolation expression">id</span><br></span><span class="token-line" style="color:#393A34"><span class="token string-literal singleline interpolation expression">                    </span><span class="token string-literal singleline interpolation interpolation-punctuation punctuation" style="color:#393A34">}</span><span class="token string-literal singleline string" style="color:#e3116c">&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token keyword" style="color:#00009f">when</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">msg</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">what</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    EVENT_INIT </span><span class="token operator" style="color:#393A34">-&gt;</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">performInit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    </span><span class="token keyword" style="color:#00009f">else</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-&gt;</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">println</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string-literal singleline string" style="color:#e3116c">&quot;Unknown Event: &quot;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> msg</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">what</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">private</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">fun</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">performInit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        Log</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">d</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">TAG</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string-literal singleline string" style="color:#e3116c">&quot;performInit() called&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token function" style="color:#d73a49">sleep</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1000</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">companion</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">object</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">const</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">val</span><span class="token plain"> EVENT_INIT</span><span class="token operator" style="color:#393A34">:</span><span class="token plain"> Int </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">private</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">const</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">val</span><span class="token plain"> TAG </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token string-literal singleline string" style="color:#e3116c">&quot;MyHandlerThread&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" 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padding-bottom--lg"><div class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><nav class="theme-doc-breadcrumbs breadcrumbsContainer_Z_bl" aria-label="页面路径"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="主页面" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">Handler</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Handler 介绍</span><meta itemprop="position" 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@@ -190,6 +190,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="message-分发和-handl
 <p>Handler.dispatchMessage()：将消息分发给接收者/回调方，由接收者/回调方进行相应处理</p>
 <div class="language-java codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-java codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic">/**</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">  * 分析：dispatchMessage(Message msg)</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">  * 作用：派发消息到对应的 Handler 实例，根据传入的 msg 作出对应的操作</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">  */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic">/**</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">     * Handle system messages here.</span><br></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">     */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">public</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">void</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">dispatchMessage</span><span class="token punctuation" style="color:#393A34">(</span><span class="token annotation punctuation" style="color:#393A34">@NonNull</span><span class="token plain"> </span><span class="token class-name">Message</span><span class="token plain"> msg</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic">// 若 msg.callback 属性不为空，则代表使用了 post(Runnable r) 发送消息</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">msg</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">callback </span><span class="token operator" style="color:#393A34">!=</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">null</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token function" style="color:#d73a49">handleCallback</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">msg</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">else</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token comment" style="color:#999988;font-style:italic">//  若 mCallback 不为空，则代表使用了 Handler(Looper looper, Callback callback) 传入了 callback 参数；之后调用 callback 自己实现的 handleMessage() 方法（必须进行 override 重写，返回 true 或 false）</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">mCallback </span><span class="token operator" style="color:#393A34">!=</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">null</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">mCallback</span><span class="token punctuation" style="color:#393A34">.</span><span class="token function" style="color:#d73a49">handleMessage</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">msg</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                    </span><span class="token keyword" style="color:#00009f">return</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">                </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token comment" style="color:#999988;font-style:italic">// 若msg.callback属性为空，则代表使用了 sendMessage（Message msg）发送消息；之后调用 handleMessage(msg)（一般都会进行 override 重写）</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token function" style="color:#d73a49">handleMessage</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">msg</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">}</span><br></span></code></pre><div 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itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/design-patterns/creational-patterns/"><span itemprop="name">创建型模式</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">抽象工厂模式</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>抽象工厂模式</h1></header>
@@ -86,6 +86,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li>当只需对客户端代码隐藏子系统创建对象的方式时，你可以使用<a href="/docs/design-patterns/abstract-factory"><strong>抽象工厂</strong></a>来代替<a href="/docs/design-patterns/facade"><strong>外观模式</strong></a>。</li>
 <li>你可以将<a href="/docs/design-patterns/abstract-factory"><strong>抽象工厂</strong></a>和<a href="/docs/design-patterns/bridge"><strong>桥接模式</strong></a>搭配使用。如果由<em>桥接</em>定义的抽象只能与特定实现合作，这一模式搭配就非常有用。在这种情况下，<em>抽象工厂</em>可以对这些关系进行封装，并且对客户端代码隐藏其复杂性。</li>
 <li><a href="/docs/design-patterns/abstract-factory"><strong>抽象工厂</strong></a>、<a href="/docs/design-patterns/builder"><strong>生成器</strong></a>和<a href="/docs/design-patterns/prototype"><strong>原型</strong></a>都可以用<a href="/docs/design-patterns/singleton"><strong>单例模式</strong></a>来实现。</li>
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class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/design-patterns/structural-patterns/"><span itemprop="name">结构型模式</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">适配器模式</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn 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@@ -90,6 +90,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="适配器模式优缺
 <li><a href="/docs/design-patterns/adapter"><strong>适配器</strong></a>能为被封装对象提供不同的接口，<a href="/docs/design-patterns/proxy"><strong>代理模式</strong></a>能为对象提供相同的接口，<a href="/docs/design-patterns/decorator"><strong>装饰</strong></a>则能为对象提供加强的接口。</li>
 <li><a href="/docs/design-patterns/facade"><strong>外观模式</strong></a>为现有对象定义了一个新接口，<a href="/docs/design-patterns/adapter"><strong>适配器</strong></a>则会试图运用已有的接口。<em>适配器</em>通常只封装一个对象，<em>外观</em>通常会作用于整个对象子系统上。</li>
 <li><a href="/docs/design-patterns/bridge"><strong>桥接</strong></a>、<a href="/docs/design-patterns/state"><strong>状态模式</strong></a>和<a href="/docs/design-patterns/strategy"><strong>策略模式</strong></a> (在某种程度上包括<a href="/docs/design-patterns/adapter"><strong>适配器</strong></a>) 模式的接口非常相似。实际上，它们都基于<a href="/docs/design-patterns/composite"><strong>组合模式</strong></a>——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。</li>
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 <p>行为模式负责对象间的高效沟通和职责委派。</p>
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-<section class="row"><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/chain-of-responsibility"><h2 class="text--truncate cardTitle_rnsV" title="责任链模式">📄️<!-- --> <!-- -->责任链模式</h2><p class="text--truncate cardDescription_PWke" title="允许你将请求沿着处理者链进行发送。收到请求后，每个处理者均可对请求进行处理，或将其传递给链上的下个处理者。">允许你将请求沿着处理者链进行发送。收到请求后，每个处理者均可对请求进行处理，或将其传递给链上的下个处理者。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/command"><h2 class="text--truncate cardTitle_rnsV" title="命令模式">📄️<!-- --> <!-- -->命令模式</h2><p class="text--truncate cardDescription_PWke" title="它可将请求转换为一个包含与请求相关的所有信息的独立对象。该转换让你能根据不同的请求将方法参数化、延迟请求执行或将其放入队列中，且能实现可撤销操作。">它可将请求转换为一个包含与请求相关的所有信息的独立对象。该转换让你能根据不同的请求将方法参数化、延迟请求执行或将其放入队列中，且能实现可撤销操作。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/iterator"><h2 class="text--truncate cardTitle_rnsV" title="迭代器模式">📄️<!-- --> <!-- -->迭代器模式</h2><p class="text--truncate cardDescription_PWke" title="让你能在不暴露集合底层表现形式（列表、栈和树等）的情况下遍历集合中所有的元素。">让你能在不暴露集合底层表现形式（列表、栈和树等）的情况下遍历集合中所有的元素。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/mediator"><h2 class="text--truncate cardTitle_rnsV" title="中介者模式">📄️<!-- --> <!-- -->中介者模式</h2><p class="text--truncate cardDescription_PWke" title="能让你减少对象之间混乱无序的依赖关系。该模式会限制对象之间的直接交互，迫使它们通过一个中介者对象进行合作。">能让你减少对象之间混乱无序的依赖关系。该模式会限制对象之间的直接交互，迫使它们通过一个中介者对象进行合作。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/memento"><h2 class="text--truncate cardTitle_rnsV" title="备忘录模式">📄️<!-- --> <!-- -->备忘录模式</h2><p class="text--truncate cardDescription_PWke" title="允许在不暴露对象实现细节的情况下保存和恢复对象之前的状态。">允许在不暴露对象实现细节的情况下保存和恢复对象之前的状态。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/observer"><h2 class="text--truncate cardTitle_rnsV" title="观察者模式">📄️<!-- --> <!-- -->观察者模式</h2><p class="text--truncate cardDescription_PWke" title="允许你定义一种订阅机制，可在对象事件发生时通知多个“观察”该对象的其他对象。">允许你定义一种订阅机制，可在对象事件发生时通知多个“观察”该对象的其他对象。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/state"><h2 class="text--truncate cardTitle_rnsV" title="状态模式">📄️<!-- --> <!-- -->状态模式</h2><p class="text--truncate cardDescription_PWke" title="让你能在一个对象的内部状态变化时改变其行为，使其看上去就像改变了自身所属的类一样。">让你能在一个对象的内部状态变化时改变其行为，使其看上去就像改变了自身所属的类一样。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/strategy"><h2 class="text--truncate cardTitle_rnsV" title="策略模式">📄️<!-- --> <!-- -->策略模式</h2><p class="text--truncate cardDescription_PWke" title="能让你定义一系列算法，并将每种算法分别放入独立的类中，以使算法的对象能够相互替换。">能让你定义一系列算法，并将每种算法分别放入独立的类中，以使算法的对象能够相互替换。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/template-method"><h2 class="text--truncate cardTitle_rnsV" title="模板方法模式">📄️<!-- --> <!-- -->模板方法模式</h2><p class="text--truncate cardDescription_PWke" title="在超类中定义一个算法的框架，允许子类在不修改结构的情况下重写算法的特定步骤。">在超类中定义一个算法的框架，允许子类在不修改结构的情况下重写算法的特定步骤。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/visitor"><h2 class="text--truncate cardTitle_rnsV" title="访问者模式">📄️<!-- --> <!-- -->访问者模式</h2><p class="text--truncate cardDescription_PWke" title="将算法与其所作用的对象隔离开来。">将算法与其所作用的对象隔离开来。</p></a></article></section></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/design-patterns/proxy"><div 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class="text--truncate cardTitle_rnsV" title="迭代器模式">📄️<!-- --> <!-- -->迭代器模式</h2><p class="text--truncate cardDescription_PWke" title="让你能在不暴露集合底层表现形式（列表、栈和树等）的情况下遍历集合中所有的元素。">让你能在不暴露集合底层表现形式（列表、栈和树等）的情况下遍历集合中所有的元素。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/mediator"><h2 class="text--truncate cardTitle_rnsV" title="中介者模式">📄️<!-- --> <!-- -->中介者模式</h2><p class="text--truncate cardDescription_PWke" title="能让你减少对象之间混乱无序的依赖关系。该模式会限制对象之间的直接交互，迫使它们通过一个中介者对象进行合作。">能让你减少对象之间混乱无序的依赖关系。该模式会限制对象之间的直接交互，迫使它们通过一个中介者对象进行合作。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/memento"><h2 class="text--truncate cardTitle_rnsV" title="备忘录模式">📄️<!-- --> <!-- -->备忘录模式</h2><p class="text--truncate cardDescription_PWke" title="允许在不暴露对象实现细节的情况下保存和恢复对象之前的状态。">允许在不暴露对象实现细节的情况下保存和恢复对象之前的状态。</p></a></article><article class="col 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title="能让你定义一系列算法，并将每种算法分别放入独立的类中，以使算法的对象能够相互替换。">能让你定义一系列算法，并将每种算法分别放入独立的类中，以使算法的对象能够相互替换。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/template-method"><h2 class="text--truncate cardTitle_rnsV" title="模板方法模式">📄️<!-- --> <!-- -->模板方法模式</h2><p class="text--truncate cardDescription_PWke" title="在超类中定义一个算法的框架，允许子类在不修改结构的情况下重写算法的特定步骤。">在超类中定义一个算法的框架，允许子类在不修改结构的情况下重写算法的特定步骤。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/visitor"><h2 class="text--truncate cardTitle_rnsV" title="访问者模式">📄️<!-- --> <!-- -->访问者模式</h2><p class="text--truncate cardDescription_PWke" title="将算法与其所作用的对象隔离开来。">将算法与其所作用的对象隔离开来。</p></a></article></section></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/design-patterns/proxy"><div 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@@ -108,6 +108,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li><a href="/docs/design-patterns/bridge"><strong>桥接</strong></a>、<a href="/docs/design-patterns/state"><strong>状态模式</strong></a>和<a href="/docs/design-patterns/strategy"><strong>策略模式</strong></a> (在某种程度上包括<a href="/docs/design-patterns/adapter"><strong>适配器</strong></a>) 模式的接口非常相似。实际上，它们都基于<a href="/docs/design-patterns/composite"><strong>组合模式</strong></a>——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。</li>
 <li>你可以将<a href="/docs/design-patterns/abstract-factory"><strong>抽象工厂模式</strong></a>和<a href="/docs/design-patterns/bridge"><strong>桥接</strong></a>搭配使用。如果由<em>桥接</em>定义的抽象只能与特定实现合作，这一模式搭配就非常有用。在这种情况下，<em>抽象工厂</em>可以对这些关系进行封装，并且对客户端代码隐藏其复杂性。</li>
 <li>你可以结合使用<a href="/docs/design-patterns/builder"><strong>生成器模式</strong></a>和<a href="/docs/design-patterns/bridge"><strong>桥接模式</strong></a>：<em>主管</em>类负责抽象工作，各种不同的<em>生成器</em>负责<em>实现</em>工作。</li>
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@@ -104,6 +104,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li>你可以在创建复杂<a href="/docs/design-patterns/composite"><strong>组合模式</strong></a>树时使用<a href="/docs/design-patterns/builder"><strong>生成器</strong></a>，因为这可使其构造步骤以递归的方式运行。</li>
 <li>你可以结合使用<a href="/docs/design-patterns/builder"><strong>生成器</strong></a>和<a href="/docs/design-patterns/bridge"><strong>桥接模式</strong></a>：<em>主管</em>类负责抽象工作，各种不同的<em>生成器</em>负责<em>实现</em>工作。</li>
 <li><a href="/docs/design-patterns/abstract-factory"><strong>抽象工厂</strong></a>、<a href="/docs/design-patterns/builder"><strong>生成器</strong></a>和<a href="/docs/design-patterns/prototype"><strong>原型</strong></a>都可以用<a href="/docs/design-patterns/singleton"><strong>单例模式</strong></a>来实现。</li>
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itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/design-patterns/behavioral-patterns/"><span itemprop="name">行为模式</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">责任链模式</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>责任链模式</h1></header>
@@ -145,6 +145,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li><a href="/docs/design-patterns/chain-of-responsibility"><strong>责任链</strong></a>通常和<a href="/docs/design-patterns/composite"><strong>组合模式</strong></a>结合使用。在这种情况下，叶组件接收到请求后，可以将请求沿包含全体父组件的链一直传递至对象树的底部。</li>
 <li><a href="/docs/design-patterns/chain-of-responsibility"><strong>责任链</strong></a>的管理者可使用<a href="/docs/design-patterns/command"><strong>命令模式</strong></a>实现。在这种情况下，你可以对由请求代表的同一个上下文对象执行许多不同的操作。还有另外一种实现方式，那就是请求自身就是一个<em>命令</em>对象。在这种情况下，你可以对由一系列不同上下文连接而成的链执行相同的操作。</li>
 <li><a href="/docs/design-patterns/chain-of-responsibility"><strong>责任链</strong></a>和<a href="/docs/design-patterns/decorator"><strong>装饰模式</strong></a>的类结构非常相似。两者都依赖递归组合将需要执行的操作传递给一系列对象。但是，两者有几点重要的不同之处。 <a href="/docs/design-patterns/chain-of-responsibility"><strong>责任链</strong></a>的管理者可以相互独立地执行一切操作，还可以随时停止传递请求。另一方面，各种<em>装饰</em>可以在遵循基本接口的情况下扩展对象的行为。此外，装饰无法中断请求的传递。</li>
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 </li>
 <li><a href="/docs/design-patterns/prototype"><strong>原型模式</strong></a>可用于保存<a href="/docs/design-patterns/command"><strong>命令</strong></a>的历史记录。</li>
 <li>你可以将<a href="/docs/design-patterns/visitor"><strong>访问者模式</strong></a>视为<a href="/docs/design-patterns/command"><strong>命令模式</strong></a>的加强版本，其对象可对不同类的多种对象执行操作。</li>
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@@ -83,6 +83,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li>你可以使用<a href="/docs/design-patterns/flyweight"><strong>享元模式</strong></a>实现<a href="/docs/design-patterns/composite"><strong>组合</strong></a>树的共享叶节点以节省内存。</li>
 <li><a href="/docs/design-patterns/composite"><strong>组合</strong></a>和<a href="/docs/design-patterns/decorator"><strong>装饰模式</strong></a>的结构图很相似，因为两者都依赖递归组合来组织无限数量的对象。 <em>装饰</em>类似于<em>组合</em>，但其只有一个子组件。此外还有一个明显不同：<em>装饰</em>为被封装对象添加了额外的职责，<em>组合</em>仅对其子节点的结果进行了“求和”。但是，模式也可以相互合作：你可以使用<em>装饰</em>来扩展<em>组合</em>树中特定对象的行为。</li>
 <li>大量使用<a href="/docs/design-patterns/composite"><strong>组合</strong></a>和<a href="/docs/design-patterns/decorator"><strong>装饰</strong></a>的设计通常可从对于<a href="/docs/design-patterns/prototype"><strong>原型模式</strong></a>的使用中获益。你可以通过该模式来复制复杂结构，而非从零开始重新构造。</li>
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@@ -104,6 +104,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li>大量使用<a href="/docs/design-patterns/composite"><strong>组合</strong></a>和<a href="/docs/design-patterns/decorator"><strong>装饰</strong></a>的设计通常可从对于<a href="/docs/design-patterns/prototype"><strong>原型模式</strong></a>的使用中获益。你可以通过该模式来复制复杂结构，而非从零开始重新构造。</li>
 <li><a href="/docs/design-patterns/decorator"><strong>装饰</strong></a>可让你更改对象的外表，<a href="/docs/design-patterns/strategy"><strong>策略模式</strong></a>则让你能够改变其本质。</li>
 <li><a href="/docs/design-patterns/decorator"><strong>装饰</strong></a>和<a href="/docs/design-patterns/proxy"><strong>代理</strong></a>有着相似的结构，但是其意图却非常不同。这两个模式的构建都基于组合原则，也就是说一个对象应该将部分工作委派给另一个对象。两者之间的不同之处在于<em>代理</em>通常自行管理其服务对象的生命周期，而<em>装饰</em>的生成则总是由客户端进行控制。</li>
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 </li>
 <li><a href="/docs/design-patterns/facade"><strong>外观</strong></a>类通常可以转换为<a href="/docs/design-patterns/singleton"><strong>单例模式</strong></a>类，因为在大部分情况下一个外观对象就足够了。</li>
 <li><a href="/docs/design-patterns/facade"><strong>外观</strong></a>与<a href="/docs/design-patterns/proxy"><strong>代理模式</strong></a>的相似之处在于它们都缓存了一个复杂实体并自行对其进行初始化。<em>代理</em>与其服务对象遵循同一接口，使得自己和服务对象可以互换，在这一点上它与<em>外观</em>不同。</li>
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@@ -103,6 +103,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li>你可以同时使用<a href="/docs/design-patterns/factory-method"><strong>工厂方法</strong></a>和<a href="/docs/design-patterns/iterator"><strong>迭代器模式</strong></a>来让子类集合返回不同类型的迭代器，并使得迭代器与集合相匹配。</li>
 <li><a href="/docs/design-patterns/prototype"><strong>原型</strong></a>并不基于继承，因此没有继承的缺点。另一方面，<em>原型</em>需要对被复制对象进行复杂的初始化。<a href="/docs/design-patterns/factory-method"><strong>工厂方法</strong></a>基于继承，但是它不需要初始化步骤。</li>
 <li><a href="/docs/design-patterns/factory-method"><strong>工厂方法</strong></a>是<a href="/docs/design-patterns/template-method"><strong>模板方法模式</strong></a>的一种特殊形式。同时，<em>工厂方法</em>可以作为一个大型<em>模板方法</em>中的一个步骤。</li>
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class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/design-patterns/structural-patterns/"><span itemprop="name">结构型模式</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">享元模式</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>享元模式</h1></header>
@@ -89,6 +89,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li><em>单例</em>对象可以是可变的。享元对象是不可变的。</li>
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 </li>
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@@ -55,6 +55,6 @@ <h1><strong>设计模式分类</strong></h1>
 <li><strong>创建型模式</strong>提供创建对象的机制，增加已有代码的灵活性和可复用性。</li>
 <li><strong>结构型模式</strong>介绍如何将对象和类组装成较大的结构，并同时保持结构的灵活和高效。</li>
 <li><strong>行为模式</strong>负责对象间的高效沟通和职责委派。</li>
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itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/design-patterns/behavioral-patterns/"><span itemprop="name">行为模式</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">迭代器模式</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>迭代器模式</h1></header>
@@ -94,6 +94,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li>你可以同时使用<a href="/docs/design-patterns/factory-method"><strong>工厂方法模式</strong></a>和<a href="/docs/design-patterns/iterator"><strong>迭代器</strong></a>来让子类集合返回不同类型的迭代器，并使得迭代器与集合相匹配。</li>
 <li>你可以同时使用<a href="/docs/design-patterns/memento"><strong>备忘录模式</strong></a>和<a href="/docs/design-patterns/iterator"><strong>迭代器</strong></a>来获取当前迭代器的状态，并且在需要的时候进行回滚。</li>
 <li>可以同时使用<a href="/docs/design-patterns/visitor"><strong>访问者模式</strong></a>和<a href="/docs/design-patterns/iterator"><strong>迭代器</strong></a>来遍历复杂数据结构，并对其中的元素执行所需操作，即使这些元素所属的类完全不同。</li>
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@@ -98,6 +98,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
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 <li><a href="/docs/design-patterns/mediator"><strong>中介者</strong></a>和<a href="/docs/design-patterns/observer"><strong>观察者</strong></a>之间的区别往往很难记住。在大部分情况下，你可以使用其中一种模式，而有时可以同时使用。让我们来看看如何做到这一点。 <em>中介者</em>的主要目标是消除一系列系统组件之间的相互依赖。这些组件将依赖于同一个中介者对象。<em>观察者</em>的目标是在对象之间建立动态的单向连接，使得部分对象可作为其他对象的附属发挥作用。有一种流行的中介者模式实现方式依赖于<em>观察者</em>。中介者对象担当发布者的角色，其他组件则作为订阅者，可以订阅中介者的事件或取消订阅。当<em>中介者</em>以这种方式实现时，它可能看上去与<em>观察者</em>非常相似。当你感到疑惑时，记住可以采用其他方式来实现中介者。例如，你可永久性地将所有组件链接到同一个中介者对象。这种实现方式和<em>观察者</em>并不相同，但这仍是一种中介者模式。假设有一个程序，其所有的组件都变成了发布者，它们之间可以相互建立动态连接。这样程序中就没有中心化的中介者对象，而只有一些分布式的观察者。</li>
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itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/design-patterns/behavioral-patterns/"><span itemprop="name">行为模式</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">备忘录模式</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>备忘录模式</h1></header>
@@ -103,6 +103,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li>你可以同时使用<a href="/docs/design-patterns/command"><strong>命令模式</strong></a>和<a href="/docs/design-patterns/memento"><strong>备忘录模式</strong></a>来实现“撤销”。在这种情况下，命令用于对目标对象执行各种不同的操作，备忘录用来保存一条命令执行前该对象的状态。</li>
 <li>你可以同时使用<a href="/docs/design-patterns/memento"><strong>备忘录</strong></a>和<a href="/docs/design-patterns/iterator"><strong>迭代器模式</strong></a>来获取当前迭代器的状态，并且在需要的时候进行回滚。</li>
 <li>有时候<a href="/docs/design-patterns/prototype"><strong>原型模式</strong></a>可以作为<a href="/docs/design-patterns/memento"><strong>备忘录</strong></a>的一个简化版本，其条件是你需要在历史记录中存储的对象的状态比较简单，不需要链接其他外部资源，或者链接可以方便地重建。</li>
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@@ -86,6 +86,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
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 <li><a href="/docs/design-patterns/mediator"><strong>中介者</strong></a>和<a href="/docs/design-patterns/observer"><strong>观察者</strong></a>之间的区别往往很难记住。在大部分情况下，你可以使用其中一种模式，而有时可以同时使用。让我们来看看如何做到这一点。 <em>中介者</em>的主要目标是消除一系列系统组件之间的相互依赖。这些组件将依赖于同一个中介者对象。<em>观察者</em>的目标是在对象之间建立动态的单向连接，使得部分对象可作为其他对象的附属发挥作用。有一种流行的中介者模式实现方式依赖于<em>观察者</em>。中介者对象担当发布者的角色，其他组件则作为订阅者，可以订阅中介者的事件或取消订阅。当<em>中介者</em>以这种方式实现时，它可能看上去与<em>观察者</em>非常相似。当你感到疑惑时，记住可以采用其他方式来实现中介者。例如，你可永久性地将所有组件链接到同一个中介者对象。这种实现方式和<em>观察者</em>并不相同，但这仍是一种中介者模式。假设有一个程序，其所有的组件都变成了发布者，它们之间可以相互建立动态连接。这样程序中就没有中心化的中介者对象，而只有一些分布式的观察者。</li>
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@@ -80,6 +80,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li><a href="/docs/design-patterns/prototype"><strong>原型</strong></a>并不基于继承，因此没有继承的缺点。另一方面，<em>原型</em>需要对被复制对象进行复杂的初始化。<a href="/docs/design-patterns/factory-method"><strong>工厂方法</strong></a>基于继承，但是它不需要初始化步骤。</li>
 <li>有时候<a href="/docs/design-patterns/prototype"><strong>原型</strong></a>可以作为<a href="/docs/design-patterns/memento"><strong>备忘录模式</strong></a>的一个简化版本，其条件是你需要在历史记录中存储的对象的状态比较简单，不需要链接其他外部资源，或者链接可以方便地重建。</li>
 <li><a href="/docs/design-patterns/abstract-factory"><strong>抽象工厂</strong></a>、<a href="/docs/design-patterns/builder"><strong>生成器</strong></a>和<a href="/docs/design-patterns/prototype"><strong>原型</strong></a>都可以用<a href="/docs/design-patterns/singleton"><strong>单例模式</strong></a>来实现。</li>
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@@ -88,6 +88,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="代理模式优缺点">
 <li><a href="/docs/design-patterns/adapter"><strong>适配器模式</strong></a>能为被封装对象提供不同的接口，<a href="/docs/design-patterns/proxy"><strong>代理模式</strong></a>能为对象提供相同的接口，<a href="/docs/design-patterns/decorator"><strong>装饰模式</strong></a>则能为对象提供加强的接口。</li>
 <li><a href="/docs/design-patterns/facade"><strong>外观模式</strong></a>与<a href="/docs/design-patterns/proxy"><strong>代理</strong></a>的相似之处在于它们都缓存了一个复杂实体并自行对其进行初始化。<em>代理</em>与其服务对象遵循同一接口，使得自己和服务对象可以互换，在这一点上它与<em>外观</em>不同。</li>
 <li><a href="/docs/design-patterns/decorator"><strong>装饰</strong></a>和<a href="/docs/design-patterns/proxy"><strong>代理</strong></a>有着相似的结构，但是其意图却非常不同。这两个模式的构建都基于组合原则，也就是说一个对象应该将部分工作委派给另一个对象。两者之间的不同之处在于<em>代理</em>通常自行管理其服务对象的生命周期，而<em>装饰</em>的生成则总是由客户端进行控制。</li>
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 <ul>
 <li><a href="/docs/design-patterns/bridge"><strong>桥接模式</strong></a>、<a href="/docs/design-patterns/state"><strong>状态模式</strong></a>和<a href="/docs/design-patterns/strategy"><strong>策略模式</strong></a> (在某种程度上包括<a href="/docs/design-patterns/adapter"><strong>适配器模式</strong></a>) 模式的接口非常相似。实际上，它们都基于<a href="/docs/design-patterns/composite"><strong>组合模式</strong></a>——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。</li>
 <li><a href="/docs/design-patterns/state"><strong>状态</strong></a>可被视为<a href="/docs/design-patterns/strategy"><strong>策略</strong></a>的扩展。两者都基于组合机制：它们都通过将部分工作委派给“帮手”对象来改变其在不同情景下的行为。<em>策略</em>使得这些对象相互之间完全独立，它们不知道其他对象的存在。但<em>状态</em>模式没有限制具体状态之间的依赖，且允许它们自行改变在不同情景下的状态。</li>
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@@ -86,6 +86,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li><a href="/docs/design-patterns/decorator"><strong>装饰模式</strong></a>可让你更改对象的外表，<a href="/docs/design-patterns/strategy"><strong>策略</strong></a>则让你能够改变其本质。</li>
 <li><a href="/docs/design-patterns/template-method"><strong>模板方法模式</strong></a>基于继承机制：它允许你通过扩展子类中的部分内容来改变部分算法。<a href="/docs/design-patterns/strategy"><strong>策略</strong></a>基于组合机制：你可以通过对相应行为提供不同的策略来改变对象的部分行为。<em>模板方法</em>在类层次上运作，因此它是静态的。<em>策略</em>在对象层次上运作，因此允许在运行时切换行为。</li>
 <li><a href="/docs/design-patterns/state"><strong>状态</strong></a>可被视为<a href="/docs/design-patterns/strategy"><strong>策略</strong></a>的扩展。两者都基于组合机制：它们都通过将部分工作委派给“帮手”对象来改变其在不同情景下的行为。<em>策略</em>使得这些对象相互之间完全独立，它们不知道其他对象的存在。但<em>状态</em>模式没有限制具体状态之间的依赖，且允许它们自行改变在不同情景下的状态。</li>
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 <p>结构型模式介绍如何将对象和类组装成较大的结构，并同时保持结构的灵活和高效。</p>
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title="你可以使用它将对象组合成树状结构，并且能像使用独立对象一样使用它们。">你可以使用它将对象组合成树状结构，并且能像使用独立对象一样使用它们。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/decorator"><h2 class="text--truncate cardTitle_rnsV" title="装饰模式">📄️<!-- --> <!-- -->装饰模式</h2><p class="text--truncate cardDescription_PWke" title="允许你通过将对象放入包含行为的特殊封装对象中来为原对象绑定新的行为。">允许你通过将对象放入包含行为的特殊封装对象中来为原对象绑定新的行为。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/facade"><h2 class="text--truncate cardTitle_rnsV" title="外观模式">📄️<!-- --> <!-- -->外观模式</h2><p class="text--truncate cardDescription_PWke" title="能为程序库、框架或其他复杂类提供一个简单的接口。">能为程序库、框架或其他复杂类提供一个简单的接口。</p></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/design-patterns/flyweight"><h2 class="text--truncate cardTitle_rnsV" title="享元模式">📄️<!-- --> <!-- 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@@ -74,6 +74,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <ul>
 <li><a href="/docs/design-patterns/factory-method"><strong>工厂方法模式</strong></a>是<a href="/docs/design-patterns/template-method"><strong>模板方法模式</strong></a>的一种特殊形式。同时，<em>工厂方法</em>可以作为一个大型<em>模板方法</em>中的一个步骤。</li>
 <li><a href="/docs/design-patterns/template-method"><strong>模板方法</strong></a>基于继承机制：它允许你通过扩展子类中的部分内容来改变部分算法。<a href="/docs/design-patterns/strategy"><strong>策略模式</strong></a>基于组合机制：你可以通过对相应行为提供不同的策略来改变对象的部分行为。<em>模板方法</em>在类层次上运作，因此它是静态的。<em>策略</em>在对象层次上运作，因此允许在运行时切换行为。</li>
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itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/design-patterns/behavioral-patterns/"><span itemprop="name">行为模式</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">访问者模式</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>访问者模式</h1></header>
@@ -85,6 +85,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="与其他模式的关
 <li>你可以将<a href="/docs/design-patterns/visitor"><strong>访问者模式</strong></a>视为<a href="/docs/design-patterns/command"><strong>命令模式</strong></a>的加强版本，其对象可对不同类的多种对象执行操作。</li>
 <li>你可以使用<a href="/docs/design-patterns/visitor"><strong>访问者</strong></a>对整个<a href="/docs/design-patterns/composite"><strong>组合模式</strong></a>树执行操作。</li>
 <li>可以同时使用<a href="/docs/design-patterns/visitor"><strong>访问者</strong></a>和<a href="/docs/design-patterns/iterator"><strong>迭代器模式</strong></a>来遍历复杂数据结构，并对其中的元素执行所需操作，即使这些元素所属的类完全不同。</li>
-</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/design-patterns/template-method"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">模板方法模式</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#意图" class="table-of-contents__link toc-highlight"><strong>意图</strong></a></li><li><a href="#问题" class="table-of-contents__link toc-highlight"><strong>问题</strong></a></li><li><a href="#解决方案" class="table-of-contents__link toc-highlight"><strong>解决方案</strong></a></li><li><a href="#真实世界类比" class="table-of-contents__link toc-highlight"><strong>真实世界类比</strong></a></li><li><a href="#访问者模式结构" class="table-of-contents__link toc-highlight"><strong>访问者模式结构</strong></a></li><li><a href="#伪代码" class="table-of-contents__link toc-highlight"><strong>伪代码</strong></a></li><li><a href="#访问者模式适合应用场景" class="table-of-contents__link toc-highlight"><strong>访问者模式适合应用场景</strong></a></li><li><a href="#访问者模式优缺点" class="table-of-contents__link toc-highlight"><strong>访问者模式优缺点</strong></a></li><li><a href="#与其他模式的关系" class="table-of-contents__link toc-highlight"><strong>与其他模式的关系</strong></a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/design-patterns/template-method"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">模板方法模式</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#意图" class="table-of-contents__link toc-highlight"><strong>意图</strong></a></li><li><a href="#问题" class="table-of-contents__link toc-highlight"><strong>问题</strong></a></li><li><a href="#解决方案" class="table-of-contents__link toc-highlight"><strong>解决方案</strong></a></li><li><a href="#真实世界类比" class="table-of-contents__link toc-highlight"><strong>真实世界类比</strong></a></li><li><a href="#访问者模式结构" class="table-of-contents__link toc-highlight"><strong>访问者模式结构</strong></a></li><li><a href="#伪代码" class="table-of-contents__link toc-highlight"><strong>伪代码</strong></a></li><li><a href="#访问者模式适合应用场景" class="table-of-contents__link toc-highlight"><strong>访问者模式适合应用场景</strong></a></li><li><a href="#访问者模式优缺点" class="table-of-contents__link toc-highlight"><strong>访问者模式优缺点</strong></a></li><li><a href="#与其他模式的关系" class="table-of-contents__link toc-highlight"><strong>与其他模式的关系</strong></a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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diff --git a/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions/index.html b/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions/index.html
index 4ab11630ef38ab57d73e639b22a8322c64b6647c..2b291a533563cf44803909514e561f8e832f973c 100644
GIT binary patch
delta 236
zcmZoUz&Lp?;|5PAvEYovy!5QhybvIzm!4UYQJSQenLl|yli6eg7PiTgm=tg;iNq!K
z&`@);A9EKo9{I_9?4J0f{g_23FJgBkpk%WVM;9Z9Wr~TVrG<s@<|CZh0h6^uxhKyQ
P<evO4R%f$B%o}C^?*CP1

delta 220
zcmbQdm$Bsl;|5PA-tzKtz2d5r)H1!~{M^YGnan1iV`iH?n@IsfCK63#BD>w@I_6Sl
zOySAy>?RnZ%@`t{n~OQ>897qT5|b<pQp`91;>-@1To$1zlb%_UQJMsDkbZDRVqSVy
yW?l%8(l5>|Nu4YZ?k4<v@5JY;XFltk@qFDv1^3JnkJ6;ganat4o0mtuVFmzysZ~t?

diff --git a/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features/index.html b/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features/index.html
index aed91ae8dd957b441c49e76921bdd42442e01270..d9e105fb1cf50d7d541f031365ac0c6c220a7270 100644
GIT binary patch
delta 220
zcmZ3zn|ap`<_*qFV!;`SdFff1c_BbbFFms)qclk`Gk<abQw(k?v&jX_yp#VhiQ!U`
z$Zowkin)#%kNji>b`#vv4Y;M;Hk)wNGjdp_m{?j`SQu~K%_)6uGS^-1$z8Y2H}Ajs
Gh8X~6WKePd

delta 252
zcmdnBgL(CC<_*qFyyfNPdc{>KsbzY}`MHx%Gnq~9XHvrujYJdqsG>R9UPX9w8FMW&
zcB#p(?8aDSgeJ#xa8JI%ZiQWTb38{EBS)%PVv>bHiuvY`oYLneTi=$RY;lcGCOxwx
zqcjQRQ2pSH#Ju#Z%)AgFrC*#`k~(><nfB!RYtq8c_fCAidgimv8PC@(RB+EM@hDB&
Tyy_Y!<7B>DPMiI1ykQ0ax5Z-r

diff --git a/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site/index.html b/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site/index.html
index d20e4f3728f6c057dab107ef47c45a861b65295f..edd8a10a44fa9dfcdd05a964fd71c26d916abc1a 100644
GIT binary patch
delta 224
zcmezQpRwaF;|6yovEYovy!5QhybvIzm!4UYQJSQenLl|iliB1A%xse<Fe%_x5{XOd
zBAfl>B`hM7eOP%nH#0jj<5pLQTgrBF54$UVY3|Kx9QBMGmMJEdmKGMqo7Zxd7i>OV
Ht;YfY0X$M@

delta 252
zcmeD9%lPv@;|6yo-tzKtz2d5r)H1!~{M^asnan2dV`ZB>lSu(XCK65Lp|a*=Id-wl
zwaiJ(SfxC$ii%9$$?l3%hI?}iM?E7)s##)^g+Yq><b|Aan;E$x3nph*Xv(B#mSmJB
zfgGwIoROH9o|Tyw0;KedGfPq@CkALwHYk@Ce!h3&^VKt-b<TLcZlQvEW{F2>(&ir(
QoQ#uWYMeIDsd~c<0CN~%i2wiq

diff --git a/docs/docusaurus-mdx/intro/index.html b/docs/docusaurus-mdx/intro/index.html
index 1cdbae6f8165ca732d664e2da1b86d2bffe4ea9e..646f31bcbb096e54242b22cdc2efce0a3e4ddf82 100644
GIT binary patch
delta 235
zcmZo|WSmmBL7Yh}I3qDHJu5RW1W4(nXO?7?Ch2A7Pwr(hn;gf?HaUSw0k@J!TvGf>
zqLcrbv2W&QR%9liW^yE(F+L^h*u3#e3vSk7uV>`2Ofj*vw6HLqT*x7}`69=C!^x3$
LPMc@iykQ0a_{CB1

delta 219
zcmbPI*V@RqL7a)Vyu4hmxGE*JOfNY<ck+BDv&nI+Y?CvY6fk5W(L@s2WH)OwD==dS
z`(ubmPkzYeiYdA|oV|;YBh@T1$-*GTeDh0=zlM{)TWHFpXO?7?CV?EJADoexm!6fG
x7Xqa8i!)17Cr>nY6MnvT;`7xrpLNc7zHXs{duEA8Y0~EV*4~VpHLTw-0|2tNQw9J4

diff --git a/docs/docusaurus-mdx/mdx-features/admonitions/index.html b/docs/docusaurus-mdx/mdx-features/admonitions/index.html
index b2f948bb135cf1410442829f4cf70fa7409dd904..7753cc2dab68f6601be8cc4ffae337cb546292ea 100644
GIT binary patch
delta 227
zcmezKkEQz$%LW4`vEYovy!5QhybvIzm!4UYQJSQenLpW<DF(Nc+2jCb-pMbS#BeFu
z$Y!wFhB<>7w|o+ADZR;l?5=pEH=kqgV&t$)F|o9?urO{;;M|_T$>?q{{k9z=_w;C6
NM)U0xtQp@h0{}5yQ5gUL

delta 258
zcmeDF!}8}J%LW4`-tzKtz2d5r)H1!~{M^Yqn9L?mU}c-!#H4^B6Nx6muc<WIUzK-r
z7;`2wcB#oM?8aDR^4SBiii&UM=cs4oNHt4LvM@+7Z=S}veHtgDyTRmc4X){ZmW+ba
zIV~9ZWYRNBGD?#`&eadjNX$#m%FGJ^Qu@W2C8^W9tQg&dpYNUceD%y{oim=VTd3fk
aS>jQew7uGbk&|)yeQQRi?ebQPZ<qnY8Cx;{

diff --git a/docs/docusaurus-mdx/mdx-features/assets/index.html b/docs/docusaurus-mdx/mdx-features/assets/index.html
index d78c6ed93cdaafa94df110f76f4de1545db839b2..a4605f64403c56ad22e8d1cc076d0e7de414d5e4 100644
GIT binary patch
delta 244
zcmZ3qon`$NmJMo5V!;`SdFff1c_BbbFFms)qclk`Gk@|NCbP-A82KibGfCi95{XNy
zkxhHEF0(r`ZuwZ;Qks+d*|{gnvs>X&vbmqVi;=@J#l+Im!os*&k#oBuC*vxf=_Qhk
ePTRMLGuAV)Jzc!v*^IvFhC+<0+Y_W1ofrY=+*Jzz

delta 276
zcmZ3#g=NupmJMo5yyfNPdc{>KsbzY}`MHzVF_}%C$HF%G03*lb1||s%*+?{z3mQtB
z?U@6ZF@-1FGjmS9z-EM1hJCUlyDN5?%}3e07&%hS5|b<pQp}sfIk$&%GOps8T&>JC
zT}FgaUM4-WB%?G5<XZjUjKsY3tjxR+Af;cNS&}+^ofxB=@bkSBpRb<ztaHZmbqf{T
vGfO;5leW(nVdP|-&Md*`wB1>Zv7U*8f#K=m4bNuuO)gXx*?vcYF_;kmod#oa

diff --git a/docs/docusaurus-mdx/mdx-features/code-blocks/index.html b/docs/docusaurus-mdx/mdx-features/code-blocks/index.html
index 501a5b2f65ceb6b68e72777a15d8400c7b515c90..248a4391511bd99a512d856355c5f64dfafc4b32 100644
GIT binary patch
delta 242
zcmezWl(+9O?*;=VvEYovy!5QhybvIzm!4UYQJSQenLpW<DF(Nc+2jCb-pMbS#BeDw
zG*+5yz|OPTiaCOrfSSo?*-Y>&3B)74c?0`2Mh?pq6H7}A3*%-#&UQaeMj&R|?#Ib|
RCwcni0%oV}!uiZ^m;u<+Q+EIW

delta 258
zcmeBs%=`Z-?*;=V-tzKtz2d5r)H1!~{M^Yqn9L?mU}c-!#H4^B6Nx6`ASXIGfL(HP
zD02k!<O5$>I1$D`r6zx5Gr=kohgDQ%^I!IQMvhdo#3T!Y6!Yd5&h{2gMj&R|-onXz
zCwX$V9M|;fY-ah%?+dsEgEJEI(z7!2LV%Qhab`*C<O4q1(=GCtrG=mGo%nq9%x9f5
hp08V|;GS9HQJS><Up6x*<MgC_W~c3oa+%*S0{~NgVT%9&

diff --git a/docs/docusaurus-mdx/mdx-features/diagrams/index.html b/docs/docusaurus-mdx/mdx-features/diagrams/index.html
index 11984115c9d34d81eea9b7dd82007bd0d2f47c9a..cc02351a573ff8677dfd6bd95cd1e4353bbf8f75 100644
GIT binary patch
delta 216
zcmdmVlJVd%#tr67V!;`SdFff1c_BbbFFms)qclk`Gk@}0CbP+X%xsezm=tg;iNqx}
zkxh5A1G5V=ZuxlJQreR>*j@2RZ(hpY#mHfqVq$4&VPU-4oO4;|<eQP)oBI=#SpbUN
BO~U{H

delta 228
zcmX?jjB(RR#tr67yyfNPdc{>KsbzY}`MHz#Gnq}E$I3RjlSu(XCK63#1H1O-NM<)?
zOyS87*i0})%_b+XTcL_>-oU<<kt5YCG0DOp#e8!v=d#err<J%S>&42;q-U07lqP{3
zr5~J;n3tZFnHK`2^ouh~QYRmXcN2cTcjEKaGoN+Nc)o6-f_r9(M`_aLjj^1JlSLDq
KHiyQ)VFmy_cUWEk

diff --git a/docs/docusaurus-mdx/mdx-features/head-metadata/index.html b/docs/docusaurus-mdx/mdx-features/head-metadata/index.html
index f3c70e4453d78c803349a2f9e28d2767a8ed06e2..b080182b5b4787080bb30db504a7399c1713276e 100644
GIT binary patch
delta 185
zcmdlulWF@jrVWjZV!;`SdFff1c_BbbFFms)qclk`Gk<a)V+?L7v&nj_ypye%#BeD|
vU^Cd<%XEwxw|psXDeKL$><<|^EK^J@EiEjJH?whGtDW51<+S-|#~Wq<Z~8-S

delta 222
zcmdl!jcMadrVWjZyyfNPdc{>KsbzY}`MHxhnan1!uuZ<t$}#yiqXdRzB$~)V6{XFy
zn65Bm3QwNJ#5dWVoqO_rHY@D1o9)@(Fmj}tB_>%Iq?k|s$RW2mkaI`vWNUS<$-V6g
zle3bz1cNgY^U||2^Fn}>esN|=>g2#yH{s`dCq7?2^I7MN=j#?KxM!AllqPK!Y~f^_
N%-!j<*}MG>GXNwkQ|JHy

diff --git a/docs/docusaurus-mdx/mdx-features/intro/index.html b/docs/docusaurus-mdx/mdx-features/intro/index.html
index 7fa88832af285bd71780e675901ffbd207a9a451..e055ba761551808843ea36a41e6698d27f604f15 100644
GIT binary patch
delta 220
zcmaF%pXuu#rVR#6V!;`SdFff1c_BbbFFms)qclk`Gk>xzQw(k?v&jmqypvxtiQ!Vh
z$gZ{7jCmh3Zh4%hGqP(;=HcL;JeS=Hw{DHiJRDt&9F{32mX;P4#+&DH7H^omYp>Jh
JU%THh0{~r9PV@i(

delta 271
zcmezRhw0gWrVR#6yyfNPdc{>KsbzY}`MHyKFquuBz{)nciAe!NCK63#f}H4N0d3yN
z8x+|$2Qcqv#w|VBkKGujEZgM$?5=oaxi|ZA)H8CVnk6P#7^IkQzQS3&Ve)P{uE`C1
z1t;Ix#V?&%l2Muja=(6XMq*xiR%TuZkkT*CEJ>aG(Mfx<{BCLC=X)nUUp@0#=Zxp;
X7Am-BmUxsVZFbo0&A7R9*BfR400(FV

diff --git a/docs/docusaurus-mdx/mdx-features/links/index.html b/docs/docusaurus-mdx/mdx-features/links/index.html
index 45403da94bb508df769d9fab4a93666f71f48948..874b74cea5b2b2778003facaf3e52cfdcc35def2 100644
GIT binary patch
delta 228
zcmdmZp7FpL#tphmV!;`SdFff1c_BbbFFms)qclk`Gk>xbQw(k?v&pioypx|XiQ!Tr
zpsqRjGo#Yx5N0K2d}`LP8RM4LnB2$CJz1XJ3XhV_ee7L~9F{32mX;P4#+wy5_e4x?
MO?BFQH2DoP05^D0ApigX

delta 244
zcmX?bhH>M0#tphmyyfNPdc{>KsbzY}`MHy~GMP=zXJngP&!m7M6Nx60sHQY|A3NJ-
zA7)o(>{64@vzcI(5uEJ9ZiOkcc^~@(Mvhdo#3T!Y6!XntoO>cB&sO7_teYS&lb%_U
zQJMsDq<(NlVqSVyW?l%8(l5>|Nu9hu$xZnA-igmw&wSQ7<N3OU3htRD9;Hc}HzaT}
OP8LaV+8mPfh8X~z`dm%`

diff --git a/docs/docusaurus-mdx/mdx-features/math-equations/index.html b/docs/docusaurus-mdx/mdx-features/math-equations/index.html
index 4d32e8cd6706bc0f3865e31b1319d9be3216c0d0..5c78f0ed47ae9779378baec95641ad77a6382d5f 100644
GIT binary patch
delta 251
zcmaE}nCbTdrVVCHV!;`SdFff1c_BbbFFms)qclk`Gk@|LCbP)`ENqi6Fmg<8XOh6J
zEE1R0!4{>-4>SZO?`BonoW?B0Oi0~+He>us_$M2%yAoEyy?GydJtK!@iixGAg@y5E
VSI$dKlf5T$Pd?pmzNzmGGXNl_USa?M

delta 240
zcmeypfa%R*rVVCHyyfNPdc{>KsbzY}`MHz#F_}$X$ILeQ0wc%d2}}|gvXN*a8`+FE
zCoo$xV+f~Wh!{?eWp~9Y%Dwpudp#pZs##)^g+Yq>=4#GMO_RTLOHZ!s;*&|wEXgQM
z0y$1UI3qDHJu5RW1W4%@XO^T+&bQQ_e4tBO`1#(6&sWcU);Z((x`hhvnI#^jNt<7H
QaWYQ!?{nJR-}8nU0Ll<wDF6Tf

diff --git a/docs/docusaurus-mdx/mdx-features/plugins/index.html b/docs/docusaurus-mdx/mdx-features/plugins/index.html
index c3bf2a1f4feae0f8f5394d7380cffc5303331286..078d112916383f1a4b8076b393143f442f9f40e6 100644
GIT binary patch
delta 236
zcmdnGnCZv@rVTnwV!;`SdFff1c_BbbFFms)qclk`Gk>xrQw(k?v&r{ac_%+*62qnB
zVYAX?A9jw-M$8S&1k_A^$!3CIi7$R>;mx<%>lryLQ%o!^Ei8;DD{#tfZs1I4n%vp%
KwE1N38)g7QL|23W

delta 237
zcmX@IfNASurVTnwyyfNPdc{>KsbzY}`MHy~Fqut0z{oebjY$GSCK62~QC(?rz6R%J
zKjwO7>{65Y*p0Eua7=Dwcf~HVnT?~1kt5YCG0DOp#eDM&&bp?_(VAS7Cv?b9K48Hu
z7@U!qm!6fG7Xqa8i!)17Cm-x^6MnvT;`7xrpLNc7zHXs{duEA8Y0_r?UT?<D5j}61
E0g=&Iy8r+H

diff --git a/docs/docusaurus-mdx/mdx-features/react/index.html b/docs/docusaurus-mdx/mdx-features/react/index.html
index 095135046c0a67a521ac69f8d312fc60d41f24f7..497da8954704a500b6dcb2c2fb324bde5f08e907 100644
GIT binary patch
delta 230
zcmdmYhyCnL_6<5rV!;`SdFff1c_BbbFFms)qclk`Gk>xrQw(k?v&k~7ypx|YiQ!Um
zkxgsz5hlgW!OVrsxYgja;Ub&H<U8!#lXKavaO>9Ce22Y@k;5{@#M08j!niq)b9){q
T<L`UZh2AhaZ4Y|I_=Xt(F9KBM

delta 270
zcmX?mlYQSE_6<5ryyfNPdc{>KsbzY}`MHy~Fqut0z{oebjY$GSCK62~K~8jXfGY21
zSLRvF*rg_mvs>Yi;o%URJPViXW*&|Sj2x+EiAfd)Ddx>fIJYn1Wc+<^a<?4U^ne$P
zg40hwW8|BzP|e6K7@U!qm!6fG7Xqa8i!)17r_bYM)Sh1cl2Kat`QC}oSI>ObIpg`d
kg$nMOB_5?o+ijmSaxzYz{g{z^`kGga=Gz~>V0^<207AfI+5i9m

diff --git a/docs/docusaurus-mdx/mdx-features/tabs/index.html b/docs/docusaurus-mdx/mdx-features/tabs/index.html
index 6f2ef45c126f6d4e1cc4120c2781f08dd75e7326..8095353deeb441b413ed1fd4917bcbc5184f43a4 100644
GIT binary patch
delta 222
zcmbRElYPNA_6>SWV!;`SdFff1c_BbbFFms)qclk`Gk>x*Qw(k?v&pioypx|ZiQ!UG
zz^=a8kU5YUkNo6qY$mv+jV5cdTj7x2T)@7Ok;5{@#M08j!nj$JbGs%d<K(x~Q-3i!
LZD0C>@eMNoyMj-O

delta 245
zcmZ4RjeX)z_6>SWyyfNPdc{>KsbzY}`MHy~F_}#+U}T%zz@&g76Nx7BP(f+4J98K_
zrtsveY?fF=Pp}J24r8~%l-YcOy`PaI)hsc|!XU-GIi7QSJSXGix06q+aZTs_$|x_B
zo>`Jnngnv8esD%&UV2t$UI>uVFU~AUoj(6Nqnq&ay%V3Wp82eE#`ARx72GpRJW7+c
WPx#8n$vFMX4@Rf$Cf^y~FarRE3t-3q

diff --git a/docs/docusaurus-mdx/mdx-features/toc/index.html b/docs/docusaurus-mdx/mdx-features/toc/index.html
index aea61eeee5e0d50b29317285bbc40b0fc5f447fe..2d6a3cab725251374d53fbcfd2d42aae4a403273 100644
GIT binary patch
delta 234
zcmbQdo@LP*mJQZSV!;`SdFff1c_BbbFFms)qclk`Gk@|%CbP-s8TlsnFiGH65{XOd
zpsM<2JLU#vJo1x2u^Ho*R-1f*oqKXJyA>WKn=i0;F>+X@m{?j`SQt-M;FN1_;N0H8
T$!NzhJzbR1Y5Q_v#y89Wu5DBY

delta 230
zcmZ3qhGp`4mJQZSyyfNPdc{>KsbzY}`MHw=nPM<R%qH`*@lIxA7DJN})KuCW!raP?
zDLh$_-2#hfBfBT2=w>F4K1PmIv&19|gB0`T8Jyc^a5BblOrI^tC_P<4fRS%<<YjKb
z;Ecq)^sLOh5Fn*roLQ1OeW4JeoAC3!6Q8f1`K)us^K}aq+%ro&N|Uy~6=L*e+-@es
H_=Xt(0Ygv{

diff --git a/docs/docusaurus-mdx/plugin-contents/blog/index.html b/docs/docusaurus-mdx/plugin-contents/blog/index.html
index 9dab790861fa8fc8201d7d0be6f39477f97ffff2..b92d6e95ae3235b9f1d1ec9c8cb632c087aa8567 100644
GIT binary patch
delta 255
zcmcc9&-S{9ZG$C~Sa3#SUV2t$UI>uVOV2FHC{5DK%%8lT$!u~zGuz}QCI#F|B5_G2
zsHjdBU}vA)%px*bo0WHS5_1hRezlhPrCBF8u)7jg!o8WDqn?q&GR4Hw(!#>HxsP*u
aA17mF#dPa-M(*jmTN%x_e`scW!wdl1VON|0

delta 254
zcmaFe!*-{iZG$BfZ+UsSUU5}QYMEYge(vOhOlFhMGV)EH%p`#!6Nx7BQAu@kDDx6#
zOyS8U?3P$WbvXnk?_jsWl-aDy(a*?{YL=K}VUS|pe1voR5l+U+ipi_xxTe2rWE7m9
z*}%vrlb%_UQJMsDrhafnVqSVyW?l%8(l5>|NuA7-r9FK^1EaL?^Su+Fub%m=bH?*^
e3l-cmOFT-Gw%=}G<Yb&~-@@p$y}pU@4Ko0n*I|AD

diff --git a/docs/docusaurus-mdx/plugin-contents/docs/index.html b/docs/docusaurus-mdx/plugin-contents/docs/index.html
index 407cc2c60f6b8afdc77bdabbe9050c843e450dc0..2fc990d68af41971f125da9cad69dbda4042ccd7 100644
GIT binary patch
delta 234
zcmdmgoc-Jp_6?RyV!;`SdFff1c_BbbFFms)qclk`Gk@}WCbP-?%xsgJm=tg;iNql_
zz2GvV>SinE4b1oyOqOA{#4F#<?nOXeV6!ksJtK!@iixGAg@tkREY9t-I2i-3OrQLa
M(P{hT`;2dx0n;8<cK`qY

delta 246
zcmX?ignj>U_6?RyyyfNPdc{>KsbzY}`MHx1GMP<2%g8r*GLr;`OeCtvW&`G{%&0<>
z4VZN%yR#c%h-yu?<KUirgxv~LX0shf7b8ciSz?lfL5g|v1<vgkI2i-3Oh0~?QF^-1
z9Y#Ls^vsfs(j<`c^n)`J^U||2^Fn}>esN~W^t)}0I@5pLW0V$tzIWpD)ia-U&Un6V
ep@Ms6iAQPD_I-C4IT@!bJz#X&o^+4#4Ko1tB3|nN

diff --git a/docs/docusaurus-mdx/plugin-contents/intro/index.html b/docs/docusaurus-mdx/plugin-contents/intro/index.html
index cf8552b1e8dd1bddab924570aedf4dc497dfd9fd..f58af5a8502abe8725cc3e2f0b322b20d6958c8f 100644
GIT binary patch
delta 240
zcmew}ow0i=;|4<}vEYovy!5QhybvIzm!4UYQJSQenLpW%DF(Nc*<?Rv-pQ|+#BeDo
zuveX|$Ih|Yiun*Tel=G3rP(GgV0R^~gnP3FM?E8lWr~TVrG<s@=JlKvHj|^hxhLQD
LG~X=X@rD@y6GT(2

delta 252
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@@ -63,6 +63,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="onehot-encoding-correla
 <p><code>sklearn.preprocessing.OneHotEncoder</code> 不提供特征列删除方法，需要转换为 numpy 数组后进行切片：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> ohe </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> OneHotEncoder</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">categorical_features</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> ohe</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit_transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">toarray</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">array</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">10.1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">13.5</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">3.</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">15.3</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" 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 <p>pandas 中的 <code>get_dummies</code> 提供参数 <code>drop_first</code>，可以很方便地删除首个特征列：</p>
-<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> pd</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">get_dummies</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">df</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&#x27;price&#x27;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;color&#x27;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;size&#x27;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain"> drop_first</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">True</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   price  size  color_green  color_red</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">0</span><span class="token plain">   </span><span class="token number" style="color:#36acaa">10.1</span><span class="token plain">     </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">            </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">          </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">1</span><span class="token plain">   </span><span class="token number" style="color:#36acaa">13.5</span><span class="token plain">     </span><span class="token number" style="color:#36acaa">2</span><span class="token plain">            </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">          </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">2</span><span class="token plain">   </span><span class="token number" style="color:#36acaa">15.3</span><span class="token plain">     </span><span class="token number" style="color:#36acaa">3</span><span class="token plain">            </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">          </span><span class="token number" style="color:#36acaa">0</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/neural-network/mcp-neuron-and-perceptron"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">MCP 神经元和感知器</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/data-preprocessing/feature-scaling"><div 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toc-highlight">独热编码的相关性</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" 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+<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> pd</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">get_dummies</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">df</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&#x27;price&#x27;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;color&#x27;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;size&#x27;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain"> drop_first</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">True</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   price  size  color_green  color_red</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">0</span><span class="token plain">   </span><span class="token number" style="color:#36acaa">10.1</span><span class="token plain">     </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">            </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">          </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">1</span><span class="token plain">   </span><span class="token number" style="color:#36acaa">13.5</span><span class="token plain">     </span><span class="token number" style="color:#36acaa">2</span><span class="token plain">            </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">          </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">2</span><span class="token plain">   </span><span class="token number" style="color:#36acaa">15.3</span><span class="token plain">     </span><span class="token number" style="color:#36acaa">3</span><span class="token plain">            </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">          </span><span class="token number" style="color:#36acaa">0</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/neural-network/mcp-neuron-and-perceptron"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">MCP 神经元和感知器</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/data-preprocessing/feature-scaling"><div 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toc-highlight">独热编码的相关性</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" 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@@ -30,6 +30,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="standardization">标准
 \end{align}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.764em;vertical-align:-1.132em"></span><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.632em"><span style="top:-3.632em"><span class="pstrut" style="height:3.628em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.3987em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">s</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">d</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3013em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.628em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.74em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mord"><span class="mord mathnormal">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em"><span></span></span></span></span></span><span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.132em"><span></span></span></span></span></span></span></span><span class="tag"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.632em"><span style="top:-3.632em"><span class="pstrut" style="height:3.628em"></span><span class="eqn-num"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.132em"><span></span></span></span></span></span></span></span></span>
 <p>其中，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup></mrow><annotation encoding="application/x-tex">x^{(i)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.888em"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mrow><mi>s</mi><mi>t</mi><mi>d</mi></mrow><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">x_{std}^{(i)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3461em;vertical-align:-0.3013em"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.3987em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">s</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">d</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3013em"><span></span></span></span></span></span></span></span></span></span> 分别表示第 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em"></span><span class="mord mathnormal">i</span></span></span></span> 个样本标准化前后的特征值，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>μ</mi><mi>x</mi></msub></mrow><annotation encoding="application/x-tex">\mu_x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord"><span class="mord mathnormal">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>σ</mi><mi>x</mi></msub></mrow><annotation encoding="application/x-tex">\sigma_x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> 分别表示该特征的平均值和标准差。</p>
 <p>在 scikit-learn 中，可通过 <a href="http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html" target="_blank" rel="noopener noreferrer">sklearn.preprocessing.StandardScaler</a> 实现：</p>
-<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">preprocessing </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> StandardScaler</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> stdsc </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> StandardScaler</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> X_train_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> stdsc</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit_transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> X_test_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> stdsc</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_test</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 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style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> stdsc </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> StandardScaler</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> X_train_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> stdsc</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit_transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token 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@@ -101,6 +101,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="replace-evaluation-metr
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">metrics </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> make_scorer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> f1_score</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">scorer </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> make_scorer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">f1_score</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> pos_label</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">gs </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> GridSearchCV</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">estimator</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">pipe_svc</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> param_grid</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">param_grid</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> scoring</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">scorer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> cv</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">10</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">gs </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">best_score_</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: 0.986202145696</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">&gt;&gt;</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">best_params_</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: {&#x27;svc__C&#x27;: 10.0, &#x27;svc__gamma&#x27;: 0.01, &#x27;svc__kernel&#x27;: &#x27;rbf&#x27;}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <blockquote>
 <p>有关评估指标的更多内容，请参见 <a href="https://en.wikipedia.org/wiki/Confusion_matrix" target="_blank" rel="noopener noreferrer">Wikipedia - Confusion matrix</a> 和 <a href="http://scikit-learn.org/stable/modules/classes.html#module-sklearn.metrics" target="_blank" rel="noopener noreferrer">sklearn.metrics</a>。</p>
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class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>ROC 和 AUC</h1></header>
@@ -22,6 +22,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="roc-plotting-in-sklearn
 <p>上面的代码通过从 SciPy 导入的 <code>interp</code> 函数插入了三次折叠的平均 ROC 曲线，并通过 <code>auc</code> 函数计算曲线下面积。</p>
 <p>三次绘制的 ROC 曲线表明不同折叠之间存在一定程度的变化，并且 ROC AUC 的平均值 (0.76) 落在完美预测 (1.0) 和随机猜测 (0.5) 之间：</p>
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-06_10.png" width="600" class="img_ev3q">
-<p>如果只需要用到 ROC AUC 分数，也可以直接导入 <code>sklearn.metrics.roc_auc_score</code> 函数。ROC AUC 分数可以对样本数量不平均的二分分类模型进行评估。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/evaluation-metrics/confusion-matrix"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">混淆矩阵</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/feature-selection/feature-extraction-lda"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">线性判别分析</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#data-loading-and-preprocessing" class="table-of-contents__link toc-highlight">数据导入和预处理</a></li><li><a href="#roc-plotting-in-sklearn" class="table-of-contents__link toc-highlight">ROC 曲线的 scikit-learn 实现</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>如果只需要用到 ROC AUC 分数，也可以直接导入 <code>sklearn.metrics.roc_auc_score</code> 函数。ROC AUC 分数可以对样本数量不平均的二分分类模型进行评估。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/evaluation-metrics/confusion-matrix"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">混淆矩阵</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/feature-selection/feature-extraction-lda"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">线性判别分析</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#data-loading-and-preprocessing" class="table-of-contents__link toc-highlight">数据导入和预处理</a></li><li><a href="#roc-plotting-in-sklearn" class="table-of-contents__link toc-highlight">ROC 曲线的 scikit-learn 实现</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -88,6 +88,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="sklearn-implementation"
 <p>在降维空间绘制已通过训练得到的决策边界，观察是否能够进行很好地分类：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">plot_decision_regions</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_test_lda</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> classifier</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">lr</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;LD 1&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;LD 2&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">legend</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">loc</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;lower left&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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-<p>可以看到逻辑回归在新的二维子空间上表现很好，在测试数据集上只有很少样本分类错误。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/evaluation-metrics/roc-and-auc"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">ROC 和 AUC</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/feature-selection/feature-extraction-pca"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">主成分分析</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#algorithm-principle" class="table-of-contents__link toc-highlight">算法思想</a></li><li><a href="#data-load-and-standardization" class="table-of-contents__link toc-highlight">数据导入和标准化</a></li><li><a href="#construct-scatter-matrix" class="table-of-contents__link toc-highlight">散布矩阵的构造</a><ul><li><a href="#mean-vector" class="table-of-contents__link toc-highlight">均值向量</a></li><li><a href="#intra-class-scatter-matrix" class="table-of-contents__link toc-highlight">类内散布矩阵</a></li><li><a href="#inter-class-scatter-matrix" class="table-of-contents__link toc-highlight">类间散布矩阵</a></li></ul></li><li><a href="#eigenvalues-and-eigenvectors" class="table-of-contents__link toc-highlight">特征值和特征向量</a></li><li><a href="#discrimination-ability-of-linear-discriminant" class="table-of-contents__link toc-highlight">线性判别式的辨别能力</a></li><li><a href="#feature-extraction" class="table-of-contents__link toc-highlight">特征提取</a></li><li><a href="#sklearn-implementation" class="table-of-contents__link toc-highlight">Scikit-learn 实现</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>可以看到逻辑回归在新的二维子空间上表现很好，在测试数据集上只有很少样本分类错误。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/evaluation-metrics/roc-and-auc"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">ROC 和 AUC</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/feature-selection/feature-extraction-pca"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">主成分分析</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#algorithm-principle" class="table-of-contents__link toc-highlight">算法思想</a></li><li><a href="#data-load-and-standardization" class="table-of-contents__link toc-highlight">数据导入和标准化</a></li><li><a href="#construct-scatter-matrix" class="table-of-contents__link toc-highlight">散布矩阵的构造</a><ul><li><a href="#mean-vector" class="table-of-contents__link toc-highlight">均值向量</a></li><li><a href="#intra-class-scatter-matrix" class="table-of-contents__link toc-highlight">类内散布矩阵</a></li><li><a href="#inter-class-scatter-matrix" class="table-of-contents__link toc-highlight">类间散布矩阵</a></li></ul></li><li><a href="#eigenvalues-and-eigenvectors" class="table-of-contents__link toc-highlight">特征值和特征向量</a></li><li><a href="#discrimination-ability-of-linear-discriminant" class="table-of-contents__link toc-highlight">线性判别式的辨别能力</a></li><li><a href="#feature-extraction" class="table-of-contents__link toc-highlight">特征提取</a></li><li><a href="#sklearn-implementation" class="table-of-contents__link toc-highlight">Scikit-learn 实现</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -122,6 +122,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="sklearn-implementation"
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-05_05.png" width="600" class="img_ev3q">
 <p>可以看到逻辑回归在新的二维子空间上表现很好，在测试数据集上只有很少样本分类错误。</p>
 <p>关于数据集的解释方差占比，可以设置 PCA 的参数 <code>n_components</code> 为 <code>None</code>，对测试集进行变换后通过 <code>explained_variance_ratio_</code> 属性得到：</p>
-<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">pca </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> PCA</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">n_components</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_train_pca </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> pca</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit_transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train_std</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">pca</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">explained_variance_ratio_</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/feature-selection/feature-extraction-lda"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">线性判别分析</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/feature-selection/feature-importance"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">特征的重要性</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#algorithm-principle" class="table-of-contents__link toc-highlight">算法思想</a></li><li><a href="#data-load-and-standardization" class="table-of-contents__link toc-highlight">数据导入和标准化</a></li><li><a href="#construct-covariance-matrix" class="table-of-contents__link toc-highlight">协方差矩阵的构造</a></li><li><a href="#eigenvalues-and-eigenvectors" class="table-of-contents__link toc-highlight">特征值和特征向量</a></li><li><a href="#explained-variance-ratio" class="table-of-contents__link toc-highlight">解释方差占比</a></li><li><a href="#feature-extraction" class="table-of-contents__link toc-highlight">特征提取</a></li><li><a href="#sklearn-implementation" class="table-of-contents__link toc-highlight">Scikit-learn 实现</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div 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+<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">pca </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> PCA</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">n_components</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_train_pca </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> pca</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit_transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train_std</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">pca</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">explained_variance_ratio_</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg 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0"></path></g></svg></button></div></div></aside><main class="docMainContainer_TBSr"><div class="container padding-top--md padding-bottom--lg"><div class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><nav class="theme-doc-breadcrumbs breadcrumbsContainer_Z_bl" aria-label="页面路径"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="主页面" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">特征选择</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">特征的重要性</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>特征的重要性</h1></header>
@@ -30,6 +30,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="feature-importance-usin
 <p>以随机森林为例，以使用以下代码将特征阈值设置为 0.1，可以筛选出最重要的五个特征：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feature_selection </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> SelectFromModel</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">sfm </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> SelectFromModel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">forest</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> threshold</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> prefit</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">True</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_selected </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> sfm</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Number of samples that meet this criterion:&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_selected</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">shape</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> f </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_selected</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">shape</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;{:2d}) {:30}{:f} &quot;</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">format</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            f </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> feat_labels</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">indices</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">f</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> importances</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">indices</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">f</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>输出如下：</p>
-<div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">Number of samples that meet this criterion: 124</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 1) Proline                       0.179927</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 2) Color intensity               0.153158</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 3) Flavanoids                    0.146123</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 4) Alcohol                       0.138224</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 5) OD280/OD315 of diluted wines  0.114818</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/feature-selection/feature-extraction-pca"><div 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+<div class="language-plain codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-plain codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">Number of samples that meet this criterion: 124</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 1) Proline                       0.179927</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 2) Color intensity               0.153158</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 3) Flavanoids                    0.146123</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 4) Alcohol                       0.138224</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"> 5) OD280/OD315 of diluted wines  0.114818</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/feature-selection/feature-extraction-pca"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">主成分分析</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/model-selection/grid-search"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">网格搜索</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#wine-dataset" class="table-of-contents__link toc-highlight">Wine 数据集</a></li><li><a href="#feature-importance-using-sklearn" class="table-of-contents__link toc-highlight">特征重要性的 Scikit-learn 实现</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -40,6 +40,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="where-to-learn">在哪
 <li>对于初学者：遵循“自顶向下”的方法，首先学习 python，然后按照<strong>在线教程</strong>或者进行编码。在小型数据集上构建您的第一个机器学习模型。</li>
 <li>对于中级开发人员：遵循“自底向上”的方法，阅读<strong>官方文档</strong>、<strong>机器学习书籍</strong>，并尝试解决 kaggle 数据集上的一些问题。选择您感兴趣的一个或一些类别，并了解该算法为何有效，了解其数学原理。</li>
 <li>对于高级开发人员：我认为高级开发人员不太需要阅读本文；如果实在有什么建议，建议多读论文和代码，多问“为什么”和“怎么做”。</li>
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@@ -33,6 +33,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="clustering">聚类 (Clu
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-01_06.png" width="300" class="img_ev3q">
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="dimensionality-reduction">降维 (Dimensionality Reduction)<a href="#dimensionality-reduction" class="hash-link" aria-label="降维 (Dimensionality Reduction)的直接链接" title="降维 (Dimensionality Reduction)的直接链接">​</a></h3>
 <p>通常，我们正在处理高维度的数据，这对于有限的存储空间和机器学习算法的计算性能是很大的挑战。降维是指在某些限定条件下，降低随机变量的维度，得到一组“不相关”的主变量，同时保留大部分有效信息。</p>
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@@ -37,6 +37,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="what-is-jupyter">什么
 <p>启动 Jupyter Lab：</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">jupyter lab</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>或者启动 Jupyter Notebook：</p>
-<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">jupyter notebook</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/ml-basics/machine-learning-major-types"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">机器学习三大类型</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/ml-basics/start-with-iris-dataset"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">入门：基于 Iris 数据集</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#what-is-python" class="table-of-contents__link toc-highlight">什么是 Python？</a></li><li><a href="#what-is-anaconda" class="table-of-contents__link toc-highlight">什么是 Anaconda？</a></li><li><a href="#what-is-jupyter" class="table-of-contents__link toc-highlight">什么是 Jupyter？</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -50,6 +50,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="evaluation-and-predicti
 <p>进行评估：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string-interpolation string" style="color:#e3116c">f&quot;Score of tree_model: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">tree_model</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">score</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation">X_validation</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">,</span><span class="token string-interpolation interpolation"> Y_validation</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Score of tree_model: 0.9666666666666667</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>对新的未知数据进行分类：</p>
-<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token string-interpolation string" style="color:#e3116c">f&quot;Prediction of [6.0, 3.1, 5.1, 1.9]: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">tree_model</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">predict</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">[</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">[</span><span class="token string-interpolation interpolation number" style="color:#36acaa">6.0</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">,</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation number" style="color:#36acaa">3.1</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">,</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation number" style="color:#36acaa">5.1</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">,</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation number" style="color:#36acaa">1.9</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">]</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">]</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">[</span><span class="token string-interpolation interpolation number" style="color:#36acaa">0</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">]</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Prediction of [6.0, 3.1, 5.1, 1.9]: Iris-virginica</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" 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+<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token string-interpolation string" style="color:#e3116c">f&quot;Prediction of [6.0, 3.1, 5.1, 1.9]: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">tree_model</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">predict</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">[</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">[</span><span class="token string-interpolation interpolation number" style="color:#36acaa">6.0</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">,</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation number" style="color:#36acaa">3.1</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">,</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation number" style="color:#36acaa">5.1</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">,</span><span class="token string-interpolation interpolation"> </span><span class="token string-interpolation interpolation number" style="color:#36acaa">1.9</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">]</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">]</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">[</span><span class="token string-interpolation interpolation number" style="color:#36acaa">0</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">]</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Prediction of [6.0, 3.1, 5.1, 1.9]: Iris-virginica</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/ml-basics/python-environment-installation"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Python 环境安装</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/ml-basics/underfitting-and-overfitting"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">欠拟合和过拟合</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#preprocessing" class="table-of-contents__link toc-highlight">预处理</a><ul><li><a href="#load-data" class="table-of-contents__link toc-highlight">加载数据</a></li><li><a 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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">机器学习基础</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">欠拟合和过拟合</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>欠拟合和过拟合</h1></header>
@@ -30,6 +30,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="underfitting">欠拟合
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="overfitting">过拟合<a href="#overfitting" class="hash-link" aria-label="过拟合的直接链接" title="过拟合的直接链接">​</a></h3>
 <p>过拟合的模型存在高方差，对已知数据表现良好，但是对未知数据表现不佳。</p>
 <p>过拟合表示对已知数据进行了过度解读，包括其中的噪音和细节，导致训练出来的模型不能很好地适用于未知数据。</p>
-<p>样本数量少、噪音数据多、模型参数过多和复杂度过高等原因，都会导致过拟合。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/ml-basics/start-with-iris-dataset"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">入门：基于 Iris 数据集</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/neural-network/adaline-and-gradient-descent"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Adaline 和梯度下降法</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#generalization" class="table-of-contents__link toc-highlight">泛化</a></li><li><a href="#fitting" class="table-of-contents__link toc-highlight">拟合</a><ul><li><a href="#underfitting" class="table-of-contents__link toc-highlight">欠拟合</a></li><li><a href="#overfitting" class="table-of-contents__link toc-highlight">过拟合</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>样本数量少、噪音数据多、模型参数过多和复杂度过高等原因，都会导致过拟合。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/ml-basics/start-with-iris-dataset"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">入门：基于 Iris 数据集</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/neural-network/adaline-and-gradient-descent"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Adaline 和梯度下降法</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#generalization" class="table-of-contents__link toc-highlight">泛化</a></li><li><a href="#fitting" class="table-of-contents__link toc-highlight">拟合</a><ul><li><a href="#underfitting" class="table-of-contents__link toc-highlight">欠拟合</a></li><li><a href="#overfitting" class="table-of-contents__link toc-highlight">过拟合</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -23,6 +23,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="grid-search-using-sklea
 <p>通过网格搜索所有超参数组合 (下面是 8 + 64 = 72 个) 中的准确率最高的一个：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">model_selection </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> GridSearchCV</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">param_range </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0.0001</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.001</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.01</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1.0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">10.0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">100.0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1000.0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">param_grid </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">{</span><span class="token string" style="color:#e3116c">&quot;svc__C&quot;</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> param_range</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;svc__kernel&quot;</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&quot;linear&quot;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">{</span><span class="token string" style="color:#e3116c">&quot;svc__C&quot;</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> param_range</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;svc__gamma&quot;</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> param_range</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;svc__kernel&quot;</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&quot;rbf&quot;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">gs </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> GridSearchCV</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">estimator</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">pipe_svc</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> param_grid</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">param_grid</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> scoring</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;accuracy&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> cv</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">10</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>网格搜索得到的最优模型的准确率、参数、以及模型调用如下：</p>
-<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">best_score_</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: 0.984615384615</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">best_params_</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: {&#x27;svc__C&#x27;: 100.0, &#x27;svc__gamma&#x27;: 0.001, &#x27;svc__kernel&#x27;: &#x27;rbf&#x27;}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">clf </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">best_estimator_</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">clf</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Test accuracy: {:.3f}&quot;</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">format</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">clf</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">score</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_test</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: Test accuracy: 0.974</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/feature-selection/feature-importance"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">特征的重要性</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/model-selection/holdout"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Holdout 验证</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#algorithm-principle" class="table-of-contents__link toc-highlight">算法思想</a></li><li><a href="#data-load-and-preprocessing" class="table-of-contents__link toc-highlight">数据导入和预处理</a></li><li><a href="#grid-search-using-sklearn" class="table-of-contents__link toc-highlight">基于 Scikit-learn 的网格搜索</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 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href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">best_score_</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: 0.984615384615</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">best_params_</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: {&#x27;svc__C&#x27;: 100.0, &#x27;svc__gamma&#x27;: 0.001, &#x27;svc__kernel&#x27;: &#x27;rbf&#x27;}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">clf </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> gs</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">best_estimator_</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">clf</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Test accuracy: {:.3f}&quot;</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">format</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">clf</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">score</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_test</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: Test accuracy: 0.974</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/feature-selection/feature-importance"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">特征的重要性</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/model-selection/holdout"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Holdout 验证</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#algorithm-principle" class="table-of-contents__link toc-highlight">算法思想</a></li><li><a href="#data-load-and-preprocessing" class="table-of-contents__link toc-highlight">数据导入和预处理</a></li><li><a href="#grid-search-using-sklearn" class="table-of-contents__link toc-highlight">基于 Scikit-learn 的网格搜索</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 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@@ -19,6 +19,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="数据集划分训练
 <p>一种更好的模型选择方法是将数据分成三部分：<strong>训练集</strong>、<strong>验证集</strong> (Validation Set) 和<strong>测试集</strong>。训练集用于拟合不同的模型，然后根据模型在验证集上的表现来进行模型选择。在整个训练过程中，测试集是不可见的，不会对测试集过拟合。</p>
 <p>下图说明了保持交叉验证的概念，使用训练集和验证集进行反复训练并将超参数调整至较优水平，再使用测试集来评估模型的泛化性能：</p>
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-06_02.png" width="600" class="img_ev3q">
-<p>Holdout 方法的缺点是算法评估对数据划分比较敏感，对于不同的数据划分比例和不同的分布，评估结果可能会有较大差异。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/model-selection/grid-search"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">网格搜索</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/model-selection/k-fold-cross-validation"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">K 折交叉验证</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#数据集划分训练集和测试集" class="table-of-contents__link toc-highlight">数据集划分：训练集和测试集</a></li><li><a href="#数据集划分训练集验证集和测试集" class="table-of-contents__link toc-highlight">数据集划分：训练集、验证集和测试集</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>Holdout 方法的缺点是算法评估对数据划分比较敏感，对于不同的数据划分比例和不同的分布，评估结果可能会有较大差异。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/model-selection/grid-search"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">网格搜索</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/model-selection/k-fold-cross-validation"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">K 折交叉验证</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#数据集划分训练集和测试集" class="table-of-contents__link toc-highlight">数据集划分：训练集和测试集</a></li><li><a href="#数据集划分训练集验证集和测试集" class="table-of-contents__link toc-highlight">数据集划分：训练集、验证集和测试集</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -43,6 +43,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="nested-cross-validation
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">gs </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> GridSearchCV</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">estimator</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">pipe_svc</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> param_grid</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">param_grid</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> scoring</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;accuracy&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> cv</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">scores </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> cross_val_score</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> scoring</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;accuracy&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> cv</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;CV accuracy: {:.3f} +/- {:.3f}&quot;</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">format</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">mean</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">scores</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">std</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">scores</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: CV accuracy: 0.974 +/- 0.015</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>基于决策树的 5×2 折叠交叉验证，实现如下：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tree </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> DecisionTreeClassifier</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">gs </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> GridSearchCV</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    estimator</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">DecisionTreeClassifier</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">om_state</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    param_grid</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">{</span><span class="token string" style="color:#e3116c">&quot;max_depth&quot;</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">4</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">6</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">7</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    scoring</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;accuracy&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    cv</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">scores </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> cross_val_score</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gs</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> scoring</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;accuracy&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> cv</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;CV accuracy: %.3f +/- %.3f&quot;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">%</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">mean</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">scores</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">std</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">scores</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: CV accuracy: 0.934 +/- 0.016</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<p>可以看到，基于 SVM 模型的嵌套交叉验证相比于基于决策树的交叉验证更优。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/model-selection/holdout"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Holdout 验证</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/model-selection/learning-and-validation-curve"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">学习曲线和验证曲线</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#kfold-cross-validation-principle" class="table-of-contents__link toc-highlight">K 折交叉验证原理</a></li><li><a href="#stratified-kfold-cross-validation-using-sklearn" class="table-of-contents__link toc-highlight">分层 K 折交叉验证的 scikit-learn 实现</a></li><li><a href="#nested-cross-validation" class="table-of-contents__link toc-highlight">嵌套交叉验证</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>可以看到，基于 SVM 模型的嵌套交叉验证相比于基于决策树的交叉验证更优。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/model-selection/holdout"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Holdout 验证</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/model-selection/learning-and-validation-curve"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">学习曲线和验证曲线</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#kfold-cross-validation-principle" class="table-of-contents__link toc-highlight">K 折交叉验证原理</a></li><li><a href="#stratified-kfold-cross-validation-using-sklearn" class="table-of-contents__link toc-highlight">分层 K 折交叉验证的 scikit-learn 实现</a></li><li><a href="#nested-cross-validation" class="table-of-contents__link toc-highlight">嵌套交叉验证</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -49,6 +49,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="validation-curve">验
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">model_selection </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> validation_curve</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">param_range </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0.001</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.01</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1.0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">10.0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">100.0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">train_scores</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_scores </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> validation_curve</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    estimator</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">pipe_lr</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    X</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    y</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">y_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    param_name</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;logisticregression__C&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    param_range</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">param_range</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    cv</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">10</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">train_mean </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">mean</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">train_scores</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> axis</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">train_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">std</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">train_scores</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> axis</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">test_mean </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">mean</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">test_scores</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> axis</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">test_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">std</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">test_scores</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> axis</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">plot</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    param_range</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    train_mean</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    color</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;blue&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    marker</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;o&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    markersize</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    label</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;training accuracy&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fill_between</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    param_range</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    train_mean </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> train_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    train_mean </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> train_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    alpha</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.15</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    color</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;blue&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">plot</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    param_range</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    test_mean</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    color</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;green&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    linestyle</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;--&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    marker</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;s&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    markersize</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    label</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;validation accuracy&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fill_between</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    param_range</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_mean </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> test_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_mean </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> test_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> alpha</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.15</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> color</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;green&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">grid</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xscale</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;log&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">legend</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">loc</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;lower right&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Parameter C&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Accuracy&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylim</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0.8</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1.03</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>得到模型的准确率随逻辑回归参数 <code>C</code> 变化的曲线：</p>
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-06_05.png" width="600" class="img_ev3q">
-<p>在正则化强度较大 (<code>C</code> 小于 0.01) 时，模型有一定程度的欠拟合 (高偏差)，但在正则化强度较小 (<code>C</code> 大于 10) 时，模型又会出现过拟合 (高方差)。超参数 <code>C</code> 的取值在 0.01 和 0.1 之间时，模型性能最优。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/model-selection/k-fold-cross-validation"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">K 折交叉验证</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/traditional-ml-algorithms/bagging"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bagging</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#variance-bias-tradeoff" class="table-of-contents__link toc-highlight">方差 - 偏差权衡</a></li><li><a href="#learning-curve" class="table-of-contents__link toc-highlight">学习曲线</a></li><li><a href="#validation-curve" class="table-of-contents__link toc-highlight">验证曲线</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>在正则化强度较大 (<code>C</code> 小于 0.01) 时，模型有一定程度的欠拟合 (高偏差)，但在正则化强度较小 (<code>C</code> 大于 10) 时，模型又会出现过拟合 (高方差)。超参数 <code>C</code> 的取值在 0.01 和 0.1 之间时，模型性能最优。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/model-selection/k-fold-cross-validation"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">K 折交叉验证</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/traditional-ml-algorithms/bagging"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bagging</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#variance-bias-tradeoff" class="table-of-contents__link toc-highlight">方差 - 偏差权衡</a></li><li><a href="#learning-curve" class="table-of-contents__link toc-highlight">学习曲线</a></li><li><a href="#validation-curve" class="table-of-contents__link toc-highlight">验证曲线</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -82,6 +82,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="adaline-implementation-
 <p>对算法训练过程进行绘图：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">ada </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> AdalineSGD</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">n_iter</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">15</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> eta</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.01</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> random_state</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">ada</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plot_decision_regions</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> classifier</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">ada</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">title</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Adaline - Stochastic Gradient Descent&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;sepal length [standardized]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;petal length [standardized]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">legend</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">loc</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;upper left&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tight_layout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">plot</span><span class="token punctuation" style="color:#393A34">(</span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">len</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">ada</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">cost_</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> ada</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">cost_</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> marker</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;o&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Epochs&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Average Cost&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tight_layout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 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+<p>从上图可以看到，随机梯度下降法每次使用单个样本训练，成本函数 SSE 也可以快速收敛。对于在线学习的场景，对单个样本调用 <code>ada.partial_fit(X_std[0, :], y[0])</code> 即可对训练模型进行更新。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/ml-basics/underfitting-and-overfitting"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">欠拟合和过拟合</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Scikit-learn 简介：使用感知器</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#adaline-principle" class="table-of-contents__link toc-highlight">Adaline 原理</a></li><li><a href="#batch-gradient-descent" class="table-of-contents__link toc-highlight">批量梯度下降法</a><ul><li><a href="#adaline-implementation-based-on-batch-gradient-descent" class="table-of-contents__link toc-highlight">基于批量梯度下降法的 Adaline 实现</a></li></ul></li><li><a href="#stochastic-gradient-descent" class="table-of-contents__link toc-highlight">随机梯度下降法</a><ul><li><a href="#adaline-implementation-based-on-stochastic-gradient-descent" class="table-of-contents__link toc-highlight">基于随机梯度下降法的 Adaline 实现</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -43,6 +43,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="plot-decistion-boundary
 <p>对算法训练过程进行绘图：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> matplotlib</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">colors </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> ListedColormap</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> matplotlib</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pyplot </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> plt</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">plot_decision_regions</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> classifier</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_idx</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> resolution</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.02</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    markers </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;s&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;x&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;o&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;^&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;v&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    colors </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;red&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;blue&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;lightgreen&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;gray&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;cyan&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    cmap </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> ListedColormap</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">colors</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> </span><span class="token builtin">len</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unique</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">y</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    x1_min</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x1_max </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> X</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">min</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    x2_min</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x2_max </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> X</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">min</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    xx1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> xx2 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">meshgrid</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">arange</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x1_min</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x1_max</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> resolution</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" 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class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlim</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">xx1</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">min</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> xx1</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylim</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">xx2</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">min</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> xx2</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> idx</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> cl </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">enumerate</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unique</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">y</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">scatter</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            x</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">X</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">y </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> cl</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            y</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">X</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">y </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> cl</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            alpha</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.8</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            c</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">colors</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">idx</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            marker</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">markers</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">idx</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            label</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">cl</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            edgecolor</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;black&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> test_idx</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        X_test</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> X</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">test_idx</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">test_idx</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">scatter</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            X_test</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            X_test</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            c</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            edgecolor</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;black&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            alpha</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1.0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            linewidth</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            marker</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;o&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            s</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">100</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            label</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;test set&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_combined_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">vstack</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_test_std</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y_combined </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">hstack</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">y_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plot_decision_regions</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    X</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">X_combined_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">y_combined</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> classifier</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">ppn</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_idx</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">105</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">150</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;petal length [standardized]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;petal width [standardized]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">legend</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">loc</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;upper left&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>绘制边界如下，其中测试集用黑色圆圈标出：</p>
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@@ -69,6 +69,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="python-implementation">
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="plotting">绘制图像<a href="#plotting" class="hash-link" aria-label="绘制图像的直接链接" title="绘制图像的直接链接">​</a></h2>
 <p>以 <em>Iris-setosa</em> (标签 0) and <em>Iris-versicolor</em> (标签 1) 为例，采用逻辑回归分类，绘制决策边界如下，</p>
 <div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">import matplotlib.pyplot as plt</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">from plot_decision_regions import plot_decision_regions</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">from sklearn import datasets</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">from sklearn.model_selection import train_test_split</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">iris = datasets.load_iris()</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X = iris.data[:, [2, 3]]</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y = iris.target</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=1, stratify=y)</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_train_01_subset = X_train[(y_train == 0) | (y_train == 1)]</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y_train_01_subset = y_train[(y_train == 0) | (y_train == 1)]</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">lrgd = LogisticRegressionGD(eta=0.05,n_iter=1000,random_state=1)</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">lrgd.fit(X_train_01_subset,y_train_01_subset)</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plot_decision_regions(X=X_train_01_subset,y=y_train_01_subset,classifier=lrgd)</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt.xlabel(&#x27;petal length [standardized]&#x27;)</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt.ylabel(&#x27;petal width [standardized]&#x27;)</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt.legend(loc=&#x27;upper left&#x27;)</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt.show()</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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@@ -134,6 +134,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="向量化">向量化<a
 W &amp; := W - \alpha \cdot dW \\
 b &amp; := b - \alpha \cdot db
 \end{align}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:13.9953em;vertical-align:-6.7476em"></span><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:7.2476em"><span style="top:-10.0077em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span></span><span style="top:-8.5077em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-6.4763em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span></span><span style="top:-4.1188em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.13889em">W</span></span></span><span style="top:-1.4814em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal">b</span></span></span><span style="top:0.9362em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em">W</span></span></span><span style="top:2.4362em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord mathnormal">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.7476em"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:7.2476em"><span style="top:-10.0077em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em">W</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.07847em">X</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mord mathnormal" style="margin-right:0.05017em">B</span></span></span><span style="top:-8.5077em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07153em">Z</span><span class="mclose">)</span></span></span><span style="top:-6.4763em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord mathnormal" style="margin-right:0.09618em">J</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">m</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mord mathnormal" style="margin-right:0.22222em">Y</span><span class="mclose">)</span></span></span><span style="top:-4.1188em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord mathnormal" style="margin-right:0.13889em">W</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord mathnormal" style="margin-right:0.09618em">J</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord mathnormal" style="margin-right:0.07847em">X</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mopen">[</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.07153em">Z</span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span></span></span><span style="top:-1.4814em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6514em"><span style="top:-1.8723em;margin-left:0em"><span class="pstrut" style="height:3.05em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em"><span class="pstrut" style="height:3.05em"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em"><span class="pstrut" style="height:3.05em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">d</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:0.9362em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">:=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord mathnormal" style="margin-right:0.13889em">W</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.13889em">W</span></span></span><span style="top:2.4362em"><span class="pstrut" style="height:3.6514em"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">:=</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mord mathnormal" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.7476em"><span></span></span></span></span></span></span></span><span class="tag"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:7.2476em"><span style="top:-10.0077em"><span class="pstrut" style="height:3.6514em"></span><span class="eqn-num"></span></span><span style="top:-8.5077em"><span class="pstrut" style="height:3.6514em"></span><span class="eqn-num"></span></span><span style="top:-6.4763em"><span class="pstrut" style="height:3.6514em"></span><span class="eqn-num"></span></span><span style="top:-4.1188em"><span class="pstrut" style="height:3.6514em"></span><span class="eqn-num"></span></span><span style="top:-1.4814em"><span class="pstrut" style="height:3.6514em"></span><span class="eqn-num"></span></span><span style="top:0.9362em"><span class="pstrut" style="height:3.6514em"></span><span class="eqn-num"></span></span><span style="top:2.4362em"><span class="pstrut" style="height:3.6514em"></span><span class="eqn-num"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.7476em"><span></span></span></span></span></span></span></span></span>
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@@ -115,6 +115,6 @@ <h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="perceptron-model-traini
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">plot_decision_regions</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> classifier</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">ppn</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;sepal length [cm]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;petal length [cm]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">legend</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">loc</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;upper left&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tight_layout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-02_08.png" width="500" class="img_ev3q">
 <p>通过学习，感知器生成了将 Iris 训练子集完全分类的决策边界。</p>
-<div class="theme-admonition theme-admonition-note admonition_xJq3 alert alert--secondary"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>备注</div><div class="admonitionContent_BuS1"><p>虽然本例中感知器能够完全分类两种花卉，但收敛仍是感知器最重要的问题之一。如果两个类线性可分，感知器算法就能够收敛。然而对于无法线性可分的类，除非我们手动设置最大训练次数，否则权重永远不会停止更新。</p></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">逻辑回归的向量化</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/data-preprocessing/categorical-data"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">分类数据的预处理</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#mcp-neuron-and-perceptron-priciple" class="table-of-contents__link toc-highlight">MCP 神经元和感知器原理</a></li><li><a href="#python-implementation-of-perceptron" class="table-of-contents__link toc-highlight">Rosenblatt 感知器的 Python 实现</a><ul><li><a href="#perceptron-model-training-based-on-iris-dataset" class="table-of-contents__link toc-highlight">基于 Iris 数据集的感知器模型训练</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<div class="theme-admonition theme-admonition-note admonition_xJq3 alert alert--secondary"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 14 16"><path fill-rule="evenodd" d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"></path></svg></span>备注</div><div class="admonitionContent_BuS1"><p>虽然本例中感知器能够完全分类两种花卉，但收敛仍是感知器最重要的问题之一。如果两个类线性可分，感知器算法就能够收敛。然而对于无法线性可分的类，除非我们手动设置最大训练次数，否则权重永远不会停止更新。</p></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">逻辑回归的向量化</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/data-preprocessing/categorical-data"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">分类数据的预处理</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#mcp-neuron-and-perceptron-priciple" class="table-of-contents__link toc-highlight">MCP 神经元和感知器原理</a></li><li><a href="#python-implementation-of-perceptron" class="table-of-contents__link toc-highlight">Rosenblatt 感知器的 Python 实现</a><ul><li><a href="#perceptron-model-training-based-on-iris-dataset" class="table-of-contents__link toc-highlight">基于 Iris 数据集的感知器模型训练</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -142,6 +142,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="images">图像<a href="
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> numpy </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> np</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> scipy</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">misc </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> imread</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> imresize</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> matplotlib</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pyplot </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> plt</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">img </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> imread</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;assets/cat.jpg&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">img_tinted </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> img </span><span class="token operator" style="color:#393A34">*</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.95</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.9</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Show the original image</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">subplot</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">imshow</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">img</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Show the tinted image</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">subplot</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># A slight gotcha with imshow is that it might give strange results</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># if presented with data that is not uint8. To work around this, we</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># explicitly cast the image to uint8 before displaying it.</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">imshow</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">uint8</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">img_tinted</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <hr>
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@@ -216,6 +216,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="excel">Excel<a href="#e
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style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;Sheet1&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> index_col</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> na_values</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&quot;NA&quot;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Out</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">140</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   Unnamed</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">2</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">3</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">4</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span 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plain"></span><span class="token number" style="color:#36acaa">8</span><span class="token plain">           </span><span class="token number" style="color:#36acaa">8</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">4</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">4</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">1</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">9</span><span class="token plain">           </span><span class="token number" style="color:#36acaa">9</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">4</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">3</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">0</span><span class="token plain">  </span><span class="token number" style="color:#36acaa">3</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="gotchas">陷阱<a href="#gotchas" class="hash-link" aria-label="陷阱的直接链接" title="陷阱的直接链接">​</a></h2>
 <p>如果您尝试对 <code>Series</code> 或 <code>DataFrame</code> 执行布尔运算，您可能会看到如下异常：</p>
-<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">In </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">141</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> pd</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Series</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">[</span><span class="token boolean" style="color:#36acaa">False</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">True</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">False</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain">      </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;I was true&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token 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class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">ValueError                                Traceback </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">most recent call last</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">ipython</span><span class="token operator" style="color:#393A34">-</span><span class="token builtin">input</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">141</span><span class="token operator" style="color:#393A34">-</span><span class="token plain">b27eb9c1dfc0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> ?</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> pd</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Series</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">[</span><span class="token boolean" style="color:#36acaa">False</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">True</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">False</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">      </span><span class="token number" style="color:#36acaa">2</span><span class="token plain">      </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;I was true&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">~</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">work</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">pandas</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">pandas</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">pandas</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">core</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">generic</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">py </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> ?</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1517</span><span class="token plain">     @final</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1518</span><span class="token plain">     </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__nonzero__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> NoReturn</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1519</span><span class="token plain">         </span><span class="token keyword" style="color:#00009f">raise</span><span class="token plain"> ValueError</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1520</span><span class="token plain">             </span><span class="token string-interpolation string" style="color:#e3116c">f&quot;The truth value of a </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation builtin">type</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation">self</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">__name__</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c"> is ambiguous. &quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1521</span><span class="token plain">             </span><span class="token string" style="color:#e3116c">&quot;Use a.empty, a.bool(), a.item(), a.any() or a.all().&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1522</span><span class="token plain">         </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">ValueError</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> The truth value of a Series </span><span class="token keyword" style="color:#00009f">is</span><span class="token plain"> ambiguous</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain"> Use a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">empty</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">bool</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">item</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">any</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">or</span><span class="token plain"> a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">all</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/numpy-pandas/numpy-quickstart"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">NumPy 快速入门</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/evaluation-metrics/confusion-matrix"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">混淆矩阵</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#basic-data-structures" class="table-of-contents__link toc-highlight">Pandas 基础数据结构</a></li><li><a href="#object-creation" class="table-of-contents__link toc-highlight">对象创建</a></li><li><a href="#viewing_data" class="table-of-contents__link toc-highlight">查看数据</a></li><li><a href="#selection" class="table-of-contents__link toc-highlight">选择数据</a><ul><li><a href="#getitem" class="table-of-contents__link toc-highlight">获取数据项 (<code>[]</code>)</a></li><li><a href="#selection-by-label" class="table-of-contents__link toc-highlight">按标签选择</a></li><li><a href="#selection-by-position" class="table-of-contents__link toc-highlight">按位置选择</a></li><li><a href="#boolean-indexing" class="table-of-contents__link toc-highlight">布尔索引</a></li><li><a href="#setting" class="table-of-contents__link toc-highlight">设置值</a></li></ul></li><li><a href="#missing-data" class="table-of-contents__link toc-highlight">缺失值</a></li><li><a href="#operations" class="table-of-contents__link toc-highlight">操作</a><ul><li><a href="#stats" class="table-of-contents__link toc-highlight">状态</a></li><li><a href="#user-defined-functions" class="table-of-contents__link toc-highlight">用户自定义函数</a></li><li><a href="#value-counts" class="table-of-contents__link toc-highlight">值计数</a></li><li><a href="#string-methods" class="table-of-contents__link toc-highlight">字符串方法</a></li></ul></li><li><a href="#merge" class="table-of-contents__link toc-highlight">合并</a><ul><li><a href="#concat" class="table-of-contents__link toc-highlight">Concat</a></li><li><a href="#join" class="table-of-contents__link toc-highlight">Join</a></li></ul></li><li><a href="#grouping" class="table-of-contents__link toc-highlight">分组</a></li><li><a href="#reshaping" class="table-of-contents__link toc-highlight">变形</a><ul><li><a href="#stack" class="table-of-contents__link toc-highlight">堆叠</a></li><li><a href="#pivot-tables" class="table-of-contents__link toc-highlight">透视表</a></li></ul></li><li><a href="#time-series" class="table-of-contents__link toc-highlight">时间序列</a></li><li><a href="#categoricals" class="table-of-contents__link toc-highlight">分类数据</a></li><li><a href="#plotting" class="table-of-contents__link toc-highlight">绘图</a></li><li><a href="#data-import-export" class="table-of-contents__link toc-highlight">数据导入/导出</a><ul><li><a href="#csv" class="table-of-contents__link toc-highlight">CSV</a></li><li><a href="#parquet" class="table-of-contents__link toc-highlight">Parquet</a></li><li><a href="#excel" class="table-of-contents__link toc-highlight">Excel</a></li></ul></li><li><a href="#gotchas" class="table-of-contents__link toc-highlight">陷阱</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 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+<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">In </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">141</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> pd</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Series</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">[</span><span class="token boolean" style="color:#36acaa">False</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">True</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">False</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain">      </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;I was true&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">.</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token 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class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">ValueError                                Traceback </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">most recent call last</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain">ipython</span><span class="token operator" style="color:#393A34">-</span><span class="token builtin">input</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">141</span><span class="token operator" style="color:#393A34">-</span><span class="token plain">b27eb9c1dfc0</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> ?</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> pd</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Series</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">[</span><span class="token boolean" style="color:#36acaa">False</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">True</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">False</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">      </span><span class="token number" style="color:#36acaa">2</span><span class="token plain">      </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;I was true&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">~</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">work</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">pandas</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">pandas</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">pandas</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">core</span><span class="token operator" style="color:#393A34">/</span><span class="token plain">generic</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">py </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> ?</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1517</span><span class="token plain">     @final</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1518</span><span class="token plain">     </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__nonzero__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> NoReturn</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token operator" style="color:#393A34">-</span><span class="token operator" style="color:#393A34">&gt;</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1519</span><span class="token plain">         </span><span class="token keyword" style="color:#00009f">raise</span><span class="token plain"> ValueError</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1520</span><span class="token plain">             </span><span class="token string-interpolation string" style="color:#e3116c">f&quot;The truth value of a </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation builtin">type</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation">self</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">__name__</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c"> is ambiguous. &quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1521</span><span class="token plain">             </span><span class="token string" style="color:#e3116c">&quot;Use a.empty, a.bool(), a.item(), a.any() or a.all().&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">   </span><span class="token number" style="color:#36acaa">1522</span><span class="token plain">         </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">ValueError</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> The truth value of a Series </span><span class="token keyword" style="color:#00009f">is</span><span class="token plain"> ambiguous</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain"> Use a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">empty</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">bool</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">item</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">any</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">or</span><span class="token plain"> a</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">all</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/numpy-pandas/numpy-quickstart"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">NumPy 快速入门</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/evaluation-metrics/confusion-matrix"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">混淆矩阵</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#basic-data-structures" class="table-of-contents__link toc-highlight">Pandas 基础数据结构</a></li><li><a href="#object-creation" class="table-of-contents__link toc-highlight">对象创建</a></li><li><a href="#viewing_data" class="table-of-contents__link toc-highlight">查看数据</a></li><li><a href="#selection" class="table-of-contents__link toc-highlight">选择数据</a><ul><li><a href="#getitem" class="table-of-contents__link toc-highlight">获取数据项 (<code>[]</code>)</a></li><li><a href="#selection-by-label" class="table-of-contents__link toc-highlight">按标签选择</a></li><li><a href="#selection-by-position" class="table-of-contents__link toc-highlight">按位置选择</a></li><li><a href="#boolean-indexing" class="table-of-contents__link toc-highlight">布尔索引</a></li><li><a href="#setting" class="table-of-contents__link toc-highlight">设置值</a></li></ul></li><li><a href="#missing-data" class="table-of-contents__link toc-highlight">缺失值</a></li><li><a href="#operations" class="table-of-contents__link toc-highlight">操作</a><ul><li><a href="#stats" class="table-of-contents__link toc-highlight">状态</a></li><li><a href="#user-defined-functions" class="table-of-contents__link toc-highlight">用户自定义函数</a></li><li><a href="#value-counts" class="table-of-contents__link toc-highlight">值计数</a></li><li><a href="#string-methods" class="table-of-contents__link toc-highlight">字符串方法</a></li></ul></li><li><a href="#merge" class="table-of-contents__link toc-highlight">合并</a><ul><li><a href="#concat" class="table-of-contents__link toc-highlight">Concat</a></li><li><a href="#join" class="table-of-contents__link toc-highlight">Join</a></li></ul></li><li><a href="#grouping" class="table-of-contents__link toc-highlight">分组</a></li><li><a href="#reshaping" class="table-of-contents__link toc-highlight">变形</a><ul><li><a href="#stack" class="table-of-contents__link toc-highlight">堆叠</a></li><li><a href="#pivot-tables" class="table-of-contents__link toc-highlight">透视表</a></li></ul></li><li><a href="#time-series" class="table-of-contents__link toc-highlight">时间序列</a></li><li><a href="#categoricals" class="table-of-contents__link toc-highlight">分类数据</a></li><li><a href="#plotting" class="table-of-contents__link toc-highlight">绘图</a></li><li><a href="#data-import-export" class="table-of-contents__link toc-highlight">数据导入/导出</a><ul><li><a href="#csv" class="table-of-contents__link toc-highlight">CSV</a></li><li><a href="#parquet" class="table-of-contents__link toc-highlight">Parquet</a></li><li><a href="#excel" class="table-of-contents__link toc-highlight">Excel</a></li></ul></li><li><a href="#gotchas" class="table-of-contents__link toc-highlight">陷阱</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 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itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="主页面" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">传统机器学习算法</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Bagging</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown 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@@ -35,6 +35,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="bagging-的-scikit-lear
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> numpy </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> np</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> matplotlib</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pyplot </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> plt</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">x_min </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> X_train</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">min</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">x_max </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> X_train</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y_min </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> X_train</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">min</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y_max </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> X_train</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">xx</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> yy </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">meshgrid</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">arange</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x_min</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x_max</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">arange</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">y_min</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_max</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">f</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> axarr </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">subplots</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nrows</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> ncols</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> sharex</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;col&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> sharey</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;row&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> figsize</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">8</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> idx</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> clf</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tt </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">zip</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">tree</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> bag</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&quot;Decision tree&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;Bagging&quot;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    clf</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    Z </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> clf</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">predict</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">c_</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">xx</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ravel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> yy</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ravel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    Z </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> Z</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">reshape</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">xx</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">shape</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    axarr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">idx</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contourf</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">xx</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> yy</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> Z</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> alpha</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.3</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    axarr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">idx</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">scatter</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        X_train</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">y_train </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_train</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">y_train </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> c</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;blue&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> marker</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;^&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    axarr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">idx</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">scatter</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        X_train</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">y_train </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_train</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">y_train </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> c</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;green&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> marker</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;o&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    axarr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">idx</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">set_title</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">tt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">axarr</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">set_ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Alcohol&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> fontsize</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">12</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">text</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token number" style="color:#36acaa">10.2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">0.5</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> s</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;OD280/OD315 of diluted wines&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> ha</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;center&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> va</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;center&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> fontsize</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">12</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tight_layout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># plt.savefig(&#x27;images/07_08.png&#x27;, dpi=300, bbox_inches=&#x27;tight&#x27;)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-07_08.png" width="800" class="img_ev3q">
 <p>从上图可以看出，bagging 的决策边界相比决策树更为平滑。</p>
-<p>在实践中，bagging 往往用于解决由于解决分类器模型的过拟合问题，降低模型的方差。需要注意的是，bagging 无法减少模型偏差 (如某些模型太简单，无法很好地捕捉数据中的趋势)。因此 bagging 更适用于低偏差的模型，如未修剪的决策树。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/model-selection/learning-and-validation-curve"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">学习曲线和验证曲线</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/traditional-ml-algorithms/decision-tree"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">决策树和随机森林</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#基本概念" class="table-of-contents__link toc-highlight">基本概念</a><ul><li><a href="#数据导入及预处理" class="table-of-contents__link toc-highlight">数据导入及预处理</a></li><li><a href="#bagging-的-scikit-learn-实现" class="table-of-contents__link toc-highlight">bagging 的 scikit-learn 实现</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>在实践中，bagging 往往用于解决由于解决分类器模型的过拟合问题，降低模型的方差。需要注意的是，bagging 无法减少模型偏差 (如某些模型太简单，无法很好地捕捉数据中的趋势)。因此 bagging 更适用于低偏差的模型，如未修剪的决策树。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/model-selection/learning-and-validation-curve"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">学习曲线和验证曲线</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/traditional-ml-algorithms/decision-tree"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">决策树和随机森林</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#基本概念" class="table-of-contents__link toc-highlight">基本概念</a><ul><li><a href="#数据导入及预处理" class="table-of-contents__link toc-highlight">数据导入及预处理</a></li><li><a href="#bagging-的-scikit-learn-实现" class="table-of-contents__link toc-highlight">bagging 的 scikit-learn 实现</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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markdown"><header><h1>决策树和随机森林</h1></header>
@@ -105,6 +105,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="随机森林">随机森
 </ol>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> matplotlib</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pyplot </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> plt</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> numpy </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> np</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> datasets</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">model_selection </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> train_test_split</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ensemble </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> RandomForestClassifier</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">iris </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> datasets</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">load_iris</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> iris</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> iris</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">target</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_test</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> train_test_split</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    X</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_size</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.3</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> random_state</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> stratify</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">y</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">forest </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> RandomForestClassifier</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    criterion</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;gini&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> n_estimators</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">25</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> random_state</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> n_jobs</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">2</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">forest</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_combined </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">vstack</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_test</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y_combined </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">hstack</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">y_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plot_decision_regions</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    X_combined</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_combined</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> classifier</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">forest</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_idx</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">105</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">150</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;petal length [standardized]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;petal width [standardized]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">legend</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">loc</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;upper left&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>上面通过 <code>n_estimators</code> 参数从 25 个决策树中训练了一个随机森林，并使用 Gini 不纯度作为分割节点的标准。<code>n_jobs</code> 参数表示可以使用计算机的多个核心 (这里是两个核心) 来并行化训练。</p>
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markdown"><header><h1>使用集合的投票分类方法</h1></header>
@@ -65,6 +65,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="加权相对多数分
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">ex </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">array</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0.9</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0.8</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.2</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0.4</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.6</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">p </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">average</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">ex</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> axis</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> weights</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0.2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.6</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">p</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: array([ 0.58, 0.42])</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">argmax</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">p</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># Output: 0</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <blockquote>
 <p>scikit-learn 中实现了投票分类，请参见 <a href="http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.VotingClassifier.html" target="_blank" rel="noopener noreferrer">sklearn.ensemble.VotingClassifier</a>。</p>
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@@ -41,6 +41,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="算法实现">算法实
 <p>若 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">p=2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">2</span></span></span></span>，则代表<strong>欧几里得距离</strong>；若 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">p=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">1</span></span></span></span>，则代表<strong>曼哈顿距离</strong>。</p>
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="算法的维度问题">算法的维度问题<a href="#算法的维度问题" class="hash-link" aria-label="算法的维度问题的直接链接" title="算法的维度问题的直接链接">​</a></h2>
 <p>如果特征空间维度非常高，空间中最相似的两个点也可能距离很远，KNN 算法很容易过拟合。</p>
-<p>在这种情况下，建议通过特征选择和降维等方法来避免维度问题。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">使用集合的投票分类方法</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/traditional-ml-algorithms/svm-linear"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">线性 SVM</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#算法思想" class="table-of-contents__link toc-highlight">算法思想</a></li><li><a href="#算法实现" class="table-of-contents__link toc-highlight">算法实现</a></li><li><a href="#算法的维度问题" class="table-of-contents__link toc-highlight">算法的维度问题</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>在这种情况下，建议通过特征选择和降维等方法来避免维度问题。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">使用集合的投票分类方法</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/traditional-ml-algorithms/svm-linear"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">线性 SVM</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#算法思想" class="table-of-contents__link toc-highlight">算法思想</a></li><li><a href="#算法实现" class="table-of-contents__link toc-highlight">算法实现</a></li><li><a href="#算法的维度问题" class="table-of-contents__link toc-highlight">算法的维度问题</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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class="button button--secondary button--outline collapseSidebarButton_PEFL"><svg width="20" height="20" aria-hidden="true" class="collapseSidebarButtonIcon_kv0_"><g fill="#7a7a7a"><path d="M9.992 10.023c0 .2-.062.399-.172.547l-4.996 7.492a.982.982 0 01-.828.454H1c-.55 0-1-.453-1-1 0-.2.059-.403.168-.551l4.629-6.942L.168 3.078A.939.939 0 010 2.528c0-.548.45-.997 1-.997h2.996c.352 0 .649.18.828.45L9.82 9.472c.11.148.172.347.172.55zm0 0"></path><path d="M19.98 10.023c0 .2-.058.399-.168.547l-4.996 7.492a.987.987 0 01-.828.454h-3c-.547 0-.996-.453-.996-1 0-.2.059-.403.168-.551l4.625-6.942-4.625-6.945a.939.939 0 01-.168-.55 1 1 0 01.996-.997h3c.348 0 .649.18.828.45l4.996 7.492c.11.148.168.347.168.55zm0 0"></path></g></svg></button></div></div></aside><main class="docMainContainer_TBSr"><div class="container padding-top--md padding-bottom--lg"><div class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><nav class="theme-doc-breadcrumbs breadcrumbsContainer_Z_bl" aria-label="页面路径"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="主页面" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">传统机器学习算法</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">线性 SVM</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>线性 SVM</h1></header>
@@ -53,6 +53,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="软间隔-svm">软间
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-03_10.png" width="600" class="img_ev3q">
 <p>以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (其中决策边界绘制函数 <code>plot_decision_regions</code> 请参见之前的文章)：</p>
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> matplotlib</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pyplot </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> plt</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> numpy </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> np</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> datasets</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">model_selection </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> train_test_split</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">svm </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> SVC</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> sklearn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">preprocessing </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> StandardScaler</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">iris </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> datasets</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">load_iris</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> iris</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> iris</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">target</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_test</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> train_test_split</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    X</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_size</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.3</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> random_state</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> stratify</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">y</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">sc </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> StandardScaler</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">sc</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_train_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> sc</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_test_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> sc</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transform</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_test</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">X_combined_std </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">vstack</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> X_test_std</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">y_combined </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> np</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">hstack</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">y_train</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_test</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">svm </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> SVC</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">kernel</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;linear&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> C</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1.0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> random_state</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">svm</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">X_train_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_train</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plot_decision_regions</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    X_combined_std</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> y_combined</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> classifier</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">svm</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> test_idx</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">105</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">150</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">xlabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;petal length [standardized]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ylabel</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;petal width [standardized]&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">legend</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">loc</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;upper left&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">plt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">show</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>核技巧和非线性 SVM</h1></header>
@@ -45,6 +45,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="非线性-svm-实现">
 <div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">svm </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> SVC</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">kernel</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;rbf&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> random_state</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> gamma</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">100.0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> C</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1.0</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <img decoding="async" loading="lazy" src="https://image.szdev.com/images/2018/12/03/book-py_ml_2nd-03_16.png" width="600" class="img_ev3q">
 <p>可以看到，类 1 和类 2 的边界非常紧凑，样本空间远远小于类 3 的样本空间。</p>
-<p>当 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.05556em">γ</span></span></span></span> 较大时，容易出现过拟合情况，在实际应用中需要控制 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.05556em">γ</span></span></span></span> 的大小在合理范围。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/traditional-ml-algorithms/svm-linear"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">线性 SVM</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-overview"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Transformer 概览</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#核技巧原理" class="table-of-contents__link toc-highlight">核技巧原理</a></li><li><a href="#数学表达" class="table-of-contents__link toc-highlight">数学表达</a></li><li><a href="#非线性-svm-实现" class="table-of-contents__link toc-highlight">非线性 SVM 实现</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>当 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.05556em">γ</span></span></span></span> 较大时，容易出现过拟合情况，在实际应用中需要控制 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.05556em">γ</span></span></span></span> 的大小在合理范围。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/traditional-ml-algorithms/svm-linear"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">线性 SVM</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-overview"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Transformer 概览</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#核技巧原理" class="table-of-contents__link toc-highlight">核技巧原理</a></li><li><a href="#数学表达" class="table-of-contents__link toc-highlight">数学表达</a></li><li><a href="#非线性-svm-实现" class="table-of-contents__link toc-highlight">非线性 SVM 实现</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">注意力机制</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>注意力机制</h1></header>
@@ -129,6 +129,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="自注意力中的-mask
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-M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1828em"><span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.74em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">Q</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.93em"><span></span></span></span></span></span><span></span></span></span></span></span> 后，将右上部分 (不包含对角线) 设置成负无穷大或者一个非常大的负值 (如 1e-9)，这样在经过 SoftMax 之后，对应位置的 attention score 接近为 0。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/transformer/transformer-positional-encoding"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">位置编码</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-split-multi-head-attention"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">分割的多头注意力机制</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#什么是注意力机制" class="table-of-contents__link toc-highlight">什么是注意力机制</a><ul><li><a href="#人类的图像注意力" class="table-of-contents__link toc-highlight">人类的图像注意力</a></li><li><a href="#人类的文本注意力" class="table-of-contents__link toc-highlight">人类的文本注意力</a></li></ul></li><li><a href="#transformer-的注意力机制" class="table-of-contents__link toc-highlight">Transformer 的注意力机制</a></li><li><a href="#理解注意力机制的-q--k--v" class="table-of-contents__link toc-highlight">理解注意力机制的 Q / K / V</a><ul><li><a href="#理解-qkt" class="table-of-contents__link toc-highlight">理解 QK^T</a></li></ul></li><li><a href="#自注意力机制" class="table-of-contents__link toc-highlight">自注意力机制</a><ul><li><a href="#自注意力中的-mask" class="table-of-contents__link toc-highlight">自注意力中的 mask</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div 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+M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1828em"><span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.74em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">Q</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">T</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.93em"><span></span></span></span></span></span><span></span></span></span></span></span> 后，将右上部分 (不包含对角线) 设置成负无穷大或者一个非常大的负值 (如 1e-9)，这样在经过 SoftMax 之后，对应位置的 attention score 接近为 0。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/transformer/transformer-positional-encoding"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">位置编码</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-split-multi-head-attention"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">分割的多头注意力机制</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#什么是注意力机制" class="table-of-contents__link toc-highlight">什么是注意力机制</a><ul><li><a href="#人类的图像注意力" class="table-of-contents__link toc-highlight">人类的图像注意力</a></li><li><a href="#人类的文本注意力" class="table-of-contents__link toc-highlight">人类的文本注意力</a></li></ul></li><li><a href="#transformer-的注意力机制" class="table-of-contents__link toc-highlight">Transformer 的注意力机制</a></li><li><a href="#理解注意力机制的-q--k--v" class="table-of-contents__link toc-highlight">理解注意力机制的 Q / K / V</a><ul><li><a href="#理解-qkt" class="table-of-contents__link toc-highlight">理解 QK^T</a></li></ul></li><li><a href="#自注意力机制" class="table-of-contents__link toc-highlight">自注意力机制</a><ul><li><a href="#自注意力中的-mask" class="table-of-contents__link toc-highlight">自注意力中的 mask</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div 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 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="pytorch-代码实现">PyTorch 代码实现<a href="#pytorch-代码实现" class="hash-link" aria-label="PyTorch 代码实现的直接链接" title="PyTorch 代码实现的直接链接">​</a></h2>
-<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">#!/usr/bin/env python3</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token triple-quoted-string string" style="color:#e3116c">&quot;&quot;&quot;</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">Implementation of Transformer: Attention Is All You Need</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="display:inline-block;color:#e3116c"></span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">References:</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">    - [Paper arXiv: Attention Is All You Need](https://arxiv.org/abs/1706.03762)</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">    - [Blog Post: The Illustrated Transformer](http://jalammar.github.io/illustrated-transformer/)</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">    - [YouTube Video: The Illustrated Transformer](https://youtu.be/ISNdQcPhsts?si=VyFfVKoITGOV78OA)</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">&quot;&quot;&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> argparse</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> math</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> os</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> sys</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> torch</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">nn </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> nn</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">optim </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> optim</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> torchinfo </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> summary</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">PositionalEncoding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">PositionalEncoding</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        pe </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">zeros</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        position </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">arange</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> max_seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dtype</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">float</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        div_term </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">exp</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">arange</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">float</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">*</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">math</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">log</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">10000.0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">/</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        pe</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">:</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">sin</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">position </span><span class="token operator" style="color:#393A34">*</span><span class="token plain"> div_term</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        pe</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">:</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">cos</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">position </span><span class="token operator" style="color:#393A34">*</span><span class="token plain"> div_term</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">register_buffer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;pe&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> pe</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pe</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">size</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Ensure that the model dimension (d_model) is divisible by the number of heads</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">assert</span><span class="token plain"> d_model </span><span class="token operator" style="color:#393A34">%</span><span class="token plain"> num_heads </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;d_model must be divisible by num_heads&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Initialize dimensions</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_model </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> d_model  </span><span class="token comment" style="color:#999988;font-style:italic"># Model&#x27;s dimension</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">num_heads </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> num_heads  </span><span class="token comment" style="color:#999988;font-style:italic"># Number of attention heads</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_k </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            d_model </span><span class="token operator" style="color:#393A34">//</span><span class="token plain"> num_heads</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Dimension of each head&#x27;s key, query, and value</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Linear layers for transforming inputs</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_q </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Query transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_k </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Key transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Value transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_o </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Output transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">scaled_dot_product_attention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> Q</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> K</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> V</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Calculate attention scores</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_scores </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">matmul</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Q</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> K</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transpose</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">/</span><span class="token plain"> math</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">sqrt</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_k</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Apply mask if provided (useful for preventing attention to certain parts like padding)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> mask </span><span class="token keyword" style="color:#00009f">is</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">not</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            attn_scores </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> attn_scores</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">masked_fill</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">mask </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1e9</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Softmax is applied to obtain attention probabilities</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_probs </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">softmax</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_scores</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dim</span><span class="token operator" style="color:#393A34">=</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Multiply by values to obtain the final output</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">matmul</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_probs</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> V</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> output</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">split_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Reshape the input to have num_heads for multi-head attention</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        batch_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">size</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">batch_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_k</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transpose</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">combine_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Combine the multiple heads back to original shape</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        batch_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> _</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_k </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">size</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transpose</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">batch_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> Q</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> K</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> V</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Apply linear transformations and split heads</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        Q </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">split_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_q</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Q</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        K </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">split_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_k</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">K</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        V </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">split_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_v</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">V</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Perform scaled dot-product attention</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">scaled_dot_product_attention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Q</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> K</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> V</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Combine heads and apply output transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_o</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">combine_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> output</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">EncoderLayer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">EncoderLayer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">self_attn </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feed_forward </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> PositionWiseFeedForward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm1 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm2 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">self_attn</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm1</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        ff_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feed_forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm2</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">ff_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">DecoderLayer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">DecoderLayer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">self_attn </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">cross_attn </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feed_forward </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> PositionWiseFeedForward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm1 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm2 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm3 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">self_attn</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm1</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">cross_attn</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm2</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        ff_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feed_forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm3</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">ff_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">PositionWiseFeedForward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">PositionWiseFeedForward</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc1 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc2 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">relu </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ReLU</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc2</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">relu</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc1</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">Transformer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        num_layers</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        max_seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        dropout</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Transformer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">encoder_embedding </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Embedding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">decoder_embedding </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Embedding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">positional_encoding </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> PositionalEncoding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">encoder_layers </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ModuleList</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">EncoderLayer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> _ </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">num_layers</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">decoder_layers </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ModuleList</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">DecoderLayer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> _ </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">num_layers</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">generate_mask</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        src_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src </span><span class="token operator" style="color:#393A34">!=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        tgt_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">tgt </span><span class="token operator" style="color:#393A34">!=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        seq_length </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> tgt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">size</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        nopeak_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">triu</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ones</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> diagonal</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">bool</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        tgt_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> tgt_mask </span><span class="token operator" style="color:#393A34">&amp;</span><span class="token plain"> nopeak_mask</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        src_mask</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">generate_mask</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        src_embedded </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">positional_encoding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">encoder_embedding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        tgt_embedded </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">positional_encoding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">decoder_embedding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">tgt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        enc_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> src_embedded</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> enc_layer </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">encoder_layers</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            enc_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> enc_layer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        dec_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> tgt_embedded</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> dec_layer </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">decoder_layers</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            dec_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> dec_layer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dec_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dec_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> output</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">args</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    transformer </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> Transformer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">num_layers</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic"># Generate random sample data</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    src_data </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">randint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">64</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># (batch_size, seq_length)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    tgt_data </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">randint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">64</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># (batch_size, seq_length)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">summary</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">transformer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> input_data</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">src_data</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_data</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> device</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;cpu&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    criterion </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">CrossEntropyLoss</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">ignore_index</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    optimizer </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> optim</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Adam</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        transformer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">parameters</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> lr</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.0001</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> betas</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0.9</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.98</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> eps</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1e-9</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    transformer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">train</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> epoch </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">10</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        optimizer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">zero_grad</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> transformer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src_data</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">:</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        loss </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> criterion</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            output</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            tgt_data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        loss</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">backward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        optimizer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">step</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string-interpolation string" style="color:#e3116c">f&quot;Epoch: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">epoch</span><span class="token string-interpolation interpolation operator" style="color:#393A34">+</span><span class="token string-interpolation interpolation number" style="color:#36acaa">1</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">, Loss: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">loss</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">item</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    transformer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">eval</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic"># Generate random sample validation data</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    val_src_data </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">randint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">64</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># (batch_size, seq_length)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    val_tgt_data </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">randint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">64</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># (batch_size, seq_length)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">with</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">no_grad</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        val_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> transformer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">val_src_data</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> val_tgt_data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">:</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        val_loss </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> criterion</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            val_output</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            val_tgt_data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string-interpolation string" style="color:#e3116c">f&quot;Validation Loss: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">val_loss</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">item</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> __name__ </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;__main__&quot;</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> argparse</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ArgumentParser</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        formatter_class</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">argparse</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ArgumentDefaultsHelpFormatter</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--src_vocab_size&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">5000</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;source vocabulary size&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--tgt_vocab_size&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">5000</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;target vocabulary size&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--d_model&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">512</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;dimensionality of model&#x27;s input and output&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--num_heads&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">8</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;number of attention heads in multi-head attention&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--num_layers&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">6</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;number of layers for both the encoder and the decoder&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--d_ff&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">2048</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;dimensionality of the inner layer in the feed-forward network&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--max_seq_length&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">100</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;the maximum length of the sequence&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--dropout&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">float</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;dropout rate for regularization&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">try</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">parse_args</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">args</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">except</span><span class="token plain"> KeyboardInterrupt</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Interrupted&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">try</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            sys</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">except</span><span class="token plain"> SystemExit</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            os</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/transformer/transformer-split-multi-head-attention"><div 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+<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-python codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">#!/usr/bin/env python3</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token triple-quoted-string string" style="color:#e3116c">&quot;&quot;&quot;</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">Implementation of Transformer: Attention Is All You Need</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="display:inline-block;color:#e3116c"></span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">References:</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">    - [Paper arXiv: Attention Is All You Need](https://arxiv.org/abs/1706.03762)</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">    - [Blog Post: The Illustrated Transformer](http://jalammar.github.io/illustrated-transformer/)</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">    - [YouTube Video: The Illustrated Transformer](https://youtu.be/ISNdQcPhsts?si=VyFfVKoITGOV78OA)</span><br></span><span class="token-line" style="color:#393A34"><span class="token triple-quoted-string string" style="color:#e3116c">&quot;&quot;&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> argparse</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> math</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> os</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> sys</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> torch</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">nn </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> nn</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">optim </span><span class="token keyword" style="color:#00009f">as</span><span class="token plain"> optim</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">from</span><span class="token plain"> torchinfo </span><span class="token keyword" style="color:#00009f">import</span><span class="token plain"> summary</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">PositionalEncoding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">PositionalEncoding</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        pe </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">zeros</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        position </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">arange</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> max_seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dtype</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">float</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        div_term </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">exp</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">arange</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">float</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">*</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">math</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">log</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">10000.0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">/</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        pe</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">:</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">sin</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">position </span><span class="token operator" style="color:#393A34">*</span><span class="token plain"> div_term</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        pe</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">:</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">cos</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">position </span><span class="token operator" style="color:#393A34">*</span><span class="token plain"> div_term</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">register_buffer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;pe&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> pe</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">pe</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">size</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Ensure that the model dimension (d_model) is divisible by the number of heads</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">assert</span><span class="token plain"> d_model </span><span class="token operator" style="color:#393A34">%</span><span class="token plain"> num_heads </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;d_model must be divisible by num_heads&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Initialize dimensions</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_model </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> d_model  </span><span class="token comment" style="color:#999988;font-style:italic"># Model&#x27;s dimension</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">num_heads </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> num_heads  </span><span class="token comment" style="color:#999988;font-style:italic"># Number of attention heads</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_k </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            d_model </span><span class="token operator" style="color:#393A34">//</span><span class="token plain"> num_heads</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Dimension of each head&#x27;s key, query, and value</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Linear layers for transforming inputs</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_q </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Query transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_k </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Key transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_v </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Value transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_o </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># Output transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">scaled_dot_product_attention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> Q</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> K</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> V</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Calculate attention scores</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_scores </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">matmul</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Q</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> K</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transpose</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">/</span><span class="token plain"> math</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">sqrt</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_k</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Apply mask if provided (useful for preventing attention to certain parts like padding)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> mask </span><span class="token keyword" style="color:#00009f">is</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">not</span><span class="token plain"> </span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            attn_scores </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> attn_scores</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">masked_fill</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">mask </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1e9</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Softmax is applied to obtain attention probabilities</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_probs </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">softmax</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_scores</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dim</span><span class="token operator" style="color:#393A34">=</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Multiply by values to obtain the final output</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">matmul</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_probs</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> V</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> output</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">split_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Reshape the input to have num_heads for multi-head attention</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        batch_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">size</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">batch_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_k</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transpose</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">combine_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Combine the multiple heads back to original shape</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        batch_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> _</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_k </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">size</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">transpose</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">batch_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> Q</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> K</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> V</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token operator" style="color:#393A34">=</span><span class="token boolean" style="color:#36acaa">None</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Apply linear transformations and split heads</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        Q </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">split_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_q</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Q</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        K </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">split_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_k</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">K</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        V </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">split_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_v</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">V</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Perform scaled dot-product attention</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">scaled_dot_product_attention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Q</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> K</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> V</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token comment" style="color:#999988;font-style:italic"># Combine heads and apply output transformation</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">W_o</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">combine_heads</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> output</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">EncoderLayer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">EncoderLayer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">self_attn </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feed_forward </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> PositionWiseFeedForward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm1 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm2 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">self_attn</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm1</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        ff_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feed_forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm2</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">ff_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">DecoderLayer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">DecoderLayer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">self_attn </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">cross_attn </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> MultiHeadAttention</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feed_forward </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> PositionWiseFeedForward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm1 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm2 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm3 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">LayerNorm</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">self_attn</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm1</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        attn_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">cross_attn</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm2</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">attn_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        ff_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">feed_forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        x </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">norm3</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">ff_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> x</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">PositionWiseFeedForward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">PositionWiseFeedForward</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc1 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc2 </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">relu </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ReLU</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc2</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">relu</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc1</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">class</span><span class="token plain"> </span><span class="token class-name">Transformer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Module</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        num_layers</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        max_seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        dropout</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">super</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Transformer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">__init__</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">encoder_embedding </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Embedding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">decoder_embedding </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Embedding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_model</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">positional_encoding </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> PositionalEncoding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">encoder_layers </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ModuleList</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">EncoderLayer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> _ </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">num_layers</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">decoder_layers </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ModuleList</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">DecoderLayer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> _ </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">num_layers</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Linear</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">generate_mask</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        src_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src </span><span class="token operator" style="color:#393A34">!=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        tgt_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">tgt </span><span class="token operator" style="color:#393A34">!=</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">unsqueeze</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">3</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        seq_length </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> tgt</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">size</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        nopeak_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">triu</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ones</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> diagonal</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">bool</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        tgt_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> tgt_mask </span><span class="token operator" style="color:#393A34">&amp;</span><span class="token plain"> nopeak_mask</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">forward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        src_mask</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">generate_mask</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        src_embedded </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">positional_encoding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">encoder_embedding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        tgt_embedded </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">positional_encoding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">decoder_embedding</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">tgt</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        enc_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> src_embedded</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> enc_layer </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">encoder_layers</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            enc_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> enc_layer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        dec_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> tgt_embedded</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> dec_layer </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">decoder_layers</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            dec_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> dec_layer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dec_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> enc_output</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> src_mask</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_mask</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> self</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">fc</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">dec_output</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">return</span><span class="token plain"> output</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">def</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">args</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    transformer </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> Transformer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_model</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">num_heads</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">num_layers</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">d_ff</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">dropout</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic"># Generate random sample data</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    src_data </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">randint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">64</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># (batch_size, seq_length)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    tgt_data </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">randint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">64</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># (batch_size, seq_length)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">summary</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">transformer</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> input_data</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">src_data</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_data</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> device</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;cpu&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    criterion </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> nn</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">CrossEntropyLoss</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">ignore_index</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    optimizer </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> optim</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">Adam</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        transformer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">parameters</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> lr</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.0001</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> betas</span><span class="token operator" style="color:#393A34">=</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0.9</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0.98</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> eps</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">1e-9</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    transformer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">train</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> epoch </span><span class="token keyword" style="color:#00009f">in</span><span class="token plain"> </span><span class="token builtin">range</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">10</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        optimizer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">zero_grad</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> transformer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">src_data</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> tgt_data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">:</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        loss </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> criterion</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            output</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            tgt_data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        loss</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">backward</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        optimizer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">step</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string-interpolation string" style="color:#e3116c">f&quot;Epoch: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">epoch</span><span class="token string-interpolation interpolation operator" style="color:#393A34">+</span><span class="token string-interpolation interpolation number" style="color:#36acaa">1</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">, Loss: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">loss</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">item</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    transformer</span><span class="token punctuation" style="color:#393A34">.</span><span class="token builtin">eval</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token comment" style="color:#999988;font-style:italic"># Generate random sample validation data</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    val_src_data </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">randint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">src_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">64</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># (batch_size, seq_length)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    val_tgt_data </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">randint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">64</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">max_seq_length</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">  </span><span class="token comment" style="color:#999988;font-style:italic"># (batch_size, seq_length)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">with</span><span class="token plain"> torch</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">no_grad</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        val_output </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> transformer</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">val_src_data</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> val_tgt_data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">:</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        val_loss </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> criterion</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            val_output</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> args</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">tgt_vocab_size</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            val_tgt_data</span><span class="token punctuation" style="color:#393A34">[</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">:</span><span class="token punctuation" style="color:#393A34">]</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">contiguous</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">view</span><span class="token punctuation" style="color:#393A34">(</span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string-interpolation string" style="color:#e3116c">f&quot;Validation Loss: </span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">{</span><span class="token string-interpolation interpolation">val_loss</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">.</span><span class="token string-interpolation interpolation">item</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">(</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">)</span><span class="token string-interpolation interpolation punctuation" style="color:#393A34">}</span><span class="token string-interpolation string" style="color:#e3116c">&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">if</span><span class="token plain"> __name__ </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;__main__&quot;</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> argparse</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ArgumentParser</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        formatter_class</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">argparse</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">ArgumentDefaultsHelpFormatter</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--src_vocab_size&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">5000</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;source vocabulary size&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--tgt_vocab_size&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">5000</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;target vocabulary size&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--d_model&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">512</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;dimensionality of model&#x27;s input and output&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--num_heads&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">8</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;number of attention heads in multi-head attention&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--num_layers&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">6</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;number of layers for both the encoder and the decoder&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--d_ff&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">2048</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;dimensionality of the inner layer in the feed-forward network&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--max_seq_length&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">int</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">100</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;the maximum length of the sequence&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">add_argument</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token string" style="color:#e3116c">&quot;--dropout&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">type</span><span class="token operator" style="color:#393A34">=</span><span class="token builtin">float</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        default</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">0.1</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token builtin">help</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;dropout rate for regularization&quot;</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">try</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        args </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> parser</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">parse_args</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        main</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">args</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">    </span><span class="token keyword" style="color:#00009f">except</span><span class="token plain"> KeyboardInterrupt</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Interrupted&quot;</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">try</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            sys</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">        </span><span class="token keyword" style="color:#00009f">except</span><span class="token plain"> SystemExit</span><span class="token punctuation" style="color:#393A34">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">            os</span><span class="token punctuation" style="color:#393A34">.</span><span class="token plain">_exit</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/transformer/transformer-split-multi-head-attention"><div 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itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">编码器和解码器</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>编码器和解码器</h1></header>
@@ -39,6 +39,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="理解编码器和解
 <li>由于几万个单词，有很多维度，人工编码不可行。</li>
 <li>固定的编码不能很好的表征其含义，在不同语境下，相同的单词可能有不同的意义。</li>
 </ol>
-<p>Transformer 的解码器和编码器，在翻译任务中，可以理解为 token 的特征提取器。解码器和编码器会自动提取源语言和目标语言中的 token 的特征。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/transformer/transformer-architecture"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Transformer 架构</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-positional-encoding"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">位置编码</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#理解编码器和解码器" class="table-of-contents__link toc-highlight">理解编码器和解码器</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>Transformer 的解码器和编码器，在翻译任务中，可以理解为 token 的特征提取器。解码器和编码器会自动提取源语言和目标语言中的 token 的特征。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/transformer/transformer-architecture"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Transformer 架构</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-positional-encoding"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">位置编码</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#理解编码器和解码器" class="table-of-contents__link toc-highlight">理解编码器和解码器</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Transformer 概览</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>Transformer 概览</h1></header>
@@ -33,6 +33,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="自然语言处理">自
 <p>我们先将整个模型视为黑盒。</p>
 <p>在机器翻译中，接收一种语言的句子作为输入，然后将其翻译成其他语言输出。</p>
 <p><img decoding="async" loading="lazy" src="/assets/images/transformer_highlevel_blackbox-8fdbf797aaae35f1679e07c451513eda.png" width="1127" height="294" class="img_ev3q"></p>
-<p>Transformer 设计之初就是为了解决 NLP 中的翻译问题。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">核技巧和非线性 SVM</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-architecture"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Transformer 架构</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#自然语言处理" class="table-of-contents__link toc-highlight">自然语言处理</a></li><li><a href="#transformer-概览-1" class="table-of-contents__link toc-highlight">Transformer 概览</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>Transformer 设计之初就是为了解决 NLP 中的翻译问题。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">核技巧和非线性 SVM</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-architecture"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Transformer 架构</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#自然语言处理" class="table-of-contents__link toc-highlight">自然语言处理</a></li><li><a href="#transformer-概览-1" class="table-of-contents__link toc-highlight">Transformer 概览</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">位置编码</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>位置编码</h1></header>
@@ -41,6 +41,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="transformer-的位置
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="transformer-编码的可视化">Transformer 编码的可视化<a href="#transformer-编码的可视化" class="hash-link" aria-label="Transformer 编码的可视化的直接链接" title="Transformer 编码的可视化的直接链接">​</a></h3>
 <p>下图为对 20 个位置编码为的示例，其中每个位置编码为 512 维的向量。左半部分是维度为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">2i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em"></span><span class="mord">2</span><span class="mord mathnormal">i</span></span></span></span> 的正弦编码，右半部分是是维度为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">2i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em"></span><span class="mord">2</span><span class="mord mathnormal">i</span></span></span></span> 的余弦编码。</p>
 <p><img decoding="async" loading="lazy" src="/assets/images/transformer_positional_encoding_example-4baaf26e596218d0cd7bf667b8026048.png" width="1238" height="907" class="img_ev3q"></p>
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+<p>将它们交叉连接，就是 Transformer 使用的位置编码向量。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/machine-learning/transformer/transformer-encoders-decoders"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">编码器和解码器</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/machine-learning/transformer/transformer-attention"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">注意力机制</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#为什么需要位置编码" class="table-of-contents__link toc-highlight">为什么需要位置编码</a></li><li><a href="#怎么实现位置编码" class="table-of-contents__link toc-highlight">怎么实现位置编码</a></li><li><a href="#transformer-的位置编码" class="table-of-contents__link toc-highlight">Transformer 的位置编码</a><ul><li><a href="#transformer-编码的可视化" class="table-of-contents__link toc-highlight">Transformer 编码的可视化</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">分割的多头注意力机制</span><meta itemprop="position" content="2"></li></ul></nav><div class="theme-doc-markdown markdown"><header><h1>分割的多头注意力机制</h1></header>
@@ -17,6 +17,6 @@
 <p>如下图所示，原始论文中使用了 8 个注意力头，每个注意力头都有自己的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em"></span><span class="mord mathnormal">Q</span></span></span></span> / <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>K</mi></mrow><annotation encoding="application/x-tex">K</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07153em">K</span></span></span></span> / <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.22222em">V</span></span></span></span> 矩阵。</p>
 <p>这可以理解为有 8 个不同的特征子空间，每个子空间可以提取不同的特征表示，最终嵌入 (投影) 到同一个向量中。</p>
 <p>对于这个合成的嵌入向量再做一次矩阵变换，得到最终的注意力矩阵 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Z</mi></mrow><annotation encoding="application/x-tex">Z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07153em">Z</span></span></span></span>。</p>
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class="breadcrumbs__link">Transformer</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Transformer 的变种</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>Transformer 的变种</h1></header>
@@ -36,6 +36,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="卷积池化减半">卷
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="单次解码器设计">单次解码器设计<a href="#单次解码器设计" class="hash-link" aria-label="单次解码器设计的直接链接" title="单次解码器设计的直接链接">​</a></h3>
 <p>经典的 Transformer 用于 NLP，很多时候每个输出结果和之前的单词具有语义上的紧密联系，因此按照一步一步的输出比较适合。</p>
 <p>在 Informer 中，由于预测未来某一些时刻的指标，这些指标之前没有类似于 NLP 中前后强关联的语义关系，因此可以采用单次输出所需要的序列，极大的提高了推理速度。</p>
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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">调试器</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">回溯和反汇编</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>回溯和反汇编</h1></header>
@@ -29,6 +29,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="从给定地址反汇
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="同时显示当前函数的源代码和反汇编代码">同时显示当前函数的源代码和反汇编代码<a href="#同时显示当前函数的源代码和反汇编代码" class="hash-link" aria-label="同时显示当前函数的源代码和反汇编代码的直接链接" title="同时显示当前函数的源代码和反汇编代码的直接链接">​</a></h3>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"></code></pre></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> disassemble </span><span class="token parameter variable" style="color:#36acaa">--frame</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--mixed</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> di </span><span class="token parameter variable" style="color:#36acaa">-f</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-m</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="反汇编当前函数">反汇编当前函数<a href="#反汇编当前函数" class="hash-link" aria-label="反汇编当前函数的直接链接" title="反汇编当前函数的直接链接">​</a></h3>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"></code></pre></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> disassemble </span><span class="token parameter variable" style="color:#36acaa">--frame</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--bytes</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> di </span><span class="token parameter variable" style="color:#36acaa">-f</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-b</span><br></span></code></pre><div 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class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">检查变量和寄存器</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#回溯-backtrace" class="table-of-contents__link toc-highlight">回溯 (backtrace)</a><ul><li><a href="#回溯当前线程调用栈" class="table-of-contents__link toc-highlight">回溯当前线程调用栈</a></li><li><a href="#回溯所有线程调用栈" class="table-of-contents__link toc-highlight">回溯所有线程调用栈</a></li><li><a href="#回溯当前线程调用栈的-backtrace-的前几帧" class="table-of-contents__link toc-highlight">回溯当前线程调用栈的 backtrace 的前几帧</a></li></ul></li><li><a href="#反汇编-disassemble" class="table-of-contents__link toc-highlight">反汇编 (disassemble)</a><ul><li><a href="#反汇编当前栈帧函数" class="table-of-contents__link toc-highlight">反汇编当前栈帧函数</a></li><li><a href="#反汇编任何名为-main-的函数" class="table-of-contents__link toc-highlight">反汇编任何名为 main 的函数</a></li><li><a href="#反汇编某个地址范围" class="table-of-contents__link toc-highlight">反汇编某个地址范围</a></li><li><a href="#从给定地址反汇编若干条指令" class="table-of-contents__link toc-highlight">从给定地址反汇编若干条指令</a></li><li><a href="#同时显示当前函数的源代码和反汇编代码" class="table-of-contents__link toc-highlight">同时显示当前函数的源代码和反汇编代码</a></li><li><a href="#反汇编当前函数" class="table-of-contents__link toc-highlight">反汇编当前函数</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" 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+<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"></code></pre></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> disassemble </span><span class="token parameter variable" style="color:#36acaa">--frame</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--bytes</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> di </span><span class="token parameter variable" style="color:#36acaa">-f</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-b</span><br></span></code></pre><div 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@@ -55,6 +55,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="设置监控的条件">
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="删除监控点">删除监控点<a href="#删除监控点" class="hash-link" aria-label="删除监控点的直接链接" title="删除监控点的直接链接">​</a></h3>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> delete </span><span class="token number" style="color:#36acaa">1</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> watchpoint delete </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">watch</span><span class="token plain"> del </span><span class="token number" style="color:#36acaa">1</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="列出所有的监控点">列出所有的监控点<a href="#列出所有的监控点" class="hash-link" aria-label="列出所有的监控点的直接链接" title="列出所有的监控点的直接链接">​</a></h3>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> info </span><span class="token builtin class-name">break</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> watchpoint list</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">watch</span><span class="token plain"> l</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/start-and-attach"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">启动调试</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/jump-in-debuggers"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">在调试器内跳转</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#断点-breakpoint" class="table-of-contents__link toc-highlight">断点 (breakpoint)</a><ul><li><a href="#根据函数名或者方法名设置断点" class="table-of-contents__link toc-highlight">根据函数名或者方法名设置断点</a></li><li><a href="#根据源文件行号设置断点" class="table-of-contents__link toc-highlight">根据源文件行号设置断点</a></li><li><a href="#设置条件断点" class="table-of-contents__link toc-highlight">设置条件断点</a></li><li><a href="#删除某个断点" class="table-of-contents__link toc-highlight">删除某个断点</a></li><li><a href="#禁用启用断点" class="table-of-contents__link toc-highlight">禁用/启用断点</a></li><li><a href="#通过正则表达式设置断点" class="table-of-contents__link toc-highlight">通过正则表达式设置断点</a></li><li><a href="#列出所有断点" class="table-of-contents__link toc-highlight">列出所有断点</a></li></ul></li><li><a href="#监控点-watchpoint" class="table-of-contents__link toc-highlight">监控点 (watchpoint)</a><ul><li><a href="#监控进程中某个变量的值" class="table-of-contents__link toc-highlight">监控进程中某个变量的值</a></li><li><a href="#监控进程中的某块内存" class="table-of-contents__link toc-highlight">监控进程中的某块内存</a></li><li><a href="#设置监控的条件" class="table-of-contents__link toc-highlight">设置监控的条件</a></li><li><a href="#删除监控点" class="table-of-contents__link toc-highlight">删除监控点</a></li><li><a href="#列出所有的监控点" class="table-of-contents__link toc-highlight">列出所有的监控点</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 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+<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> info </span><span class="token builtin class-name">break</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> watchpoint list</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">watch</span><span class="token plain"> l</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/start-and-attach"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">启动调试</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/jump-in-debuggers"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">在调试器内跳转</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#断点-breakpoint" class="table-of-contents__link toc-highlight">断点 (breakpoint)</a><ul><li><a href="#根据函数名或者方法名设置断点" class="table-of-contents__link toc-highlight">根据函数名或者方法名设置断点</a></li><li><a href="#根据源文件行号设置断点" class="table-of-contents__link toc-highlight">根据源文件行号设置断点</a></li><li><a href="#设置条件断点" class="table-of-contents__link toc-highlight">设置条件断点</a></li><li><a href="#删除某个断点" class="table-of-contents__link toc-highlight">删除某个断点</a></li><li><a href="#禁用启用断点" class="table-of-contents__link toc-highlight">禁用/启用断点</a></li><li><a href="#通过正则表达式设置断点" class="table-of-contents__link toc-highlight">通过正则表达式设置断点</a></li><li><a href="#列出所有断点" class="table-of-contents__link toc-highlight">列出所有断点</a></li></ul></li><li><a href="#监控点-watchpoint" class="table-of-contents__link toc-highlight">监控点 (watchpoint)</a><ul><li><a href="#监控进程中某个变量的值" class="table-of-contents__link toc-highlight">监控进程中某个变量的值</a></li><li><a href="#监控进程中的某块内存" class="table-of-contents__link toc-highlight">监控进程中的某块内存</a></li><li><a href="#设置监控的条件" class="table-of-contents__link toc-highlight">设置监控的条件</a></li><li><a href="#删除监控点" class="table-of-contents__link toc-highlight">删除监控点</a></li><li><a href="#列出所有的监控点" class="table-of-contents__link toc-highlight">列出所有的监控点</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 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4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -3,10 +3,10 @@
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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">调试器</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">检查内存地址的数据</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>检查内存地址的数据</h1></header>
@@ -40,6 +40,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="读取若干十六进
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="从内存指定地址读取若干字节并保存到本地文件">从内存指定地址读取若干字节，并保存到本地文件<a href="#从内存指定地址读取若干字节并保存到本地文件" class="hash-link" aria-label="从内存指定地址读取若干字节，并保存到本地文件的直接链接" title="从内存指定地址读取若干字节，并保存到本地文件的直接链接">​</a></h3>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">set</span><span class="token plain"> logging on</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">set</span><span class="token plain"> logging </span><span class="token function" style="color:#d73a49">file</span><span class="token plain"> /tmp/mem.txt</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> x/512bx 0xbffff3c0</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">set</span><span class="token plain"> logging off</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> memory </span><span class="token builtin class-name">read</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--outfile</span><span class="token plain"> /tmp/mem.txt </span><span class="token parameter variable" style="color:#36acaa">--count</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">512</span><span class="token plain"> 0xbffff3c0</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> me r -o/tmp/mem.txt </span><span class="token parameter variable" style="color:#36acaa">-c512</span><span class="token plain"> 0xbffff3c0</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> x/512bx -o/tmp/mem.txt 0xbffff3c0</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="从内存指定地址范围读取字节并保存到本地文件">从内存指定地址范围读取字节，并保存到本地文件<a href="#从内存指定地址范围读取字节并保存到本地文件" class="hash-link" aria-label="从内存指定地址范围读取字节，并保存到本地文件的直接链接" title="从内存指定地址范围读取字节，并保存到本地文件的直接链接">​</a></h3>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> dump memory /tmp/mem.bin 0x1000 0x2000</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> memory </span><span class="token builtin class-name">read</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--outfile</span><span class="token plain"> /tmp/mem.bin </span><span class="token parameter variable" style="color:#36acaa">--binary</span><span class="token plain"> 0x1000 0x2000</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> me r </span><span class="token parameter variable" style="color:#36acaa">-o</span><span class="token plain"> /tmp/mem.bin </span><span class="token parameter variable" style="color:#36acaa">-b</span><span class="token plain"> 0x1000 0x2000</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/check-variables-and-registers"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">检查变量和寄存器</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/check-executable-and-libraries"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">可执行文件和共享库信息查询</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#读取内存" class="table-of-contents__link toc-highlight">读取内存</a></li><li><a href="#读取若干十六进制的内存" class="table-of-contents__link toc-highlight">读取若干十六进制的内存</a></li><li><a href="#从内存指定地址读取若干字节并保存到本地文件" class="table-of-contents__link toc-highlight">从内存指定地址读取若干字节，并保存到本地文件</a></li><li><a href="#从内存指定地址范围读取字节并保存到本地文件" class="table-of-contents__link toc-highlight">从内存指定地址范围读取字节，并保存到本地文件</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row 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+<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> dump memory /tmp/mem.bin 0x1000 0x2000</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> memory </span><span class="token builtin class-name">read</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--outfile</span><span class="token plain"> /tmp/mem.bin </span><span class="token parameter variable" style="color:#36acaa">--binary</span><span class="token plain"> 0x1000 0x2000</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> me r </span><span class="token parameter variable" style="color:#36acaa">-o</span><span class="token plain"> /tmp/mem.bin </span><span class="token parameter variable" style="color:#36acaa">-b</span><span class="token plain"> 0x1000 0x2000</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/check-variables-and-registers"><div class="pagination-nav__sublabel">上一页</div><div 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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">调试器</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">可执行文件和共享库信息查询</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>可执行文件和共享库信息查询</h1></header>
@@ -21,6 +21,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="查找完整的源代
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="仅在-aout-中查找地址信息">仅在 <code>a.out</code> 中查找地址信息<a href="#仅在-aout-中查找地址信息" class="hash-link" aria-label="仅在-aout-中查找地址信息的直接链接" title="仅在-aout-中查找地址信息的直接链接">​</a></h3>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"></code></pre></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> image lookup </span><span class="token parameter variable" style="color:#36acaa">--address</span><span class="token plain"> 0x1ec4 a.out</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> im loo </span><span class="token parameter variable" style="color:#36acaa">-a</span><span class="token plain"> 0x1ec4 a.out</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="按名称查找类型-point-的信息">按名称查找类型 <code>Point</code> 的信息<a href="#按名称查找类型-point-的信息" class="hash-link" aria-label="按名称查找类型-point-的信息的直接链接" title="按名称查找类型-point-的信息的直接链接">​</a></h3>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> ptype Point</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> image lookup </span><span class="token parameter variable" style="color:#36acaa">--type</span><span class="token plain"> Point</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> im loo </span><span class="token parameter variable" style="color:#36acaa">-t</span><span class="token plain"> Point</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/check-data-in-memory-address"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">检查内存地址的数据</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/image-dump"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">dump 信息</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul 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+<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> ptype Point</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> image lookup </span><span class="token parameter variable" style="color:#36acaa">--type</span><span class="token plain"> Point</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> im loo </span><span class="token parameter variable" style="color:#36acaa">-t</span><span class="token plain"> Point</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/check-data-in-memory-address"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">检查内存地址的数据</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/image-dump"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">dump 信息</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul 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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">调试器</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">检查变量和寄存器</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>检查变量和寄存器</h1></header>
@@ -27,6 +27,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="显示当前线程中
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="显示当前线程中指定寄存器的值格式为二进制">显示当前线程中指定寄存器的值，格式为二进制<a href="#显示当前线程中指定寄存器的值格式为二进制" class="hash-link" aria-label="显示当前线程中指定寄存器的值，格式为二进制的直接链接" title="显示当前线程中指定寄存器的值，格式为二进制的直接链接">​</a></h3>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> p/t </span><span class="token variable" style="color:#36acaa">$rax</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> register </span><span class="token builtin class-name">read</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--format</span><span class="token plain"> binary rax</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> re r </span><span class="token parameter variable" style="color:#36acaa">-f</span><span class="token plain"> b rax</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># LLDB now supports the GDB shorthand format syntax but there can’t be space after the command</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> register read/t rax</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> p/t </span><span class="token variable" style="color:#36acaa">$rax</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="打印表达式结果的动态类型-c">打印表达式结果的动态类型 (C++)<a href="#打印表达式结果的动态类型-c" class="hash-link" aria-label="打印表达式结果的动态类型 (C++)的直接链接" title="打印表达式结果的动态类型 (C++)的直接链接">​</a></h2>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">set</span><span class="token plain"> print object </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> p someCPPObjectPtrOrReference</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Only works </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> C++ objects</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">expr</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-d</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> -- </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">SomeClass returnAnObject</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">expr</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-d</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> -- someCPPObjectPtrOrReference</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># or set dynamic type printing to be the default:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> settings </span><span class="token builtin class-name">set</span><span class="token plain"> target.prefer-dynamic run-target</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">回溯和反汇编</div></a><a 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toc-highlight">显示当前线程的所有寄存器</a></li><li><a href="#显示当前线程中指定寄存器的值" class="table-of-contents__link toc-highlight">显示当前线程中指定寄存器的值</a></li><li><a href="#显示当前线程中指定寄存器的值格式为二进制" class="table-of-contents__link toc-highlight">显示当前线程中指定寄存器的值，格式为二进制</a></li></ul></li><li><a href="#打印表达式结果的动态类型-c" class="table-of-contents__link toc-highlight">打印表达式结果的动态类型 (C++)</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 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+<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">set</span><span class="token plain"> print object </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> p someCPPObjectPtrOrReference</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">Only works </span><span class="token keyword" style="color:#00009f">for</span><span class="token plain"> C++ objects</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">expr</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-d</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> -- </span><span class="token punctuation" style="color:#393A34">[</span><span class="token plain">SomeClass returnAnObject</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">expr</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-d</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> -- someCPPObjectPtrOrReference</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># or set dynamic type printing to be the default:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> settings </span><span class="token builtin class-name">set</span><span class="token plain"> target.prefer-dynamic run-target</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">回溯和反汇编</div></a><a 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toc-highlight">显示当前线程的所有寄存器</a></li><li><a href="#显示当前线程中指定寄存器的值" class="table-of-contents__link toc-highlight">显示当前线程中指定寄存器的值</a></li><li><a href="#显示当前线程中指定寄存器的值格式为二进制" class="table-of-contents__link toc-highlight">显示当前线程中指定寄存器的值，格式为二进制</a></li></ul></li><li><a href="#打印表达式结果的动态类型-c" class="table-of-contents__link toc-highlight">打印表达式结果的动态类型 (C++)</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 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class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">调试器</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">GEF - GDB 增强工具</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>GEF - GDB 增强工具</h1></header>
@@ -34,6 +34,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="gef-命令">GEF 命令<
 <li><code>vmmap</code>：内存映射</li>
 <li><code>dereferece</code>：解引用</li>
 </ul>
-<p>更多的命令可以在 <a href="https://hugsy.github.io/gef/commands/aliases" target="_blank" rel="noopener noreferrer">GEF - Commands</a> 内查看。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/misc"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">其他项</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#安装" class="table-of-contents__link toc-highlight">安装</a></li><li><a href="#gef-命令" class="table-of-contents__link toc-highlight">GEF 命令</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>更多的命令可以在 <a href="https://hugsy.github.io/gef/commands/aliases" target="_blank" rel="noopener noreferrer">GEF - Commands</a> 内查看。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/misc"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">其他项</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#安装" class="table-of-contents__link toc-highlight">安装</a></li><li><a href="#gef-命令" class="table-of-contents__link toc-highlight">GEF 命令</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -17,6 +17,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="dump-可执行文件的
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="dump-可执行文件和所有共享库的-symtab-符号">dump 可执行文件和所有共享库的 symtab 符号<a href="#dump-可执行文件和所有共享库的-symtab-符号" class="hash-link" aria-label="dump 可执行文件和所有共享库的 symtab 符号的直接链接" title="dump 可执行文件和所有共享库的 symtab 符号的直接链接">​</a></h2>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"></code></pre></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> image dump symtab</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="dump-可执行文件和指定共享库的-symtab-符号">dump 可执行文件和指定共享库的 symtab 符号<a href="#dump-可执行文件和指定共享库的-symtab-符号" class="hash-link" aria-label="dump 可执行文件和指定共享库的 symtab 符号的直接链接" title="dump 可执行文件和指定共享库的 symtab 符号的直接链接">​</a></h2>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"></code></pre></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> image dump symtab a.out liba.so</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a 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+<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"></code></pre></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> image dump symtab a.out liba.so</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a 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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">调试器</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">在调试器内跳转</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>在调试器内跳转</h1></header>
@@ -51,6 +51,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="从栈帧返回可以
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="调用带有断点的函数并在断点处停止">调用带有断点的函数并在断点处停止<a href="#调用带有断点的函数并在断点处停止" class="hash-link" aria-label="调用带有断点的函数并在断点处停止的直接链接" title="调用带有断点的函数并在断点处停止的直接链接">​</a></h3>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">set</span><span class="token plain"> unwindonsignal </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> p function_with_a_breakpoint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">expr</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-i</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"> -- function_with_a_breakpoint</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="调用-crash-的函数并在-crash-时停止">调用 crash 的函数并在 crash 时停止<a href="#调用-crash-的函数并在-crash-时停止" class="hash-link" aria-label="调用 crash 的函数并在 crash 时停止的直接链接" title="调用 crash 的函数并在 crash 时停止的直接链接">​</a></h3>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">set</span><span class="token plain"> unwindonsignal </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> p function_which_crashes</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">expr</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-u</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"> -- function_which_crashes</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">断点和监控点</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">回溯和反汇编</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#设置断点和启动进程" class="table-of-contents__link toc-highlight">设置断点和启动进程</a></li><li><a href="#单步调试" class="table-of-contents__link toc-highlight">单步调试</a><ul><li><a href="#step-in-单步调试-源码级别" class="table-of-contents__link toc-highlight">step-in 单步调试 (源码级别)</a></li><li><a href="#step-over-单步调试-源码级别" class="table-of-contents__link toc-highlight">step-over 单步调试 (源码级别)</a></li><li><a href="#step-in-单步调试-汇编指令级别" class="table-of-contents__link toc-highlight">step-in 单步调试 (汇编指令级别)</a></li><li><a href="#step-over-单步调试-汇编指令级别" class="table-of-contents__link toc-highlight">step-over 单步调试 (汇编指令级别)</a></li><li><a href="#step-over-跳出栈帧" class="table-of-contents__link toc-highlight">step-over 跳出栈帧</a></li></ul></li><li><a href="#断点调试" class="table-of-contents__link toc-highlight">断点调试</a><ul><li><a href="#跳转到下一个断点" class="table-of-contents__link toc-highlight">跳转到下一个断点</a></li><li><a href="#运行到指定行数" class="table-of-contents__link toc-highlight">运行到指定行数</a></li></ul></li><li><a href="#线程切换" class="table-of-contents__link toc-highlight">线程切换</a><ul><li><a href="#列出程序中的线程" class="table-of-contents__link toc-highlight">列出程序中的线程</a></li><li><a href="#设置后续命令的默认线程" class="table-of-contents__link toc-highlight">设置后续命令的默认线程</a></li></ul></li><li><a href="#栈帧切换" class="table-of-contents__link toc-highlight">栈帧切换</a><ul><li><a href="#显示当前栈帧简略信息" class="table-of-contents__link toc-highlight">显示当前栈帧简略信息</a></li><li><a href="#显示当前栈帧源代码行" class="table-of-contents__link toc-highlight">显示当前栈帧源代码行</a></li><li><a href="#通过栈帧号选择栈帧" class="table-of-contents__link toc-highlight">通过栈帧号选择栈帧</a></li><li><a href="#选择调用当前栈帧的栈帧" class="table-of-contents__link toc-highlight">选择调用当前栈帧的栈帧</a></li><li><a href="#选择被当前栈帧调用的栈帧" class="table-of-contents__link toc-highlight">选择被当前栈帧调用的栈帧</a></li><li><a href="#使用栈帧相对偏移选择栈帧" class="table-of-contents__link toc-highlight">使用栈帧相对偏移选择栈帧</a></li><li><a href="#从栈帧返回可以带有返回值" class="table-of-contents__link toc-highlight">从栈帧返回，可以带有返回值</a></li><li><a href="#调用带有断点的函数并在断点处停止" class="table-of-contents__link toc-highlight">调用带有断点的函数并在断点处停止</a></li><li><a href="#调用-crash-的函数并在-crash-时停止" class="table-of-contents__link toc-highlight">调用 crash 的函数并在 crash 时停止</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col 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+<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">set</span><span class="token plain"> unwindonsignal </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> p function_which_crashes</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">expr</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-u</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token plain"> -- function_which_crashes</span><span class="token punctuation" style="color:#393A34">(</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">断点和监控点</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">回溯和反汇编</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#设置断点和启动进程" class="table-of-contents__link toc-highlight">设置断点和启动进程</a></li><li><a href="#单步调试" class="table-of-contents__link toc-highlight">单步调试</a><ul><li><a href="#step-in-单步调试-源码级别" class="table-of-contents__link toc-highlight">step-in 单步调试 (源码级别)</a></li><li><a href="#step-over-单步调试-源码级别" class="table-of-contents__link toc-highlight">step-over 单步调试 (源码级别)</a></li><li><a href="#step-in-单步调试-汇编指令级别" class="table-of-contents__link toc-highlight">step-in 单步调试 (汇编指令级别)</a></li><li><a href="#step-over-单步调试-汇编指令级别" class="table-of-contents__link toc-highlight">step-over 单步调试 (汇编指令级别)</a></li><li><a href="#step-over-跳出栈帧" class="table-of-contents__link toc-highlight">step-over 跳出栈帧</a></li></ul></li><li><a href="#断点调试" class="table-of-contents__link toc-highlight">断点调试</a><ul><li><a href="#跳转到下一个断点" class="table-of-contents__link toc-highlight">跳转到下一个断点</a></li><li><a href="#运行到指定行数" class="table-of-contents__link toc-highlight">运行到指定行数</a></li></ul></li><li><a href="#线程切换" class="table-of-contents__link toc-highlight">线程切换</a><ul><li><a href="#列出程序中的线程" class="table-of-contents__link toc-highlight">列出程序中的线程</a></li><li><a href="#设置后续命令的默认线程" class="table-of-contents__link toc-highlight">设置后续命令的默认线程</a></li></ul></li><li><a href="#栈帧切换" class="table-of-contents__link toc-highlight">栈帧切换</a><ul><li><a href="#显示当前栈帧简略信息" class="table-of-contents__link toc-highlight">显示当前栈帧简略信息</a></li><li><a href="#显示当前栈帧源代码行" class="table-of-contents__link toc-highlight">显示当前栈帧源代码行</a></li><li><a href="#通过栈帧号选择栈帧" class="table-of-contents__link toc-highlight">通过栈帧号选择栈帧</a></li><li><a href="#选择调用当前栈帧的栈帧" class="table-of-contents__link toc-highlight">选择调用当前栈帧的栈帧</a></li><li><a href="#选择被当前栈帧调用的栈帧" class="table-of-contents__link toc-highlight">选择被当前栈帧调用的栈帧</a></li><li><a href="#使用栈帧相对偏移选择栈帧" class="table-of-contents__link toc-highlight">使用栈帧相对偏移选择栈帧</a></li><li><a href="#从栈帧返回可以带有返回值" class="table-of-contents__link toc-highlight">从栈帧返回，可以带有返回值</a></li><li><a href="#调用带有断点的函数并在断点处停止" class="table-of-contents__link toc-highlight">调用带有断点的函数并在断点处停止</a></li><li><a href="#调用-crash-的函数并在-crash-时停止" class="table-of-contents__link toc-highlight">调用 crash 的函数并在 crash 时停止</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col 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@@ -26,6 +26,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="创建临时变量并
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="在当前帧中的计算表达式">在当前帧中的计算表达式<a href="#在当前帧中的计算表达式" class="hash-link" aria-label="在当前帧中的计算表达式的直接链接" title="在当前帧中的计算表达式的直接链接">​</a></h3>
 <div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> print </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">int</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">printf</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Print nine: %d.&quot;</span><span class="token plain">, </span><span class="token number" style="color:#36acaa">4</span><span class="token plain"> + </span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># or if you don’t want to see void returns:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> call </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">int</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">printf</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Print nine: %d.&quot;</span><span class="token plain">, </span><span class="token number" style="color:#36acaa">4</span><span class="token plain"> + </span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">expr</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">int</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">printf</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Print nine: %d.&quot;</span><span class="token plain">, </span><span class="token number" style="color:#36acaa">4</span><span class="token plain"> + </span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># or using the print alias:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> print </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">int</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">printf</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Print nine: %d.&quot;</span><span class="token plain">, </span><span class="token number" style="color:#36acaa">4</span><span class="token plain"> + </span><span class="token number" style="color:#36acaa">5</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div>
 <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="打印信息到屏幕">打印信息到屏幕<a href="#打印信息到屏幕" class="hash-link" aria-label="打印信息到屏幕的直接链接" title="打印信息到屏幕的直接链接">​</a></h3>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token builtin class-name">echo</span><span class="token plain"> Here is some text</span><span class="token punctuation" style="color:#393A34">\</span><span class="token plain">n</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> script print</span><span class="token punctuation" style="color:#393A34">(</span><span class="token string" style="color:#e3116c">&quot;Here is some text&quot;</span><span class="token punctuation" style="color:#393A34">)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/gdb-lldb/image-dump"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">dump 信息</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/gef"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">GEF - 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@@ -58,6 +58,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="attach-到已有进程"
 </li>
 </ol>
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="显示参数">显示参数<a href="#显示参数" class="hash-link" aria-label="显示参数的直接链接" title="显示参数的直接链接">​</a></h2>
-<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> show args</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Argument list to give program being debugged when it is started is </span><span class="token string" style="color:#e3116c">&quot;1 2 3&quot;</span><span class="token builtin class-name">.</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> settings show target.run-args</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">target.run-args </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">array of strings</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">: </span><span class="token string" style="color:#e3116c">&quot;1&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">: </span><span class="token string" style="color:#e3116c">&quot;2&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">: </span><span class="token string" style="color:#e3116c">&quot;3&quot;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/intro"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">现代 C++</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">断点和监控点</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#启动新的进程" class="table-of-contents__link toc-highlight">启动新的进程</a><ul><li><a href="#设置进程的运行参数" class="table-of-contents__link toc-highlight">设置进程的运行参数</a></li><li><a href="#环境变量设置" class="table-of-contents__link toc-highlight">环境变量设置</a></li></ul></li><li><a href="#attach-到已有进程" class="table-of-contents__link toc-highlight">attach 到已有进程</a></li><li><a href="#显示参数" class="table-of-contents__link toc-highlight">显示参数</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div 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+<div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">gdb</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">lldb</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">gdb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> show args</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">Argument list to give program being debugged when it is started is </span><span class="token string" style="color:#e3116c">&quot;1 2 3&quot;</span><span class="token builtin class-name">.</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">lldb</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> settings show target.run-args</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">target.run-args </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">array of strings</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">: </span><span class="token string" style="color:#e3116c">&quot;1&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">: </span><span class="token string" style="color:#e3116c">&quot;2&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">[</span><span class="token number" style="color:#36acaa">2</span><span class="token punctuation" style="color:#393A34">]</span><span class="token plain">: </span><span class="token string" style="color:#e3116c">&quot;3&quot;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-cpp/intro"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">现代 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@@ -143,6 +143,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="let-命令">let 命令<
 <p><code>let</code>命令用于将算术运算的结果，赋予一个变量。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">let</span><span class="token plain"> </span><span class="token assign-left variable" style="color:#36acaa">x</span><span class="token operator" style="color:#393A34">=</span><span class="token number" style="color:#36acaa">2</span><span class="token plain">+3</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">$x</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">5</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>上面例子中，变量<code>x</code>等于<code>2+3</code>的运算结果。</p>
-<p>注意，<code>x=2+3</code>这个式子里面不能有空格，否则会报错。<code>let</code>命令的详细用法参见《变量》一章。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/string"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">字符串操作</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/history"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">操作历史</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#算术表达式" class="table-of-contents__link toc-highlight">算术表达式</a></li><li><a href="#数值的进制" class="table-of-contents__link toc-highlight">数值的进制</a></li><li><a href="#位运算" class="table-of-contents__link toc-highlight">位运算</a></li><li><a href="#逻辑运算" class="table-of-contents__link toc-highlight">逻辑运算</a></li><li><a href="#赋值运算" class="table-of-contents__link toc-highlight">赋值运算</a></li><li><a href="#求值运算" class="table-of-contents__link toc-highlight">求值运算</a></li><li><a href="#expr-命令" class="table-of-contents__link toc-highlight">expr 命令</a></li><li><a href="#let-命令" class="table-of-contents__link toc-highlight">let 命令</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>注意，<code>x=2+3</code>这个式子里面不能有空格，否则会报错。<code>let</code>命令的详细用法参见《变量》一章。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/string"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">字符串操作</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/history"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">操作历史</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#算术表达式" class="table-of-contents__link toc-highlight">算术表达式</a></li><li><a href="#数值的进制" class="table-of-contents__link toc-highlight">数值的进制</a></li><li><a href="#位运算" class="table-of-contents__link toc-highlight">位运算</a></li><li><a href="#逻辑运算" class="table-of-contents__link toc-highlight">逻辑运算</a></li><li><a href="#赋值运算" class="table-of-contents__link toc-highlight">赋值运算</a></li><li><a href="#求值运算" class="table-of-contents__link toc-highlight">求值运算</a></li><li><a href="#expr-命令" class="table-of-contents__link toc-highlight">expr 命令</a></li><li><a href="#let-命令" class="table-of-contents__link toc-highlight">let 命令</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -116,6 +116,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="关联数组">关联数
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token builtin class-name">declare</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-A</span><span class="token plain"> colors</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">colors</span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&quot;red&quot;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;#ff0000&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">colors</span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&quot;green&quot;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;#00ff00&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">colors</span><span class="token punctuation" style="color:#393A34">[</span><span class="token string" style="color:#e3116c">&quot;blue&quot;</span><span class="token punctuation" style="color:#393A34">]</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;#0000ff&quot;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>关联数组必须用带有<code>-A</code>选项的<code>declare</code>命令声明创建。相比之下，整数索引的数组，可以直接使用变量名创建数组，关联数组就不行。</p>
 <p>访问关联数组成员的方式，几乎与整数索引数组相同。</p>
-<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">${colors</span><span class="token variable punctuation" style="color:#393A34">[</span><span class="token variable" style="color:#36acaa">&quot;blue&quot;</span><span class="token variable punctuation" style="color:#393A34">]</span><span class="token variable" style="color:#36acaa">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/function"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 函数</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/set"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">set 命令，shopt 命令</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#创建数组" class="table-of-contents__link toc-highlight">创建数组</a></li><li><a href="#读取数组" class="table-of-contents__link toc-highlight">读取数组</a><ul><li><a href="#读取单个元素" class="table-of-contents__link toc-highlight">读取单个元素</a></li><li><a href="#读取所有成员" class="table-of-contents__link toc-highlight">读取所有成员</a></li><li><a href="#默认位置" class="table-of-contents__link toc-highlight">默认位置</a></li></ul></li><li><a href="#数组的长度" class="table-of-contents__link toc-highlight">数组的长度</a></li><li><a href="#提取数组序号" class="table-of-contents__link toc-highlight">提取数组序号</a></li><li><a href="#提取数组成员" class="table-of-contents__link toc-highlight">提取数组成员</a></li><li><a href="#追加数组成员" class="table-of-contents__link toc-highlight">追加数组成员</a></li><li><a href="#删除数组" class="table-of-contents__link toc-highlight">删除数组</a></li><li><a href="#关联数组" class="table-of-contents__link 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+<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">${colors</span><span class="token variable punctuation" style="color:#393A34">[</span><span class="token variable" style="color:#36acaa">&quot;blue&quot;</span><span class="token variable punctuation" style="color:#393A34">]</span><span class="token variable" style="color:#36acaa">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 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fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/modern-linux/bash-tutorial/"><span itemprop="name">Bash 教程</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">条件判断</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>条件判断</h1></header>
@@ -189,6 +189,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="case-结构">case 结
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考链接">参考链接<a href="#参考链接" class="hash-link" aria-label="参考链接的直接链接" title="参考链接的直接链接">​</a></h2>
 <ul>
 <li><a href="http://linuxcommand.org/tlcl.php" target="_blank" rel="noopener noreferrer">The Linux Command Line</a>, William Shotts</li>
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@@ -70,6 +70,6 @@ <h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="bash_lineno">BASH_LINEN
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token shebang important">#!/bin/bash</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># main.sh</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">source</span><span class="token plain"> lib1.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">source</span><span class="token plain"> lib2.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">func1</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>执行主脚本<code>main.sh</code>，会得到下面的结果。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ ./main.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">func1: </span><span class="token environment constant" style="color:#36acaa">BASH_LINENO</span><span class="token plain"> is </span><span class="token number" style="color:#36acaa">7</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">func1: FUNCNAME is func1</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">func1: </span><span class="token environment constant" style="color:#36acaa">BASH_SOURCE</span><span class="token plain"> is main.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">func2: </span><span class="token environment constant" style="color:#36acaa">BASH_LINENO</span><span class="token plain"> is </span><span class="token number" style="color:#36acaa">8</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">func2: FUNCNAME is func2</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">func2: </span><span class="token environment constant" style="color:#36acaa">BASH_SOURCE</span><span class="token plain"> is lib1.sh</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<p>上面例子中，函数<code>func1</code>是在<code>main.sh</code>的第 7 行调用，函数<code>func2</code>是在<code>lib1.sh</code>的第 8 行调用的。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/set"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">set 命令，shopt 命令</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/mktemp"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">mktemp 命令，trap 命令</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#常见错误" class="table-of-contents__link toc-highlight">常见错误</a></li><li><a href="#bash的-x参数" class="table-of-contents__link toc-highlight"><code>bash</code>的<code>-x</code>参数</a></li><li><a href="#环境变量" class="table-of-contents__link toc-highlight">环境变量</a><ul><li><a href="#lineno" class="table-of-contents__link toc-highlight">LINENO</a></li><li><a href="#funcname" class="table-of-contents__link toc-highlight">FUNCNAME</a></li><li><a href="#bash_source" class="table-of-contents__link toc-highlight">BASH_SOURCE</a></li><li><a href="#bash_lineno" class="table-of-contents__link toc-highlight">BASH_LINENO</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>上面例子中，函数<code>func1</code>是在<code>main.sh</code>的第 7 行调用，函数<code>func2</code>是在<code>lib1.sh</code>的第 8 行调用的。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/set"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">set 命令，shopt 命令</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/mktemp"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">mktemp 命令，trap 命令</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#常见错误" class="table-of-contents__link toc-highlight">常见错误</a></li><li><a href="#bash的-x参数" class="table-of-contents__link toc-highlight"><code>bash</code>的<code>-x</code>参数</a></li><li><a href="#环境变量" class="table-of-contents__link toc-highlight">环境变量</a><ul><li><a href="#lineno" class="table-of-contents__link toc-highlight">LINENO</a></li><li><a href="#funcname" class="table-of-contents__link toc-highlight">FUNCNAME</a></li><li><a href="#bash_source" class="table-of-contents__link toc-highlight">BASH_SOURCE</a></li><li><a href="#bash_lineno" class="table-of-contents__link toc-highlight">BASH_LINENO</a></li></ul></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -278,6 +278,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考链接">参考链
 <ul>
 <li><a href="https://medium.com/@leedowthwaite/why-most-people-only-think-they-understand-wildcards-63bb9c2024ab" target="_blank" rel="noopener noreferrer">Think You Understand Wildcards? Think Again</a></li>
 <li><a href="https://appcodelabs.com/advanced-wildcard-patterns-most-people-dont-know" target="_blank" rel="noopener noreferrer">Advanced Wildcard Patterns Most People Don’t Know</a></li>
-</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/grammar"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 的基本语法</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/quotation"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">引号和转义</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#简介" class="table-of-contents__link toc-highlight">简介</a></li><li><a href="#波浪线扩展" class="table-of-contents__link toc-highlight">波浪线扩展</a></li><li><a href="#-字符扩展" class="table-of-contents__link toc-highlight"><code>?</code> 字符扩展</a></li><li><a href="#-字符扩展-1" class="table-of-contents__link toc-highlight"><code>*</code> 字符扩展</a></li><li><a href="#方括号扩展" class="table-of-contents__link toc-highlight">方括号扩展</a></li><li><a href="#start-end-扩展" class="table-of-contents__link toc-highlight">[start-end] 扩展</a></li><li><a href="#大括号扩展" class="table-of-contents__link toc-highlight">大括号扩展</a></li><li><a href="#startend-扩展" class="table-of-contents__link toc-highlight">{start..end} 扩展</a></li><li><a href="#变量扩展" class="table-of-contents__link toc-highlight">变量扩展</a></li><li><a href="#子命令扩展" class="table-of-contents__link toc-highlight">子命令扩展</a></li><li><a href="#算术扩展" class="table-of-contents__link toc-highlight">算术扩展</a></li><li><a href="#字符类" class="table-of-contents__link toc-highlight">字符类</a></li><li><a href="#使用注意点" class="table-of-contents__link toc-highlight">使用注意点</a></li><li><a href="#量词语法" class="table-of-contents__link toc-highlight">量词语法</a></li><li><a href="#shopt-命令" class="table-of-contents__link toc-highlight">shopt 命令</a></li><li><a href="#参考链接" class="table-of-contents__link toc-highlight">参考链接</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/grammar"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 的基本语法</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/quotation"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">引号和转义</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#简介" class="table-of-contents__link toc-highlight">简介</a></li><li><a href="#波浪线扩展" class="table-of-contents__link toc-highlight">波浪线扩展</a></li><li><a href="#-字符扩展" class="table-of-contents__link toc-highlight"><code>?</code> 字符扩展</a></li><li><a href="#-字符扩展-1" class="table-of-contents__link toc-highlight"><code>*</code> 字符扩展</a></li><li><a href="#方括号扩展" class="table-of-contents__link toc-highlight">方括号扩展</a></li><li><a href="#start-end-扩展" class="table-of-contents__link toc-highlight">[start-end] 扩展</a></li><li><a href="#大括号扩展" class="table-of-contents__link toc-highlight">大括号扩展</a></li><li><a href="#startend-扩展" class="table-of-contents__link toc-highlight">{start..end} 扩展</a></li><li><a href="#变量扩展" class="table-of-contents__link toc-highlight">变量扩展</a></li><li><a href="#子命令扩展" class="table-of-contents__link toc-highlight">子命令扩展</a></li><li><a href="#算术扩展" class="table-of-contents__link toc-highlight">算术扩展</a></li><li><a href="#字符类" class="table-of-contents__link toc-highlight">字符类</a></li><li><a href="#使用注意点" class="table-of-contents__link toc-highlight">使用注意点</a></li><li><a href="#量词语法" class="table-of-contents__link toc-highlight">量词语法</a></li><li><a href="#shopt-命令" class="table-of-contents__link toc-highlight">shopt 命令</a></li><li><a href="#参考链接" class="table-of-contents__link toc-highlight">参考链接</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -76,6 +76,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="全局变量和局部
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考链接">参考链接<a href="#参考链接" class="hash-link" aria-label="参考链接的直接链接" title="参考链接的直接链接">​</a></h2>
 <ul>
 <li><a href="https://www.linuxtechi.com/define-use-functions-linux-shell-script/" target="_blank" rel="noopener noreferrer">How to define and use functions in Linux Shell Script</a>, by Pradeep Kumar</li>
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@@ -92,6 +92,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="快捷键">快捷键<a
 <li><code>↑</code>，<code>↓</code>：浏览已执行命令的历史记录。</li>
 </ul>
 <p>除了上面的快捷键，Bash 还具有自动补全功能。命令输入到一半的时候，可以按下 Tab 键，Bash 会自动完成剩下的部分。比如，输入<code>tou</code>，然后按一下 Tab 键，Bash 会自动补上<code>ch</code>。</p>
-<p>除了命令的自动补全，Bash 还支持路径的自动补全。有时，需要输入很长的路径，这时只需要输入前面的部分，然后按下 Tab 键，就会自动补全后面的部分。如果有多个可能的选择，按两次 Tab 键，Bash 会显示所有选项，让你选择。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/intro"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 简介</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/expansion"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bash 的模式扩展</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#echo-命令" class="table-of-contents__link toc-highlight">echo 命令</a><ul><li><a href="#-n参数" class="table-of-contents__link toc-highlight"><code>-n</code>参数</a></li><li><a href="#-e参数" class="table-of-contents__link toc-highlight"><code>-e</code>参数</a></li></ul></li><li><a href="#命令格式" class="table-of-contents__link toc-highlight">命令格式</a></li><li><a href="#空格" class="table-of-contents__link toc-highlight">空格</a></li><li><a href="#分号" class="table-of-contents__link toc-highlight">分号</a></li><li><a href="#命令的组合符和" class="table-of-contents__link toc-highlight">命令的组合符<code>&amp;&amp;</code>和<code>||</code></a></li><li><a href="#type-命令" class="table-of-contents__link toc-highlight">type 命令</a></li><li><a href="#快捷键" class="table-of-contents__link toc-highlight">快捷键</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>除了命令的自动补全，Bash 还支持路径的自动补全。有时，需要输入很长的路径，这时只需要输入前面的部分，然后按下 Tab 键，就会自动补全后面的部分。如果有多个可能的选择，按两次 Tab 键，Bash 会显示所有选项，让你选择。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/intro"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 简介</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/expansion"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bash 的模式扩展</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#echo-命令" class="table-of-contents__link toc-highlight">echo 命令</a><ul><li><a href="#-n参数" class="table-of-contents__link toc-highlight"><code>-n</code>参数</a></li><li><a href="#-e参数" class="table-of-contents__link toc-highlight"><code>-e</code>参数</a></li></ul></li><li><a href="#命令格式" class="table-of-contents__link toc-highlight">命令格式</a></li><li><a href="#空格" class="table-of-contents__link toc-highlight">空格</a></li><li><a href="#分号" class="table-of-contents__link toc-highlight">分号</a></li><li><a href="#命令的组合符和" class="table-of-contents__link toc-highlight">命令的组合符<code>&amp;&amp;</code>和<code>||</code></a></li><li><a href="#type-命令" class="table-of-contents__link toc-highlight">type 命令</a></li><li><a href="#快捷键" class="table-of-contents__link toc-highlight">快捷键</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -118,6 +118,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="快捷键">快捷键<a
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考链接">参考链接<a href="#参考链接" class="hash-link" aria-label="参考链接的直接链接" title="参考链接的直接链接">​</a></h2>
 <ul>
 <li><a href="https://www.redhat.com/sysadmin/bash-bang-commands" target="_blank" rel="noopener noreferrer">Bash bang commands: A must-know trick for the Linux command line</a></li>
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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Bash 教程</span><meta itemprop="position" content="1"></li></ul></nav><div class="theme-doc-markdown markdown"><header><h1>Bash 教程</h1></header>
 <p>本教程介绍 Linux 命令行 Bash 的基本用法和脚本编程。</p>
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-->引号和转义</h2></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/modern-linux/bash-tutorial/variable"><h2 class="text--truncate cardTitle_rnsV" title="Bash 变量">📄️<!-- --> <!-- -->Bash 变量</h2></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/modern-linux/bash-tutorial/string"><h2 class="text--truncate cardTitle_rnsV" title="字符串操作">📄️<!-- --> <!-- -->字符串操作</h2></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/modern-linux/bash-tutorial/arithmetic"><h2 class="text--truncate cardTitle_rnsV" title="Bash 的算术运算">📄️<!-- --> <!-- -->Bash 的算术运算</h2></a></article><article class="col col--6 margin-bottom--lg"><a class="card padding--lg cardContainer_fWXF" href="/docs/modern-linux/bash-tutorial/history"><h2 class="text--truncate cardTitle_rnsV" title="操作历史">📄️<!-- --> <!-- 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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/docs/modern-linux/bash-tutorial/"><span itemprop="name">Bash 教程</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Bash 简介</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>Bash 简介</h1></header>
@@ -83,6 +83,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="shell-和-bash-的历
 <p>2009 年，Bash 发布 4.0 版。</p>
 <p>2019 年，Bash 发布 5.0 版。</p>
 <p>用户可以通过<code>bash</code>命令的<code>--version</code>参数或者环境变量<code>$BASH_VERSION</code>，查看本机的 Bash 版本。</p>
-<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token function" style="color:#d73a49">bash</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--version</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">GNU bash，版本 </span><span class="token number" style="color:#36acaa">5.0</span><span class="token plain">.3</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">-release </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x86_64-pc-linux-gnu</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># 或者</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token environment constant" style="color:#36acaa">$BASH_VERSION</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">5.0</span><span class="token plain">.3</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">-release</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link 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+<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token function" style="color:#d73a49">bash</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">--version</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">GNU bash，版本 </span><span class="token number" style="color:#36acaa">5.0</span><span class="token plain">.3</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">-release </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">x86_64-pc-linux-gnu</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># 或者</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token environment constant" style="color:#36acaa">$BASH_VERSION</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">5.0</span><span class="token plain">.3</span><span class="token punctuation" style="color:#393A34">(</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain">-release</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link 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@@ -106,6 +106,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="select-结构">select 
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考链接">参考链接<a href="#参考链接" class="hash-link" aria-label="参考链接的直接链接" title="参考链接的直接链接">​</a></h2>
 <ul>
 <li><a href="https://linuxhint.com/bash_select_command/" target="_blank" rel="noopener noreferrer">Bash Select Command</a>, Fahmida Yesmin</li>
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@@ -77,6 +77,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考链接">参考链
 <li><a href="https://www.putorius.net/working-with-temporary-files.html" target="_blank" rel="noopener noreferrer">Working with Temporary Files and Directories in Shell Scripts</a>, Steven Vona</li>
 <li><a href="https://www.putorius.net/using-trap-to-exit-bash-scripts-cleanly.html" target="_blank" rel="noopener noreferrer">Using Trap to Exit Bash Scripts Cleanly</a></li>
 <li><a href="https://mywiki.wooledge.org/SignalTrap" target="_blank" rel="noopener noreferrer">Sending and Trapping Signals</a></li>
-</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/debug"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">脚本除错</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/startup"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bash 启动环境</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#临时文件的安全问题" class="table-of-contents__link toc-highlight">临时文件的安全问题</a></li><li><a href="#mktemp-命令的用法" class="table-of-contents__link toc-highlight">mktemp 命令的用法</a></li><li><a href="#mktemp-命令的参数" class="table-of-contents__link toc-highlight">mktemp 命令的参数</a></li><li><a href="#trap-命令" class="table-of-contents__link toc-highlight">trap 命令</a></li><li><a href="#参考链接" class="table-of-contents__link toc-highlight">参考链接</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -96,6 +96,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="环境变量-ps2ps3ps4"
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token shebang important">#!/bin/bash</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;hello world&quot;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>使用<code>-x</code>参数执行这个脚本。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token function" style="color:#d73a49">bash</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-x</span><span class="token plain"> test.sh</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">+ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;hello world&#x27;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">hello world</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<p>上面例子中，输出的第一行前面有一个<code>+ </code>，这就是变量<code>PS4</code>定义的。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/startup"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 启动环境</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#环境变量-ps1" class="table-of-contents__link toc-highlight">环境变量 PS1</a></li><li><a href="#颜色" class="table-of-contents__link toc-highlight">颜色</a></li><li><a href="#环境变量-ps2ps3ps4" class="table-of-contents__link toc-highlight">环境变量 PS2，PS3，PS4</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>上面例子中，输出的第一行前面有一个<code>+ </code>，这就是变量<code>PS4</code>定义的。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/startup"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 启动环境</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#环境变量-ps1" class="table-of-contents__link toc-highlight">环境变量 PS1</a></li><li><a href="#颜色" class="table-of-contents__link toc-highlight">颜色</a></li><li><a href="#环境变量-ps2ps3ps4" class="table-of-contents__link toc-highlight">环境变量 PS2，PS3，PS4</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -91,6 +91,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="here-字符串">Here 
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token function" style="color:#d73a49">cat</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;&lt;&lt;</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;hi there&#x27;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># 等同于</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;hi there&#x27;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">|</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">cat</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>上面的第一种语法使用了 Here 字符串，要比第二种语法看上去语义更好，也更简洁。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ md5sum </span><span class="token operator" style="color:#393A34">&lt;&lt;&lt;</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;ddd&#x27;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># 等同于</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&#x27;ddd&#x27;</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">|</span><span class="token plain"> md5sum</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<p>上面例子中，<code>md5sum</code>命令只能接受标准输入作为参数，不能直接将字符串放在命令后面，会被当作文件名，即<code>md5sum ddd</code>里面的<code>ddd</code>会被解释成文件名。这时就可以用 Here 字符串，将字符串传给<code>md5sum</code>命令。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/expansion"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 的模式扩展</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/variable"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bash 变量</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#转义" class="table-of-contents__link toc-highlight">转义</a></li><li><a href="#单引号" class="table-of-contents__link toc-highlight">单引号</a></li><li><a href="#双引号" class="table-of-contents__link toc-highlight">双引号</a></li><li><a href="#here-文档" class="table-of-contents__link toc-highlight">Here 文档</a></li><li><a href="#here-字符串" class="table-of-contents__link toc-highlight">Here 字符串</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>上面例子中，<code>md5sum</code>命令只能接受标准输入作为参数，不能直接将字符串放在命令后面，会被当作文件名，即<code>md5sum ddd</code>里面的<code>ddd</code>会被解释成文件名。这时就可以用 Here 字符串，将字符串传给<code>md5sum</code>命令。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/expansion"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 的模式扩展</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/variable"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bash 变量</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#转义" class="table-of-contents__link toc-highlight">转义</a></li><li><a href="#单引号" class="table-of-contents__link toc-highlight">单引号</a></li><li><a href="#双引号" class="table-of-contents__link toc-highlight">双引号</a></li><li><a href="#here-文档" class="table-of-contents__link toc-highlight">Here 文档</a></li><li><a href="#here-字符串" class="table-of-contents__link toc-highlight">Here 字符串</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -72,6 +72,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="ifs-变量">IFS 变量<
 <p>另外，上面例子中，<code>&lt;&lt;&lt;</code>是 Here 字符串，用于将变量值转为标准输入，因为<code>read</code>命令只能解析标准输入。</p>
 <p>如果<code>IFS</code>设为空字符串，就等同于将整行读入一个变量。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token shebang important">#!/bin/bash</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token assign-left variable" style="color:#36acaa">input</span><span class="token operator" style="color:#393A34">=</span><span class="token string" style="color:#e3116c">&quot;/path/to/txt/file&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">while</span><span class="token plain"> </span><span class="token assign-left variable environment constant" style="color:#36acaa">IFS</span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token builtin class-name">read</span><span class="token plain"> </span><span class="token parameter variable" style="color:#36acaa">-r</span><span class="token plain"> line</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">do</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">  </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;</span><span class="token string variable" style="color:#36acaa">$line</span><span class="token string" style="color:#e3116c">&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">done</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">&lt;</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;</span><span class="token string variable" style="color:#36acaa">$input</span><span class="token string" style="color:#e3116c">&quot;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<p>上面的命令可以逐行读取文件，每一行存入变量<code>line</code>，打印出来以后再读取下一行。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/script"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 脚本入门</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/condition"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">条件判断</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#用法" class="table-of-contents__link toc-highlight">用法</a></li><li><a href="#参数" class="table-of-contents__link toc-highlight">参数</a></li><li><a href="#ifs-变量" class="table-of-contents__link toc-highlight">IFS 变量</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>上面的命令可以逐行读取文件，每一行存入变量<code>line</code>，打印出来以后再读取下一行。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/script"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Bash 脚本入门</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/condition"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">条件判断</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#用法" class="table-of-contents__link toc-highlight">用法</a></li><li><a href="#参数" class="table-of-contents__link toc-highlight">参数</a></li><li><a href="#ifs-变量" class="table-of-contents__link toc-highlight">IFS 变量</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -89,6 +89,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="其他快捷键">其他
 </ul>
 <p>上面的<code>Alt + .</code>快捷键，对于很长的文件路径，有时会非常方便。因为 Unix 命令的最后一个参数通常是文件路径。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token function" style="color:#d73a49">mkdir</span><span class="token plain"> foo_bar</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">cd</span><span class="token plain"> </span><span class="token comment" style="color:#999988;font-style:italic">#按下 Alt + .</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<p>上面例子中，在<code>cd</code>命令后按下<code>Alt + .</code>，就会自动插入<code>foo_bar</code>。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/history"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">操作历史</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/stack"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">目录堆栈</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#简介" class="table-of-contents__link toc-highlight">简介</a></li><li><a href="#光标移动" class="table-of-contents__link toc-highlight">光标移动</a></li><li><a href="#清除屏幕" class="table-of-contents__link toc-highlight">清除屏幕</a></li><li><a href="#编辑操作" class="table-of-contents__link toc-highlight">编辑操作</a></li><li><a href="#自动补全" class="table-of-contents__link toc-highlight">自动补全</a></li><li><a href="#其他快捷键" class="table-of-contents__link toc-highlight">其他快捷键</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>上面例子中，在<code>cd</code>命令后按下<code>Alt + .</code>，就会自动插入<code>foo_bar</code>。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/history"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">操作历史</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/stack"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">目录堆栈</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#简介" class="table-of-contents__link toc-highlight">简介</a></li><li><a href="#光标移动" class="table-of-contents__link toc-highlight">光标移动</a></li><li><a href="#清除屏幕" class="table-of-contents__link toc-highlight">清除屏幕</a></li><li><a href="#编辑操作" class="table-of-contents__link toc-highlight">编辑操作</a></li><li><a href="#自动补全" class="table-of-contents__link toc-highlight">自动补全</a></li><li><a href="#其他快捷键" class="table-of-contents__link toc-highlight">其他快捷键</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -167,6 +167,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="别名alias-命令">别
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考链接">参考链接<a href="#参考链接" class="hash-link" aria-label="参考链接的直接链接" title="参考链接的直接链接">​</a></h2>
 <ul>
 <li><a href="https://linuxconfig.org/how-to-use-getopts-to-parse-a-script-options" target="_blank" rel="noopener noreferrer">How to use getopts to parse a script options</a>, Egidio Docile</li>
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@@ -133,6 +133,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="参考链接">参考链
 <li><a href="https://www.gnu.org/software/bash/manual/html_node/The-Set-Builtin.html" target="_blank" rel="noopener noreferrer">The Set Builtin</a></li>
 <li><a href="https://vaneyckt.io/posts/safer_bash_scripts_with_set_euxo_pipefail/" target="_blank" rel="noopener noreferrer">Safer bash scripts with &#x27;set -euxo pipefail&#x27;</a></li>
 <li><a href="http://www.davidpashley.com/articles/writing-robust-shell-scripts/" target="_blank" rel="noopener noreferrer">Writing Robust Bash Shell Scripts</a></li>
-</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/array"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">数组</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/debug"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">脚本除错</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#简介" class="table-of-contents__link toc-highlight">简介</a></li><li><a href="#set--u" class="table-of-contents__link toc-highlight">set -u</a></li><li><a href="#set--x" class="table-of-contents__link toc-highlight">set -x</a></li><li><a href="#bash-的错误处理" class="table-of-contents__link toc-highlight">Bash 的错误处理</a></li><li><a href="#set--e" class="table-of-contents__link toc-highlight">set -e</a></li><li><a href="#set--o-pipefail" class="table-of-contents__link toc-highlight">set -o pipefail</a></li><li><a href="#set--e-1" class="table-of-contents__link toc-highlight">set -E</a></li><li><a href="#其他参数" class="table-of-contents__link toc-highlight">其他参数</a></li><li><a href="#set-命令总结" class="table-of-contents__link toc-highlight">set 命令总结</a></li><li><a href="#shopt-命令" class="table-of-contents__link toc-highlight">shopt 命令</a></li><li><a href="#参考链接" class="table-of-contents__link toc-highlight">参考链接</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/array"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">数组</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/debug"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">脚本除错</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#简介" class="table-of-contents__link toc-highlight">简介</a></li><li><a href="#set--u" class="table-of-contents__link toc-highlight">set -u</a></li><li><a href="#set--x" class="table-of-contents__link toc-highlight">set -x</a></li><li><a href="#bash-的错误处理" class="table-of-contents__link toc-highlight">Bash 的错误处理</a></li><li><a href="#set--e" class="table-of-contents__link toc-highlight">set -e</a></li><li><a href="#set--o-pipefail" class="table-of-contents__link toc-highlight">set -o pipefail</a></li><li><a href="#set--e-1" class="table-of-contents__link toc-highlight">set -E</a></li><li><a href="#其他参数" class="table-of-contents__link toc-highlight">其他参数</a></li><li><a href="#set-命令总结" class="table-of-contents__link toc-highlight">set 命令总结</a></li><li><a href="#shopt-命令" class="table-of-contents__link toc-highlight">shopt 命令</a></li><li><a href="#参考链接" class="table-of-contents__link toc-highlight">参考链接</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -49,6 +49,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="dirs-命令">dirs 命
 <li><code>-v</code>：每行一个条目，每个条目之前显示位置编号（从 0 开始）。</li>
 <li><code>+N</code>：<code>N</code>为整数，表示显示堆顶算起的第 N 个目录，从零开始。</li>
 <li><code>-N</code>：<code>N</code>为整数，表示显示堆底算起的第 N 个目录，从零开始。</li>
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@@ -57,6 +57,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="启动选项">启动选
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="键盘绑定">键盘绑定<a href="#键盘绑定" class="hash-link" aria-label="键盘绑定的直接链接" title="键盘绑定的直接链接">​</a></h2>
 <p>Bash 允许用户定义自己的快捷键。全局的键盘绑定文件默认为<code>/etc/inputrc</code>，你可以在主目录创建自己的键盘绑定文件<code>.inputrc</code>文件。如果定义了这个文件，需要在其中加入下面这行，保证全局绑定不会被遗漏。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token variable" style="color:#36acaa">$include</span><span class="token plain"> /etc/inputrc</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
-<p><code>.inputrc</code>文件里面的快捷键，可以像这样定义，<code>&quot;\C-t&quot;:&quot;pwd\n&quot;</code>表示将<code>Ctrl + t</code>绑定为运行<code>pwd</code>命令。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/mktemp"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">mktemp 命令，trap 命令</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/prompt"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">命令提示符</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#session" class="table-of-contents__link toc-highlight">Session</a><ul><li><a href="#登录-session" class="table-of-contents__link toc-highlight">登录 Session</a></li><li><a href="#非登录-session" class="table-of-contents__link toc-highlight">非登录 Session</a></li><li><a href="#bash_logout" class="table-of-contents__link toc-highlight">.bash_logout</a></li></ul></li><li><a href="#启动选项" class="table-of-contents__link toc-highlight">启动选项</a></li><li><a href="#键盘绑定" class="table-of-contents__link toc-highlight">键盘绑定</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p><code>.inputrc</code>文件里面的快捷键，可以像这样定义，<code>&quot;\C-t&quot;:&quot;pwd\n&quot;</code>表示将<code>Ctrl + t</code>绑定为运行<code>pwd</code>命令。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/mktemp"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">mktemp 命令，trap 命令</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/prompt"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">命令提示符</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#session" class="table-of-contents__link toc-highlight">Session</a><ul><li><a href="#登录-session" class="table-of-contents__link toc-highlight">登录 Session</a></li><li><a href="#非登录-session" class="table-of-contents__link toc-highlight">非登录 Session</a></li><li><a href="#bash_logout" class="table-of-contents__link toc-highlight">.bash_logout</a></li></ul></li><li><a href="#启动选项" class="table-of-contents__link toc-highlight">启动选项</a></li><li><a href="#键盘绑定" class="table-of-contents__link toc-highlight">键盘绑定</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -93,6 +93,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="改变大小写">改变
 <p>下面的语法可以改变变量的大小写。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"># 转为大写</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token variable" style="color:#36acaa">${varname</span><span class="token variable operator" style="color:#393A34">^^</span><span class="token variable" style="color:#36acaa">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token comment" style="color:#999988;font-style:italic"># 转为小写</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token variable" style="color:#36acaa">${varname</span><span class="token variable operator" style="color:#393A34">,,</span><span class="token variable" style="color:#36acaa">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>下面是一个例子。</p>
-<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token assign-left variable" style="color:#36acaa">foo</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">heLLo</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">${foo</span><span class="token variable operator" style="color:#393A34">^^</span><span class="token variable" style="color:#36acaa">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">HELLO</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">${foo</span><span class="token variable operator" style="color:#393A34">,,</span><span class="token variable" style="color:#36acaa">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">hello</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" 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+<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token assign-left variable" style="color:#36acaa">foo</span><span class="token operator" style="color:#393A34">=</span><span class="token plain">heLLo</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">${foo</span><span class="token variable operator" style="color:#393A34">^^</span><span class="token variable" style="color:#36acaa">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">HELLO</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">${foo</span><span class="token variable operator" style="color:#393A34">,,</span><span class="token variable" style="color:#36acaa">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">hello</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" 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@@ -213,6 +213,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="let-命令">let 命令<
 <p><code>let</code>可以同时对多个变量赋值，赋值表达式之间使用空格分隔。</p>
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">let</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;v1 = 1&quot;</span><span class="token plain"> </span><span class="token string" style="color:#e3116c">&quot;v2 = v1++&quot;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain">$ </span><span class="token builtin class-name">echo</span><span class="token plain"> </span><span class="token variable" style="color:#36acaa">$v1</span><span class="token plain">,</span><span class="token variable" style="color:#36acaa">$v2</span><span class="token plain"></span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token number" style="color:#36acaa">2,1</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>上面例子中，<code>let</code>声明了两个变量<code>v1</code>和<code>v2</code>，其中<code>v2</code>等于<code>v1++</code>，表示先返回<code>v1</code>的值，然后<code>v1</code>自增。</p>
-<p>这种语法支持的运算符，参考《Bash 的算术运算》一章。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/quotation"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">引号和转义</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/string"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">字符串操作</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#简介" class="table-of-contents__link toc-highlight">简介</a><ul><li><a href="#环境变量" class="table-of-contents__link toc-highlight">环境变量</a></li><li><a href="#自定义变量" class="table-of-contents__link toc-highlight">自定义变量</a></li></ul></li><li><a href="#创建变量" class="table-of-contents__link toc-highlight">创建变量</a></li><li><a href="#读取变量" class="table-of-contents__link toc-highlight">读取变量</a></li><li><a href="#删除变量" class="table-of-contents__link toc-highlight">删除变量</a></li><li><a href="#输出变量export-命令" class="table-of-contents__link toc-highlight">输出变量，export 命令</a></li><li><a href="#特殊变量" class="table-of-contents__link toc-highlight">特殊变量</a></li><li><a href="#变量的默认值" class="table-of-contents__link toc-highlight">变量的默认值</a></li><li><a href="#declare-命令" class="table-of-contents__link toc-highlight">declare 命令</a></li><li><a href="#readonly-命令" class="table-of-contents__link toc-highlight">readonly 命令</a></li><li><a href="#let-命令" class="table-of-contents__link toc-highlight">let 命令</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p>这种语法支持的运算符，参考《Bash 的算术运算》一章。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/bash-tutorial/quotation"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">引号和转义</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/string"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">字符串操作</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#简介" class="table-of-contents__link toc-highlight">简介</a><ul><li><a href="#环境变量" class="table-of-contents__link toc-highlight">环境变量</a></li><li><a href="#自定义变量" class="table-of-contents__link toc-highlight">自定义变量</a></li></ul></li><li><a href="#创建变量" class="table-of-contents__link toc-highlight">创建变量</a></li><li><a href="#读取变量" class="table-of-contents__link toc-highlight">读取变量</a></li><li><a href="#删除变量" class="table-of-contents__link toc-highlight">删除变量</a></li><li><a href="#输出变量export-命令" class="table-of-contents__link toc-highlight">输出变量，export 命令</a></li><li><a href="#特殊变量" class="table-of-contents__link toc-highlight">特殊变量</a></li><li><a href="#变量的默认值" class="table-of-contents__link toc-highlight">变量的默认值</a></li><li><a href="#declare-命令" class="table-of-contents__link toc-highlight">declare 命令</a></li><li><a href="#readonly-命令" class="table-of-contents__link toc-highlight">readonly 命令</a></li><li><a href="#let-命令" class="table-of-contents__link toc-highlight">let 命令</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -37,6 +37,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="fzf"><a href="https://g
 <p>It offers key bindings <strong>CTRL-T</strong> to search for filenames with fuzzy in an interactive way.</p>
 <p><img decoding="async" loading="lazy" src="/assets/images/fzf-preview-086d5387c23ba6a8f18b3acabff8b826.png" width="2560" height="1600" class="img_ev3q"></p>
 <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="eza-or-lsd"><a href="https://github.com/eza-community/eza" target="_blank" rel="noopener noreferrer">eza</a> or <a href="https://github.com/lsd-rs/lsd" target="_blank" rel="noopener noreferrer">lsd</a>.<a href="#eza-or-lsd" class="hash-link" aria-label="eza-or-lsd的直接链接" title="eza-or-lsd的直接链接">​</a></h2>
-<p><strong><em><code>eza</code> and <code>lsd</code> are git-aware ls replacements with clever utilization of colour. <code>eza</code> is a fork of original project <code>exa</code> which is not under maintained anymore.</em></strong></p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/linux-user-guide/linux-installation"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Linux Installation</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/zsh/use-zsh"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Use ZSH</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#mise" class="table-of-contents__link toc-highlight">mise</a></li><li><a href="#rg" class="table-of-contents__link toc-highlight">rg</a></li><li><a href="#fd" class="table-of-contents__link toc-highlight">fd</a></li><li><a href="#fzf" class="table-of-contents__link toc-highlight">fzf</a></li><li><a href="#eza-or-lsd" class="table-of-contents__link toc-highlight">eza or lsd.</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<p><strong><em><code>eza</code> and <code>lsd</code> are git-aware ls replacements with clever utilization of colour. <code>eza</code> is a fork of original project <code>exa</code> which is not under maintained anymore.</em></strong></p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/linux-user-guide/linux-installation"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Linux Installation</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/zsh/use-zsh"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Use ZSH</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#mise" class="table-of-contents__link toc-highlight">mise</a></li><li><a href="#rg" class="table-of-contents__link toc-highlight">rg</a></li><li><a href="#fd" class="table-of-contents__link toc-highlight">fd</a></li><li><a href="#fzf" class="table-of-contents__link toc-highlight">fzf</a></li><li><a href="#eza-or-lsd" class="table-of-contents__link toc-highlight">eza or lsd.</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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@@ -72,6 +72,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="how-to-version-control-
 </ol>
 <p>Once git repository is created, you can upload it to GitHub or GitLab so it won&#x27;t be lost.</p>
 <div class="theme-admonition theme-admonition-danger admonition_xJq3 alert alert--danger"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>危险</div><div class="admonitionContent_BuS1"><p>Do you create <code>public</code> repository if you want to store some privacy data, such as GitHub token, ssh keys, etc.</p></div></div>
-<div class="theme-admonition theme-admonition-info admonition_xJq3 alert alert--info"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>信息</div><div class="admonitionContent_BuS1"><p>These link procedure are done by hand and hard to maintain across different environments; for automatically installation with config files, I recommend to use <a href="https://github.com/anishathalye/dotbot" target="_blank" rel="noopener noreferrer">GitHub - dotbot</a>.</p></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/nvim/use-nvim"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Use NVIM</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bash 教程</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#what-are-dotfiles" class="table-of-contents__link toc-highlight">What are dotfiles?</a></li><li><a href="#why-use-dotfiles" class="table-of-contents__link toc-highlight">Why Use Dotfiles?</a></li><li><a href="#how-to-create-dotfiles" class="table-of-contents__link toc-highlight">How to Create Dotfiles</a></li><li><a href="#how-to-symlink-your-dotfiles" class="table-of-contents__link toc-highlight">How to Symlink your Dotfiles</a></li><li><a href="#how-to-version-control-your-dotfiles" class="table-of-contents__link toc-highlight">How to Version Control your Dotfiles</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
+<div class="theme-admonition theme-admonition-info admonition_xJq3 alert alert--info"><div class="admonitionHeading_Gvgb"><span class="admonitionIcon_Rf37"><svg viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>信息</div><div class="admonitionContent_BuS1"><p>These link procedure are done by hand and hard to maintain across different environments; for automatically installation with config files, I recommend to use <a href="https://github.com/anishathalye/dotbot" target="_blank" rel="noopener noreferrer">GitHub - dotbot</a>.</p></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/nvim/use-nvim"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Use NVIM</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/bash-tutorial/"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Bash 教程</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#what-are-dotfiles" class="table-of-contents__link toc-highlight">What are dotfiles?</a></li><li><a href="#why-use-dotfiles" class="table-of-contents__link toc-highlight">Why Use Dotfiles?</a></li><li><a href="#how-to-create-dotfiles" class="table-of-contents__link toc-highlight">How to Create Dotfiles</a></li><li><a href="#how-to-symlink-your-dotfiles" class="table-of-contents__link toc-highlight">How to Symlink your Dotfiles</a></li><li><a href="#how-to-version-control-your-dotfiles" class="table-of-contents__link toc-highlight">How to Version Control your Dotfiles</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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 <p>It is based on Ubuntu Latest LTS (currently 22.04) or ArchLinux.</p>
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1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">Linux User Guide</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Linux Installation</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>Linux Installation</h1></header>
@@ -92,6 +92,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="step-4---after-installi
 <li>Get familiar with the preferred package manager used by your chosen Linux distribution. Linux uses package manager&#x27;s to download and update any software that you plan to use. For example, Ubuntu uses the Advanced Packaging Tool (<code>apt</code>), ArchLinux uses the Package Manager (<code>pacman</code>).</li>
 <li>Use your distribution&#x27;s package manager to update and upgrade your distribution. Software packages in a stable release of a Linux distribution are often outdated. It is recommended to regularly run an update. You may also want to run an upgrade, which installs newer versions of any packages that you&#x27;ve already installed. For example, if you&#x27;re using Ubuntu, run: <code>sudo apt update &amp;&amp; sudo apt upgrade</code>; if you&#x27;re using ArchLinux, run: <code>sudo pacman -Syu</code>.</li>
 <li>Learn more about the Linux tools, such as Visual Studio Code, vim, git to speed up your development and usage.</li>
-</ol></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/intro"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Modern Linux</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/command-line-tools/modern-cli-tools"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Modern CLI Tools</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#step-1---choose-a-method-to-install-linux" class="table-of-contents__link toc-highlight">Step 1 - Choose a method to install Linux</a><ul><li><a href="#step-2---choose-a-linux-distribution-choose-wsl" class="table-of-contents__link toc-highlight">Windows Subsystem for Linux (WSL)</a></li><li><a href="#step-2---choose-a-linux-distribution-create-vm" class="table-of-contents__link toc-highlight">Create a Virtual Machine (VM)</a></li><li><a href="#step-2---choose-a-linux-distribution-bare-metal-linux" class="table-of-contents__link toc-highlight">Bare metal Linux</a></li></ul></li><li><a href="#step-2---choose-a-linux-distribution" class="table-of-contents__link toc-highlight">Step 2 - Choose a Linux distribution</a><ul><li><a href="#required-linux-experience" class="table-of-contents__link toc-highlight">Required Linux experience</a></li><li><a href="#system-requirements" class="table-of-contents__link toc-highlight">System requirements</a></li><li><a href="#community-support" class="table-of-contents__link toc-highlight">Community support</a></li></ul></li><li><a href="#step-3---follow-install-method-instructions" class="table-of-contents__link toc-highlight">Step 3 - Follow install method instructions</a><ul><li><a href="#install-linux-with-windows-subsystem-for-linux" class="table-of-contents__link toc-highlight">Install Linux with Windows Subsystem for Linux</a></li><li><a href="#install-linux-command-options" class="table-of-contents__link toc-highlight">Install Linux command options</a></li><li><a href="#create-a-linux-virtual-machine-locally-using-a-hypervisor" class="table-of-contents__link toc-highlight">Create a Linux Virtual Machine locally using a hypervisor</a></li><li><a href="#create-a-bootable-usb-drive-to-install-bare-metal-linux" class="table-of-contents__link toc-highlight">Create a bootable USB drive to install bare-metal Linux</a></li></ul></li><li><a href="#step-4---after-installing-linux" class="table-of-contents__link toc-highlight">Step 4 - 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+</ol></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/intro"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Modern Linux</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/command-line-tools/modern-cli-tools"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Modern CLI Tools</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#step-1---choose-a-method-to-install-linux" class="table-of-contents__link toc-highlight">Step 1 - Choose a method to install Linux</a><ul><li><a href="#step-2---choose-a-linux-distribution-choose-wsl" class="table-of-contents__link toc-highlight">Windows Subsystem for Linux (WSL)</a></li><li><a href="#step-2---choose-a-linux-distribution-create-vm" class="table-of-contents__link toc-highlight">Create a Virtual Machine (VM)</a></li><li><a href="#step-2---choose-a-linux-distribution-bare-metal-linux" class="table-of-contents__link toc-highlight">Bare metal Linux</a></li></ul></li><li><a href="#step-2---choose-a-linux-distribution" class="table-of-contents__link toc-highlight">Step 2 - Choose a Linux distribution</a><ul><li><a href="#required-linux-experience" class="table-of-contents__link toc-highlight">Required Linux experience</a></li><li><a href="#system-requirements" class="table-of-contents__link toc-highlight">System requirements</a></li><li><a href="#community-support" class="table-of-contents__link toc-highlight">Community support</a></li></ul></li><li><a href="#step-3---follow-install-method-instructions" class="table-of-contents__link toc-highlight">Step 3 - Follow install method instructions</a><ul><li><a href="#install-linux-with-windows-subsystem-for-linux" class="table-of-contents__link toc-highlight">Install Linux with Windows Subsystem for Linux</a></li><li><a href="#install-linux-command-options" class="table-of-contents__link toc-highlight">Install Linux command options</a></li><li><a href="#create-a-linux-virtual-machine-locally-using-a-hypervisor" class="table-of-contents__link toc-highlight">Create a Linux Virtual Machine locally using a hypervisor</a></li><li><a href="#create-a-bootable-usb-drive-to-install-bare-metal-linux" class="table-of-contents__link toc-highlight">Create a bootable USB drive to install bare-metal Linux</a></li></ul></li><li><a href="#step-4---after-installing-linux" class="table-of-contents__link toc-highlight">Step 4 - After installing Linux</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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3.078A.939.939 0 010 2.528c0-.548.45-.997 1-.997h2.996c.352 0 .649.18.828.45L9.82 9.472c.11.148.172.347.172.55zm0 0"></path><path d="M19.98 10.023c0 .2-.058.399-.168.547l-4.996 7.492a.987.987 0 01-.828.454h-3c-.547 0-.996-.453-.996-1 0-.2.059-.403.168-.551l4.625-6.942-4.625-6.945a.939.939 0 01-.168-.55 1 1 0 01.996-.997h3c.348 0 .649.18.828.45l4.996 7.492c.11.148.168.347.168.55zm0 0"></path></g></svg></button></div></div></aside><main class="docMainContainer_TBSr"><div class="container padding-top--md padding-bottom--lg"><div class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><nav class="theme-doc-breadcrumbs breadcrumbsContainer_Z_bl" aria-label="页面路径"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="主页面" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li class="breadcrumbs__item"><span class="breadcrumbs__link">Zsh</span><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Use ZSH</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">本页总览</button></div><div class="theme-doc-markdown markdown"><header><h1>Use ZSH</h1></header>
@@ -51,6 +51,6 @@ <h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="recommend-plugins">Reco
 <div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token function" style="color:#d73a49">git</span><span class="token plain"> clone https://github.com/zsh-users/zsh-autosuggestions.git </span><span class="token variable" style="color:#36acaa">$ZSH</span><span class="token plain">/plugins/zsh-autosuggestions</span><br></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token function" style="color:#d73a49">git</span><span class="token plain"> clone https://github.com/zsh-users/zsh-syntax-highlighting.git </span><span class="token variable" style="color:#36acaa">$ZSH</span><span class="token plain">/plugins/zsh-syntax-highlighting</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
 <p>Open the <code>.zshrc</code> file, replace the line <code>plugins=(git z)</code> by <code>plugins=(git z zsh-autosuggestions zsh-syntax-highlighting)</code>.</p>
 <p>Reload ZSH to make it work:</p>
-<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token builtin class-name">exec</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">zsh</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/command-line-tools/modern-cli-tools"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Modern CLI Tools</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/nvim/use-nvim"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Use NVIM</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#what-is-zsh" class="table-of-contents__link toc-highlight">What is ZSH?</a></li><li><a href="#how-to-install-zsh" class="table-of-contents__link toc-highlight">How to install ZSH?</a></li><li><a href="#install-zsh-on-other-linux-systems" class="table-of-contents__link toc-highlight">Install ZSH on Other Linux Systems</a></li><li><a href="#how-to-use-zsh-themes" class="table-of-contents__link toc-highlight">How to Use ZSH Themes</a></li><li><a href="#recommend-plugins" class="table-of-contents__link toc-highlight">Recommend Plugins</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li><li class="footer__item"><a href="https://github.com/ShangjinTang/site" target="_blank" rel="noopener noreferrer" class="footer__link-item">网站托管 GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div 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+<div class="language-bash codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-bash codeBlock_bY9V thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#393A34"><span class="token builtin class-name">exec</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">zsh</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="复制代码到剪贴板" title="复制" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="文件选项卡"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/modern-linux/command-line-tools/modern-cli-tools"><div class="pagination-nav__sublabel">上一页</div><div class="pagination-nav__label">Modern CLI Tools</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/modern-linux/nvim/use-nvim"><div class="pagination-nav__sublabel">下一页</div><div class="pagination-nav__label">Use NVIM</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#what-is-zsh" class="table-of-contents__link toc-highlight">What is ZSH?</a></li><li><a href="#how-to-install-zsh" class="table-of-contents__link toc-highlight">How to install ZSH?</a></li><li><a href="#install-zsh-on-other-linux-systems" class="table-of-contents__link toc-highlight">Install ZSH on Other Linux Systems</a></li><li><a href="#how-to-use-zsh-themes" class="table-of-contents__link toc-highlight">How to Use ZSH Themes</a></li><li><a href="#recommend-plugins" class="table-of-contents__link toc-highlight">Recommend Plugins</a></li></ul></div></div></div></div></main></div></div></div><footer class="footer"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">本站构建</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/docs/docusaurus-mdx/intro">Docusaurus 特性</a></li><li class="footer__item"><a href="https://docusaurus.io/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">Docusaurus 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://mdxjs.com/docs" target="_blank" rel="noopener noreferrer" class="footer__link-item">MDX 官方文档<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a class="footer__link-item" href="/latex">Latex 语法</a></li></ul></div><div class="col footer__col"><div class="footer__title">常用链接</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://google.com" target="_blank" rel="noopener noreferrer" class="footer__link-item">Google<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">更多</div><ul class="footer__items clean-list"><li class="footer__item"><a class="footer__link-item" href="/license">版权声明</a></li><li class="footer__item"><a class="footer__link-item" href="/about-site">关于本站</a></li><li class="footer__item"><a class="footer__link-item" href="/contact-me">联系信息</a></li></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 by Sol</div></div></div></footer></div>
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(watchpoint)","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控点-watchpoint","p":1325},{"i":1342,"t":"监控进程中某个变量的值","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控进程中某个变量的值","p":1325},{"i":1344,"t":"监控进程中的某块内存","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控进程中的某块内存","p":1325},{"i":1346,"t":"设置监控的条件","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#设置监控的条件","p":1325},{"i":1348,"t":"删除监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#删除监控点","p":1325},{"i":1350,"t":"列出所有的监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#列出所有的监控点","p":1325},{"i":1354,"t":"读取内存","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#读取内存","p":1352},{"i":1356,"t":"读取若干十六进制的内存","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#读取若干十六进制的内存","p":1352},{"i":1358,"t":"从内存指定地址读取若干字节，并保存到本地文件","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#从内存指定地址读取若干字节并保存到本地文件","p":1352},{"i":1360,"t":"从内存指定地址范围读取字节，并保存到本地文件","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#从内存指定地址范围读取字节并保存到本地文件","p":1352},{"i":1363,"t":"列出可执行文件和所有依赖的共享库","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#列出可执行文件和所有依赖的共享库","p":1362},{"i":1365,"t":"查找可执行文件或任何共享库中原始地址信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#查找可执行文件或任何共享库中原始地址信息","p":1362},{"i":1367,"t":"在二进制文件中查找与正则表达式匹配的函数","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#在二进制文件中查找与正则表达式匹配的函数","p":1362},{"i":1369,"t":"查找完整的源代码行信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#查找完整的源代码行信息","p":1362},{"i":1371,"t":"仅在 a.out 中查找地址信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#仅在-aout-中查找地址信息","p":1362},{"i":1373,"t":"按名称查找类型 Point 的信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#按名称查找类型-point-的信息","p":1362},{"i":1376,"t":"检查变量","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#检查变量","p":1375},{"i":1377,"t":"显示变量的内容","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示变量的内容","p":1375},{"i":1379,"t":"显示当前栈帧的参数和局部变量","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前栈帧的参数和局部变量","p":1375},{"i":1381,"t":"检查数组","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#检查数组","p":1375},{"i":1383,"t":"检查寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#检查寄存器","p":1375},{"i":1384,"t":"显示当前线程的通用寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程的通用寄存器","p":1375},{"i":1386,"t":"显示当前线程的所有寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程的所有寄存器","p":1375},{"i":1388,"t":"显示当前线程中指定寄存器的值","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程中指定寄存器的值","p":1375},{"i":1390,"t":"显示当前线程中指定寄存器的值，格式为二进制","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程中指定寄存器的值格式为二进制","p":1375},{"i":1392,"t":"打印表达式结果的动态类型 (C++)","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#打印表达式结果的动态类型-c","p":1375},{"i":1396,"t":"安装","u":"/docs/modern-cpp/gdb-lldb/gef","h":"#安装","p":1394},{"i":1398,"t":"GEF 命令","u":"/docs/modern-cpp/gdb-lldb/gef","h":"#gef-命令","p":1394},{"i":1401,"t":"dump 可执行文件和所有共享库的 section 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和所有共享库的-section-信息","p":1400},{"i":1403,"t":"dump 可执行文件的 section 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件的-section-信息","p":1400},{"i":1405,"t":"dump 可执行文件和所有共享库的 symtab 符号","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和所有共享库的-symtab-符号","p":1400},{"i":1407,"t":"dump 可执行文件和指定共享库的 symtab 符号","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和指定共享库的-symtab-符号","p":1400},{"i":1410,"t":"重新映射调试对话的源文件路径","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#重新映射调试对话的源文件路径","p":1409},{"i":1412,"t":"调试服务器设置","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#调试服务器设置","p":1409},{"i":1413,"t":"连接到远程调试服务器","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#连接到远程调试服务器","p":1409},{"i":1415,"t":"连接到本地调试服务器","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#连接到本地调试服务器","p":1409},{"i":1417,"t":"临时变量和打印","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#临时变量和打印","p":1409},{"i":1418,"t":"创建临时变量并赋值","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#创建临时变量并赋值","p":1409},{"i":1420,"t":"在当前帧中的计算表达式","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#在当前帧中的计算表达式","p":1409},{"i":1422,"t":"打印信息到屏幕","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#打印信息��到屏幕","p":1409},{"i":1425,"t":"设置断点和启动进程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#设置断点和启动进程","p":1424},{"i":1427,"t":"单步调试","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#单步调试","p":1424},{"i":1428,"t":"step-in 单步调试 (源码级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-in-单步调试-源码级别","p":1424},{"i":1430,"t":"step-over 单步调试 (源码级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-单步调试-源码级别","p":1424},{"i":1432,"t":"step-in 单步调试 (汇编指令级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-in-单步调试-汇编指令级别","p":1424},{"i":1434,"t":"step-over 单步调试 (汇编指令级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-单步调试-汇编指令级别","p":1424},{"i":1436,"t":"step-over 跳出栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-跳出栈帧","p":1424},{"i":1438,"t":"断点调试","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#断点调试","p":1424},{"i":1439,"t":"跳转到下一个断点","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#跳转到下一个断点","p":1424},{"i":1441,"t":"运行到指定行数","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#运行到指定行数","p":1424},{"i":1443,"t":"线程切换","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#线程切换","p":1424},{"i":1444,"t":"列出程序中的线程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#列出程序中的线程","p":1424},{"i":1446,"t":"设置后续命令的默认线程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#设置后续命令的默认线程","p":1424},{"i":1448,"t":"栈帧切换","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#栈帧切换","p":1424},{"i":1449,"t":"显示当前栈帧简略信息","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#显示当前栈帧简略信息","p":1424},{"i":1451,"t":"显示当前栈帧源代码行","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#显示当前栈帧源代码行","p":1424},{"i":1453,"t":"通过栈帧号选择栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#通过栈帧号选择栈帧","p":1424},{"i":1455,"t":"选择调用当前栈帧的栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#选择调用当前栈帧的栈帧","p":1424},{"i":1457,"t":"选择被当前栈帧调用的栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#选择被当前栈帧调用的栈帧","p":1424},{"i":1459,"t":"使用栈帧相对偏移选择栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#使用栈帧相对偏移选择栈帧","p":1424},{"i":1461,"t":"从栈帧返回，可以带有返回值","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#从栈帧返回可以带有返回值","p":1424},{"i":1463,"t":"调用带有断点的函数并在断点处停止","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#调用带有断点的函数并在断点处停止","p":1424},{"i":1465,"t":"调用 crash 的函数并在 crash 时停止","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#调用-crash-的函数并在-crash-时停止","p":1424},{"i":1469,"t":"启动新的进程","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#启动新的进程","p":1468},{"i":1471,"t":"设置进程的运行参数","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#设置进程的运行参数","p":1468},{"i":1473,"t":"环境变量设置","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#环境变量设置","p":1468},{"i":1475,"t":"attach 到已有进程","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#attach-到已有进程","p":1468},{"i":1477,"t":"显示参数","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#显示参数","p":1468},{"i":1481,"t":"📄️ Bash 简介","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1482,"t":"📄️ Bash 的基本语法","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1483,"t":"📄️ Bash 的模式扩展","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1484,"t":"📄️ 引号和转义","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1485,"t":"📄️ Bash 变量","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1486,"t":"📄️ 字符串操作","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1487,"t":"📄️ Bash 的算术运算","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1488,"t":"📄️ 操作历史","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1489,"t":"📄️ Bash 行操作","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1490,"t":"📄️ 目录堆栈","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1491,"t":"📄️ Bash 脚本入门","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1492,"t":"📄️ read 命令","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1493,"t":"📄️ 条件判断","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1494,"t":"📄️ 循环","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1495,"t":"📄️ Bash 函数","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1496,"t":"📄️ 数组","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1497,"t":"📄️ set 命令，shopt 命令","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1498,"t":"📄️ 脚本除错","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1499,"t":"📄️ mktemp 命令，trap 命令","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1500,"t":"📄️ Bash 启动环境","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1501,"t":"📄️ 命令提示符","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1503,"t":"算术表达式","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#算术表达式","p":1502},{"i":1505,"t":"数值的进制","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#数值的进制","p":1502},{"i":1507,"t":"位运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#位运算","p":1502},{"i":1509,"t":"逻辑运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#逻辑运算","p":1502},{"i":1511,"t":"赋值运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#赋值运算","p":1502},{"i":1513,"t":"求值运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#求值运算","p":1502},{"i":1515,"t":"expr 命令","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#expr-命令","p":1502},{"i":1517,"t":"let 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类似，本文中的逻辑回归也是二元分类的线性模型。","s":"逻辑回归","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","p":1129},{"i":1141,"t":"本文介绍了逻辑回归 (Logistic Regression) 相关的数学知识，重点在于参数和变量的向量化。","s":"逻辑回归的向量化","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","p":1141},{"i":1155,"t":"本文介绍了 MCP 神经元和感知器，以及对应的算法实现。","s":"MCP 神经元和感知器","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","p":1155},{"i":1163,"t":"NumPy 是用于 Python 中多维数组计算的软件库。","s":"NumPy 快速入门","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","p":1163},{"i":1197,"t":"套袋算法 (Bagging) 是一种集成学习技术，与 MajorityVoteClassifier 相似，不同之处在于 bagging 不是每次使用相同的训练集来拟合单个分类器，而是对初始训练集进行 bootstrap 抽样。这也是 bagging 称为引导聚合 (Bootstrap Aggregating) 的原因。","s":"Bagging","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","p":1197},{"i":1205,"t":"决策树 (Decision Tree) 是一种特殊的树结构，代表的是样本特征与样本标签之间的一种映射关系。","s":"决策树和随机森林","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","p":1205},{"i":1219,"t":"本文介绍懒惰学习的一个典型示例：K-近邻 (K-Nearest Neighbors，KNN) 算法。之所以称为懒惰，是因为它不从训练样本中学习判别函数，而是在记住已有的样本数据集的基础上对新样本进行分类。","s":"K-近邻","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","p":1219},{"i":1227,"t":"支持向量机 (Support Vector Machine，SVM) 是一种监督式学习方法，其学习策略为最大化样本与超平面 (即决策边界) 之间的间隔。本文介绍线性 SVM 的原理及实现。","s":"线性 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-linear","p":1227},{"i":1233,"t":"集合 (Ensemble) 方法的目标是将不同的分类器组合到一起，相比每个单独的分类器具有更好的泛化性能。","s":"使用集合的投票分类方法","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","p":1233},{"i":1241,"t":"架构总览","s":"Transformer 架构","u":"/docs/machine-learning/transformer/transformer-architecture","p":1241},{"i":1246,"t":"在原始 SVM 只支持线性样本的基础上，引入核技巧 (Kernel Trick) 可以对非线性的样本进行分类。算法思想为将输入向量映射到高维空间，然后用超平面划分。本文中有举例说明。","s":"核技巧和非线性 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","p":1246},{"i":1254,"t":"什么是注意力机制","s":"注意力机制","u":"/docs/machine-learning/transformer/transformer-attention","p":1254},{"i":1270,"t":"总体来看，Transformer 模型主要由两个块组成：","s":"编码器和解码器","u":"/docs/machine-learning/transformer/transformer-encoders-decoders","p":1270},{"i":1274,"t":"Transformer 是一种采用自注意力机制 (self-attention) 的深度学习模型架构，这一机制可以按输入数据各部分重要性的不同而分配不同的权重。该模型由 Google 机器翻译团队于 2017 年发表于论文 Attention is all you need 中，为 OpenAI 开发的 ChatGPT、Google 的 Gemini、Meta 的 LLaMA 等大语言模型的核心基础架构。","s":"Transformer 概览","u":"/docs/machine-learning/transformer/transformer-overview","p":1274},{"i":1279,"t":"PyTorch 代码实现","s":"代码实现","u":"/docs/machine-learning/transformer/transformer-code-implementation","p":1279},{"i":1282,"t":"论文通过添加一种称为“多头”注意力的机制进一步细化了自注意力。它扩展了模型关注不同位置的能力。","s":"分割的多头注意力机制","u":"/docs/machine-learning/transformer/transformer-split-multi-head-attention","p":1282},{"i":1284,"t":"为什么需要位置编码","s":"位置编码","u":"/docs/machine-learning/transformer/transformer-positional-encoding","p":1284},{"i":1293,"t":"Informer","s":"Transformer 的变种","u":"/docs/machine-learning/transformer/transformer-variants","p":1293},{"i":1304,"t":"回溯 (backtrace)","s":"回溯和反汇编","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","p":1304},{"i":1325,"t":"断点 (breakpoint)","s":"断点和监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","p":1325},{"i":1352,"t":"形式：x/count fmt size address","s":"检查内存地址的数据","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","p":1352},{"i":1362,"t":"列出可执行文件和所有依赖的共享库","s":"可执行文件和共享库信息查询","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","p":1362},{"i":1375,"t":"检查变量","s":"检查变量和寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","p":1375},{"i":1394,"t":"GEF 是对 GDB 的增强，使用 Python API 为 GDB 提供附加功能，在动态分析和漏洞开发过程中提供更容易理解的二进制布局，并且安装简单，无外部依赖。","s":"GEF - GDB 增强工具","u":"/docs/modern-cpp/gdb-lldb/gef","p":1394},{"i":1400,"t":"dump 可执行文件和所有共享库的 section 信息","s":"dump 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","p":1400},{"i":1409,"t":"重新映射调试对话的源文件路径","s":"其他项","u":"/docs/modern-cpp/gdb-lldb/misc","p":1409},{"i":1424,"t":"设置断点和启动进程","s":"在调试器内跳转","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","p":1424},{"i":1468,"t":"启动新的进程","s":"启动调试","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","p":1468},{"i":1479,"t":"本教程介绍 Linux 命令行 Bash 的基本用法和脚本编程。","s":"Bash 教程","u":"/docs/modern-linux/bash-tutorial/","p":1479},{"i":1877,"t":"It is based on Ubuntu Latest LTS (currently 22.04) or ArchLinux.","s":"Modern Linux","u":"/docs/modern-linux/intro","p":1877},{"i":1879,"t":"For modern CLI Tools on x86_64 Linux distros, see: CLI Prebuilts.","s":"Modern CLI Tools","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","p":1879},{"i":1891,"t":"I've created a dotfiles for multi softwares including multi configurations, see GitHub - ShangjinTang/dotfiles. You can clone it or take it as a dotfiles sample.","s":"Manage Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","p":1891},{"i":1903,"t":"Linux is an operating system, similar to Windows, but with many different versions due to the nature of being open source and fully customizable. To install Linux, you must choose an install method and choose a Linux distribution.","s":"Linux Installation","u":"/docs/modern-linux/linux-user-guide/linux-installation","p":1903},{"i":1932,"t":"What is NVIM?","s":"Use NVIM","u":"/docs/modern-linux/nvim/use-nvim","p":1932},{"i":1941,"t":"Bash, or the Bourne Again Shell, is a hallmark of Linux systems. However, there are other shells out there that may offer extra functionality. 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模板元编程可以解决这个问题，在编译时计算斐波那契数列，从而提高执行效率。 斐波那契数列有两种： 从 000 开始： 0,1,1,2,3,5,8,...0,1,1,2,3,5,8,...0,1,1,2,3,5,8,... 从 111 开始： 1,1,2,3,5,8,...1,1,2,3,5,8,...1,1,2,3,5,8,... 我们假设从 000 开始，即 f(0)=0，f(1)=1，f(2)=1，... f(0) = 0，f(1) = 1，f(2) = 1，...f(0)=0，f(1)=1，f(2)=1，...。","s":"模板元编程：斐波那契数列","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"","p":3},{"i":6,"t":"/** * @file fibonacci_recursive.cpp * @brief calculate fibonacci value recursively */ #include <iostream> unsigned int calc_fibonacci(unsigned int i) { if (i == 0 || i == 1) { return i; } return calc_fibonacci(i - 1) + calc_fibonacci(i - 2); }; int main() { std::cout << calc_fibonacci(42) << '\\n'; return 0; } > g++ -O0 -g a.out fibonacci_recursive.cpp -o prog_fibonacci_recursive > ./prog_fibonacci_recursive 267914296 > hyperfine \"./prog_fibonacci_recursive\" Benchmark 1: ./prog_fibonacci_recursive Time (mean ± σ): 1.657 s ± 0.015 s [User: 1.652 s, System: 0.002 s] Range (min … max): 1.647 s … 1.696 s 10 runs","s":"传统递归","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#传统递归","p":3},{"i":9,"t":"首先，我们定义一个模板类 fibonacci，它具有一个静态成员变量 value，用于存储斐波那契数列的值。该模板类使用递归定义，根据给定的大小计算斐波那契数列值。 template <int size> struct fibonacci { static constexpr unsigned int value = fibonacci<size - 1>::value + fibonacci<size - 2>::value; }; template <> struct fibonacci<0> { static constexpr unsigned int value = 0; }; template <> struct fibonacci<1> { static constexpr unsigned int value = 1; }; 使用 fibonacci<42>::value 则可以得到对应的结果。这个语法类似于传统的递归，但是会在编译期进行求值。 使用模板元编程的斐波那契数列计算方法相比于传统的递归方法具有更高的效率。它在编译时完成计算，避免了运行时的重复计算，从而提高了程序的性能。 这里使用了编译期求值的关键字 constexpr，因此需要 C++11 版本及以上。 > g++ -O0 -g -std=c++11 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp > ./prog_fibonacci_tmp 267914296 > hyperfine \"./prog_fibonacci_tmp\" Benchmark 1: ./prog_fibonacci_tmp Time (mean ± σ): 0.8 ms ± 0.1 ms [User: 0.9 ms, System: 0.2 ms] Range (min … max): 0.6 ms … 1.5 ms 1605 runs 在计算第 42 个斐波那契数的时候，运行时间仅需 ~0.8ms，相当于传统递归方法 ~1.6s 的 1/2000。","s":"C++11","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#c11","p":3},{"i":11,"t":"在 C++17 中，通常使用 _v 结尾当作 value 类型 (参见这篇 proposal)，比如： template <struct T> constexpr bool is_integral_v = is_integral<T>::value; 类似的，我们可以定义一个模板变量 fibonacci_v，用于方便地获取斐波那契数列的值。 template <int size> constexpr auto fibonacci_v = fibonacci<size>::value; 注意，这种 _v 的实现并不需要 C++17 的编译器；C++14 的编译器即可以满足需求。 编译： > g++ -O0 -g -std=c++14 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp","s":"C++14","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#c14","p":3},{"i":13,"t":"C++20 中，我们可以使用 concept / requires，合并两个偏特化模板。 template <int size> concept FibonacciBaseCase = (size == 0) || (size == 1); template <int size> requires FibonacciBaseCase<size> struct fibonacci<size> { public: static constexpr unsigned int value = size; }; 编译： > g++ -O0 -g -std=c++20 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp","s":"C++20","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#c20","p":3},{"i":15,"t":"c++11 c++14 c++20 #include <iostream> template <int size> struct fibonacci { public: static constexpr unsigned int value = fibonacci<size - 1>::value + fibonacci<size - 2>::value; }; template <> struct fibonacci<0> { public: static constexpr unsigned int value = 0; }; template <> struct fibonacci<1> { public: static constexpr unsigned int value = 1; }; int main() { std::cout << fibonacci<42>::value << '\\n'; return 0; } #include <iostream> template <int size> struct fibonacci { public: static constexpr unsigned int value = fibonacci<size - 1>::value + fibonacci<size - 2>::value; }; template <> struct fibonacci<0> { public: static constexpr unsigned int value = 0; }; template <> struct fibonacci<1> { public: static constexpr unsigned int value = 1; }; template <int size> constexpr auto fibonacci_v = fibonacci<size>::value; int main() { // std::cout << fibonacci<42>::value << '\\n'; std::cout << fibonacci_v<42> << '\\n'; return 0; } #include <iostream> template <int size> struct fibonacci { public: static constexpr unsigned int value = fibonacci<size - 1>::value + fibonacci<size - 2>::value; }; // template <> // struct fibonacci<0> { // public: // static constexpr unsigned int value = 0; // }; // template <> // struct fibonacci<1> { // public: // static constexpr unsigned int value = 1; // }; template <int size> concept FibonacciBaseCase = (size == 0) || (size == 1); template <int size> requires FibonacciBaseCase<size> struct fibonacci<size> { public: static constexpr unsigned int value = size; }; template <int size> constexpr auto fibonacci_v = fibonacci<size>::value; int main() { std::cout << fibonacci_v<42> << '\\n'; return 0; } 通过使用模板元编程技术，我们可以在编译时计算斐波那契数列，避免了递归函数的重复计算，在一些需要高效计算斐波那契数列的场景下，这种方法可以提供更好的性能。 希望这篇博客能帮助你理解如何使用模板元编程实现斐波那契数列的编译期计算，并对此有所启发。","s":"完整代码","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#完整代码","p":3},{"i":17,"t":"Ubuntu 22.04 默认使用 g++-11 和 clang++-14 作为默认的 g++ 和 clang++。 本文说明如何升级 C++ 编译器并设置默认版本，从而使用最新的 C++ 语言特性。","s":"Ubuntu 22.04 更新 C++ 编译器","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"","p":16},{"i":20,"t":"sudo apt update sudo add-apt-repository ppa:ubuntu-toolchain-r/test sudo apt install gcc-12 g++-12 -y sudo apt install gcc-13 g++-13 -y","s":"安装最新的 g++","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#install-latest-g++","p":16},{"i":22,"t":"参见 LLVM Debian/Ubuntu Packages 中的安装指南： wget https://apt.llvm.org/llvm.sh chmod +x llvm.sh # sudo ./llvm.sh <version number> all # or # sudo ./llvm.sh all sudo ./llvm.sh 18 all","s":"安装最新的 clang++","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#install-latest-clang++","p":16},{"i":24,"t":"上述命令执行之后，我们会发现，g++ 仍然是 g++11，clang++ 仍然是 clang++-14。 这里介绍一下 update-alternatives，由于管理 Ubuntu 上软件版本的切换，使其多版本共存。语法： 注册可选的软件版本： sudo update-alternatives --install link name path priority \\ [--slave link name path] 切换默认的软件版本： sudo update-alternatives --config name 注意 切换编译器软件包可能有风险，建议只在个人计算机上使用。","s":"切换编译器的默认版本","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#change-default-version","p":16},{"i":26,"t":"注册 gcc / g++ 版本： sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-11 11 --slave /usr/bin/g++ g++ /usr/bin/g++-11 sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-12 12 --slave /usr/bin/g++ g++ /usr/bin/g++-12 sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-13 13 --slave /usr/bin/g++ g++ /usr/bin/g++-13 选择默认 gcc / g++ 版本： sudo update-alternatives --config gcc 会弹出以下选项： There are 3 choices for the alternative gcc (providing /usr/bin/gcc). Selection Path Priority Status ------------------------------------------------------------ * 0 /usr/bin/gcc-13 13 auto mode 1 /usr/bin/gcc-11 11 manual mode 2 /usr/bin/gcc-12 12 manual mode 3 /usr/bin/gcc-13 13 manual mode Press <enter> to keep the current choice[*], or type selection number: 输入序号即可。","s":"切换 g++ 的默认版本","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#change-g++-default-version","p":16},{"i":28,"t":"clang / clang++ 是 LLVM 工具链的一部分，更新的时候，建议把 llvm 所有工具一起更新。 这里使用以下脚本 update-alternatives-clang.sh 进行批量注册： #!/usr/bin/env bash # Colors RESET=$(tput sgr0) RED=$(tput setaf 1) GREEN=$(tput setaf 2) BOLD=$(tput bold) # Get available versions from /lib/llvm-* # You can also use specific versions, e.g. VERSIONS=(\"14\" \"17\" \"18\"), but not recommend VERSIONS=() for dir in /lib/llvm-*; do if [[ -d \"$dir\" ]]; then version=$(basename \"$dir\" | cut -d'-' -f2) VERSIONS+=(\"$version\") fi done # Loop through versions for VERSION in \"${VERSIONS[@]}\"; do # Check if /lib/llvm-${VERSION} directory exists if [[ -d \"/lib/llvm-${VERSION}\" ]]; then # Scan paths and generate string alternative_string=\"\" alternative_cmds=() for cmd in \"/lib/llvm-${VERSION}/bin/\"*; do if [[ -x \"$cmd\" ]] && [[ \"$(basename \"$cmd\")\" != \"clang\" ]]; then base_cmd=$(basename \"$cmd\") symlink=\"/usr/bin/${base_cmd}-${VERSION}\" if [[ -x \"${symlink}\" ]]; then alternative_cmds+=($(basename ${symlink})) alternative_string+=\"--slave /usr/bin/${base_cmd} ${base_cmd} ${symlink} \" fi fi done # Remove specific alternative configuration sudo update-alternatives --remove clang \"/usr/bin/clang-${VERSION}\" > /dev/null # Install alternatives install_command=\"sudo update-alternatives \\ --quiet \\ --install /usr/bin/clang clang /usr/bin/clang-${VERSION} ${VERSION} \\ ${alternative_string}\" # Print the concatenated string echo \"${BOLD}${GREEN}[Adding alternative /usr/bin/clang-${VERSION} ...]${RESET}\" echo \"Master command: clang-${VERSION}\" echo \"Slave commands: ${alternative_cmds[*]}\" eval \"$install_command\" # Check eval command's return value if [[ $? -eq 0 ]]; then echo \"${BOLD}${GREEN}[Adding alternative /usr/bin/clang-${VERSION}: succeeded]${RESET}\" else echo \"${BOLD}${RED}[Adding alternative /usr/bin/clang-${VERSION}: failed]${RESET}\" fi echo \"\" else # Remove specific alternative configuration if /lib/llvm-${VERSION} directory does not exist sudo update-alternatives --remove clang \"/usr/bin/clang-${VERSION}\" &> /dev/null fi done clang_path=$(sudo update-alternatives --get-selections | grep ^clang | awk '{print $NF}') echo \"======================================================================\" echo \"${GREEN}clang alternative is set to: ${clang_path}${RESET}\" echo \"======================================================================\" # print helps echo \"\" echo \"Info:\" num_versions=${#VERSIONS[@]} if [[ num_versions -gt 1 ]]; then echo \" use '${GREEN}sudo update-alternatives --config clang${RESET}' to change default clang alternative\" fi echo \" use '${GREEN}sudo update-alternatives --remove clang /usr/bin/clang-*${RESET}' to delete a clang alternative\" echo \" use '${GREEN}sudo update-alternatives --remove-all clang${RESET}' to delete all clang alternatives\" sudo bash update-alternatives-clang.sh 结果如下： [Adding alternative /usr/bin/clang-14 ...] Master command: clang-14 Slave commands: analyze-build-14 bugpoint-14 ... [Adding alternative /usr/bin/clang-14: succeeded] [Adding alternative /usr/bin/clang-18 ...] Master command: clang-18 Slave commands: amdgpu-arch-18 analyze-build-18 ... [Adding alternative /usr/bin/clang-18: succeeded] ====================================================================== clang alternative is set to: /usr/bin/clang-18 ====================================================================== ... 同上面的 gcc/g++ 版本切换，切换 clang / llvm 工具链版本命令如下： sudo update-alternatives --config clang 会弹出以下选项： There are 2 choices for the alternative clang (providing /usr/bin/clang). Selection Path Priority Status ------------------------------------------------------------ * 0 /usr/bin/clang-18 18 auto mode 1 /usr/bin/clang-14 14 manual mode 2 /usr/bin/clang-18 18 manual mode Press <enter> to keep the current choice[*], or type selection number: 输入序号即可。","s":"切换 clang++ 的默认版本","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#change-clang++-default-version","p":16},{"i":30,"t":"Leaflet 是地理信息系统（GIS）中流行的开源 JavaScript 库。 本文在 MDX 中使用 Leaflet 绘制交互式地图。","s":"使用 Leaflet 绘制地图","u":"/blog/mdx/interactive-map-with-leaflet","h":"","p":29},{"i":32,"t":"博客文章支持 Docusaurus Markdown 功能，例如 MDX。","s":"React 支持","u":"/blog/mdx/react-support","h":"","p":31},{"i":34,"t":"提示 使用 React 的强大功能来创建交互式博客文章。 <button onClick={() => alert('按钮被点击了!')}>点击这里！</button> 点击这里！","s":"交互式","u":"/blog/mdx/react-support","h":"#interactive","p":31},{"i":36,"t":"提示 使用 React 的强大功能来创建图表。 import {Chart} from './_asset/snowfall.js'; export const year = 2013; # 去年降雪 {year} 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。 <Chart year={year} color=\"#fcb32c\" />; 去年降雪 2013 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。","s":"图表式","u":"/blog/mdx/react-support","h":"#diagram","p":31},{"i":38,"t":"2013 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。","s":"去年降雪","u":"/blog/mdx/react-support","h":"","p":31},{"i":40,"t":"现在可以在 mdx 中使用 Font Awesome 图标。 <FontAwesomeIcon icon=\"fa-brands fa-react\" /> 这是 React 图标。 <FontAwesomeIcon icon=\"fa-brands fa-github\" size=\"xl\" /> 这是加大的 GitHub 图标。 这是 React 图标。 这是加大的 GitHub 图标。 默认情况下，图标继承其父容器的字体大小。现代浏览器使用默认字体大小 16px。 要更改字体大小，请在 FontAwesomeIcon 中添加以下 size 属性： 2xs: 0.625em (10px) xs: 0.75em (12px) sm: 0.875em (14px) lg: 1.25em (20px) xl: 1.5em (24px) 2xl: 2em (32px) 1x ~ 10x: 1em ~ 10em","s":"支持 Font Awesome","u":"/blog/mdx/support-fontawesome","h":"","p":39},{"i":42,"t":"Docusaurus 提供了 <Tabs> 和 <TabItem> 组件，可以通过 MDX 在 Markdown 中使用该组件。 我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。 <Tabs> <TabItem value=\"apple\" label=\"Apple\" default> This is an apple 🍎 </TabItem> <TabItem value=\"orange\" label=\"Orange\"> This is an orange 🍊 </TabItem> <TabItem value=\"banana\" label=\"Banana\"> This is a banana 🍌 </TabItem> </Tabs> This is an apple 🍎 This is an orange 🍊 This is a banana 🍌","s":"支持全局 Tabs 和 TabItem","u":"/blog/mdx/support-global-tabs-tabitem","h":"","p":41},{"i":44,"t":"数学公式可以使用 KaTeX 渲染，目前本站已经支持。","s":"支持 LaTeX 数学公式","u":"/blog/mdx/support-math-latex","h":"","p":43},{"i":46,"t":"请阅读 KaTeX 文档了解更多详细信息。","s":"用法","u":"/blog/mdx/support-math-latex","h":"#usage","p":43},{"i":48,"t":"对于行内数学公式，将 LaTeX 包裹在 $ 之间： 假设 $f\\colon[a,b]\\to\\R$ 是黎曼可积的，定义 $F\\colon[a,b]\\to\\R$ 为 $F(x)=\\int_{a}^{x} f(t)\\,dt$。那么， $F$ 是连续的；并且 $x$ 在 $f$ 在 $x$ 处连续；$F$ 在 $x$ 处可微，且 $F'(x)=f(x)$。 假设 f ⁣:[a,b]→Rf\\colon[a,b]\\to\\Rf:[a,b]→R 是黎曼可积的，定义 F ⁣:[a,b]→RF\\colon[a,b]\\to\\RF:[a,b]→R 为 F(x)=∫axf(t) dtF(x)=\\int_{a}^{x} f(t)\\,dtF(x)=∫ax​f(t)dt。那么， FFF 是连续的；并且 xxx 在 fff 在 xxx 处连续；FFF 在 xxx 处可微，且 F′(x)=f(x)F'(x)=f(x)F′(x)=f(x)。","s":"行内公式","u":"/blog/mdx/support-math-latex","h":"#inline","p":43},{"i":50,"t":"对于公式块，使用换行符和 $$ 隔开： $$ I = \\int_0^{2\\pi} \\sin(x)\\,dx $$ I=∫02πsin⁡(x) dxI = \\int_0^{2\\pi} \\sin(x)\\,dxI=∫02π​sin(x)dx","s":"公式块","u":"/blog/mdx/support-math-latex","h":"#blocks","p":43},{"i":52,"t":"Mermaid 是一个绘制图表的工具。 请参阅 Mermaid 教程 并使用 Mermaid 实时编辑 来进行绘图。","s":"支持 Mermaid 图表","u":"/blog/mdx/support-mermaid-diagrams","h":"","p":51},{"i":54,"t":"Example Mermaid sequence diagram ```mermaid graph TD; A-->B; A-->C; B-->D; C-->D; ```","s":"序列图","u":"/blog/mdx/support-mermaid-diagrams","h":"#序列图","p":51},{"i":56,"t":"Example Mermaid flowchart ```mermaid flowchart TD A[Christmas] -->|Get money| B(Go shopping) B --> C{Let me think} C -->|One| D[Laptop] C -->|Two| E[iPhone] C -->|Three| F[fa:fa-car Car] ```","s":"流程图","u":"/blog/mdx/support-mermaid-diagrams","h":"#流程图","p":51},{"i":58,"t":"基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。","s":"支持嵌入 YouTube 和 Bilibili 视频","u":"/blog/mdx/support-video-link","h":"","p":57},{"i":60,"t":"React 组件： YouTube / Bilibili 组件参数： id: 必选 YouTube: https://www.youtube.com/watch?v=<id>?... 或者 https://youtu.be/<id>?... Bilibili: https://www.bilibili.com/video/<id>/?...，由 BV 开头。 title: 可选。位置在视频上方；左对齐。","s":"参数说明","u":"/blog/mdx/support-video-link","h":"#参数说明","p":57},{"i":63,"t":"<YouTube id=\"sEQf5lcnj_o\" title=\"Animenz - Unravel [Piano Ver.]\" /> Animenz - Unravel [Piano Ver.]","s":"YouTube 嵌入","u":"/blog/mdx/support-video-link","h":"#youtube-嵌入","p":57},{"i":65,"t":"<Bilibili id=\"BV1bi4y1675m\" title=\"Animenz - Unravel [钢琴版]\" /> Animenz - Unravel [钢琴版]","s":"Bilibili 嵌入","u":"/blog/mdx/support-video-link","h":"#bilibili-嵌入","p":57},{"i":68,"t":"2023年11月24日 Sol 千里之行，始于足下。","s":"支持 LaTeX 数学公式","u":"/blog/page/2","h":"","p":66},{"i":70,"t":"2023年11月23日 Sol 千里之行，始于足下。","s":"React 支持","u":"/blog/page/2","h":"","p":66},{"i":72,"t":"2019年5月28日 Sol 千里之行，始于足下。","s":"欢迎","u":"/blog/page/2","h":"","p":66},{"i":74,"t":"本站默认字体现已更改为 LxgwWenKai Screen.","s":"更改默认字体","u":"/blog/site/change-default-fonts","h":"","p":73},{"i":76,"t":"删除所有的文章的国际化支持。之前所有文章均有双语版本，后续所有文章只会有单个语言版本。 由于难以长期维护和保证内容的一致性，删除所有的双语文章和 docusaurus i18n 国际化配置： 双语文章需要额外的翻译时间。 本站使用 docusaurus 部署，但是 docusaurus 在全局化存在各种问题，包括但不限于： 需要保证文章链接的一致性，否则无法相互跳转。 需要保证锚点 (anchor tag) 的一致性。 假设配置是英文为主语言，这种情况下，不可以单独发表中文文章。如果要写中文文章，必须先存在的英文文章。 中英文链接在不同目录，且层级不同，来回切换不方便。 翻译不是一劳永逸的事情，每次更新某个语言的文章的时候，需要更新同时两种语言。","s":"停止国际化支持","u":"/blog/site/remove-i18n-support","h":"","p":75},{"i":78,"t":"本站使用 autocorrect 对中文内容进行统一排版和修正。","s":"统一中文排版","u":"/blog/tools/cli/autocorrect","h":"","p":77},{"i":80,"t":"Docusaurus 博客功能由 blog 插件提供支持。 使用 <!-- truncate --> 注释来限制博客预览。 只需要将 Markdown 文件 (或文件夹) 添加到 blog 目录即可。 常用的博客作者可以添加到 authors.yml 中。 可以从文件名中提取博客文章日期，例如： 2019-05-30-welcome.md 2019-05-30-welcome/index.md 写博客时，可以方便地在同级文件夹内引用图像： 博客也支持标签！ 如果不需要博客：删除此目录，并在 Docusaurus 配置中使用 blog: false 即可。","s":"欢迎","u":"/blog/welcome","h":"","p":79},{"i":83,"t":"MainActivity.kt 内的 onCreate() 最后添加： val looperThread = LooperThread() looperThread.start() thread { Thread.sleep(3000) val message = Message() message.what = LooperThread.EVENT_INIT message.target = looperThread.getHandler() Log.d( \"MainActivity\", \"send message ${message.what} at thread id ${Thread.currentThread().id}\" ) message.sendToTarget() } 新建 LooperThread.kt： package com.example.myapplication import android.os.Handler import android.os.Looper import android.os.Message import android.util.Log class LooperThread : Thread() { private var handler: Handler? = null private var isInitialized = false fun getHandler(): Handler? { return handler } override fun run() { Looper.prepare() handler = object : Handler(Looper.myLooper()!!) { override fun handleMessage(msg: Message) { Log.d( TAG, \"Received message ${msg.what} at thread id ${ currentThread().id }\" ) when (msg.what) { EVENT_INIT -> { performInit() } else -> println(\"Unknown Event: \" + msg.what) } } } isInitialized = true Looper.loop() } fun isInitialized(): Boolean { return isInitialized } private fun performInit() { Log.d(TAG, \"performInit() called\") sleep(1000); } companion object { const val EVENT_INIT: Int = 1 private const val TAG = \"LooperThread\" } }","s":"方法一：创建一个 Thread 线程","u":"/docs/android-framework/handler/create-a-thread-with-looper","h":"#方法一创建一个-thread-线程","p":81},{"i":85,"t":"MainActivity.kt 内的 onCreate() 最后添加： val myHandlerThread = MyHandlerThread(\"MyHandlerThreadA\") myHandlerThread.start() thread { Thread.sleep(3000) val message = Message() message.what = MyHandlerThread.EVENT_INIT message.target = myHandlerThread.handler Log.d( \"MainActivity\", \"send message ${message.what} at thread id ${Thread.currentThread().id}\" ) message.sendToTarget() } 新建 MyHandlerThread.kt： package com.example.myapplication import android.os.Handler import android.os.HandlerThread import android.os.Looper import android.os.Message import android.util.Log public class MyHandlerThread(name: String?) : HandlerThread(name) { lateinit var handler: Handler; override fun onLooperPrepared() { super.onLooperPrepared() handler = object : Handler(Looper.myLooper()!!) { override fun handleMessage(msg: Message) { Log.d( TAG, \"Received message ${msg.what} at thread id ${ currentThread().id }\" ) when (msg.what) { EVENT_INIT -> performInit() else -> println(\"Unknown Event: \" + msg.what) } } } } private fun performInit() { Log.d(TAG, \"performInit() called\") sleep(1000); } companion object { const val EVENT_INIT: Int = 1 private const val TAG = \"MyHandlerThread\" } }","s":"方法二：创建一个 HandlerThread 线程","u":"/docs/android-framework/handler/create-a-thread-with-looper","h":"#方法二创建一个-handlerthread-线程","p":81},{"i":88,"t":"一套 Android 消息传递机制 / 异步通信机制","s":"定义","u":"/docs/android-framework/handler/handler-introduction","h":"#定义","p":86},{"i":90,"t":"在 Android 开发中，UI 线程 (主线程) 负责处理用户界面的交互和更新。 如果 UI 线程被长时间阻塞或执行耗时操作，将会导致用户界面的响应性降低，用户体验很差。 如果在主线程进行大量耗时操作，没有响应用户输入事件 (如点击、滑动等) 时，Android 系统会认为应用程序无响应，并弹出 ANR (Application Not Responding) 对话框提醒用户。这个时间阈值通常为 5 秒。","s":"背景","u":"/docs/android-framework/handler/handler-introduction","h":"#背景","p":86},{"i":92,"t":"UI 线程 (主线程) 不能进行大量耗时的工作，需要使用子线程 (工作线程) 处理。 如果工作线程直接尝试更新 UI 组件，就会违反 Android 的线程安全规定，可能会导致应用程序崩溃或界面异常。","s":"问题","u":"/docs/android-framework/handler/handler-introduction","h":"#问题","p":86},{"i":94,"t":"使用 Handler 机制进行线程间通信： 启动一个子线程 (工作线程) 进行耗时的任务处理，可以向 UI 线程的 Handler 发送消息。 UI 线程的 Handler 收到消息后，在主线程中更新 UI 组件。 这样可以保证 UI 操作在主线程中执行，从而避免线程安全问题。","s":"解决方案","u":"/docs/android-framework/handler/handler-introduction","h":"#解决方案","p":86},{"i":96,"t":"下图说明了子线程进行耗时操作，并且更新主线程的流程。 流程 Handler 类流程 真实世界类比 1 创建 Looper 对象并启动 创建一个工厂车间的传送带系统 2 创建 MessageQueue 对象 准备用于存放货物的货物槽链 3 创建 Handler 对象并和 Looper 对象关联 为传送带指派一名专门的处理人员 4 在工作线程中执行耗时操作 在另一个车间进行耗时的生产加工 5 将需要通知主线程的更新信息封装在 Message 对象中 将需要通知处理人员的货物信息打包到货物槽 6 将 Message 对象添加到 MessageQueue 中 将打包好的货物放入货物槽 7 Looper 不断循环读取 MessageQueue 中的 Message 传送带不断运转，读取其中的货物槽的信息 8 Looper 取出 Message 对象，并分发给关联的 Handler 处理 处理人员取出货物槽，交给对应的处理人员进行处理 9 Handler 的 handleMessage() 方法中更新 UI 组件 处理人员根据货物槽内的信息，执行相应的处理操作","s":"和真实世界类比","u":"/docs/android-framework/handler/handler-introduction","h":"#和真实世界类比","p":86},{"i":98,"t":"一个线程最多只有一个 Looper 对象，一个 Looper 对象只和一个线程关联 主线程创建 Looper：Android 主线程都是 Activity，在 ActivityThread 内会自动创建 子线程创建 Looper： 继承于 Thread，在 run() 里面调用 Looper.prepare() 和 Looper.loop() 继承于 HandlerThread，自动创建 一个 Looper 对象中必须有且仅有一个 MessageQueue 对象 一个 Looper 对象可以关联 0 到多个 Handler 对象","s":"Handler / Looper / Thread 的关系","u":"/docs/android-framework/handler/handler-introduction","h":"#handler--looper--thread-的关系","p":86},{"i":101,"t":"创建 Looper 时会同步创建 MessageQueue 对象 主线程 Looper 的创建​ ActivityThread.main() 调用 Looper.prepareMainLooper() 和 Looper.loop() /** * 源码分析：Looper.prepareMainLooper() * 作用：为主线程（UI 线程）创建 1 个循环器对象（Looper），同时也生成了 1 个消息队列对象（MessageQueue） * 注：该方法在主线程（UI 线程）创建时自动调用，即 主线程的 Looper 对象自动生成，不需手动生成 */ // 在Android应用进程启动时，会默认创建1个主线程（ActivityThread，也叫 UI 线程） // 创建时，会自动调用 ActivityThread 的1个静态的 main() 方法 = 应用程序的入口 // main() 内则会调用 Looper.prepareMainLooper() 为主线程生成 1 个 Looper 对象 public static void main(String[] args) { ... // 1. 为主线程创建 1 个 Looper 对象，同时生成 1 个消息队列对象（MessageQueue） // 方法逻辑类似 Looper.prepare() // 注：prepare()：为子线程中创建 1 个 Looper 对象 Looper.prepareMainLooper(); ... // 2. 创建主线程 ActivityThread thread = new ActivityThread(); ... // 3. 自动开启消息循环 Looper.loop(); } Looper.prepareMainLooper()：在主线程中创建 1 个 Looper 对象 (自动生成) /** * Initialize the current thread as a looper, marking it as an * application's main looper. See also: {@link #prepare()} * * @deprecated The main looper for your application is created by the Android environment, * so you should never need to call this function yourself. */ @Deprecated public static void prepareMainLooper() { prepare(false); synchronized (Looper.class) { if (sMainLooper != null) { throw new IllegalStateException(\"The main Looper has already been prepared.\"); } sMainLooper = myLooper(); } } Looper.myLooper() /** * Return the Looper object associated with the current thread. Returns * null if the calling thread is not associated with a Looper. */ public static @Nullable Looper myLooper() { return sThreadLocal.get(); } sThreadLocal // sThreadLocal.get() will return null unless you've called prepare(). @UnsupportedAppUsage static final ThreadLocal<Looper> sThreadLocal= new ThreadLocal<Looper>(); 子线程 Looper 的创建​ Looper.prepare()：在子线程中创建 1 个 Looper 对象 (手动创建) /** Initialize the current thread as a looper. * This gives you a chance to create handlers that then reference * this looper, before actually starting the loop. Be sure to call * {@link #loop()} after calling this method, and end it by calling * {@link #quit()}. */ public static void prepare() { prepare(true); } private static void prepare(boolean quitAllowed) { // 1. 判断 sThreadLocal 是否为 null，否则抛出异常 // 即 Looper.prepare() 方法不能被调用两次， 1 个线程中只能对应 1 个 Looper 实例 // 注：sThreadLocal 为 ThreadLocal 对象，用于存储线程的变量 if (sThreadLocal.get() != null) { throw new RuntimeException(\"Only one Looper may be created per thread\"); } sThreadLocal.set(new Looper(quitAllowed)); } Looper.Looper() private Looper(boolean quitAllowed) { // 创建 1 个 Looper 实例时，会自动创建 1 个与之配对的 MessageQueue mQueue = new MessageQueue(quitAllowed); mThread = Thread.currentThread(); }","s":"Looper 对象创建 & MessageQueue 对象创建","u":"/docs/android-framework/handler/handler-introduction","h":"#looper-对象创建--messagequeue-对象创建","p":86},{"i":103,"t":"Handler 对象创建 private Handler mHandler = new Handler(Looper.myLooper()){ }; Handler() 创建时，关联 Looper 对象和 Queue 对象。 public Handler(@NonNull Looper looper) { this(looper, null, false); } Handler() final Looper mLooper; final MessageQueue mQueue; @UnsupportedAppUsage public Handler(@NonNull Looper looper, @Nullable Callback callback, boolean async) { mLooper = looper; mQueue = looper.mQueue; mCallback = callback; mAsynchronous = async; }","s":"Handler 对象创建","u":"/docs/android-framework/handler/handler-introduction","h":"#handler-对象创建","p":86},{"i":105,"t":"Handler.sendMessageAtTime(Message msg，long uptimeMillis)：调用 enqueueMessage() /** * 分析：sendMessageAtTime(Message msg, long uptimeMillis) * 作用：在指定时间发出消息，消息会加入到消息队列 MessageQueue */ /** * Enqueue a message into the message queue after all pending messages * before the absolute time (in milliseconds) <var>uptimeMillis</var>. * <b>The time-base is {@link android.os.SystemClock#uptimeMillis}.</b> * Time spent in deep sleep will add an additional delay to execution. * You will receive it in {@link #handleMessage}, in the thread attached * to this handler. * * @param uptimeMillis The absolute time at which the message should be * delivered, using the * {@link android.os.SystemClock#uptimeMillis} time-base. * * @return Returns true if the message was successfully placed in to the * message queue. Returns false on failure, usually because the * looper processing the message queue is exiting. Note that a * result of true does not mean the message will be processed -- if * the looper is quit before the delivery time of the message * occurs then the message will be dropped. */ public boolean sendMessageAtTime(@NonNull Message msg, long uptimeMillis) { MessageQueue queue = mQueue; if (queue == null) { RuntimeException e = new RuntimeException( this + \" sendMessageAtTime() called with no mQueue\"); Log.w(\"Looper\", e.getMessage(), e); return false; } return enqueueMessage(queue, msg, uptimeMillis); } Handler.enqueueMessage(MessageQueue queue, Message msg, long uptimeMillis) private boolean enqueueMessage(@NonNull MessageQueue queue, @NonNull Message msg, long uptimeMillis) { msg.target = this; msg.workSourceUid = ThreadLocalWorkSource.getUid(); if (mAsynchronous) { msg.setAsynchronous(true); } return queue.enqueueMessage(msg, uptimeMillis); } MessageQueue.enqueueMessage(Message msg，long when)：将 Message 对象加入消息队列 /** * 分析：MessageQueue.enqueueMessage() * 作用：入队消息，即将新的消息加入消息队列 */ // mMessages 为链表结构，头部为优先执行 // 即优先执行 mMessages，执行完之后 mMessages = mMessages.next，直到 mMessages 为空为止 Message mMessages; ... boolean enqueueMessage(Message msg, long when) { // msg.target 即目标 Handler，如果为 null 则抛出异常 if (msg.target == null) { throw new IllegalArgumentException(\"Message must have a target.\"); } // 可能出现存在多个线程同时插入消息多情况，用 synchronized 同步 synchronized (this) { if (msg.isInUse()) { throw new IllegalStateException(msg + \" This message is already in use.\"); } ... // msg：当前（需要加入消息队列的）消息 msg.markInUse(); msg.when = when; // p (mMessages)：指针，指向当前队列的头部 Message p = mMessages; boolean needWake; // 如果以下出现情况之一：当前队列为空；当前 msg 需要马上执行；当前 msg 需要执行的时间 < 头部消息需要执行的时间，则将当前消息插入队列头部；反止插入队列头部之后（中间或尾部）。 if (p == null || when == 0 || when < p.when) { // 将当前消息插入队列头部 // New head, wake up the event queue if blocked. msg.next = p; mMessages = msg; needWake = mBlocked; } else { // Inserted within the middle of the queue. Usually we don't have to wake // up the event queue unless there is a barrier at the head of the queue // and the message is the earliest asynchronous message in the queue. // 是否需要队列保持唤醒状态 needWake = mBlocked && p.target == null && msg.isAsynchronous(); // 将当前消息插入队列中间 Message prev; for (;;) { prev = p; p = p.next; if (p == null || when < p.when) { break; } if (needWake && p.isAsynchronous()) { needWake = false; } } msg.next = p; // invariant: p == prev.next prev.next = msg; } // We can assume mPtr != 0 because mQuitting is false. if (needWake) { nativeWake(mPtr); } } return true; }","s":"Message 发送","u":"/docs/android-framework/handler/handler-introduction","h":"#message-发送","p":86},{"i":107,"t":"Looper.loop()：取出 Looper 中的消息队列，使用 MessageQueue.next() 无限循环取出 msg 并发送到对应的 handler /** * 作用：消息循环，即从消息队列中获取消息、分发消息到 Handler * 特别注意： * a. 主线程的消息循环不允许退出，即无限循环 * b. 子线程的消息循环允许退出：调用消息队列 MessageQueue 的 quit() */ /** * Run the message queue in this thread. Be sure to call * {@link #quit()} to end the loop. */ public static void loop() { // 1. 获取当前Looper的消息队列 // myLooper()作用：返回 sThreadLocal 存储的 Looper 实例；若为 null 则抛出异常 final Looper me = myLooper(); // 若为 null 则抛出异常，即 loop（）执行前必须执行 prepare() 创建 Looper 实例 if (me == null) { throw new RuntimeException(\"No Looper; Looper.prepare() wasn't called on this thread.\"); } ... me.mInLoop = true; // 获取Looper实例中的消息队列对象 (MessageQueue) final MessageQueue queue = me.mQueue; // 2. 消息循环（for 无限循环） for (;;) { // 2.1 从消息队列取出消息 msg，若取出消息为空则线程阻塞 Message msg = queue.next(); // might block if (msg == null) { // No message indicates that the message queue is quitting. return; } try { // 2.2 把消息 msg 派发给消息对象 msg.target（实际是 handler 对象） msg.target.dispatchMessage(msg); ... } ... ... // 3. 释放资源 msg.recycleUnchecked(); } } MessageQueue.next()：从消息队列中取出下一个 Message 对象 /** * 分析：MessageQueue.next() * 作用：出队消息，即从消息队列中移出头部消息 */ // mMessages 为链表结构，头部为优先执行 // 即优先执行 mMessages，执行完之后 mMessages = mMessages.next，直到 mMessages 为空为止 Message mMessages; ... Message next() { // 该参数用于确定消息队列中是否还有消息 // 从而决定消息队列应处于出队消息状态 or 等待状态 int nextPollTimeoutMillis = 0; for (;;) { if (nextPollTimeoutMillis != 0) { Binder.flushPendingCommands(); } // nativePollOnce 方法在 native 层，若是 nextPollTimeoutMillis 为 -1，此时消息队列处于等待状态 nativePollOnce(ptr, nextPollTimeoutMillis); synchronized (this) { final long now = SystemClock.uptimeMillis(); Message prevMsg = null; // 从消息队列中取出头部消息对象作为当前的 msg Message msg = mMessages; if (msg != null) { // 如果当前 msg 时间大于当前时间，重新计算 nextPollTimeoutMillis 并设置超时唤醒 if (now < msg.when) { nextPollTimeoutMillis = (int) Math.min(msg.when - now, Integer.MAX_VALUE); } else { // 如果当前 msg 时间等于或者小于当前时间，取出当前 msg mBlocked = false; if (prevMsg != null) { prevMsg.next = msg.next; } else { mMessages = msg.next; } msg.next = null; if (DEBUG) Log.v(TAG, \"Returning message: \" + msg); msg.markInUse(); return msg; } } else { // 若消息队列中已无消息，则将 nextPollTimeoutMillis 参数设为 -1 // 下次循环时，消息队列则处于等待状态 nextPollTimeoutMillis = -1; } ... } ... } } Handler.dispatchMessage()：将消息分发给接收者/回调方，由接收者/回调方进行相应处理 /** * 分析：dispatchMessage(Message msg) * 作用：派发消息到对应的 Handler 实例，根据传入的 msg 作出对应的操作 */ /** * Handle system messages here. */ public void dispatchMessage(@NonNull Message msg) { // 若 msg.callback 属性不为空，则代表使用了 post(Runnable r) 发送消息 if (msg.callback != null) { handleCallback(msg); } else { // 若 mCallback 不为空，则代表使用了 Handler(Looper looper, Callback callback) 传入了 callback 参数；之后调用 callback 自己实现的 handleMessage() 方法（必须进行 override 重写，返回 true 或 false） if (mCallback != null) { if (mCallback.handleMessage(msg)) { return; } } // 若msg.callback属性为空，则代表使用了 sendMessage（Message msg）发送消息；之后调用 handleMessage(msg)（一般都会进行 override 重写） handleMessage(msg); } }","s":"Message 分发和 Handler 处理","u":"/docs/android-framework/handler/handler-introduction","h":"#message-分发和-handler-处理","p":86},{"i":110,"t":"亦称：Abstract Factory","s":"抽象工厂模式","u":"/docs/design-patterns/abstract-factory","h":"","p":109},{"i":112,"t":"抽象工厂模式是一种创建型设计模式，它能创建一系列相关的对象，而无需指定其具体类。","s":"意图","u":"/docs/design-patterns/abstract-factory","h":"#意图","p":109},{"i":114,"t":"假设你正在开发一款家具商店模拟器。你的代码中包括一些类，用于表示： 一系列相关产品，例如 椅子 Chair、沙发 Sofa 和 咖啡桌 Coffee­Table。 系列产品的不同变体。例如，你可以使用 现代 Modern、维多利亚 Victorian、装饰风艺术 Art­Deco 等风格生成 椅子、沙发 和 咖啡桌。 系列产品及其不同变体。 你需要设法单独生成每件家具对象，这样才能确保其风格一致。如果顾客收到的家具风格不一样，他们可不会开心。 现代风格的沙发和维多利亚风格的椅子不搭。 此外，你也不希望在添加新产品或新风格时修改已有代码。家具供应商对于产品目录的更新非常频繁，你不会想在每次更新时都去修改核心代码的。","s":"问题","u":"/docs/design-patterns/abstract-factory","h":"#问题","p":109},{"i":116,"t":"首先，抽象工厂模式建议为系列中的每件产品明确声明接口 (例如椅子、沙发或咖啡桌)。然后，确保所有产品变体都继承这些接口。例如，所有风格的椅子都实现 椅子 接口；所有风格的咖啡桌都实现 咖啡桌 接口，以此类推。 同一对象的所有变体都必须放置在同一个类层次结构之中。 接下来，我们需要声明抽象工厂——包含系列中所有产品构造方法的接口。例如 create­Chair 创建椅子、create­Sofa 创建沙发和 create­Coffee­Table 创建咖啡桌。这些方法必须返回抽象产品类型，即我们之前抽取的那些接口：椅子，沙发 和 咖啡桌 等等。 每个具体工厂类都对应一个特定的产品变体。 那么该如何处理产品变体呢？对于系列产品的每个变体，我们都将基于 抽象工厂 接口创建不同的工厂类。每个工厂类都只能返回特定类别的产品，例如，现代家具工厂 Modern­Furniture­Factory 只能创建 现代椅子 Modern­Chair、现代沙发 Modern­Sofa 和 现代咖啡桌 Modern­Coffee­Table 对象。 客户端代码可以通过相应的抽象接口调用工厂和产品类。你无需修改实际客户端代码，就能更改传递给客户端的工厂类，也能更改客户端代码接收的产品变体。 客户端无需了解其所调用工厂的具体类信息。 假设客户端想要工厂创建一把椅子。客户端无需了解工厂类，也不用管工厂类创建出的椅子类型。无论是现代风格，还是维多利亚风格的椅子，对于客户端来说没有分别，它只需调用抽象 椅子 接口就可以了。这样一来，客户端只需知道椅子以某种方式实现了 sit­On 坐下方法就足够了。此外，无论工厂返回的是何种椅子变体，它都会和由同一工厂对象创建的沙发或咖啡桌风格一致。 最后一点说明：如果客户端仅接触抽象接口，那么谁来创建实际的工厂对象呢？一般情况下，应用程序会在初始化阶段创建具体工厂对象。而在此之前，应用程序必须根据配置文件或环境设定选择工厂类别。","s":"解决方案","u":"/docs/design-patterns/abstract-factory","h":"#解决方案","p":109},{"i":118,"t":"抽象产品 (Abstract Product) 为构成系列产品的一组不同但相关的产品声明接口。 具体产品 (Concrete Product) 是抽象产品的多种不同类型实现。所有变体 (维多利亚/现代) 都必须实现相应的抽象产品 (椅子/沙发)。 抽象工厂 (Abstract Factory) 接口声明了一组创建各种抽象产品的方法。 具体工厂 (Concrete Factory) 实现抽象工厂的构建方法。每个具体工厂都对应特定产品变体，且仅创建此种产品变体。 尽管具体工厂会对具体产品进行初始化，其构建方法签名必须返回相应的抽象产品。这样，使用工厂类的客户端代码就不会与工厂创建的特定产品变体耦合。客户端 (Client) 只需通过抽象接口调用工厂和产品对象，就能与任何具体工厂/产品变体交互。","s":"抽象工厂模式结构","u":"/docs/design-patterns/abstract-factory","h":"#抽象工厂模式结构","p":109},{"i":120,"t":"下面例子通过应用抽象工厂模式，使得客户端代码无需与具体 UI 类耦合，就能创建跨平台的 UI 元素，同时确保所创建的元素与指定的操作系统匹配。 跨平台 UI 类示例。 跨平台应用中的相同 UI 元素功能类似，但是在不同操作系统下的外观有一定差异。此外，你需要确保 UI 元素与当前操作系统风格一致。你一定不希望在 Windows 系统下运行的应用程序中显示 macOS 的控件。 抽象工厂接口声明一系列构建方法，客户端代码可调用它们生成不同风格的 UI 元素。每个具体工厂对应特定操作系统，并负责生成符合该操作系统风格的 UI 元素。 其运作方式如下：应用程序启动后检测当前操作系统。根据该信息，应用程序通过与该操作系统对应的类创建工厂对象。其余代码使用该工厂对象创建 UI 元素。这样可以避免生成错误类型的元素。 使用这种方法，客户端代码只需调用抽象接口，而无需了解具体工厂类和 UI 元素。此外，客户端代码还支持未来添加新的工厂或 UI 元素。 这样一来，每次在应用程序中添加新的 UI 元素变体时，你都无需修改客户端代码。你只需创建一个能够生成这些 UI 元素的工厂类，然后稍微修改应用程序的初始代码，使其能够选择合适的工厂类即可。 // 抽象工厂接口声明了一组能返回不同抽象产品的方法。这些产品属于同一个系列 // 且在高层主题或概念上具有相关性。同系列的产品通常能相互搭配使用。系列产 // 品可有多个变体，但不同变体的产品不能搭配使用。 interface GUIFactory is method createButton():Button method createCheckbox():Checkbox // 具体工厂可生成属于同一变体的系列产品。工厂会确保其创建的产品能相互搭配 // 使用。具体工厂方法签名会返回一个抽象产品，但在方法内部则会对具体产品进 // 行实例化。 class WinFactory implements GUIFactory is method createButton():Button is return new WinButton() method createCheckbox():Checkbox is return new WinCheckbox() // 每个具体工厂中都会包含一个相应的产品变体。 class MacFactory implements GUIFactory is method createButton():Button is return new MacButton() method createCheckbox():Checkbox is return new MacCheckbox() // 系列产品中的特定产品必须有一个基础接口。所有产品变体都必须实现这个接口。 interface Button is method paint() // 具体产品由相应的具体工厂创建。 class WinButton implements Button is method paint() is // 根据 Windows 样式渲染按钮。 class MacButton implements Button is method paint() is // 根据 macOS 样式渲染按钮 // 这是另一个产品的基础接口。所有产品都可以互动，但是只有相同具体变体的产 // 品之间才能够正确地进行交互。 interface Checkbox is method paint() class WinCheckbox implements Checkbox is method paint() is // 根据 Windows 样式渲染复选框。 class MacCheckbox implements Checkbox is method paint() is // 根据 macOS 样式渲染复选框。 // 客户端代码仅通过抽象类型（GUIFactory、Button 和 Checkbox）使用工厂 // 和产品。这让你无需修改任何工厂或产品子类就能将其传递给客户端代码。 class Application is private field factory: GUIFactory private field button: Button constructor Application(factory: GUIFactory) is this.factory = factory method createUI() is this.button = factory.createButton() method paint() is button.paint() // 程序会根据当前配置或环境设定选择工厂类型，并在运行时创建工厂（通常在初 // 始化阶段）。 class ApplicationConfigurator is method main() is config = readApplicationConfigFile() if (config.OS == \"Windows\") then factory = new WinFactory() else if (config.OS == \"Mac\") then factory = new MacFactory() else throw new Exception(\"错误！未知的操作系统。\") Application app = new Application(factory)","s":"伪代码","u":"/docs/design-patterns/abstract-factory","h":"#伪代码","p":109},{"i":122,"t":"如果代码需要与多个不同系列的相关产品交互，但是由于无法提前获取相关信息，或者出于对未来扩展性的考虑，你不希望代码基于产品的具体类进行构建，在这种情况下，你可以使用抽象工厂。 抽象工厂为你提供了一个接口，可用于创建每个系列产品的对象。只要代码通过该接口创建对象，那么你就不会生成与应用程序已生成的产品类型不一致的产品。 如果你有一个基于一组抽象方法的类，且其主要功能因此变得不明确，那么在这种情况下可以考虑使用抽象工厂模式。 在设计良好的程序中，每个类仅负责一件事。如果一个类与多种类型产品交互，就可以考虑将工厂方法抽取到独立的工厂类或具备完整功能的抽象工厂类中。 实现方式 以不同的产品类型与产品变体为维度绘制矩阵。 为所有产品声明抽象产品接口。然后让所有具体产品类实现这些接口。 声明抽象工厂接口，并且在接口中为所有抽象产品提供一组构建方法。 为每种产品变体实现一个具体工厂类。 在应用程序中开发初始化代码。该代码根据应用程序配置或当前环境，对特定具体工厂类进行初始化。然后将该工厂对象传递给所有需要创建产品的类。 找出代码中所有对产品构造函数的直接调用，将其替换为对工厂对象中相应构建方法的调用。","s":"抽象工厂模式适合应用场景","u":"/docs/design-patterns/abstract-factory","h":"#抽象工厂模式适合应用场景","p":109},{"i":124,"t":"✔️ 你可以确保同一工厂生成的产品相互匹配。 ✔️ 你可以避免客户端和具体产品代码的耦合。 ✔️ 单一职责原则。你可以将产品生成代码抽取到同一位置，使得代码易于维护。 ✔️ 开闭原则。向应用程序中引入新产品变体时，你无需修改客户端代码。 ❌ 由于采用该模式需要向应用中引入众多接口和类，代码可能会比之前更加复杂。","s":"抽象工厂模式优缺点","u":"/docs/design-patterns/abstract-factory","h":"#抽象工厂模式优缺点","p":109},{"i":126,"t":"在许多设计工作的初期都会使用工厂方法模式 (较为简单，而且可以更方便地通过子类进行定制)，随后演化为使用抽象工厂模式、原型模式或生成器模式 (更灵活但更加复杂)。 生成器重点关注如何分步生成复杂对象。抽象工厂专门用于生产一系列相关对象。抽象工厂会马上返回产品，生成器则允许你在获取产品前执行一些额外构造步骤。 抽象工厂模式通常基于一组工厂方法，但你也可以使用原型模式来生成这些类的方法。 当只需对客户端代码隐藏子系统创建对象的方式时，你可以使用抽象工厂来代替外观模式。 你可以将抽象工厂和桥接模式搭配使用。如果由桥接定义的抽象只能与特定实现合作，这一模式搭配就非常有用。在这种情况下，抽象工厂可以对这些关系进行封装，并且对客户端代码隐藏其复杂性。 抽象工厂、生成器和原型都可以用单例模式来实现。","s":"与其他模式的关系","u":"/docs/design-patterns/abstract-factory","h":"#与其他模式的关系","p":109},{"i":128,"t":"亦称：封装器模式、Wrapper、Adapter","s":"适配器模式","u":"/docs/design-patterns/adapter","h":"","p":127},{"i":130,"t":"适配器模式是一种结构型设计模式，它能使接口不兼容的对象能够相互合作。","s":"意图","u":"/docs/design-patterns/adapter","h":"#意图","p":127},{"i":132,"t":"假如你正在开发一款股票市场监测程序，它会从不同来源下载 XML 格式的股票数据，然后向用户呈现出美观的图表。 在开发过程中，你决定在程序中整合一个第三方智能分析函数库。但是遇到了一个问题，那就是分析函数库只兼容 JSON 格式的数据。 你无法“直接”使用分析函数库，因为它所需的输入数据格式与你的程序不兼容。 你可以修改程序库来支持 XML。但是，这可能需要修改部分依赖该程序库的现有代码。甚至还有更糟糕的情况，你可能根本没有程序库的源代码，从而无法对其进行修改。","s":"问题","u":"/docs/design-patterns/adapter","h":"#问题","p":127},{"i":134,"t":"你可以创建一个适配器。这是一个特殊的对象，能够转换对象接口，使其能与其他对象进行交互。 适配器模式通过封装对象将复杂的转换过程隐藏于幕后。被封装的对象甚至察觉不到适配器的存在。例如，你可以使用一个将所有数据转换为英制单位 (如英尺和英里) 的适配器封装运行于米和千米单位制中的对象。 适配器不仅可以转换不同格式的数据，其还有助于采用不同接口的对象之间的合作。它的运作方式如下： 适配器实现与其中一个现有对象兼容的接口。 现有对象可以使用该接口安全地调用适配器方法。 适配器方法被调用后将以另一个对象兼容的格式和顺序将请求传递给该对象。 有时你甚至可以创建一个双向适配器来实现双向转换调用。 让我们回到股票市场程序。为了解决数据格式不兼容的问题，你可以为分析函数库中的每个类创建将 XML 转换为 JSON 格式的适配器，然后让客户端仅通过这些适配器来与函数库进行交流。当某个适配器被调用时，它会将传入的 XML 数据转换为 JSON 结构，并将其传递给被封装分析对象的相应方法。","s":"解决方案","u":"/docs/design-patterns/adapter","h":"#解决方案","p":127},{"i":136,"t":"出国旅行前后的旅行箱。 如果你是第一次从美国到欧洲旅行，那么在给笔记本充电时可能会大吃一惊。不同国家的电源插头和插座标准不同。美国插头和德国插座不匹配。同时提供美国标准插座和欧洲标准插头的电源适配器可以解决你的难题。","s":"真实世界类比","u":"/docs/design-patterns/adapter","h":"#真实世界类比","p":127},{"i":139,"t":"实现时使用了构成原则：适配器实现了其中一个对象的接口，并对另一个对象进行封装。所有流行的编程语言都可以实现适配器。 客户端 (Client) 是包含当前程序业务逻辑的类。 客户端接口 (Client Interface) 描述了其他类与客户端代码合作时必须遵循的协议。 服务 (Service) 中有一些功能类 (通常来自第三方或遗留系统)。客户端与其接口不兼容，因此无法直接调用其功能。 适配器 (Adapter) 是一个可以同时与客户端和服务交互的类：它在实现客户端接口的同时封装了服务对象。适配器接受客户端通过适配器接口发起的调用，并将其转换为适用于被封装服务对象的调用。 客户端代码只需通过接口与适配器交互即可，无需与具体的适配器类耦合。因此，你可以向程序中添加新类型的适配器而无需修改已有代码。这在服务类的接口被更改或替换时很有用：你无需修改客户端代码就可以创建新的适配器类。","s":"对象适配器","u":"/docs/design-patterns/adapter","h":"#对象适配器","p":127},{"i":141,"t":"这一实现使用了继承机制：适配器同时继承两个对象的接口。请注意，这种方式仅能在支持多重继承的编程语言中实现，例如 C++。 类适配器不需要封装任何对象，因为它同时继承了客户端和服务的行为。适配功能在重写的方法中完成。最后生成的适配器可替代已有的客户端类进行使用。","s":"类适配器","u":"/docs/design-patterns/adapter","h":"#类适配器","p":127},{"i":143,"t":"下列适配器模式演示基于经典的“方钉和圆孔”问题。 让方钉适配圆孔。 适配器假扮成一个圆钉 (Round­Peg)，其半径等于方钉 (Square­Peg) 横截面对角线的一半 (即能够容纳方钉的最小外接圆的半径)。 // 假设你有两个接口相互兼容的类：圆孔（Round­Hole）和圆钉（Round­Peg）。 class RoundHole is constructor RoundHole(radius) { …… } method getRadius() is // 返回孔的半径。 method fits(peg: RoundPeg) is return this.getRadius() >= peg.getRadius() class RoundPeg is constructor RoundPeg(radius) { …… } method getRadius() is // 返回钉子的半径。 // 但还有一个不兼容的类：方钉（Square­Peg）。 class SquarePeg is constructor SquarePeg(width) { …… } method getWidth() is // 返回方钉的宽度。 // 适配器类让你能够将方钉放入圆孔中。它会对 RoundPeg 类进行扩展，以接收适 // 配器对象作为圆钉。 class SquarePegAdapter extends RoundPeg is // 在实际情况中，适配器中会包含一个 SquarePeg 类的实例。 private field peg: SquarePeg constructor SquarePegAdapter(peg: SquarePeg) is this.peg = peg method getRadius() is // 适配器会假扮为一个圆钉，其半径刚好能与适配器实际封装的方钉搭配 // 起来。 return peg.getWidth() * Math.sqrt(2) / 2 // 客户端代码中的某个位置。 hole = new RoundHole(5) rpeg = new RoundPeg(5) hole.fits(rpeg) // true small_sqpeg = new SquarePeg(5) large_sqpeg = new SquarePeg(10) hole.fits(small_sqpeg) // 此处无法编译（类型不一致）。 small_sqpeg_adapter = new SquarePegAdapter(small_sqpeg) large_sqpeg_adapter = new SquarePegAdapter(large_sqpeg) hole.fits(small_sqpeg_adapter) // true hole.fits(large_sqpeg_adapter) // false","s":"伪代码","u":"/docs/design-patterns/adapter","h":"#伪代码","p":127},{"i":145,"t":"当你希望使用某个类，但是其接口与其他代码不兼容时，可以使用适配器类。 适配器模式允许你创建一个中间层类，其可作为代码与遗留类、第三方类或提供怪异接口的类之间的转换器。 如果您需要复用这样一些类，他们处于同一个继承体系，并且他们又有了额外的一些共同的方法，但是这些共同的方法不是所有在这一继承体系中的子类所具有的共性。 你可以扩展每个子类，将缺少的功能添加到新的子类中。但是，你必须在所有新子类中重复添加这些代码，这样会使得代码有坏味道。 将缺失功能添加到一个适配器类中是一种优雅得多的解决方案。然后你可以将缺少功能的对象封装在适配器中，从而动态地获取所需功能。如要这一点正常运作，目标类必须要有通用接口，适配器的成员变量应当遵循该通用接口。这种方式同装饰模式非常相似。 实现方式 确保至少有两个类的接口不兼容： 一个无法修改 (通常是第三方、遗留系统或者存在众多已有依赖的类) 的功能性服务类。 一个或多个将受益于使用服务类的客户端类。 声明客户端接口，描述客户端如何与服务交互。 创建遵循客户端接口的适配器类。所有方法暂时都为空。 在适配器类中添加一个成员变量用于保存对于服务对象的引用。通常情况下会通过构造函数对该成员变量进行初始化，但有时在调用其方法时将该变量传递给适配器会更方便。 依次实现适配器类客户端接口的所有方法。适配器会将实际工作委派给服务对象，自身只负责接口或数据格式的转换。 客户端必须通过客户端接口使用适配器。这样一来，你就可以在不影响客户端代码的情况下修改或扩展适配器。","s":"适配器模式适合应用场景","u":"/docs/design-patterns/adapter","h":"#适配器模式适合应用场景","p":127},{"i":147,"t":"✔️ 单一职责原则你可以将接口或数据转换代码从程序主要业务逻辑中分离。 ✔️ 开闭原则。只要客户端代码通过客户端接口与适配器进行交互，你就能在不修改现有客户端代码的情况下在程序中添加新类型的适配器。 ❌ 代码整体复杂度增加，因为你需要新增一系列接口和类。有时直接更改服务类使其与其他代码兼容会更简单。","s":"适配器模式优缺点","u":"/docs/design-patterns/adapter","h":"#适配器模式优缺点","p":127},{"i":149,"t":"桥接模式通常会于开发前期进行设计，使你能够将程序的各个部分独立开来以便开发。另一方面，适配器模式通常在已有程序中使用，让相互不兼容的类能很好地合作。 适配器可以对已有对象的接口进行修改，装饰模式则能在不改变对象接口的前提下强化对象功能。此外，装饰还支持递归组合，适配器则无法实现。 适配器能为被封装对象提供不同的接口，代理模式能为对象提供相同的接口，装饰则能为对象提供加强的接口。 外观模式为现有对象定义了一个新接口，适配器则会试图运用已有的接口。适配器通常只封装一个对象，外观通常会作用于整个对象子系统上。 桥接、状态模式和策略模式 (在某种程度上包括适配器) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。","s":"与其他模式的关系","u":"/docs/design-patterns/adapter","h":"#与其他模式的关系","p":127},{"i":151,"t":"行为模式负责对象间的高效沟通和职责委派。","s":"行为模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":153,"t":"允许你将请求沿着处理者链进行发送。收到请求后，每个处理者均可对请求进行处理，或将其传递给链上的下个处理者。","s":"📄️ 责任链模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":155,"t":"它可将请求转换为一个包含与请求相关的所有信息的独立对象。该转换让你能根据不同的请求将方法参数化、延迟请求执行或将其放入队列中，且能实现可撤销操作。","s":"📄️ 命令模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":157,"t":"让你能在不暴露集合底层表现形式（列表、栈和树等）的情况下遍历集合中所有的元素。","s":"📄️ 迭代器模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":159,"t":"能让你减少对象之间混乱无序的依赖关系。该模式会限制对象之间的直接交互，迫使它们通过一个中介者对象进行合作。","s":"📄️ 中介者模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":161,"t":"允许在不暴露对象实现细节的情况下保存和恢复对象之前的状态。","s":"📄️ 备忘录模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":163,"t":"允许你定义一种订阅机制，可在对象事件发生时通知多个“观察”该对象的其他对象。","s":"📄️ 观察者模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":165,"t":"让你能在一个对象的内部状态变化时改变其行为，使其看上去就像改变了自身所属的类一样。","s":"📄️ 状态模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":167,"t":"能让你定义一系列算法，并将每种算法分别放入独立的类中，以使算法的对象能够相互替换。","s":"📄️ 策略模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":169,"t":"在超类中定义一个算法的框架，允许子类在不修改结构的情况下重写算法的特定步骤。","s":"📄️ 模板方法模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":171,"t":"将算法与其所作用的对象隔离开来。","s":"📄️ 访问者模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":173,"t":"亦称：Bridge","s":"桥接模式","u":"/docs/design-patterns/bridge","h":"","p":172},{"i":175,"t":"桥接模式是一种结构型设计模式，可将一个大类或一系列紧密相关的类拆分为抽象和实现两个独立的层次结构，从而能在开发时分别使用。","s":"意图","u":"/docs/design-patterns/bridge","h":"#意图","p":172},{"i":177,"t":"*抽象？实现？*听上去挺吓人？让我们慢慢来，先考虑一个简单的例子。 假如你有一个几何 形状 Shape 类，从它能扩展出两个子类：圆形 Circle 和 方形 Square。你希望对这样的类层次结构进行扩展以使其包含颜色，所以你打算创建名为 红色 Red 和 蓝色 Blue 的形状子类。但是，由于你已有两个子类，所以总共需要创建四个类才能覆盖所有组合，例如 蓝色圆形 Blue­Circle 和 红色方形 Red­Square。 所有组合类的数量将以几何级数增长。 在层次结构中新增形状和颜色将导致代码复杂程度指数增长。例如添加三角形状，你需要新增两个子类，也就是每种颜色一个；此后新增一种新颜色需要新增三个子类，即每种形状一个。如此以往，情况会越来越糟糕。","s":"问题","u":"/docs/design-patterns/bridge","h":"#问题","p":172},{"i":179,"t":"问题的根本原因是我们试图在两个独立的维度——形状与颜色——上扩展形状类。这在处理类继承时是很常见的问题。 桥接模式通过将继承改为组合的方式来解决这个问题。具体来说，就是抽取其中一个维度并使之成为独立的类层次，这样就可以在初始类中引用这个新层次的对象，从而使得一个类不必拥有所有的状态和行为。 将一个类层次转化为多个相关的类层次，避免单个类层次的失控。 根据该方法，我们可以将颜色相关的代码抽取到拥有 红色 和 蓝色 两个子类的颜色类中，然后在 形状 类中添加一个指向某一颜色对象的引用成员变量。现在，形状类可以将所有与颜色相关的工作委派给连入的颜色对象。这样的引用就成为了 形状 和 颜色 之间的桥梁。此后，新增颜色将不再需要修改形状的类层次，反之亦然。","s":"解决方案","u":"/docs/design-patterns/bridge","h":"#解决方案","p":172},{"i":181,"t":"设计模式四人组的著作在桥接定义中提出了抽象部分和实现部分两个术语。我觉得这些术语过于学术了，反而让模式看上去比实际情况更加复杂。在介绍过形状和颜色的简单例子后，我们来看看四人组著作中让人望而生畏的词语的含义。 抽象部分 (也被称为接口) 是一些实体的高阶控制层。该层自身不完成任何具体的工作，它需要将工作委派给实现部分层 (也被称为平台)。 注意，这里提到的内容与编程语言中的接口或抽象类无关。它们并不是一回事。 在实际的程序中，抽象部分是图形用户界面 (GUI)，而实现部分则是底层操作系统代码 (API)，GUI 层调用 API 层来对用户的各种操作做出响应。 一般来说，你可以在两个独立方向上扩展这种应用： 开发多个不同的 GUI (例如面向普通用户和管理员进行分别配置) 支持多个不同的 API (例如，能够在 Windows、Linux 和 macOS 上运行该程序)。 在最糟糕的情况下，程序可能会是一团乱麻，其中包含数百种条件语句，连接着代码各处不同种类的 GUI 和各种 API。 在庞杂的代码中，即使是很小的改动都非常难以完成，因为你必须要在整体上对代码有充分的理解。而在较小且定义明确的模块中，进行修改则要容易得多。 你可以将特定接口 - 平台的组合代码抽取到独立的类中，以在混乱中建立一些秩序。但是，你很快会发现这种类的数量很多。类层次将以指数形式增长，因为每次添加一个新的 GUI 或支持一种新的 API 都需要创建更多的类。 让我们试着用桥接模式来解决这个问题。该模式建议将类拆分为两个类层次结构： 抽象部分：程序的 GUI 层。 实现部分：操作系统的 API。 创建跨平台应用程序的一种方法 抽象对象控制程序的外观，并将真实工作委派给连入的实现对象。不同的实现只要遵循相同的接口就可以互换，使同一 GUI 可在 Windows 和 Linux 下运行。 最后的结果是：你无需改动与 API 相关的类就可以修改 GUI 类。此外如果想支持一个新的操作系统，只需在实现部分层次中创建一个子类即可。","s":"抽象部分和实现部分","u":"/docs/design-patterns/bridge","h":"#抽象部分和实现部分","p":172},{"i":183,"t":"抽象部分 (Abstraction) 提供高层控制逻辑，依赖于完成底层实际工作的实现对象。 实现部分 (Implementation) 为所有具体实现声明通用接口。抽象部分仅能通过在这里声明的方法与实现对象交互。 抽象部分可以列出和实现部分一样的方法，但是抽象部分通常声明一些复杂行为，这些行为依赖于多种由实现部分声明的原语操作。 具体实现 (Concrete Implementations) 中包括特定于平台的代码。 精确抽象 (Refined Abstraction) 提供控制逻辑的变体。与其父类一样，它们通过通用实现接口与不同的实现进行交互。 通常情况下，客户端 (Client) 仅关心如何与抽象部分合作。但是，客户端需要将抽象对象与一个实现对象连接起来。","s":"桥接模式结构","u":"/docs/design-patterns/bridge","h":"#桥接模式结构","p":172},{"i":185,"t":"示例演示了桥接模式如何拆分程序中同时管理设备及其遥控器的庞杂代码。设备 Device 类作为实现部分，而 遥控器 Remote 类则作为抽象部分。 最初类层次结构被拆分为两个部分：设备和遥控器。 遥控器基类声明了一个指向设备对象的引用成员变量。所有遥控器通过通用设备接口与设备进行交互，使得同一个遥控器可以支持不同类型的设备。 你可以开发独立于设备类的遥控器类，只需新建一个遥控器子类即可。例如，基础遥控器可能只有两个按钮，但你可在其基础上扩展新功能，比如额外的一节电池或一块触摸屏。 客户端代码通过遥控器构造函数将特定种类的遥控器与设备对象连接起来。 // “抽象部分”定义了两个类层次结构中“控制”部分的接口。它管理着一个指向“实 // 现部分”层次结构中对象的引用，并会将所有真实工作委派给该对象。 class RemoteControl is protected field device: Device constructor RemoteControl(device: Device) is this.device = device method togglePower() is if (device.isEnabled()) then device.disable() else device.enable() method volumeDown() is device.setVolume(device.getVolume() - 10) method volumeUp() is device.setVolume(device.getVolume() + 10) method channelDown() is device.setChannel(device.getChannel() - 1) method channelUp() is device.setChannel(device.getChannel() + 1) // 你可以独立于设备类的方式从抽象层中扩展类。 class AdvancedRemoteControl extends RemoteControl is method mute() is device.setVolume(0) // “实现部分”接口声明了在所有具体实现类中通用的方法。它不需要与抽象接口相 // 匹配。实际上，这两个接口可以完全不一样。通常实现接口只提供原语操作，而 // 抽象接口则会基于这些操作定义较高层次的操作。 interface Device is method isEnabled() method enable() method disable() method getVolume() method setVolume(percent) method getChannel() method setChannel(channel) // 所有设备都遵循相同的接口。 class Tv implements Device is // …… class Radio implements Device is // …… // 客户端代码中的某个位置。 tv = new Tv() remote = new RemoteControl(tv) remote.togglePower() radio = new Radio() remote = new AdvancedRemoteControl(radio)","s":"伪代码","u":"/docs/design-patterns/bridge","h":"#伪代码","p":172},{"i":187,"t":"如果你想要拆分或重组一个具有多重功能的庞杂类 (例如能与多个数据库服务器进行交互的类)，可以使用桥接模式。 类的代码行数越多，弄清其运作方式就越困难，对其进行修改所花费的时间就越长。一个功能上的变化可能需要在整个类范围内进行修改，而且常常会产生错误，甚至还会有一些严重的副作用。 桥接模式可以将庞杂类拆分为几个类层次结构。此后，你可以修改任意一个类层次结构而不会影响到其他类层次结构。这种方法可以简化代码的维护工作，并将修改已有代码的风险降到最低。 如果你希望在几个独立维度上扩展一个类，可使用该模式。 桥接建议将每个维度抽取为独立的类层次。初始类将相关工作委派给属于对应类层次的对象，无需自己完成所有工作。 如果你需要在运行时切换不同实现方法，可使用桥接模式。 当然并不是说一定要实现这一点，桥接模式可替换抽象部分中的实现对象，具体操作就和给成员变量赋新值一样简单。 顺便提一句，最后一点是很多人混淆桥接模式和策略模式的主要原因。记住，设计模式并不仅是一种对类进行组织的方式，它还能用于沟通意图和解决问题。 实现方式 明确类中独立的维度。独立的概念可能是：抽象/平台，域/基础设施，前端/后端或接口/实现。 了解客户端的业务需求，并在抽象基类中定义它们。 确定在所有平台上都可执行的业务。并在通用实现接口中声明抽象部分所需的业务。 为你域内的所有平台创建实现类，但需确保它们遵循实现部分的接口。 在抽象类中添加指向实现类型的引用成员变量。抽象部分会将大部分工作委派给该成员变量所指向的实现对象。 如果你的高层逻辑有多个变体，则可通过扩展抽象基类为每个变体创建一个精确抽象。 客户端代码必须将实现对象传递给抽象部分的构造函数才能使其能够相互关联。此后，客户端只需与抽象对象进行交互，无需和实现对象打交道。","s":"桥接模式适合应用场景","u":"/docs/design-patterns/bridge","h":"#桥接模式适合应用场景","p":172},{"i":189,"t":"✔️ 你可以创建与平台无关的类和程序。 ✔️ 客户端代码仅与高层抽象部分进行互动，不会接触到平台的详细信息。 ✔️ 开闭原则。你可以新增抽象部分和实现部分，且它们之间不会相互影响。 ✔️ 单一职责原则。抽象部分专注于处理高层逻辑，实现部分处理平台细节。 ❌ 对高内聚的类使用该模式可能会让代码更加复杂。","s":"桥接模式优缺点","u":"/docs/design-patterns/bridge","h":"#桥接模式优缺点","p":172},{"i":191,"t":"桥接模式通常会于开发前期进行设计，使你能够将程序的各个部分独立开来以便开发。另一方面，适配器模式通常在已有程序中使用，让相互不兼容的类能很好地合作。 桥接、状态模式和策略模式 (在某种程度上包括适配器) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。 你可以将抽象工厂模式和桥接搭配使用。如果由桥接定义的抽象只能与特定实现合作，这一模式搭配就非常有用。在这种情况下，抽象工厂可以对这些关系进行封装，并且对客户端代码隐藏其复杂性。 你可以结合使用生成器模式和桥接模式：主管类负责抽象工作，各种不同的生成器负责实现工作。","s":"与其他模式的关系","u":"/docs/design-patterns/bridge","h":"#与其他模式的关系","p":172},{"i":193,"t":"亦称：建造者模式、Builder","s":"生成器模式","u":"/docs/design-patterns/builder","h":"","p":192},{"i":195,"t":"生成器模式是一种创建型设计模式，使你能够分步骤创建复杂对象。该模式允许你使用相同的创建代码生成不同类型和形式的对象。","s":"意图","u":"/docs/design-patterns/builder","h":"#意图","p":192},{"i":197,"t":"假设有这样一个复杂对象，在对其进行构造时需要对诸多成员变量和嵌套对象进行繁复的初始化工作。这些初始化代码通常深藏于一个包含众多参数且让人基本看不懂的构造函数中；甚至还有更糟糕的情况，那就是这些代码散落在客户端代码的多个位置。 如果为每种可能的对象都创建一个子类，这可能会导致程序变得过于复杂。 例如，我们来思考如何创建一个 房屋 House 对象。建造一栋简单的房屋，首先你需要建造四面墙和地板，安装房门和一套窗户，然后再建造一个屋顶。但是如果你想要一栋更宽敞更明亮的房屋，还要有院子和其他设施 (例如暖气、排水和供电设备)，那又该怎么办呢？ 最简单的方法是扩展 房屋 基类，然后创建一系列涵盖所有参数组合的子类。但最终你将面对相当数量的子类。任何新增的参数 (例如门廊类型) 都会让这个层次结构更加复杂。 另一种方法则无需生成子类。你可以在 房屋 基类中创建一个包括所有可能参数的超级构造函数，并用它来控制房屋对象。这种方法确实可以避免生成子类，但它却会造成另外一个问题。 拥有大量输入参数的构造函数也有缺陷：这些参数也不是每次都要全部用上的。 通常情况下，绝大部分的参数都没有使用，这使得对于构造函数的调用十分不简洁。例如，只有很少的房子有游泳池，因此与游泳池相关的参数十之八九是毫无用处的。","s":"问题","u":"/docs/design-patterns/builder","h":"#问题","p":192},{"i":199,"t":"生成器模式建议将对象构造代码从产品类中抽取出来，并将其放在一个名为生成器的独立对象中。 生成器模式让你能够分步骤创建复杂对象。生成器不允许其他对象访问正在创建中的产品。 该模式会将对象构造过程划分为一组步骤，比如 build­Walls 创建墙壁和 build­Door 创建房门创建房门等。每次创建对象时，你都需要通过生成器对象执行一系列步骤。重点在于你无需调用所有步骤，而只需调用创建特定对象配置所需的那些步骤即可。 当你需要创建不同形式的产品时，其中的一些构造步骤可能需要不同的实现。例如，木屋的房门可能需要使用木头制造，而城堡的房门则必须使用石头制造。 在这种情况下，你可以创建多个不同的生成器，用不同方式实现一组相同的创建步骤。然后你就可以在创建过程中使用这些生成器 (例如按顺序调用多个构造步骤) 来生成不同类型的对象。 不同生成器以不同方式执行相同的任务。 例如，假设第一个建造者使用木头和玻璃制造房屋，第二个建造者使用石头和钢铁，而第三个建造者使用黄金和钻石。在调用同一组步骤后，第一个建造者会给你一栋普通房屋，第二个会给你一座小城堡，而第三个则会给你一座宫殿。但是，只有在调用构造步骤的客户端代码可以通过通用接口与建造者进行交互时，这样的调用才能返回需要的房屋。","s":"解决方案","u":"/docs/design-patterns/builder","h":"#解决方案","p":192},{"i":201,"t":"你可以进一步将用于创建产品的一系列生成器步骤调用抽取成为单独的主管类。主管类可定义创建步骤的执行顺序，而生成器则提供这些步骤的实现。 主管知道需要哪些创建步骤才能获得可正常使用的产品。 严格来说，你的程序中并不一定需要主管类。客户端代码可直接以特定顺序调用创建步骤。不过，主管类中非常适合放入各种例行构造流程，以便在程序中反复使用。 此外，对于客户端代码来说，主管类完全隐藏了产品构造细节。客户端只需要将一个生成器与主管类关联，然后使用主管类来构造产品，就能从生成器处获得构造结果了。","s":"主管","u":"/docs/design-patterns/builder","h":"#主管","p":192},{"i":203,"t":"生成器 (Builder) 接口声明在所有类型生成器中通用的产品构造步骤。 具体生成器 (Concrete Builders) 提供构造过程的不同实现。具体生成器也可以构造不遵循通用接口的产品。 产品 (Products) 是最终生成的对象。由不同生成器构造的产品无需属于同一类层次结构或接口。 主管 (Director) 类定义调用构造步骤的顺序，这样你就可以创建和复用特定的产品配置。 客户端 (Client) 必须将某个生成器对象与主管类关联。一般情况下，你只需通过主管类构造函数的参数进行一次性关联即可。此后主管类就能使用生成器对象完成后续所有的构造任务。但在客户端将生成器对象传递给主管类制造方法时还有另一种方式。在这种情况下，你在使用主管类生产产品时每次都可以使用不同的生成器。","s":"生成器模式结构","u":"/docs/design-patterns/builder","h":"#生成器模式结构","p":192},{"i":205,"t":"下面关于生成器模式的例子演示了你可以如何复用相同的对象构造代码来生成不同类型的产品——例如汽车 (Car)——及其相应的使用手册 (Manual)。 分步骤制造汽车并制作对应型号用户使用手册的示例 汽车是一个复杂对象，有数百种不同的制造方法。我们没有在 汽车 类中塞入一个巨型构造函数，而是将汽车组装代码抽取到单独的汽车生成器类中。该类中有一组方法可用来配置汽车的各种部件。 如果客户端代码需要组装一辆与众不同、精心调教的汽车，它可以直接调用生成器。或者，客户端可以将组装工作委托给主管类，因为主管类知道如何使用生成器制造最受欢迎的几种型号汽车。 你或许会感到吃惊，但确实每辆汽车都需要一本使用手册 (说真的，谁会去读它们呢？)。使用手册会介绍汽车的每一项功能，因此不同型号的汽车，其使用手册内容也不一样。因此，你可以复用现有流程来制造实际的汽车及其对应的手册。当然，编写手册和制造汽车不是一回事，所以我们需要另外一个生成器对象来专门编写使用手册。该类与其制造汽车的兄弟类都实现了相同的制造方法，但是其功能不是制造汽车部件，而是描述每个部件。将这些生成器传递给相同的主管对象，我们就能够生成一辆汽车或是一本使用手册了。 最后一个部分是获取结果对象。尽管金属汽车和纸质手册存在关联，但它们却是完全不同的东西。我们无法在主管类和具体产品类不发生耦合的情况下，在主管类中提供获取结果对象的方法。因此，我们只能通过负责制造过程的生成器来获取结果对象。 // 只有当产品较为复杂且需要详细配置时，使用生成器模式才有意义。下面的两个 // 产品尽管没有同样的接口，但却相互关联。 class Car is // 一辆汽车可能配备有 GPS 设备、行车电脑和几个座位。不同型号的汽车（ // 运动型轿车、SUV 和敞篷车）可能会安装或启用不同的功能。 class Manual is // 用户使用手册应该根据汽车配置进行编制，并介绍汽车的所有功能。 // 生成器接口声明了创建产品对象不同部件的方法。 interface Builder is method reset() method setSeats(……) method setEngine(……) method setTripComputer(……) method setGPS(……) // 具体生成器类将遵循生成器接口并提供生成步骤的具体实现。你的程序中可能会 // 有多个以不同方式实现的生成器变体。 class CarBuilder implements Builder is private field car:Car // 一个新的生成器实例必须包含一个在后续组装过程中使用的空产品对象。 constructor CarBuilder() is this.reset() // reset（重置）方法可清除正在生成的对象。 method reset() is this.car = new Car() // 所有生成步骤都会与同一个产品实例进行交互。 method setSeats(……) is // 设置汽车座位的数量。 method setEngine(……) is // 安装指定的引擎。 method setTripComputer(……) is // 安装行车电脑。 method setGPS(……) is // 安装全球定位系统。 // 具体生成器需要自行提供获取结果的方法。这是因为不同类型的生成器可能 // 会创建不遵循相同接口的、完全不同的产品。所以也就无法在生成器接口中 // 声明这些方法（至少在静态类型的编程语言中是这样的）。 // // 通常在生成器实例将结果返回给客户端后，它们应该做好生成另一个产品的 // 准备。因此生成器实例通常会在 `getProduct（获取产品）` 方法主体末尾 // 调用重置方法。但是该行为并不是必需的，你也可让生成器等待客户端明确 // 调用重置方法后再去处理之前的结果。 method getProduct():Car is product = this.car this.reset() return product // 生成器与其他创建型模式的不同之处在于：它让你能创建不遵循相同接口的产品。 class CarManualBuilder implements Builder is private field manual:Manual constructor CarManualBuilder() is this.reset() method reset() is this.manual = new Manual() method setSeats(……) is // 添加关于汽车座椅功能的文档。 method setEngine(……) is // 添加关于引擎的介绍。 method setTripComputer(……) is // 添加关于行车电脑的介绍。 method setGPS(……) is // 添加关于 GPS 的介绍。 method getProduct():Manual is // 返回使用手册并重置生成器。 // 主管只负责按照特定顺序执行生成步骤。其在根据特定步骤或配置来生成产品时 // 会很有帮助。由于客户端可以直接控制生成器，所以严格意义上来说，主管类并 // 不是必需的。 class Director is // 主管可同由客户端代码传递给自身的任何生成器实例进行交互。客户端可通 // 过这种方式改变最新组装完毕的产品的最终类型。主管可使用同样的生成步 // 骤创建多个产品变体。 method constructSportsCar(builder: Builder) is builder.reset() builder.setSeats(2) builder.setEngine(new SportEngine()) builder.setTripComputer(true) builder.setGPS(true) method constructSUV(builder: Builder) is // …… // 客户端代码会创建生成器对象并将其传递给主管，然后执行构造过程。最终结果 // 将需要从生成器对象中获取。 class Application is method makeCar() is director = new Director() CarBuilder builder = new CarBuilder() director.constructSportsCar(builder) Car car = builder.getProduct() CarManualBuilder builder = new CarManualBuilder() director.constructSportsCar(builder) // 最终产品通常需要从生成器对象中获取，因为主管不知晓具体生成器和 // 产品的存在，也不会对其产生依赖。 Manual manual = builder.getProduct()","s":"伪代码","u":"/docs/design-patterns/builder","h":"#伪代码","p":192},{"i":207,"t":"使用生成器模式可避免“重叠构造函数 (telescoping function)”的出现。 假设你的构造函数中有十个可选参数，那么调用该函数会非常不方便；因此，你需要重载这个构造函数，新建几个只有较少参数的简化版。但这些构造函数仍需调用主构造函数，传递一些默认数值来替代省略掉的参数。 class Pizza { Pizza(int size) { …… } Pizza(int size, boolean cheese) { …… } Pizza(int size, boolean cheese, boolean pepperoni) { …… } // …… 只有在 C# 或 Java 等支持方法重载的编程语言中才能写出如此复杂的构造函数。 生成器模式让你可以分步骤生成对象，而且允许你仅使用必须的步骤。应用该模式后，你再也不需要将几十个参数塞进构造函数里了。 当你希望使用代码创建不同形式的产品 (例如石头或木头房屋) 时，可使用生成器模式。 如果你需要创建的各种形式的产品，它们的制造过程相似且仅有细节上的差异，此时可使用生成器模式。 基本生成器接口中定义了所有可能的制造步骤，具体生成器将实现这些步骤来制造特定形式的产品。同时，主管类将负责管理制造步骤的顺序。 使用生成器构造组合树或其他复杂对象。 生成器模式让你能分步骤构造产品。你可以延迟执行某些步骤而不会影响最终产品。你甚至可以递归调用这些步骤，这在创建对象树时非常方便。 生成器在执行制造步骤时，不能对外发布未完成的产品。这可以避免客户端代码获取到不完整结果对象的情况。","s":"生成器模式适合应用场景","u":"/docs/design-patterns/builder","h":"#生成器模式适合应用场景","p":192},{"i":209,"t":"清晰地定义通用步骤，确保它们可以制造所有形式的产品。否则你将无法进一步实施该模式。 在基本生成器接口中声明这些步骤。 为每个形式的产品创建具体生成器类，并实现其构造步骤。 不要忘记实现获取构造结果对象的方法。你不能在生成器接口中声明该方法，因为不同生成器构造的产品可能没有公共接口，因此你就不知道该方法返回的对象类型。但是，如果所有产品都位于单一类层次中，你就可以安全地在基本接口中添加获取生成对象的方法。 考虑创建主管类。它可以使用同一生成器对象来封装多种构造产品的方式。 客户端代码会同时创建生成器和主管对象。构造开始前，客户端必须将生成器对象传递给主管对象。通常情况下，客户端只需调用主管类构造函数一次即可。主管类使用生成器对象完成后续所有制造任务。还有另一种方式，那就是客户端可以将生成器对象直接传递给主管类的制造方法。 只有在所有产品都遵循相同接口的情况下，构造结果可以直接通过主管类获取。否则，客户端应当通过生成器获取构造结果。","s":"实现方法","u":"/docs/design-patterns/builder","h":"#实现方法","p":192},{"i":211,"t":"✔️ 你可以分步创建对象，暂缓创建步骤或递归运行创建步骤。 ✔️ 生成不同形式的产品时，你可以复用相同的制造代码。 ✔️ 单一职责原则。你可以将复杂构造代码从产品的业务逻辑中分离出来。 ❌ 由于该模式需要新增多个类，因此代码整体复杂程度会有所增加。","s":"生成器模式优缺点","u":"/docs/design-patterns/builder","h":"#生成器模式优缺点","p":192},{"i":213,"t":"在许多设计工作的初期都会使用工厂方法模式 (较为简单，而且可以更方便地通过子类进行定制)，随后演化为使用抽象工厂模式、原型模式或生成器模式 (更灵活但更加复杂)。 生成器重点关注如何分步生成复杂对象。抽象工厂专门用于生产一系列相关对象。抽象工厂会马上返回产品，生成器则允许你在获取产品前执行一些额外构造步骤。 你可以在创建复杂组合模式树时使用生成器，因为这可使其构造步骤以递归的方式运行。 你可以结合使用生成器和桥接模式：主管类负责抽象工作，各种不同的生成器负责实现工作。 抽象工厂、生成器和原型都可以用单例模式来实现。","s":"与其他模式的关系","u":"/docs/design-patterns/builder","h":"#与其他模式的关系","p":192},{"i":215,"t":"亦称：职责链模式、命令链、CoR、Chain of Command、Chain of Responsibility","s":"责任链模式","u":"/docs/design-patterns/chain-of-responsibility","h":"","p":214},{"i":217,"t":"责任链模式是一种行为设计模式，允许你将请求沿着处理者链进行发送。收到请求后，每个处理者均可对请求进行处理，或将其传递给链上的下个处理者。","s":"意图","u":"/docs/design-patterns/chain-of-responsibility","h":"#意图","p":214},{"i":219,"t":"假如你正在开发一个在线订购系统。你希望对系统访问进行限制，只允许认证用户创建订单。此外，拥有管理权限的用户也拥有所有订单的完全访问权限。 简单规划后，你会意识到这些检查必须依次进行。只要接收到包含用户凭据的请求，应用程序就可尝试对进入系统的用户进行认证。但如果由于用户凭据不正确而导致认证失败，那就没有必要进行后续检查了。 请求必须经过一系列检查后才能由订购系统来处理。 在接下来的几个月里，你实现了后续的几个检查步骤。 一位同事认为直接将原始数据传递给订购系统存在安全隐患。因此你新增了额外的验证步骤来清理请求中的数据。 过了一段时间，有人注意到系统无法抵御暴力密码破解方式的攻击。为了防范这种情况，你立刻添加了一个检查步骤来过滤来自同一 IP 地址的重复错误请求。 又有人提议你可以对包含同样数据的重复请求返回缓存中的结果，从而提高系统响应速度。因此，你新增了一个检查步骤，确保只有没有满足条件的缓存结果时请求才能通过并被发送给系统。 代码变得越来越多，也越来越混乱。 检查代码本来就已经混乱不堪，而每次新增功能都会使其更加臃肿。修改某个检查步骤有时会影响其他的检查步骤。最糟糕的是，当你希望复用这些检查步骤来保护其他系统组件时，你只能复制部分代码，因为这些组件只需部分而非全部的检查步骤。 系统会变得让人非常费解，而且其维护成本也会激增。你在艰难地和这些代码共处一段时间后，有一天终于决定对整个系统进行重构。","s":"问题","u":"/docs/design-patterns/chain-of-responsibility","h":"#问题","p":214},{"i":221,"t":"与许多其他行为设计模式一样，责任链会将特定行为转换为被称作处理者的独立对象。在上述示例中，每个检查步骤都可被抽取为仅有单个方法的类，并执行检查操作。请求及其数据则会被作为参数传递给该方法。 模式建议你将这些处理者连成一条链。链上的每个处理者都有一个成员变量来保存对于下一处理者的引用。除了处理请求外，处理者还负责沿着链传递请求。请求会在链上移动，直至所有处理者都有机会对其进行处理。 最重要的是：处理者可以决定不再沿着链传递请求，这可高效地取消所有后续处理步骤。 在我们的订购系统示例中，处理者会在进行请求处理工作后决定是否继续沿着链传递请求。如果请求中包含正确的数据，所有处理者都将执行自己的主要行为，无论该行为是身份验证还是数据缓存。 处理者依次排列，组成一条链。 不过还有一种稍微不同的方式 (也是更经典一种)，那就是处理者接收到请求后自行决定是否能够对其进行处理。如果自己能够处理，处理者就不再继续传递请求。因此在这种情况下，每个请求要么最多有一个处理者对其进行处理，要么没有任何处理者对其进行处理。在处理图形用户界面元素栈中的事件时，这种方式非常常见。 例如，当用户点击按钮时，按钮产生的事件将沿着 GUI 元素链进行传递，最开始是按钮的容器 (如窗体或面板)，直至应用程序主窗口。链上第一个能处理该事件的元素会对其进行处理。此外，该例还有另一个值得我们关注的地方：它表明我们总能从对象树中抽取出链来。 对象树的枝干可以组成一条链。 所有处理者类均实现同一接口是关键所在。每个具体处理者仅关心下一个包含 execute 执行方法的处理者。这样一来，你就可以在运行时使用不同的处理者来创建链，而无需将相关代码与处理者的具体类进行耦合。","s":"解决方案","u":"/docs/design-patterns/chain-of-responsibility","h":"#解决方案","p":214},{"i":223,"t":"给技术支持打电话时你可能得应对多名接听人员。 最近，你刚为自己的电脑购买并安装了一个新的硬件设备。身为一名极客，你显然在电脑上安装了多个操作系统，所以你会试着启动所有操作系统来确认其是否支持新的硬件设备。Windows 检测到了该硬件设备并对其进行了自动启用。但是你喜爱的 Linux 系统并不支持新硬件设备。抱着最后一点希望，你决定拨打包装盒上的技术支持电话。 首先你会听到自动回复器的机器合成语音，它提供了针对各种问题的九个常用解决方案，但其中没有一个与你遇到的问题相关。过了一会儿，机器人将你转接到人工接听人员处。 这位接听人员同样无法提供任何具体的解决方案。他不断地引用手册中冗长的内容，并不会仔细聆听你的回应。在第 10 次听到“你是否关闭计算机后重新启动呢？”这句话后，你要求与一位真正的工程师通话。 最后，接听人员将你的电话转接给了工程师，他或许正缩在某幢办公大楼的阴暗地下室中，坐在他所深爱的服务器机房里，焦躁不安地期待着同一名真人交流。工程师告诉了你新硬件设备驱动程序的下载网址，以及如何在 Linux 系统上进行安装。问题终于解决了！你挂断了电话，满心欢喜。","s":"真实世界类比","u":"/docs/design-patterns/chain-of-responsibility","h":"#真实世界类比","p":214},{"i":225,"t":"处理者 (Handler) 声明了所有具体处理者的通用接口。该接口通常仅包含单个方法用于请求处理，但有时其还会包含一个设置链上下个处理者的方法。 基础处理者 (Base Handler) 是一个可选的类，你可以将所有处理者共用的样本代码放置在其中。 通常情况下，该类中定义了一个保存对于下个处理者引用的成员变量。客户端可通过将处理者传递给上个处理者的构造函数或设定方法来创建链。该类还可以实现默认的处理行为：确定下个处理者存在后再将请求传递给它。 具体处理者 (Concrete Handlers) 包含处理请求的实际代码。每个处理者接收到请求后，都必须决定是否进行处理，以及是否沿着链传递请求。 处理者通常是独立且不可变的，需要通过构造函数一次性地获得所有必要地数据。 客户端 (Client) 可根据程序逻辑一次性或者动态地生成链。值得注意的是，请求可发送给链上的任意一个处理者，而非必须是第一个处理者。","s":"责任链模式结构","u":"/docs/design-patterns/chain-of-responsibility","h":"#责任链模式结构","p":214},{"i":227,"t":"在本例中，责任链模式负责为活动的 GUI 元素显示上下文帮助信息。 GUI 类使用组合模式生成。每个元素都链接到自己的容器元素。你可随时构建从当前元素开始的、遍历其所有容器的元素链。 应用程序的 GUI 通常为对象树结构。例如，负责渲染程序主窗口的 对话框 类就是对象树的根节点。对话框包含 面板，而面板可能包含其他面板，或是 按钮 和 文本框 等下层元素。 只要给一个简单的组件指定帮助文本，它就可显示简短的上下文提示。但更复杂的组件可自定义上下文帮助文本的显示方式，例如显示手册摘录内容或在浏览器中打开一个网页。 帮助请求如何在 GUI 对象中移动。 当用户将鼠标指针移动到某个元素并按下 F1 键时，程序检测到指针下的组件并对其发送帮助请求。该请求不断向上传递到该元素所有的容器，直至某个元素能够显示帮助信息。 `// 处理者接口声明了一个创建处理者链的方法。还声明了一个执行请求的方法。 interface ComponentWithContextualHelp ismethod showHelp() // 简单组件的基础类。 abstract class Component implements ComponentWithContextualHelp isfield tooltipText：string // 组件容器在处理者链中作为“下一个”链接。 protected field container: Container // 如果组件设定了帮助文字，那它将会显示提示信息。如果组件没有帮助文字 // 且其容器存在，那它会将调用传递给容器。 method showHelp() isif (tooltipText != null) // 显示提示信息。 elsecontainer.showHelp() // 容器可以将简单组件和其他容器作为其子项目。链关系将在这里建立。该类将从 // 其父类处继承 showHelp (显示帮助) 的行为。 abstract class Container extends Component isprotected field children：array of Component method add(child) ischildren.add(child) child.container = this// 原始组件应该能够使用帮助操作的默认实现…… class Button extends Component is// …… // 但复杂组件可能会对默认实现进行重写。如果无法以新的方式来提供帮助文字，// 那组件总是还能调用基础实现的 (参见 Component 类)。 class Panel extends Container isfield modalHelpText：string method showHelp() isif (modalHelpText != null) // 显示包含帮助文字的模态窗口。 elsesuper.showHelp() // ……同上…… class Dialog extends Container isfield wikiPageURL：string method showHelp() isif (wikiPageURL != null) // 打开百科帮助页面。 elsesuper.showHelp() // 客户端代码。 class Application is// 每个程序都能以不同方式对链进行配置。 method createUI() isdialog = new Dialog (“预算报告”) dialog.wikiPageURL = “http://……”panel = new Panel(0，0，400，800) panel.modalHelpText = “本面板用于……”ok = new Button(250，760，50，20，“确认”) ok.tooltipText = “这是一个确认按钮……”cancel = new Button(320，760，50，20，“取消”) // …… panel.add(ok) panel.add(cancel) dialog.add(panel) // 想象这里会发生什么。 method onF1KeyPress() iscomponent = this.getComponentAtMouseCoords() component.showHelp()`","s":"伪代码","u":"/docs/design-patterns/chain-of-responsibility","h":"#伪代码","p":214},{"i":229,"t":"当程序需要使用不同方式处理不同种类请求，而且请求类型和顺序预先未知时，可以使用责任链模式。 该模式能将多个处理者连接成一条链。接收到请求后，它会“询问”每个处理者是否能够对其进行处理。这样所有处理者都有机会来处理请求。 当必须按顺序执行多个处理者时，可以使用该模式。 无论你以何种顺序将处理者连接成一条链，所有请求都会严格按照顺序通过链上的处理者。 如果所需处理者及其顺序必须在运行时进行改变，可以使用责任链模式。 如果在处理者类中有对引用成员变量的设定方法，你将能动态地插入和移除处理者，或者改变其顺序。 实现方式 声明处理者接口并描述请求处理方法的签名。确定客户端如何将请求数据传递给方法。最灵活的方式是将请求转换为对象，然后将其以参数的形式传递给处理函数。 为了在具体处理者中消除重复的样本代码，你可以根据处理者接口创建抽象处理者基类。该类需要有一个成员变量来存储指向链上下个处理者的引用。你可以将其设置为不可变类。但如果你打算在运行时对链进行改变，则需要定义一个设定方法来修改引用成员变量的值。为了使用方便，你还可以实现处理方法的默认行为。如果还有剩余对象，该方法会将请求传递给下个对象。具体处理者还能够通过调用父对象的方法来使用这一行为。 依次创建具体处理者子类并实现其处理方法。每个处理者在接收到请求后都必须做出两个决定： 是否自行处理这个请求。 是否将该请求沿着链进行传递。 客户端可以自行组装链，或者从其他对象处获得预先组装好的链。在后一种情况下，你必须实现工厂类以根据配置或环境设置来创建链。 客户端可以触发链中的任意处理者，而不仅仅是第一个。请求将通过链进行传递，直至某个处理者拒绝继续传递，或者请求到达链尾。 由于链的动态性，客户端需要准备好处理以下情况： 链中可能只有单个链接。 部分请求可能无法到达链尾。 其他请求可能直到链尾都未被处理。","s":"责任链模式适合应用场景","u":"/docs/design-patterns/chain-of-responsibility","h":"#责任链模式适合应用场景","p":214},{"i":231,"t":"✔️ 你可以控制请求处理的顺序。 ✔️ 单一职责原则。你可对发起操作和执行操作的类进行解耦。 ✔️ 开闭原则。你可以在不更改现有代码的情况下在程序中新增处理者。 ❌ 部分请求可能未被处理。","s":"责任链模式优缺点","u":"/docs/design-patterns/chain-of-responsibility","h":"#责任链模式优缺点","p":214},{"i":233,"t":"责任链模式、命令模式、中介者模式和观察者模式用于处理请求发送者和接收者之间的不同连接方式： 责任链按照顺序将请求动态传递给一系列的潜在接收者，直至其中一名接收者对请求进行处理。 命令在发送者和请求者之间建立单向连接。 中介者清除了发送者和请求者之间的直接连接，强制它们通过一个中介对象进行间接沟通。 观察者允许接收者动态地订阅或取消接收请求。 责任链通常和组合模式结合使用。在这种情况下，叶组件接收到请求后，可以将请求沿包含全体父组件的链一直传递至对象树的底部。 责任链的管理者可使用命令模式实现。在这种情况下，你可以对由请求代表的同一个上下文对象执行许多不同的操作。还有另外一种实现方式，那就是请求自身就是一个命令对象。在这种情况下，你可以对由一系列不同上下文连接而成的链执行相同的操作。 责任链和装饰模式的类结构非常相似。两者都依赖递归组合将需要执行的操作传递给一系列对象。但是，两者有几点重要的不同之处。 责任链的管理者可以相互独立地执行一切操作，还可以随时停止传递请求。另一方面，各种装饰可以在遵循基本接口的情况下扩展对象的行为。此外，装饰无法中断请求的传递。","s":"与其他模式的关系","u":"/docs/design-patterns/chain-of-responsibility","h":"#与其他模式的关系","p":214},{"i":235,"t":"亦称：动作、事务、Action、Transaction、Command","s":"命令模式","u":"/docs/design-patterns/command","h":"","p":234},{"i":237,"t":"命令模式是一种行为设计模式，它可将请求转换为一个包含与请求相关的所有信息的独立对象。该转换让你能根据不同的请求将方法参数化、延迟请求执行或将其放入队列中，且能实现可撤销操作。","s":"意图","u":"/docs/design-patterns/command","h":"#意图","p":234},{"i":239,"t":"假如你正在开发一款新的文字编辑器，当前的任务是创建一个包含多个按钮的工具栏，并让每个按钮对应编辑器的不同操作。你创建了一个非常简洁的 按钮 类，它不仅可用于生成工具栏上的按钮，还可用于生成各种对话框的通用按钮。 应用中的所有按钮都可以继承相同的类 尽管所有按钮看上去都很相似，但它们可以完成不同的操作 (打开、保存、打印和应用等)。你会在哪里放置这些按钮的点击处理代码呢？最简单的解决方案是在使用按钮的每个地方都创建大量的子类。这些子类中包含按钮点击后必须执行的代码。 大量的按钮子类。没关系的。 你很快就意识到这种方式有严重缺陷。首先，你创建了大量的子类，当每次修改基类 按钮 时，你都有可能需要修改所有子类的代码。简单来说，GUI 代码以一种拙劣的方式依赖于业务逻辑中的不稳定代码。 多个类实现同一功能。 还有一个部分最难办。复制/粘贴文字等操作可能会在多个地方被调用。例如用户可以点击工具栏上小小的“复制”按钮，或者通过上下文菜单复制一些内容，又或者直接使用键盘上的 Ctrl+C。 我们的程序最初只有工具栏，因此可以使用按钮子类来实现各种不同操作。换句话来说，复制按钮 Copy­Button 子类包含复制文字的代码是可行的。在实现了上下文菜单、快捷方式和其他功能后，你要么需要将操作代码复制进许多个类中，要么需要让菜单依赖于按钮，而后者是更糟糕的选择。","s":"问题","u":"/docs/design-patterns/command","h":"#问题","p":234},{"i":241,"t":"优秀的软件设计通常会将关注点进行分离，而这往往会导致软件的分层。最常见的例子：一层负责用户图像界面；另一层负责业务逻辑。GUI 层负责在屏幕上渲染美观的图形，捕获所有输入并显示用户和程序工作的结果。当需要完成一些重要内容时 (比如计算月球轨道或撰写年度报告)，GUI 层则会将工作委派给业务逻辑底层。 这在代码中看上去就像这样：一个 GUI 对象传递一些参数来调用一个业务逻辑对象。这个过程通常被描述为一个对象发送请求给另一个对象。 GUI 层可以直接访问业务逻辑层。 命令模式建议 GUI 对象不直接提交这些请求。你应该将请求的所有细节 (例如调用的对象、方法名称和参数列表) 抽取出来组成命令类，该类中仅包含一个用于触发请求的方法。 命令对象负责连接不同的 GUI 和业务逻辑对象。此后，GUI 对象无需了解业务逻辑对象是否获得了请求，也无需了解其对请求进行处理的方式。GUI 对象触发命令即可，命令对象会自行处理所有细节工作。 通过命令访问业务逻辑层。 下一步是让所有命令实现相同的接口。该接口通常只有一个没有任何参数的执行方法，让你能在不和具体命令类耦合的情况下使用同一请求发送者执行不同命令。此外还有额外的好处，现在你能在运行时切换连接至发送者的命令对象，以此改变发送者的行为。 你可能会注意到遗漏的一块拼图——请求的参数。GUI 对象可以给业务层对象提供一些参数。但执行命令方法没有任何参数，所以我们如何将请求的详情发送给接收者呢？答案是：使用数据对命令进行预先配置，或者让其能够自行获取数据。 GUI 对象将命令委派给命令对象。 让我们回到文本编辑器。应用命令模式后，我们不再需要任何按钮子类来实现点击行为。我们只需在 按钮 Button 基类中添加一个成员变量来存储对于命令对象的引用，并在点击后执行该命令即可。 你需要为每个可能的操作实现一系列命令类，并且根据按钮所需行为将命令和按钮连接起来。 其他菜单、快捷方式或整个对话框等 GUI 元素都可以通过相同方式来实现。当用户与 GUI 元素交互时，与其连接的命令将会被执行。现在你很可能已经猜到了，与相同操作相关的元素将会被连接到相同的命令，从而避免了重复代码。 最后，命令成为了减少 GUI 和业务逻辑层之间耦合的中间层。而这仅仅是命令模式所提供的一小部分好处！","s":"解决方案","u":"/docs/design-patterns/command","h":"#解决方案","p":234},{"i":243,"t":"在餐厅里点餐。 在市中心逛了很久的街后，你找到了一家不错的餐厅，坐在了临窗的座位上。一名友善的服务员走近你，迅速记下你点的食物，写在一张纸上。服务员来到厨房，把订单贴在墙上。过了一段时间，厨师拿到了订单，他根据订单来准备食物。厨师将做好的食物和订单一起放在托盘上。服务员看到托盘后对订单进行检查，确保所有食物都是你要的，然后将食物放到了你的桌上。 那张纸就是一个命令，它在厨师开始烹饪前一直位于队列中。命令中包含与烹饪这些食物相关的所有信息。厨师能够根据它马上开始烹饪，而无需跑来直接和你确认订单详情。","s":"真实世界类比","u":"/docs/design-patterns/command","h":"#真实世界类比","p":234},{"i":245,"t":"发送者 (Sender)——亦称“触发者 (Invoker)”——类负责对请求进行初始化，其中必须包含一个成员变量来存储对于命令对象的引用。发送者触发命令，而不向接收者直接发送请求。注意，发送者并不负责创建命令对象：它通常会通过构造函数从客户端处获得预先生成的命令。 命令 (Command) 接口通常仅声明一个执行命令的方法。 具体命令 (Concrete Commands) 会实现各种类型的请求。具体命令自身并不完成工作，而是会将调用委派给一个业务逻辑对象。但为了简化代码，这些类可以进行合并。 接收对象执行方法所需的参数可以声明为具体命令的成员变量。你可以将命令对象设为不可变，仅允许通过构造函数对这些成员变量进行初始化。 接收者 (Receiver) 类包含部分业务逻辑。几乎任何对象都可以作为接收者。绝大部分命令只处理如何将请求传递到接收者的细节，接收者自己会完成实际的工作。 客户端 (Client) 会创建并配置具体命令对象。客户端必须将包括接收者实体在内的所有请求参数传递给命令的构造函数。此后，生成的命令就可以与一个或多个发送者相关联了。","s":"命令模式结构","u":"/docs/design-patterns/command","h":"#命令模式结构","p":234},{"i":247,"t":"在本例中，命令模式会记录已执行操作的历史记录，以在需要时撤销操作。 文本编辑器中的可撤销操作。 有些命令会改变编辑器的状态 (例如剪切和粘贴)，它们可在执行相关操作前对编辑器的状态进行备份。命令执行后会和当前点备份的编辑器状态一起被放入命令历史 (命令对象栈)。此后，如果用户需要进行回滚操作，程序可从历史记录中取出最近的命令，读取相应的编辑器状态备份，然后进行恢复。 客户端代码 (GUI 元素和命令历史等) 没有和具体命令类相耦合，因为它通过命令接口来使用命令。这使得你能在无需修改已有代码的情况下在程序中增加新的命令。 // 命令基类会为所有具体命令定义通用接口。 abstract class Command is protected field app: Application protected field editor: Editor protected field backup: text constructor Command(app: Application, editor: Editor) is this.app = app this.editor = editor // 备份编辑器状态。 method saveBackup() is backup = editor.text // 恢复编辑器状态。 method undo() is editor.text = backup // 执行方法被声明为抽象以强制所有具体命令提供自己的实现。该方法必须根 // 据命令是否更改编辑器的状态返回 true 或 false。 abstract method execute() // 这里是具体命令。 class CopyCommand extends Command is // 复制命令不会被保存到历史记录中，因为它没有改变编辑器的状态。 method execute() is app.clipboard = editor.getSelection() return false class CutCommand extends Command is // 剪切命令改变了编辑器的状态，因此它必须被保存到历史记录中。只要方法 // 返回 true，它就会被保存。 method execute() is saveBackup() app.clipboard = editor.getSelection() editor.deleteSelection() return true class PasteCommand extends Command is method execute() is saveBackup() editor.replaceSelection(app.clipboard) return true // 撤销操作也是一个命令。 class UndoCommand extends Command is method execute() is app.undo() return false // 全局命令历史记录就是一个堆桟。 class CommandHistory is private field history: array of Command // 后进…… method push(c: Command) is // 将命令压入历史记录数组的末尾。 // ……先出 method pop():Command is // 从历史记录中取出最近的命令。 // 编辑器类包含实际的文本编辑操作。它会担任接收者的角色：最后所有命令都会 // 将执行工作委派给编辑器的方法。 class Editor is field text: string method getSelection() is // 返回选中的文字。 method deleteSelection() is // 删除选中的文字。 method replaceSelection(text) is // 在当前位置插入剪贴板中的内容。 // 应用程序类会设置对象之间的关系。它会担任发送者的角色：当需要完成某些工 // 作时，它会创建并执行一个命令对象。 class Application is field clipboard: string field editors: array of Editors field activeEditor: Editor field history: CommandHistory // 将命令分派给 UI 对象的代码可能会是这样的。 method createUI() is // …… copy = function() { executeCommand( new CopyCommand(this, activeEditor)) } copyButton.setCommand(copy) shortcuts.onKeyPress(\"Ctrl+C\", copy) cut = function() { executeCommand( new CutCommand(this, activeEditor)) } cutButton.setCommand(cut) shortcuts.onKeyPress(\"Ctrl+X\", cut) paste = function() { executeCommand( new PasteCommand(this, activeEditor)) } pasteButton.setCommand(paste) shortcuts.onKeyPress(\"Ctrl+V\", paste) undo = function() { executeCommand( new UndoCommand(this, activeEditor)) } undoButton.setCommand(undo) shortcuts.onKeyPress(\"Ctrl+Z\", undo) // 执行一个命令并检查它是否需要被添加到历史记录中。 method executeCommand(command) is if (command.execute()) history.push(command) // 从历史记录中取出最近的命令并运行其 undo（撤销）方法。请注意，你并 // 不知晓该命令所属的类。但是我们不需要知晓，因为命令自己知道如何撤销 // 其动作。 method undo() is command = history.pop() if (command != null) command.undo()","s":"伪代码","u":"/docs/design-patterns/command","h":"#伪代码","p":234},{"i":249,"t":"如果你需要通过操作来参数化对象，可使用命令模式。 命令模式可将特定的方法调用转化为独立对象。这一改变也带来了许多有趣的应用：你可以将命令作为方法的参数进行传递、将命令保存在其他对象中，或者在运行时切换已连接的命令等。 举个例子：你正在开发一个 GUI 组件 (例如上下文菜单)，你希望用户能够配置菜单项，并在点击菜单项时触发操作。 如果你想要将操作放入队列中、操作的执行或者远程执行操作，可使用命令模式。 同其他对象一样，命令也可以实现序列化 (序列化的意思是转化为字符串)，从而能方便地写入文件或数据库中。一段时间后，该字符串可被恢复成为最初的命令对象。因此，你可以延迟或计划命令的执行。但其功能远不止如此！使用同样的方式，你还可以将命令放入队列、记录命令或者通过网络发送命令。 如果你想要实现操作回滚功能，可使用命令模式。 尽管有很多方法可以实现撤销和恢复功能，但命令模式可能是其中最常用的一种。 为了能够回滚操作，你需要实现已执行操作的历史记录功能。命令历史记录是一种包含所有已执行命令对象及其相关程序状态备份的栈结构。 这种方法有两个缺点。首先，程序状态的保存功能并不容易实现，因为部分状态可能是私有的。你可以使用备忘录模式来在一定程度上解决这个问题。 其次，备份状态可能会占用大量内存。因此，有时你需要借助另一种实现方式：命令无需恢复原始状态，而是执行反向操作。反向操作也有代价：它可能会很难甚至是无法实现。 实现方式 声明仅有一个执行方法的命令接口。 抽取请求并使之成为实现命令接口的具体命令类。每个类都必须有一组成员变量来保存请求参数和对于实际接收者对象的引用。所有这些变量的数值都必须通过命令构造函数进行初始化。 找到担任发送者职责的类。在这些类中添加保存命令的成员变量。发送者只能通过命令接口与其命令进行交互。发送者自身通常并不创建命令对象，而是通过客户端代码获取。 修改发送者使其执行命令，而非直接将请求发送给接收者。 客户端必须按照以下顺序来初始化对象： 创建接收者。 创建命令，如有需要可将其关联至接收者。 创建发送者并将其与特定命令关联。","s":"命令模式适合应用场景","u":"/docs/design-patterns/command","h":"#命令模式适合应用场景","p":234},{"i":251,"t":"✔️ 单一职责原则。你可以解耦触发和执行操作的类。 ✔️ 开闭原则。你可以在不修改已有客户端代码的情况下在程序中创建新的命令。 ✔️ 你可以实现撤销和恢复功能。 ✔️ 你可以实现操作的延迟执行。 ✔️ 你可以将一组简单命令组合成一个复杂命令。 ❌ 代码可能会变得更加复杂，因为你在发送者和接收者之间增加了一个全新的层次。","s":"命令模式优缺点","u":"/docs/design-patterns/command","h":"#命令模式优缺点","p":234},{"i":253,"t":"责任链模式、命令模式、中介者模式和观察者模式用于处理请求发送者和接收者之间的不同连接方式： 责任链按照顺序将请求动态传递给一系列的潜在接收者，直至其中一名接收者对请求进行处理。 命令在发送者和请求者之间建立单向连接。 中介者清除了发送者和请求者之间的直接连接，强制它们通过一个中介对象进行间接沟通。 观察者允许接收者动态地订阅或取消接收请求。 责任链的管理者可使用命令模式实现。在这种情况下，你可以对由请求代表的同一个上下文对象执行许多不同的操作。还有另外一种实现方式，那就是请求自身就是一个命令对象。在这种情况下，你可以对由一系列不同上下文连接而成的链执行相同的操作。 你可以同时使用命令和备忘录模式来实现“撤销”。在这种情况下，命令用于对目标对象执行各种不同的操作，备忘录用来保存一条命令执行前该对象的状态。 命令和策略模式看上去很像，因为两者都能通过某些行为来参数化对象。但是，它们的意图有非常大的不同。 你可以使用命令来将任何操作转换为对象。操作的参数将成为对象的成员变量。你可以通过转换来延迟操作的执行、将操作放入队列、保存历史命令或者向远程服务发送命令等。 另一方面，策略通常可用于描述完成某件事的不同方式，让你能够在同一个上下文类中切换算法。 原型模式可用于保存命令的历史记录。 你可以将访问者模式视为命令模式的加强版本，其对象可对不同类的多种对象执行操作。","s":"与其他模式的关系","u":"/docs/design-patterns/command","h":"#与其他模式的关系","p":234},{"i":255,"t":"亦称：对象树、Object Tree、Composite","s":"组合模式","u":"/docs/design-patterns/composite","h":"","p":254},{"i":257,"t":"组合模式是一种结构型设计模式，你可以使用它将对象组合成树状结构，并且能像使用独立对象一样使用它们。","s":"意图","u":"/docs/design-patterns/composite","h":"#意图","p":254},{"i":259,"t":"如果应用的核心模型能用树状结构表示，在应用中使用组合模式才有价值。 例如，你有两类对象：产品 和 盒子。一个盒子中可以包含多个 产品 或者几个较小的 盒子。这些小 盒子 中同样可以包含一些 产品 或更小的 盒子，以此类推。 假设你希望在这些类的基础上开发一个定购系统。订单中可以包含无包装的简单产品，也可以包含装满产品的盒子…… 以及其他盒子。此时你会如何计算每张订单的总价格呢？ 订单中可能包括各种产品，这些产品放置在盒子中，然后又被放入一层又一层更大的盒子中。整个结构看上去像是一棵倒过来的树。 你可以尝试直接计算：打开所有盒子，找到每件产品，然后计算总价。这在真实世界中或许可行，但在程序中，你并不能简单地使用循环语句来完成该工作。你必须事先知道所有 产品 和 盒子 的类别，所有盒子的嵌套层数以及其他繁杂的细节信息。因此，直接计算极不方便，甚至完全不可行。","s":"问题","u":"/docs/design-patterns/composite","h":"#问题","p":254},{"i":261,"t":"组合模式建议使用一个通用接口来与 产品 和 盒子 进行交互，并且在该接口中声明一个计算总价的方法。 那么方法该如何设计呢？对于一个产品，该方法直接返回其价格；对于一个盒子，该方法遍历盒子中的所有项目，询问每个项目的价格，然后返回该盒子的总价格。如果其中某个项目是小一号的盒子，那么当前盒子也会遍历其中的所有项目，以此类推，直到计算出所有内部组成部分的价格。你甚至可以在盒子的最终价格中增加额外费用，作为该盒子的包装费用。 组合模式以递归方式处理对象树中的所有项目 该方式的最大优点在于你无需了解构成树状结构的对象的具体类。你也无需了解对象是简单的产品还是复杂的盒子。你只需调用通用接口以相同的方式对其进行处理即可。当你调用该方法后，对象会将请求沿着树结构传递下去。","s":"解决方案","u":"/docs/design-patterns/composite","h":"#解决方案","p":254},{"i":263,"t":"部队结构的例子。 大部分国家的军队都采用层次结构管理。每支部队包括几个师，师由旅构成，旅由团构成，团可以继续划分为排。最后，每个排由一小队实实在在的士兵组成。军事命令由最高层下达，通过每个层级传递，直到每位士兵都知道自己应该服从的命令。","s":"真实世界类比","u":"/docs/design-patterns/composite","h":"#真实世界类比","p":254},{"i":265,"t":"组件 (Component) 接口描述了树中简单项目和复杂项目所共有的操作。 叶节点 (Leaf) 是树的基本结构，它不包含子项目。 一般情况下，叶节点最终会完成大部分的实际工作，因为它们无法将工作指派给其他部分。 容器 (Container)——又名“组合 (Composite)”——是包含叶节点或其他容器等子项目的单位。容器不知道其子项目所属的具体类，它只通过通用的组件接口与其子项目交互。 容器接收到请求后会将工作分配给自己的子项目，处理中间结果，然后将最终结果返回给客户端。 客户端 (Client) 通过组件接口与所有项目交互。因此，客户端能以相同方式与树状结构中的简单或复杂项目交互。","s":"组合模式结构","u":"/docs/design-patterns/composite","h":"#组合模式结构","p":254},{"i":267,"t":"在本例中，我们将借助组合模式帮助你在图形编辑器中实现一系列的几何图形。 几何形状编辑器示例。 组合图形 Compound­Graphic 是一个容器，它可以由多个包括容器在内的子图形构成。组合图形与简单图形拥有相同的方法。但是，组合图形自身并不完成具体工作，而是将请求递归地传递给自己的子项目，然后“汇总”结果。 通过所有图形类所共有的接口，客户端代码可以与所有图形互动。因此，客户端不知道与其交互的是简单图形还是组合图形。客户端可以与非常复杂的对象结构进行交互，而无需与组成该结构的实体类紧密耦合。 // 组件接口会声明组合中简单和复杂对象的通用操作。 interface Graphic is method move(x, y) method draw() // 叶节点类代表组合的终端对象。叶节点对象中不能包含任何子对象。叶节点对象 // 通常会完成实际的工作，组合对象则仅会将工作委派给自己的子部件。 class Dot implements Graphic is field x, y constructor Dot(x, y) { …… } method move(x, y) is this.x += x, this.y += y method draw() is // 在坐标位置 (X,Y) 处绘制一个点。 // 所有组件类都可以扩展其他组件。 class Circle extends Dot is field radius constructor Circle(x, y, radius) { …… } method draw() is // 在坐标位置 (X,Y) 处绘制一个半径为 R 的圆。 // 组合类表示可能包含子项目的复杂组件。组合对象通常会将实际工作委派给子项 // 目，然后“汇总”结果。 class CompoundGraphic implements Graphic is field children: array of Graphic // 组合对象可在其项目列表中添加或移除其他组件（简单的或复杂的皆可）。 method add(child: Graphic) is // 在子项目数组中添加一个子项目。 method remove(child: Graphic) is // 从子项目数组中移除一个子项目。 method move(x, y) is foreach (child in children) do child.move(x, y) // 组合会以特定的方式执行其主要逻辑。它会递归遍历所有子项目，并收集和 // 汇总其结果。由于组合的子项目也会将调用传递给自己的子项目，以此类推， // 最后组合将会完成整个对象树的遍历工作。 method draw() is // 1. 对于每个子部件： // - 绘制该部件。 // - 更新边框坐标。 // 2. 根据边框坐标绘制一个虚线长方形。 // 客户端代码会通过基础接口与所有组件进行交互。这样一来，客户端代码便可同 // 时支持简单叶节点组件和复杂组件。 class ImageEditor is field all: CompoundGraphic method load() is all = new CompoundGraphic() all.add(new Dot(1, 2)) all.add(new Circle(5, 3, 10)) // …… // 将所需组件组合为复杂的组合组件。 method groupSelected(components: array of Graphic) is group = new CompoundGraphic() foreach (component in components) do group.add(component) all.remove(component) all.add(group) // 所有组件都将被绘制。 all.draw()","s":"伪代码","u":"/docs/design-patterns/composite","h":"#伪代码","p":254},{"i":269,"t":"如果你需要实现树状对象结构，可以使用组合模式。 组合模式为你提供了两种共享公共接口的基本元素类型：简单叶节点和复杂容器。容器中可以包含叶节点和其他容器。这使得你可以构建树状嵌套递归对象结构。 如果你希望客户端代码以相同方式处理简单和复杂元素，可以使用该模式。 组合模式中定义的所有元素共用同一个接口。在这一接口的帮助下，客户端不必在意其所使用的对象的具体类。 实现方式 确保应用的核心模型能够以树状结构表示。尝试将其分解为简单元素和容器。记住，容器必须能够同时包含简单元素和其他容器。 声明组件接口及其一系列方法，这些方法对简单和复杂元素都有意义。 创建一个叶节点类表示简单元素。程序中可以有多个不同的叶节点类。 创建一个容器类表示复杂元素。在该类中，创建一个数组成员变量来存储对于其子元素的引用。该数组必须能够同时保存叶节点和容器，因此请确保将其声明为组合接口类型。实现组件接口方法时，记住容器应该将大部分工作交给其子元素来完成。 最后，在容器中定义添加和删除子元素的方法。记住，这些操作可在组件接口中声明。这将会违反接口隔离原则，因为叶节点类中的这些方法为空。但是，这可以让客户端无差别地访问所有元素，即使是组成树状结构的元素。","s":"组合模式适合应用场景","u":"/docs/design-patterns/composite","h":"#组合模式适合应用场景","p":254},{"i":271,"t":"✔️ 你可以利用多态和递归机制更方便地使用复杂树结构。 ✔️ 开闭原则。无需更改现有代码，你就可以在应用中添加新元素，使其成为对象树的一部分。 ❌ 对于功能差异较大的类，提供公共接口或许会有困难。在特定情况下，你需要过度一般化组件接口，使其变得令人难以理解。","s":"组合模式优缺点","u":"/docs/design-patterns/composite","h":"#组合模式优缺点","p":254},{"i":273,"t":"桥接模式、状态模式和策略模式 (在某种程度上包括适配器模式) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。 你可以在创建复杂组合树时使用生成器模式，因为这可使其构造步骤以递归的方式运行。 责任链模式通常和组合模式结合使用。在这种情况下，叶组件接收到请求后，可以将请求沿包含全体父组件的链一直传递至对象树的底部。 你可以使用迭代器模式来遍历组合树。 你可以使用访问者模式对整个组合树执行操作。 你可以使用享元模式实现组合树的共享叶节点以节省内存。 组合和装饰模式的结构图很相似，因为两者都依赖递归组合来组织无限数量的对象。 装饰类似于组合，但其只有一个子组件。此外还有一个明显不同：装饰为被封装对象添加了额外的职责，组合仅对其子节点的结果进行了“求和”。但是，模式也可以相互合作：你可以使用装饰来扩展组合树中特定对象的行为。 大量使用组合和装饰的设计通常可从对于原型模式的使用中获益。你可以通过该模式来复制复杂结构，而非从零开始重新构造。","s":"与其他模式的关系","u":"/docs/design-patterns/composite","h":"#与其他模式的关系","p":254},{"i":275,"t":"创建型模式提供了创建对象的机制，能够提升已有代码的灵活性和可复用性。","s":"创建型模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":277,"t":"在父类中提供一个创建对象的接口以允许子类决定实例化对象的类型。","s":"📄️ 工厂方法模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":279,"t":"让你能创建一系列相关的对象，而无需指定其具体类。","s":"📄️ 抽象工厂模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":281,"t":"使你能够分步骤创建复杂对象。该模式允许你使用相同的创建代码生成不同类型和形式的对象。","s":"📄️ 生成器模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":283,"t":"让你能够复制已有对象，而又无需使代码依赖它们所属的类。","s":"📄️ 原型模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":285,"t":"让你能够保证一个类只有一个实例，并提供一个访问该实例的全局节点。","s":"📄️ 单例模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":287,"t":"亦称：装饰者模式、装饰器模式、Wrapper、Decorator","s":"装饰模式","u":"/docs/design-patterns/decorator","h":"","p":286},{"i":289,"t":"装饰模式是一种结构型设计模式，允许你通过将对象放入包含行为的特殊封装对象中来为原对象绑定新的行为。","s":"意图","u":"/docs/design-patterns/decorator","h":"#意图","p":286},{"i":291,"t":"假设你正在开发一个提供通知功能的库，其他程序可使用它向用户发送关于重要事件的通知。 库的最初版本基于 通知器 Notifier 类，其中只有很少的几个成员变量，一个构造函数和一个 send 发送方法。该方法可以接收来自客户端的消息参数，并将该消息发送给一系列的邮箱，邮箱列表则是通过构造函数传递给通知器的。作为客户端的第三方程序仅会创建和配置通知器对象一次，然后在有重要事件发生时对其进行调用。 程序可以使用通知器类向预定义的邮箱发送重要事件通知。 此后某个时刻，你会发现库的用户希望使用除邮件通知之外的功能。许多用户会希望接收关于紧急事件的手机短信，还有些用户希望在微信上接收消息，而公司用户则希望在 QQ 上接收消息。 每种通知类型都将作为通知器的一个子类得以实现。 这有什么难的呢？首先扩展 通知器 类，然后在新的子类中加入额外的通知方法。现在客户端要对所需通知形式的对应类进行初始化，然后使用该类发送后续所有的通知消息。 但是很快有人会问：“为什么不同时使用多种通知形式呢？如果房子着火了，你大概会想在所有渠道中都收到相同的消息吧。” 你可以尝试创建一个特殊子类来将多种通知方法组合在一起以解决该问题。但这种方式会使得代码量迅速膨胀，不仅仅是程序库代码，客户端代码也会如此。 子类组合数量爆炸。 你必须找到其他方法来规划通知类的结构，否则它们的数量会在不经意之间打破吉尼斯纪录。","s":"问题","u":"/docs/design-patterns/decorator","h":"#问题","p":286},{"i":293,"t":"当你需要更改一个对象的行为时，第一个跳入脑海的想法就是扩展它所属的类。但是，你不能忽视继承可能引发的几个严重问题。 继承是静态的。你无法在运行时更改已有对象的行为，只能使用由不同子类创建的对象来替代当前的整个对象。 子类只能有一个父类。大部分编程语言不允许一个类同时继承多个类的行为。 其中一种方法是用聚合或组合，而不是继承。两者的工作方式几乎一模一样：一个对象包含指向另一个对象的引用，并将部分工作委派给引用对象；继承中的对象则继承了父类的行为，它们自己能够完成这些工作。 你可以使用这个新方法来轻松替换各种连接的“小帮手”对象，从而能在运行时改变容器的行为。一个对象可以使用多个类的行为，包含多个指向其他对象的引用，并将各种工作委派给引用对象。聚合 (或组合) 组合是许多设计模式背后的关键原则 (包括装饰在内)。记住这一点后，让我们继续关于模式的讨论。 继承与聚合的对比 封装器是装饰模式的别称，这个称谓明确地表达了该模式的主要思想。“封装器”是一个能与其他“目标”对象连接的对象。封装器包含与目标对象相同的一系列方法，它会将所有接收到的请求委派给目标对象。但是，封装器可以在将请求委派给目标前后对其进行处理，所以可能会改变最终结果。 那么什么时候一个简单的封装器可以被称为是真正的装饰呢？正如之前提到的，封装器实现了与其封装对象相同的接口。因此从客户端的角度来看，这些对象是完全一样的。封装器中的引用成员变量可以是遵循相同接口的任意对象。这使得你可以将一个对象放入多个封装器中，并在对象中添加所有这些封装器的组合行为。 比如在消息通知示例中，我们可以将简单邮件通知行为放在基类 通知器 中，但将所有其他通知方法放入装饰中。 将各种通知方法放入装饰。 客户端代码必须将基础通知器放入一系列自己所需的装饰中。因此最后的对象将形成一个栈结构。 程序可以配置由通知装饰构成的复杂栈。 实际与客户端进行交互的对象将是最后一个进入栈中的装饰对象。由于所有的装饰都实现了与通知基类相同的接口，客户端的其他代码并不在意自己到底是与“纯粹”的通知器对象，还是与装饰后的通知器对象进行交互。 我们可以使用相同方法来完成其他行为 (例如设置消息格式或者创建接收人列表)。只要所有装饰都遵循相同的接口，客户端就可以使用任意自定义的装饰来装饰对象。","s":"解决方案","u":"/docs/design-patterns/decorator","h":"#解决方案","p":286},{"i":295,"t":"穿上多件衣服将获得组合性的效果。 穿衣服是使用装饰的一个例子。觉得冷时，你可以穿一件毛衣。如果穿毛衣还觉得冷，你可以再套上一件夹克。如果遇到下雨，你还可以再穿一件雨衣。所有这些衣物都“扩展”了你的基本行为，但它们并不是你的一部分，如果你不再需要某件衣物，可以方便地随时脱掉。","s":"真实世界类比","u":"/docs/design-patterns/decorator","h":"#真实世界类比","p":286},{"i":297,"t":"部件 (Component) 声明封装器和被封装对象的公用接口。 具体部件 (Concrete Component) 类是被封装对象所属的类。它定义了基础行为，但装饰类可以改变这些行为。 基础装饰 (Base Decorator) 类拥有一个指向被封装对象的引用成员变量。该变量的类型应当被声明为通用部件接口，这样它就可以引用具体的部件和装饰。装饰基类会将所有操作委派给被封装的对象。 具体装饰类 (Concrete Decorators) 定义了可动态添加到部件的额外行为。具体装饰类会重写装饰基类的方法，并在调用父类方法之前或之后进行额外的行为。 客户端 (Client) 可以使用多层装饰来封装部件，只要它能使用通用接口与所有对象互动即可。","s":"装饰模式结构","u":"/docs/design-patterns/decorator","h":"#装饰模式结构","p":286},{"i":299,"t":"在本例中，装饰模式能够对敏感数据进行压缩和加密，从而将数据从使用数据的代码中独立出来。 加密和压缩装饰的示例。 程序使用一对装饰来封装数据源对象。这两个封装器都改变了从磁盘读写数据的方式： 当数据即将被写入磁盘前，装饰对数据进行加密和压缩。在原始类对改变毫无察觉的情况下，将加密后的受保护数据写入文件。 当数据刚从磁盘读出后，同样通过装饰对数据进行解压和解密。 装饰和数据源类实现同一接口，从而能在客户端代码中相互替换。 // 装饰可以改变组件接口所定义的操作。 interface DataSource is method writeData(data) method readData():data // 具体组件提供操作的默认实现。这些类在程序中可能会有几个变体。 class FileDataSource implements DataSource is constructor FileDataSource(filename) { …… } method writeData(data) is // 将数据写入文件。 method readData():data is // 从文件读取数据。 // 装饰基类和其他组件遵循相同的接口。该类的主要任务是定义所有具体装饰的封 // 装接口。封装的默认实现代码中可能会包含一个保存被封装组件的成员变量，并 // 且负责对其进行初始化。 class DataSourceDecorator implements DataSource is protected field wrappee: DataSource constructor DataSourceDecorator(source: DataSource) is wrappee = source // 装饰基类会直接将所有工作分派给被封装组件。具体装饰中则可以新增一些 // 额外的行为。 method writeData(data) is wrappee.writeData(data) // 具体装饰可调用其父类的操作实现，而不是直接调用被封装对象。这种方式 // 可简化装饰类的扩展工作。 method readData():data is return wrappee.readData() // 具体装饰必须在被封装对象上调用方法，不过也可以自行在结果中添加一些内容。 // 装饰必须在调用封装对象之前或之后执行额外的行为。 class EncryptionDecorator extends DataSourceDecorator is method writeData(data) is // 1. 对传递数据进行加密。 // 2. 将加密后数据传递给被封装对象 writeData（写入数据）方法。 method readData():data is // 1. 通过被封装对象的 readData（读取数据）方法获取数据。 // 2. 如果数据被加密就尝试解密。 // 3. 返回结果。 // 你可以将对象封装在多层装饰中。 class CompressionDecorator extends DataSourceDecorator is method writeData(data) is // 1. 压缩传递数据。 // 2. 将压缩后数据传递给被封装对象 writeData（写入数据）方法。 method readData():data is // 1. 通过被封装对象的 readData（读取数据）方法获取数据。 // 2. 如果数据被压缩就尝试解压。 // 3. 返回结果。 // 选项 1：装饰组件的简单示例 class Application is method dumbUsageExample() is source = new FileDataSource(\"somefile.dat\") source.writeData(salaryRecords) // 已将明码数据写入目标文件。 source = new CompressionDecorator(source) source.writeData(salaryRecords) // 已将压缩数据写入目标文件。 source = new EncryptionDecorator(source) // 源变量中现在包含： // Encryption > Compression > FileDataSource source.writeData(salaryRecords) // 已将压缩且加密的数据写入目标文件。 // 选项 2：客户端使用外部数据源。SalaryManager（工资管理器）对象并不关心 // 数据如何存储。它们会与提前配置好的数据源进行交互，数据源则是通过程序配 // 置器获取的。 class SalaryManager is field source: DataSource constructor SalaryManager(source: DataSource) { …… } method load() is return source.readData() method save() is source.writeData(salaryRecords) // ……其他有用的方法…… // 程序可在运行时根据配置或环境组装不同的装饰堆桟。 class ApplicationConfigurator is method configurationExample() is source = new FileDataSource(\"salary.dat\") if (enabledEncryption) source = new EncryptionDecorator(source) if (enabledCompression) source = new CompressionDecorator(source) logger = new SalaryManager(source) salary = logger.load() // ……","s":"伪代码","u":"/docs/design-patterns/decorator","h":"#伪代码","p":286},{"i":301,"t":"如果你希望在无需修改代码的情况下即可使用对象，且希望在运行时为对象新增额外的行为，可以使用装饰模式。 装饰能将业务逻辑组织为层次结构，你可为各层创建一个装饰，在运行时将各种不同逻辑组合成对象。由于这些对象都遵循通用接口，客户端代码能以相同的方式使用这些对象。 如果用继承来扩展对象行为的方案难以实现或者根本不可行，你可以使用该模式。 许多编程语言使用 final 最终关键字来限制对某个类的进一步扩展。复用最终类已有行为的唯一方法是使用装饰模式：用封装器对其进行封装。 实现方式 确保业务逻辑可用一个基本组件及多个额外可选层次表示。 找出基本组件和可选层次的通用方法。创建一个组件接口并在其中声明这些方法。 创建一个具体组件类，并定义其基础行为。 创建装饰基类，使用一个成员变量存储指向被封装对象的引用。该成员变量必须被声明为组件接口类型，从而能在运行时连接具体组件和装饰。装饰基类必须将所有工作委派给被封装的对象。 确保所有类实现组件接口。 将装饰基类扩展为具体装饰。具体装饰必须在调用父类方法 (总是委派给被封装对象) 之前或之后执行自身的行为。 客户端代码负责创建装饰并将其组合成客户端所需的形式。","s":"装饰模式适合应用场景","u":"/docs/design-patterns/decorator","h":"#装饰模式适合应用场景","p":286},{"i":303,"t":"✔️ 你无需创建新子类即可扩展对象的行为。 ✔️ 你可以在运行时添加或删除对象的功能。 ✔️ 你可以用多个装饰封装对象来组合几种行为。 ✔️ 单一职责原则。你可以将实现了许多不同行为的一个大类拆分为多个较小的类。 ❌ 在封装器栈中删除特定封装器比较困难。 ❌ 实现行为不受装饰栈顺序影响的装饰比较困难。 ❌ 各层的初始化配置代码看上去可能会很糟糕。","s":"装饰模式优缺点","u":"/docs/design-patterns/decorator","h":"#装饰模式优缺点","p":286},{"i":305,"t":"适配器模式可以对已有对象的接口进行修改，装饰模式则能在不改变对象接口的前提下强化对象功能。此外，装饰还支持递归组合，适配器则无法实现。 适配器能为被封装对象提供不同的接口，代理模式能为对象提供相同的接口，装饰则能为对象提供加强的接口。 责任链模式和装饰模式的类结构非常相似。两者都依赖递归组合将需要执行的操作传递给一系列对象。但是，两者有几点重要的不同之处。 责任链的管理者可以相互独立地执行一切操作，还可以随时停止传递请求。另一方面，各种装饰可以在遵循基本接口的情况下扩展对象的行为。此外，装饰无法中断请求的传递。 组合模式和装饰的结构图很相似，因为两者都依赖递归组合来组织无限数量的对象。 装饰类似于组合，但其只有一个子组件。此外还有一个明显不同：装饰为被封装对象添加了额外的职责，组合仅对其子节点的结果进行了“求和”。但是，模式也可以相互合作：你可以使用装饰来扩展组合树中特定对象的行为。 大量使用组合和装饰的设计通常可从对于原型模式的使用中获益。你可以通过该模式来复制复杂结构，而非从零开始重新构造。 装饰可让你更改对象的外表，策略模式则让你能够改变其本质。 装饰和代理有着相似的结构，但是其意图却非常不同。这两个模式的构建都基于组合原则，也就是说一个对象应该将部分工作委派给另一个对象。两者之间的不同之处在于代理通常自行管理其服务对象的生命周期，而装饰的生成则总是由客户端进行控制。","s":"与其他模式的关系","u":"/docs/design-patterns/decorator","h":"#与其他模式的关系","p":286},{"i":307,"t":"亦称：Facade","s":"外观模式","u":"/docs/design-patterns/facade","h":"","p":306},{"i":309,"t":"外观模式是一种结构型设计模式，能为程序库、框架或其他复杂类提供一个简单的接口。","s":"意图","u":"/docs/design-patterns/facade","h":"#意图","p":306},{"i":311,"t":"假设你必须在代码中使用某个复杂的库或框架中的众多对象。正常情况下，你需要负责所有对象的初始化工作、管理其依赖关系并按正确的顺序执行方法等。 最终，程序中类的业务逻辑将与第三方类的实现细节紧密耦合，使得理解和维护代码的工作很难进行。","s":"问题","u":"/docs/design-patterns/facade","h":"#问题","p":306},{"i":313,"t":"外观类为包含许多活动部件的复杂子系统提供一个简单的接口。与直接调用子系统相比，外观提供的功能可能比较有限，但它却包含了客户端真正关心的功能。 如果你的程序需要与包含几十种功能的复杂库整合，但只需使用其中非常少的功能，那么使用外观模式会非常方便， 例如，上传猫咪搞笑短视频到社交媒体网站的应用可能会用到专业的视频转换库，但它只需使用一个包含 encode­(filename, format) 方法 (以文件名与文件格式为参数进行编码的方法) 的类即可。在创建这个类并将其连接到视频转换库后，你就拥有了自己的第一个外观。","s":"解决方案","u":"/docs/design-patterns/facade","h":"#解决方案","p":306},{"i":315,"t":"电话购物。 当你通过电话给商店下达订单时，接线员就是该商店的所有服务和部门的外观。接线员为你提供了一个同购物系统、支付网关和各种送货服务进行互动的简单语音接口。","s":"真实世界类比","u":"/docs/design-patterns/facade","h":"#真实世界类比","p":306},{"i":317,"t":"外观 (Facade) 提供了一种访问特定子系统功能的便捷方式，其了解如何重定向客户端请求，知晓如何操作一切活动部件。 创建附加外观 (Additional Facade) 类可以避免多种不相关的功能污染单一外观，使其变成又一个复杂结构。客户端和其他外观都可使用附加外观。 复杂子系统 (Complex Subsystem) 由数十个不同对象构成。如果要用这些对象完成有意义的工作，你必须深入了解子系统的实现细节，比如按照正确顺序初始化对象和为其提供正确格式的数据。 子系统类不会意识到外观的存在，它们在系统内运作并且相互之间可直接进行交互。 客户端 (Client) 使用外观代替对子系统对象的直接调用。","s":"外观模式结构","u":"/docs/design-patterns/facade","h":"#外观模式结构","p":306},{"i":319,"t":"在本例中，外观模式简化了客户端与复杂视频转换框架之间的交互。 使用单个外观类隔离多重依赖的示例 你可以创建一个封装所需功能并隐藏其他代码的外观类，从而无需使全部代码直接与数十个框架类进行交互。该结构还能将未来框架升级或更换所造成的影响最小化，因为你只需修改程序中外观方法的实现即可。 // 这里有复杂第三方视频转换框架中的一些类。我们不知晓其中的代码，因此无法 // 对其进行简化。 class VideoFile // …… class OggCompressionCodec // …… class MPEG4CompressionCodec // …… class CodecFactory // …… class BitrateReader // …… class AudioMixer // …… // 为了将框架的复杂性隐藏在一个简单接口背后，我们创建了一个外观类。它是在 // 功能性和简洁性之间做出的权衡。 class VideoConverter is method convert(filename, format):File is file = new VideoFile(filename) sourceCodec = (new CodecFactory).extract(file) if (format == \"mp4\") destinationCodec = new MPEG4CompressionCodec() else destinationCodec = new OggCompressionCodec() buffer = BitrateReader.read(filename, sourceCodec) result = BitrateReader.convert(buffer, destinationCodec) result = (new AudioMixer()).fix(result) return new File(result) // 应用程序的类并不依赖于复杂框架中成千上万的类。同样，如果你决定更换框架， // 那只需重写外观类即可。 class Application is method main() is convertor = new VideoConverter() mp4 = convertor.convert(\"funny-cats-video.ogg\", \"mp4\") mp4.save()","s":"伪代码","u":"/docs/design-patterns/facade","h":"#伪代码","p":306},{"i":321,"t":"如果你需要一个指向复杂子系统的直接接口，且该接口的功能有限，则可以使用外观模式。 子系统通常会随着时间的推进变得越来越复杂。即便是应用了设计模式，通常你也会创建更多的类。尽管在多种情形中子系统可能是更灵活或易于复用的，但其所需的配置和样板代码数量将会增长得更快。为了解决这个问题，外观将会提供指向子系统中最常用功能的快捷方式，能够满足客户端的大部分需求。 如果需要将子系统组织为多层结构，可以使用外观。 创建外观来定义子系统中各层次的入口。你可以要求子系统仅使用外观来进行交互，以减少子系统之间的耦合。 让我们回到视频转换框架的例子。该框架可以拆分为两个层次：音频相关和视频相关。你可以为每个层次创建一个外观，然后要求各层的类必须通过这些外观进行交互。这种方式看上去与中介者模式非常相似。 实现方式 考虑能否在现有子系统的基础上提供一个更简单的接口。如果该接口能让客户端代码独立于众多子系统类，那么你的方向就是正确的。 在一个新的外观类中声明并实现该接口。外观应将客户端代码的调用重定向到子系统中的相应对象处。如果客户端代码没有对子系统进行初始化，也没有对其后续生命周期进行管理，那么外观必须完成此类工作。 如果要充分发挥这一模式的优势，你必须确保所有客户端代码仅通过外观来与子系统进行交互。此后客户端代码将不会受到任何由子系统代码修改而造成的影响，比如子系统升级后，你只需修改外观中的代码即可。 如果外观变得过于臃肿，你可以考虑将其部分行为抽取为一个新的专用外观类。","s":"外观模式适合应用场景","u":"/docs/design-patterns/facade","h":"#外观模式适合应用场景","p":306},{"i":323,"t":"✔️ 你可以让自己的代码独立于复杂子系统。 ❌ 外观可能成为与程序中所有类都耦合的上帝对象。","s":"外观模式优缺点","u":"/docs/design-patterns/facade","h":"#外观模式优缺点","p":306},{"i":325,"t":"外观模式为现有对象定义了一个新接口，适配器模式则会试图运用已有的接口。适配器通常只封装一个对象，外观通常会作用于整个对象子系统上。 当只需对客户端代码隐藏子系统创建对象的方式时，你可以使用抽象工厂模式来代替外观。 享元模式展示了如何生成大量的小型对象，外观则展示了如何用一个对象来代表整个子系统。 外观和中介者模式的职责类似：它们都尝试在大量紧密耦合的类中组织起合作。 外观为子系统中的所有对象定义了一个简单接口，但是它不提供任何新功能。子系统本身不会意识到外观的存在。子系统中的对象可以直接进行交流。 中介者将系统中组件的沟通行为中心化。各组件只知道中介者对象，无法直接相互交流。 外观类通常可以转换为单例模式类，因为在大部分情况下一个外观对象就足够了。 外观与代理模式的相似之处在于它们都缓存了一个复杂实体并自行对其进行初始化。代理与其服务对象遵循同一接口，使得自己和服务对象可以互换，在这一点上它与外观不同。","s":"与其他模式的关系","u":"/docs/design-patterns/facade","h":"#与其他模式的关系","p":306},{"i":327,"t":"亦称：虚拟构造函数、Virtual Constructor、Factory Method","s":"工厂方法模式","u":"/docs/design-patterns/factory-method","h":"","p":326},{"i":329,"t":"工厂方法模式是一种创建型设计模式，其在父类中提供一个创建对象的方法，允许子类决定实例化对象的类型。","s":"意图","u":"/docs/design-patterns/factory-method","h":"#意图","p":326},{"i":331,"t":"假设你正在开发一款物流管理应用。最初版本只能处理卡车运输，因此大部分代码都在位于名为 卡车 的类中。 一段时间后，这款应用变得极受欢迎。你每天都能收到十几次来自海运公司的请求，希望应用能够支持海上物流功能。 如果代码其余部分与现有类已经存在耦合关系，那么向程序中添加新类其实并没有那么容易。 这可是个好消息。但是代码问题该如何处理呢？目前，大部分代码都与 卡车 类相关。在程序中添加 轮船 类需要修改全部代码。更糟糕的是，如果你以后需要在程序中支持另外一种运输方式，很可能需要再次对这些代码进行大幅修改。 最后，你将不得不编写繁复的代码，根据不同的运输对象类，在应用中进行不同的处理。","s":"问题","u":"/docs/design-patterns/factory-method","h":"#问题","p":326},{"i":333,"t":"工厂方法模式建议使用特殊的工厂方法代替对于对象构造函数的直接调用 (即使用 new 运算符)。不用担心，对象仍将通过 new 运算符创建，只是该运算符改在工厂方法中调用罢了。工厂方法返回的对象通常被称作“产品”。 子类可以修改工厂方法返回的对象类型。 乍看之下，这种更改可能毫无意义：我们只是改变了程序中调用构造函数的位置而已。但是，仔细想一下，现在你可以在子类中重写工厂方法，从而改变其创建产品的类型。 但有一点需要注意：仅当这些产品具有共同的基类或者接口时，子类才能返回不同类型的产品，同时基类中的工厂方法还应将其返回类型声明为这一共有接口。 所有产品都必须使用同一接口。 举例来说，卡车 Truck 和 轮船 Ship 类都必须实现 运输 Transport 接口，该接口声明了一个名为 deliver 交付的方法。每个类都将以不同的方式实现该方法：卡车走陆路交付货物，轮船走海路交付货物。陆路运输 Road­Logistics 类中的工厂方法返回卡车对象，而 海路运输 Sea­Logistics 类则返回轮船对象。 只要产品类实现一个共同的接口，你就可以将其对象传递给客户代码，而无需提供额外数据。 调用工厂方法的代码 (通常被称为客户端代码) 无需了解不同子类返回实际对象之间的差别。客户端将所有产品视为抽象的 运输。客户端知道所有运输对象都提供 交付 方法，但是并不关心其具体实现方式。","s":"解决方案","u":"/docs/design-patterns/factory-method","h":"#解决方案","p":326},{"i":335,"t":"产品 (Product) 将会对接口进行声明。对于所有由创建者及其子类构建的对象，这些接口都是通用的。 具体产品 (Concrete Products) 是产品接口的不同实现。 创建者 (Creator) 类声明返回产品对象的工厂方法。该方法的返回对象类型必须与产品接口相匹配。 你可以将工厂方法声明为抽象方法，强制要求每个子类以不同方式实现该方法。或者，你也可以在基础工厂方法中返回默认产品类型。 注意，尽管它的名字是创建者，但它最主要的职责并不是创建产品。一般来说，创建者类包含一些与产品相关的核心业务逻辑。工厂方法将这些逻辑处理从具体产品类中分离出来。打个比方，大型软件开发公司拥有程序员培训部门。但是，这些公司的主要工作还是编写代码，而非生产程序员。 具体创建者 (Concrete Creators) 将会重写基础工厂方法，使其返回不同类型的产品。 注意，并不一定每次调用工厂方法都会创建新的实例。工厂方法也可以返回缓存、对象池或其他来源的已有对象。","s":"工厂方法模式结构","u":"/docs/design-patterns/factory-method","h":"#工厂方法模式结构","p":326},{"i":337,"t":"以下示例演示了如何使用工厂方法开发跨平台 UI (用户界面) 组件，并同时避免客户代码与具体 UI 类之间的耦合。 跨平台对话框示例。 基础对话框类使用不同的 UI 组件渲染窗口。在不同的操作系统下，这些组件外观或许略有不同，但其功能保持一致。Windows 系统中的按钮在 Linux 系统中仍然是按钮。 如果使用工厂方法，就不需要为每种操作系统重写对话框逻辑。如果我们声明了一个在基本对话框类中生成按钮的工厂方法，那么我们就可以创建一个对话框子类，并使其通过工厂方法返回 Windows 样式按钮。子类将继承对话框基础类的大部分代码，同时在屏幕上根据 Windows 样式渲染按钮。 如需该模式正常工作，基础对话框类必须使用抽象按钮 (例如基类或接口)，以便将其扩展为具体按钮。这样一来，无论对话框中使用何种类型的按钮，其代码都可以正常工作。 你可以使用此方法开发其他 UI 组件。不过，每向对话框中添加一个新的工厂方法，你就离抽象工厂模式更近一步。我们将在稍后谈到这个模式。 // 创建者类声明的工厂方法必须返回一个产品类的对象。创建者的子类通常会提供 // 该方法的实现。 class Dialog is // 创建者还可提供一些工厂方法的默认实现。 abstract method createButton():Button // 请注意，创建者的主要职责并非是创建产品。其中通常会包含一些核心业务 // 逻辑，这些逻辑依赖于由工厂方法返回的产品对象。子类可通过重写工厂方 // 法并使其返回不同类型的产品来间接修改业务逻辑。 method render() is // 调用工厂方法创建一个产品对象。 Button okButton = createButton() // 现在使用产品。 okButton.onClick(closeDialog) okButton.render() // 具体创建者将重写工厂方法以改变其所返回的产品类型。 class WindowsDialog extends Dialog is method createButton():Button is return new WindowsButton() class WebDialog extends Dialog is method createButton():Button is return new HTMLButton() // 产品接口中将声明所有具体产品都必须实现的操作。 interface Button is method render() method onClick(f) // 具体产品需提供产品接口的各种实现。 class WindowsButton implements Button is method render(a, b) is // 根据 Windows 样式渲染按钮。 method onClick(f) is // 绑定本地操作系统点击事件。 class HTMLButton implements Button is method render(a, b) is // 返回一个按钮的 HTML 表述。 method onClick(f) is // 绑定网络浏览器的点击事件。 class Application is field dialog: Dialog // 程序根据当前配置或环境设定选择创建者的类型。 method initialize() is config = readApplicationConfigFile() if (config.OS == \"Windows\") then dialog = new WindowsDialog() else if (config.OS == \"Web\") then dialog = new WebDialog() else throw new Exception(\"错误！未知的操作系统。\") // 当前客户端代码会与具体创建者的实例进行交互，但是必须通过其基本接口 // 进行。只要客户端通过基本接口与创建者进行交互，你就可将任何创建者子 // 类传递给客户端。 method main() is this.initialize() dialog.render()","s":"伪代码","u":"/docs/design-patterns/factory-method","h":"#伪代码","p":326},{"i":339,"t":"当你在编写代码的过程中，如果无法预知对象确切类别及其依赖关系时，可使用工厂方法。 工厂方法将创建产品的代码与实际使用产品的代码分离，从而能在不影响其他代码的情况下扩展产品创建部分代码。 例如，如果需要向应用中添加一种新产品，你只需要开发新的创建者子类，然后重写其工厂方法即可。 如果你希望用户能扩展你软件库或框架的内部组件，可使用工厂方法。 继承可能是扩展软件库或框架默认行为的最简单方法。但是当你使用子类替代标准组件时，框架如何辨识出该子类？ 解决方案是将各框架中构造组件的代码集中到单个工厂方法中，并在继承该组件之外允许任何人对该方法进行重写。 让我们看看具体是如何实现的。假设你使用开源 UI 框架编写自己的应用。你希望在应用中使用圆形按钮，但是原框架仅支持矩形按钮。你可以使用 圆形按钮 Round­Button 子类来继承标准的 按钮 Button 类。但是，你需要告诉 UI框架 UIFramework 类使用新的子类按钮代替默认按钮。 为了实现这个功能，你可以根据基础框架类开发子类 圆形按钮 UI UIWith­Round­Buttons，并且重写其 create­Button 创建按钮方法。基类中的该方法返回 按钮 对象，而你开发的子类返回 圆形按钮 对象。现在，你就可以使用 圆形按钮 UI 类代替 UI框架 类。就是这么简单！ 如果你希望复用现有对象来节省系统资源，而不是每次都重新创建对象，可使用工厂方法。 在处理大型资源密集型对象 (比如数据库连接、文件系统和网络资源) 时，你会经常碰到这种资源需求。 让我们思考复用现有对象的方法： 首先，你需要创建存储空间来存放所有已经创建的对象。 当他人请求一个对象时，程序将在对象池中搜索可用对象。 … 然后将其返回给客户端代码。 如果没有可用对象，程序则创建一个新对象 (并将其添加到对象池中)。 这些代码可不少！而且它们必须位于同一处，这样才能确保重复代码不会污染程序。 可能最显而易见，也是最方便的方式，就是将这些代码放置在我们试图重用的对象类的构造函数中。但是从定义上来讲，构造函数始终返回的是新对象，其无法返回现有实例。 因此，你需要有一个既能够创建新对象，又可以重用现有对象的普通方法。这听上去和工厂方法非常相像。 实现方式 让所有产品都遵循同一接口。该接口必须声明对所有产品都有意义的方法。 在创建类中添加一个空的工厂方法。该方法的返回类型必须遵循通用的产品接口。 在创建者代码中找到对于产品构造函数的所有引用。将它们依次替换为对于工厂方法的调用，同时将创建产品的代码移入工厂方法。你可能需要在工厂方法中添加临时参数来控制返回的产品类型。工厂方法的代码看上去可能非常糟糕。其中可能会有复杂的 switch 分支运算符，用于选择各种需要实例化的产品类。但是不要担心，我们很快就会修复这个问题。 现在，为工厂方法中的每种产品编写一个创建者子类，然后在子类中重写工厂方法，并将基本方法中的相关创建代码移动到工厂方法中。 如果应用中的产品类型太多，那么为每个产品创建子类并无太大必要，这时你也可以在子类中复用基类中的控制参数。例如，设想你有以下一些层次结构的类。基类 邮件 及其子类 航空邮件 和 陆路邮件；运输 及其子类 飞机，卡车 和 火车。航空邮件 仅使用 飞机 对象，而 陆路邮件 则会同时使用 卡车 和 火车 对象。你可以编写一个新的子类 (例如 火车邮件) 来处理这两种情况，但是还有其他可选的方案。客户端代码可以给 陆路邮件 类传递一个参数，用于控制其希望获得的产品。 如果代码经过上述移动后，基础工厂方法中已经没有任何代码，你可以将其转变为抽象类。如果基础工厂方法中还有其他语句，你可以将其设置为该方法的默认行为。","s":"工厂方法模式适合应用场景","u":"/docs/design-patterns/factory-method","h":"#工厂方法模式适合应用场景","p":326},{"i":341,"t":"✔️ 你可以避免创建者和具体产品之间的紧密耦合。 ✔️ 单一职责原则。你可以将产品创建代码放在程序的单一位置，从而使得代码更容易维护。 ✔️ 开闭原则。无需更改现有客户端代码，你就可以在程序中引入新的产品类型。 ❌ 应用工厂方法模式需要引入许多新的子类，代码可能会因此变得更复杂。最好的情况是将该模式引入创建者类的现有层次结构中。","s":"工厂方法模式优缺点","u":"/docs/design-patterns/factory-method","h":"#工厂方法模式优缺点","p":326},{"i":343,"t":"在许多设计工作的初期都会使用工厂方法模式 (较为简单，而且可以更方便地通过子类进行定制)，随后演化为使用抽象工厂模式、原型模式或生成器模式 (更灵活但更加复杂)。 抽象工厂模式通常基于一组工厂方法，但你也可以使用原型模式来生成这些类的方法。 你可以同时使用工厂方法和迭代器模式来让子类集合返回不同类型的迭代器，并使得迭代器与集合相匹配。 原型并不基于继承，因此没有继承的缺点。另一方面，原型需要对被复制对象进行复杂的初始化。工厂方法基于继承，但是它不需要初始化步骤。 工厂方法是模板方法模式的一种特殊形式。同时，工厂方法可以作为一个大型模板方法中的一个步骤。","s":"与其他模式的关系","u":"/docs/design-patterns/factory-method","h":"#与其他模式的关系","p":326},{"i":345,"t":"亦称：缓存、Cache、Flyweight","s":"享元模式","u":"/docs/design-patterns/flyweight","h":"","p":344},{"i":347,"t":"享元模式是一种结构型设计模式，它摒弃了在每个对象中保存所有数据的方式，通过共享多个对象所共有的相同状态，让你能在有限的内存容量中载入更多对象。","s":"意图","u":"/docs/design-patterns/flyweight","h":"#意图","p":344},{"i":349,"t":"假如你希望在长时间工作后放松一下，所以开发了一款简单的游戏：玩家们在地图上移动并相互射击。你决定实现一个真实的粒子系统，并将其作为游戏的特色。大量的子弹、导弹和爆炸弹片会在整个地图上穿行，为玩家提供紧张刺激的游戏体验。 开发完成后，你推送提交了最新版本的程序，并在编译游戏后将其发送给了一个朋友进行测试。尽管该游戏在你的电脑上完美运行，但是你的朋友却无法长时间进行游戏：游戏总是会在他的电脑上运行几分钟后崩溃。在研究了几个小时的调试消息记录后，你发现导致游戏崩溃的原因是内存容量不足。朋友的设备性能远比不上你的电脑，因此游戏运行在他的电脑上时很快就会出现问题。 真正的问题与粒子系统有关。每个粒子 (一颗子弹、一枚导弹或一块弹片) 都由包含完整数据的独立对象来表示。当玩家在游戏中鏖战进入高潮后的某一时刻，游戏将无法在剩余内存中载入新建粒子，于是程序就崩溃了。","s":"问题","u":"/docs/design-patterns/flyweight","h":"#问题","p":344},{"i":351,"t":"仔细观察 粒子 Particle 类，你可能会注意到颜色 (color) 和精灵图 (sprite) 这两个成员变量所消耗的内存要比其他变量多得多。更糟糕的是，对于所有的粒子来说，这两个成员变量所存储的数据几乎完全一样 (比如所有子弹的颜色和精灵图都一样)。 每个粒子的另一些状态 (坐标、移动矢量和速度) 则是不同的。因为这些成员变量的数值会不断变化。这些数据代表粒子在存续期间不断变化的情景，但每个粒子的颜色和精灵图则会保持不变。 对象的常量数据通常被称为内在状态，其位于对象中，其他对象只能读取但不能修改其数值。而对象的其他状态常常能被其他对象“从外部”改变，因此被称为外在状态。 享元模式建议不在对象中存储外在状态，而是将其传递给依赖于它的一个特殊方法。程序只在对象中保存内在状态，以方便在不同情景下重用。这些对象的区别仅在于其内在状态 (与外在状态相比，内在状态的变体要少很多)，因此你所需的对象数量会大大削减。 让我们回到游戏中。假如能从粒子类中抽出外在状态，那么我们只需三个不同的对象 (子弹、导弹和弹片) 就能表示游戏中的所有粒子。你现在很可能已经猜到了，我们将这样一个仅存储内在状态的对象称为享元。","s":"解决方案","u":"/docs/design-patterns/flyweight","h":"#解决方案","p":344},{"i":353,"t":"那么外在状态会被移动到什么地方呢？总得有类来存储它们，对不对？在大部分情况中，它们会被移动到容器对象中，也就是我们应用享元模式前的聚合对象中。 在我们的例子中，容器对象就是主要的 游戏 Game 对象，其会将所有粒子存储在名为 粒子 particles 的成员变量中。为了能将外在状态移动到这个类中，你需要创建多个数组成员变量来存储每个粒子的坐标、方向矢量和速度。除此之外，你还需要另一个数组来存储指向代表粒子的特定享元的引用。这些数组必须保持同步，这样你才能够使用同一索引来获取关于某个粒子的所有数据。 更优雅的解决方案是创建独立的情景类来存储外在状态和对享元对象的引用。在该方法中，容器类只需包含一个数组。 稍等！这样的话情景对象数量不是会和不采用该模式时的对象数量一样多吗？的确如此，但这些对象要比之前小很多。消耗内存最多的成员变量已经被移动到很少的几个享元对象中了。现在，一个享元大对象会被上千个情境小对象复用，因此无需再重复存储数千个大对象的数据。","s":"外在状态存储","u":"/docs/design-patterns/flyweight","h":"#外在状态存储","p":344},{"i":355,"t":"由于享元对象可在不同的情景中使用，你必须确保其状态不能被修改。享元类的状态只能由构造函数的参数进行一次性初始化，它不能对其他对象公开其设置器或公有成员变量。","s":"享元与不可变性","u":"/docs/design-patterns/flyweight","h":"#享元与不可变性","p":344},{"i":357,"t":"为了能更方便地访问各种享元，你可以创建一个工厂方法来管理已有享元对象的缓存池。工厂方法从客户端处接收目标享元对象的内在状态作为参数，如果它能在缓存池中找到所需享元，则将其返回给客户端；如果没有找到，它就会新建一个享元，并将其添加到缓存池中。 你可以选择在程序的不同地方放入该函数。最简单的选择就是将其放置在享元容器中。除此之外，你还可以新建一个工厂类，或者创建一个静态的工厂方法并将其放入实际的享元类中。","s":"享元工厂","u":"/docs/design-patterns/flyweight","h":"#享元工厂","p":344},{"i":359,"t":"享元模式只是一种优化。在应用该模式之前，你要确定程序中存在与大量类似对象同时占用内存相关的内存消耗问题，并且确保该问题无法使用其他更好的方式来解决。 享元 (Flyweight) 类包含原始对象中部分能在多个对象中共享的状态。同一享元对象可在许多不同情景中使用。享元中存储的状态被称为“内在状态”。传递给享元方法的状态被称为“外在状态”。 情景 (Context) 类包含原始对象中各不相同的外在状态。情景与享元对象组合在一起就能表示原始对象的全部状态。 通常情况下，原始对象的行为会保留在享元类中。因此调用享元方法必须提供部分外在状态作为参数。但你也可将行为移动到情景类中，然后将连入的享元作为单纯的数据对象。 客户端 (Client) 负责计算或存储享元的外在状态。在客户端看来，享元是一种可在运行时进行配置的模板对象，具体的配置方式为向其方法中传入一些情景数据参数。 享元工厂 (Flyweight Factory) 会对已有享元的缓存池进行管理。有了工厂后，客户端就无需直接创建享元，它们只需调用工厂并向其传递目标享元的一些内在状态即可。工厂会根据参数在之前已创建的享元中进行查找，如果找到满足条件的享元就将其返回；如果没有找到就根据参数新建享元。","s":"享元模式结构","u":"/docs/design-patterns/flyweight","h":"#享元模式结构","p":344},{"i":361,"t":"在本例中，享元模式能有效减少在画布上渲染数百万个树状对象时所需的内存。 该模式从主要的 树 Tree 类中抽取内在状态，并将其移动到享元类 树种类 Tree­Type 之中。 最初程序需要在多个对象中存储相同数据，而现在仅需在几个享元对象中保存数据，然后在作为情景的 树 对象中连入享元即可。客户端代码使用享元工厂创建树对象并封装搜索指定对象的复杂行为，并能在需要时复用对象。 // 享元类包含一个树的部分状态。这些成员变量保存的数值对于特定树而言是唯一 // 的。例如，你在这里找不到树的坐标。但这里有很多树木之间所共有的纹理和颜 // 色。由于这些数据的体积通常非常大，所以如果让每棵树都其进行保存的话将耗 // 费大量内存。因此，我们可将纹理、颜色和其他重复数据导出到一个单独的对象 // 中，然后让众多的单个树对象去引用它。 class TreeType is field name field color field texture constructor TreeType(name, color, texture) { …… } method draw(canvas, x, y) is // 1. 创建特定类型、颜色和纹理的位图。 // 2. 在画布坐标 (X,Y) 处绘制位图。 // 享元工厂决定是否复用已有享元或者创建一个新的对象。 class TreeFactory is static field treeTypes: collection of tree types static method getTreeType(name, color, texture) is type = treeTypes.find(name, color, texture) if (type == null) type = new TreeType(name, color, texture) treeTypes.add(type) return type // 情景对象包含树状态的外在部分。程序中可以创建数十亿个此类对象，因为它们 // 体积很小：仅有两个整型坐标和一个引用成员变量。 class Tree is field x,y field type: TreeType constructor Tree(x, y, type) { …… } method draw(canvas) is type.draw(canvas, this.x, this.y) // 树（Tree）和森林（Forest）类是享元的客户端。如果不打算继续对树类进行开 // 发，你可以将它们合并。 class Forest is field trees: collection of Trees method plantTree(x, y, name, color, texture) is type = TreeFactory.getTreeType(name, color, texture) tree = new Tree(x, y, type) trees.add(tree) method draw(canvas) is foreach (tree in trees) do tree.draw(canvas)","s":"伪代码","u":"/docs/design-patterns/flyweight","h":"#伪代码","p":344},{"i":363,"t":"仅在程序必须支持大量对象且没有足够的内存容量时使用享元模式。 应用该模式所获的收益大小取决于使用它的方式和情景。它在下列情况中最有效： 程序需要生成数量巨大的相似对象 这将耗尽目标设备的所有内存 对象中包含可抽取且能在多个对象间共享的重复状态。 实现方式 将需要改写为享元的类成员变量拆分为两个部分： 内在状态：包含不变的、可在许多对象中重复使用的数据的成员变量。 外在状态：包含每个对象各自不同的情景数据的成员变量 保留类中表示内在状态的成员变量，并将其属性设置为不可修改。这些变量仅可在构造函数中获得初始数值。 找到所有使用外在状态成员变量的方法，为在方法中所用的每个成员变量新建一个参数，并使用该参数代替成员变量。 你可以有选择地创建工厂类来管理享元缓存池，它负责在新建享元时检查已有的享元。如果选择使用工厂，客户端就只能通过工厂来请求享元，它们需要将享元的内在状态作为参数传递给工厂。 客户端必须存储和计算外在状态 (情景) 的数值，因为只有这样才能调用享元对象的方法。为了使用方便，外在状态和引用享元的成员变量可以移动到单独的情景类中。","s":"享元模式适合应用场景","u":"/docs/design-patterns/flyweight","h":"#享元模式适合应用场景","p":344},{"i":365,"t":"✔️ 如果程序中有很多相似对象，那么你将可以节省大量内存。 ❌ 你可能需要牺牲执行速度来换取内存，因为他人每次调用享元方法时都需要重新计算部分情景数据。 ❌ 代码会变得更加复杂。团队中的新成员总是会问：“为什么要像这样拆分一个实体的状态？”。","s":"享元模式优缺点","u":"/docs/design-patterns/flyweight","h":"#享元模式优缺点","p":344},{"i":367,"t":"你可以使用享元模式实现组合模式树的共享叶节点以节省内存。 享元展示了如何生成大量的小型对象，外观模式则展示了如何用一个对象来代表整个子系统。 如果你能将对象的所有共享状态简化为一个享元对象，那么享元就和单例模式类似了。但这两个模式有两个根本性的不同。 只会有一个单例实体，但是享元类可以有多个实体，各实体的内在状态也可以不同。 单例对象可以是可变的。享元对象是不可变的。","s":"与其他模式的关系","u":"/docs/design-patterns/flyweight","h":"#与其他模式的关系","p":344},{"i":369,"t":"设计模式是软件设计中常见问题的典型解决方案。它们就像能根据需求进行调整的预制蓝图，可用于解决代码中反复出现的设计问题。 设计模式与方法或库的使用方式不同，你很难直接在自己的程序中套用某个设计模式。模式并不是一段特定的代码，而是解决特定问题的一般性概念。你可以根据模式来实现符合自己程序实际所需的解决方案。 人们常常会混淆模式和算法，因为两者在概念上都是已知特定问题的典型解决方案。但算法总是明确定义达成特定目标所需的一系列步骤，而模式则是对解决方案的更高层次描述。同一模式在两个不同程序中的实现代码可能会不一样。 算法更像是菜谱：提供达成目标的明确步骤。而模式更像是蓝图：你可以看到最终的结果和模式的功能，但需要自己确定实现步骤。","s":"设计模式是什么？","u":"/docs/design-patterns/intro","h":"","p":368},{"i":371,"t":"大部分模式都有正规的描述方式，以便在不同情况下使用。模式的描述通常会包括以下部分： 意图部分简单描述问题和解决方案。 动机部分将进一步解释问题并说明模式会如何提供解决方案。 结构部分展示模式的每个部分和它们之间的关系。 在不同语言中的实现提供流行编程语言的代码，让读者更好地理解模式背后的思想。 部分模式介绍中还列出其他的一些实用细节，例如模式的适用性、实现步骤以及与其他模式的关系。","s":"模式包含哪些内容？","u":"/docs/design-patterns/intro","h":"#模式包含哪些内容","p":368},{"i":373,"t":"谁发明了设计模式？这是一个很好的问题，但也有点不太准确。设计模式并不是晦涩的、复杂的概念——事实恰恰相反。模式是面向对象设计中常见问题的典型解决方案。同样的解决方案在各种项目中得到了反复使用，所以最终有人给它们起了名字，并对其进行了详细描述。这基本上就是模式被发现的历程了。 模式的概念是由克里斯托佛·亚历山大在其著作《建筑模式语言》中首次提出的。本书介绍了城市设计的“语言”，而此类“语言”的基本单元就是模式。模式中可能会包含对窗户应该在多高、一座建筑应该有多少层以及一片街区应该有多大面积的植被等信息的描述。 埃里希·伽玛、约翰·弗利赛德斯、拉尔夫·约翰逊和理查德·赫尔姆这四位作者接受了模式的概念。1994 年，他们出版了《设计模式：可复用面向对象软件的基础》一书，将设计模式的概念应用到程序开发领域中。该书提供了 23 个模式来解决面向对象程序设计中的各种问题，很快便成为了畅销书。由于书名太长，人们将其简称为“四人组 (Gang of Four，GoF) 的书”，并且很快进一步简化为“GoF 的书”。 此后，人们又发现了几十种面向对象的模式。“模式方法”开始在其他程序开发领域中流行起来。如今，在面向对象设计领域之外，人们也提出了许多其他的模式。","s":"模式的历史","u":"/docs/design-patterns/intro","h":"","p":368},{"i":375,"t":"或许你已从事程序开发工作多年，却完全不知道单例模式是什么。很多人都是这样。即便如此，你可能也在不自知的情况下已经使用过一些设计模式了。所以为什么不花些时间来更进一步学习它们呢？ 设计模式是针对软件设计中常见问题的工具箱，其中的工具就是各种经过实践验证的解决方案。即使你从未遇到过这些问题，了解模式仍然非常有用，因为它能指导你如何使用面向对象的设计原则来解决各种问题。 设计模式定义了一种让你和团队成员能够更高效沟通的通用语言。你只需说“哦，这里用单例就可以了”，所有人都会理解这条建议背后的想法。只要知晓模式及其名称，你就无需解释什么是单例。","s":"为什么以及如何学习设计模式？","u":"/docs/design-patterns/intro","h":"","p":368},{"i":377,"t":"设计模式自其诞生之初似乎就饱受争议，所以让我们来看看针对模式的最常见批评吧。","s":"关于模式的争议","u":"/docs/design-patterns/intro","h":"","p":368},{"i":379,"t":"通常当所选编程语言或技术缺少必要的抽象功能时，人们才需要设计模式。在这种情况下，模式是一种可为语言提供更优功能的蹩脚解决方案。 例如，策略模式在绝大部分现代编程语言中可以简单地使用匿名 (lambda) 函数来实现。","s":"一种针对不完善编程语言的蹩脚解决方案","u":"/docs/design-patterns/intro","h":"#一种针对不完善编程语言的蹩脚解决方案","p":368},{"i":381,"t":"模式试图将已经广泛使用的方式系统化。许多人会将这样的统一化认为是某种教条，他们会“全心全意”地实施这样的模式，而不会根据项目的实际情况对其进行调整。","s":"低效的解决方案","u":"/docs/design-patterns/intro","h":"#低效的解决方案","p":368},{"i":383,"t":"如果你只有一把铁锤，那么任何东西看上去都像是钉子。 这个问题常常会给初学模式的人们带来困扰：在学习了某个模式后，他们会在所有地方使用该模式，即便是在较为简单的代码也能胜任的地方也是如此。","s":"不当使用","u":"/docs/design-patterns/intro","h":"#不当使用","p":368},{"i":385,"t":"不同设计模式的复杂程度、细节层次以及在整个系统中的应用范围等方面各不相同。我喜欢将其类比于道路的建造：如果你希望让十字路口更加安全，那么可以安装一些交通信号灯，或者修建包含行人地下通道在内的多层互通式立交桥。 最基础的、底层的模式通常被称为惯用技巧。这类模式一般只能在一种编程语言中使用。 最通用的、高层的模式是构架模式。开发者可以在任何编程语言中使用这类模式。与其他模式不同，它们可用于整个应用程序的架构设计。 此外，所有模式可以根据其意图或目的来分类。本书覆盖了三种主要的模式类别： 创建型模式提供创建对象的机制，增加已有代码的灵活性和可复用性。 结构型模式介绍如何将对象和类组装成较大的结构，并同时保持结构的灵活和高效。 行为模式负责对象间的高效沟通和职责委派。","s":"设计模式分类","u":"/docs/design-patterns/intro","h":"","p":368},{"i":387,"t":"亦称：Iterator","s":"迭代器模式","u":"/docs/design-patterns/iterator","h":"","p":386},{"i":389,"t":"迭代器模式是一种行为设计模式，让你能在不暴露集合底层表现形式 (列表、栈和树等) 的情况下遍历集合中所有的元素。","s":"意图","u":"/docs/design-patterns/iterator","h":"#意图","p":386},{"i":391,"t":"集合是编程中最常使用的数据类型之一。尽管如此，集合只是一组对象的容器而已。 各种类型的集合。 大部分集合使用简单列表存储元素。但有些集合还会使用栈、树、图和其他复杂的数据结构。 无论集合的构成方式如何，它都必须提供某种访问元素的方式，便于其他代码使用其中的元素。集合应提供一种能够遍历元素的方式，且保证它不会周而复始地访问同一个元素。 如果你的集合基于列表，那么这项工作听上去仿佛很简单。但如何遍历复杂数据结构 (例如树) 中的元素呢？例如，今天你需要使用深度优先算法来遍历树结构，明天可能会需要广度优先算法；下周则可能会需要其他方式 (比如随机存取树中的元素)。 可通过不同的方式遍历相同的集合。 不断向集合中添加遍历算法会模糊其“高效存储数据”的主要职责。此外，有些算法可能是根据特定应用订制的，将其加入泛型集合类中会显得非常奇怪。 另一方面，使用多种集合的客户端代码可能并不关心存储数据的方式。不过由于集合提供不同的元素访问方式，你的代码将不得不与特定集合类进行耦合。","s":"问题","u":"/docs/design-patterns/iterator","h":"#问题","p":386},{"i":393,"t":"迭代器模式的主要思想是将集合的遍历行为抽取为单独的迭代器对象。 迭代器可实现多种遍历算法。多个迭代器对象可同时遍历同一个集合。 除实现自身算法外，迭代器还封装了遍历操作的所有细节，例如当前位置和末尾剩余元素的数量。因此，多个迭代器可以在相互独立的情况下同时访问集合。 迭代器通常会提供一个获取集合元素的基本方法。客户端可不断调用该方法直至它不返回任何内容，这意味着迭代器已经遍历了所有元素。 所有迭代器必须实现相同的接口。这样一来，只要有合适的迭代器，客户端代码就能兼容任何类型的集合或遍历算法。如果你需要采用特殊方式来遍历集合，只需创建一个新的迭代器类即可，无需对集合或客户端进行修改。","s":"解决方案","u":"/docs/design-patterns/iterator","h":"#解决方案","p":386},{"i":395,"t":"漫步罗马的不同方式。 你计划在罗马游览数天，参观所有主要的旅游景点。但在到达目的地后，你可能会浪费很多时间绕圈子，甚至找不到罗马斗兽场在哪里。 或者你可以购买一款智能手机上的虚拟导游程序。这款程序非常智能而且价格不贵，你想在景点待多久都可以。 第三种选择是用部分旅行预算雇佣一位对城市了如指掌的当地向导。向导能根据你的喜好来安排行程，为你介绍每个景点并讲述许多激动人心的故事。这样的旅行可能会更有趣，但所需费用也会更高。 所有这些选择 (自由漫步、智能手机导航或真人向导) 都是这个由众多罗马景点组成的集合的迭代器。","s":"真实世界类比","u":"/docs/design-patterns/iterator","h":"#真实世界类比","p":386},{"i":397,"t":"迭代器 (Iterator) 接口声明了遍历集合所需的操作：获取下一个元素、获取当前位置和重新开始迭代等。 具体迭代器 (Concrete Iterators) 实现遍历集合的一种特定算法。迭代器对象必须跟踪自身遍历的进度。这使得多个迭代器可以相互独立地遍历同一集合。 集合 (Collection) 接口声明一个或多个方法来获取与集合兼容的迭代器。请注意，返回方法的类型必须被声明为迭代器接口，因此具体集合可以返回各种不同种类的迭代器。 具体集合 (Concrete Collections) 会在客户端请求迭代器时返回一个特定的具体迭代器类实体。你可能会琢磨，剩下的集合代码在什么地方呢？不用担心，它也会在同一个类中。只是这些细节对于实际模式来说并不重要，所以我们将其省略了而已。 客户端 (Client) 通过集合和迭代器的接口与两者进行交互。这样一来客户端无需与具体类进行耦合，允许同一客户端代码使用各种不同的集合和迭代器。 客户端通常不会自行创建迭代器，而是会从集合中获取。但在特定情况下，客户端可以直接创建一个迭代器 (例如当客户端需要自定义特殊迭代器时)。","s":"迭代器模式结构","u":"/docs/design-patterns/iterator","h":"#迭代器模式结构","p":386},{"i":399,"t":"在本例中，迭代器模式用于遍历一个封装了访问微信好友关系功能的特殊集合。该集合提供使用不同方式遍历档案资料的多个迭代器。 遍历社交档案的示例 “好友 (friends)”迭代器可用于遍历指定档案的好友。“同事 (colleagues)”迭代器也提供同样的功能，但仅包括与目标用户在同一家公司工作的好友。这两个迭代器都实现了同一个通用接口，客户端能在不了解认证和发送 REST 请求等实现细节的情况下获取档案。 客户端仅通过接口与集合和迭代器交互，也就不会同具体类耦合。如果你决定将应用连接到全新的社交网络，只需提供新的集合和迭代器类即可，无需修改现有代码。 // 集合接口必须声明一个用于生成迭代器的工厂方法。如果程序中有不同类型的迭 // 代器，你也可以声明多个方法。 interface SocialNetwork is method createFriendsIterator(profileId):ProfileIterator method createCoworkersIterator(profileId):ProfileIterator // 每个具体集合都与其返回的一组具体迭代器相耦合。但客户并不是这样的，因为 // 这些方法的签名将会返回迭代器接口。 class WeChat implements SocialNetwork is // ……大量的集合代码应该放在这里…… // 迭代器创建代码。 method createFriendsIterator(profileId) is return new WeChatIterator(this, profileId, \"friends\") method createCoworkersIterator(profileId) is return new WeChatIterator(this, profileId, \"coworkers\") // 所有迭代器的通用接口。 interface ProfileIterator is method getNext():Profile method hasMore():bool // 具体迭代器类。 class WeChatIterator implements ProfileIterator is // 迭代器需要一个指向其遍历集合的引用。 private field weChat: WeChat private field profileId, type: string // 迭代器对象会独立于其他迭代器来对集合进行遍历。因此它必须保存迭代器 // 的状态。 private field currentPosition private field cache: array of Profile constructor WeChatIterator(weChat, profileId, type) is this.weChat = weChat this.profileId = profileId this.type = type private method lazyInit() is if (cache == null) cache = weChat.socialGraphRequest(profileId, type) // 每个具体迭代器类都会自行实现通用迭代器接口。 method getNext() is if (hasMore()) result = cache[currentPosition] currentPosition++ return result method hasMore() is lazyInit() return currentPosition < cache.length // 这里还有一个有用的绝招：你可将迭代器传递给客户端类，无需让其拥有访问整 // 个集合的权限。这样一来，你就无需将集合暴露给客户端了。 // // 还有另一个好处：你可在运行时将不同的迭代器传递给客户端，从而改变客户端 // 与集合互动的方式。这一方法可行的原因是客户端代码并没有和具体迭代器类相 // 耦合。 class SocialSpammer is method send(iterator: ProfileIterator, message: string) is while (iterator.hasMore()) profile = iterator.getNext() System.sendEmail(profile.getEmail(), message) // 应用程序（Application）类可对集合和迭代器进行配置，然后将其传递给客户 // 端代码。 class Application is field network: SocialNetwork field spammer: SocialSpammer method config() is if working with WeChat this.network = new WeChat() if working with LinkedIn this.network = new LinkedIn() this.spammer = new SocialSpammer() method sendSpamToFriends(profile) is iterator = network.createFriendsIterator(profile.getId()) spammer.send(iterator, \"非常重要的消息\") method sendSpamToCoworkers(profile) is iterator = network.createCoworkersIterator(profile.getId()) spammer.send(iterator, \"非常重要的消息\")","s":"伪代码","u":"/docs/design-patterns/iterator","h":"#伪代码","p":386},{"i":401,"t":"当集合背后为复杂的数据结构，且你希望对客户端隐藏其复杂性时 (出于使用便利性或安全性的考虑)，可以使用迭代器模式。 迭代器封装了与复杂数据结构进行交互的细节，为客户端提供多个访问集合元素的简单方法。这种方式不仅对客户端来说非常方便，而且能避免客户端在直接与集合交互时执行错误或有害的操作，从而起到保护集合的作用。 使用该模式可以减少程序中重复的遍历代码。 重要迭代算法的代码往往体积非常庞大。当这些代码被放置在程序业务逻辑中时，它会让原始代码的职责模糊不清，降低其可维护性。因此，将遍历代码移到特定的迭代器中可使程序代码更加精炼和简洁。 如果你希望代码能够遍历不同的甚至是无法预知的数据结构，可以使用迭代器模式。 该模式为集合和迭代器提供了一些通用接口。如果你在代码中使用了这些接口，那么将其他实现了这些接口的集合和迭代器传递给它时，它仍将可以正常运行。 实现方式 声明迭代器接口。该接口必须提供至少一个方法来获取集合中的下个元素。但为了使用方便，你还可以添加一些其他方法，例如获取前一个元素、记录当前位置和判断迭代是否已结束。 声明集合接口并描述一个获取迭代器的方法。其返回值必须是迭代器接口。如果你计划拥有多组不同的迭代器，则可以声明多个类似的方法。 为希望使用迭代器进行遍历的集合实现具体迭代器类。迭代器对象必须与单个集合实体链接。链接关系通常通过迭代器的构造函数建立。 在你的集合类中实现集合接口。其主要思想是针对特定集合为客户端代码提供创建迭代器的快捷方式。集合对象必须将自身传递给迭代器的构造函数来创建两者之间的链接。 检查客户端代码，使用迭代器替代所有集合遍历代码。每当客户端需要遍历集合元素时都会获取一个新的迭代器。","s":"迭代器模式适合应用场景","u":"/docs/design-patterns/iterator","h":"#迭代器模式适合应用场景","p":386},{"i":403,"t":"✔️ 单一职责原则。通过将体积庞大的遍历算法代码抽取为独立的类，你可对客户端代码和集合进行整理。 ✔️ 开闭原则。你可实现新型的集合和迭代器并将其传递给现有代码，无需修改现有代码。 ✔️ 你可以并行遍历同一集合，因为每个迭代器对象都包含其自身的遍历状态。 ✔️ 相似的，你可以暂停遍历并在需要时继续。 ❌ 如果你的程序只与简单的集合进行交互，应用该模式可能会矫枉过正。 ❌ 对于某些特殊集合，使用迭代器可能比直接遍历的效率低。","s":"迭代器模式优缺点","u":"/docs/design-patterns/iterator","h":"#迭代器模式优缺点","p":386},{"i":405,"t":"你可以使用迭代器模式来遍历组合模式树。 你可以同时使用工厂方法模式和迭代器来让子类集合返回不同类型的迭代器，并使得迭代器与集合相匹配。 你可以同时使用备忘录模式和迭代器来获取当前迭代器的状态，并且在需要的时候进行回滚。 可以同时使用访问者模式和迭代器来遍历复杂数据结构，并对其中的元素执行所需操作，即使这些元素所属的类完全不同。","s":"与其他模式的关系","u":"/docs/design-patterns/iterator","h":"#与其他模式的关系","p":386},{"i":407,"t":"亦称：调解人、控制器、Intermediary、Controller、Mediator","s":"中介者模式","u":"/docs/design-patterns/mediator","h":"","p":406},{"i":409,"t":"中介者模式是一种行为设计模式，能让你减少对象之间混乱无序的依赖关系。该模式会限制对象之间的直接交互，迫使它们通过一个中介者对象进行合作。","s":"意图","u":"/docs/design-patterns/mediator","h":"#意图","p":406},{"i":411,"t":"假如你有一个创建和修改客户资料的对话框，它由各种控件组成，例如文本框 (Text­Field)、复选框 (Checkbox) 和按钮 (Button) 等。 用户界面中各元素间的关系会随程序发展而变得混乱。 某些表单元素可能会直接进行互动。例如，选中“我有一只狗”复选框后可能会显示一个隐藏文本框用于输入狗狗的名字。另一个例子是提交按钮必须在保存数据前校验所有输入内容。 元素间存在许多关联。因此，对某些元素进行修改可能会影响其他元素。 如果直接在表单元素代码中实现业务逻辑，你将很难在程序其他表单中复用这些元素类。例如，由于复选框类与狗狗的文本框相耦合，所以将无法在其他表单中使用它。你要么使用渲染资料表单时用到的所有类，要么一个都不用。","s":"问题","u":"/docs/design-patterns/mediator","h":"#问题","p":406},{"i":413,"t":"中介者模式建议你停止组件之间的直接交流并使其相互独立。这些组件必须调用特殊的中介者对象，通过中介者对象重定向调用行为，以间接的方式进行合作。最终，组件仅依赖于一个中介者类，无需与多个其他组件相耦合。 在资料编辑表单的例子中，对话框 (Dialog) 类本身将作为中介者，其很可能已知自己所有的子元素，因此你甚至无需在该类中引入新的依赖关系。 UI 元素必须通过中介者对象进行间接沟通。 绝大部分重要的修改都在实际表单元素中进行。让我们想想提交按钮。之前，当用户点击按钮后，它必须对所有表单元素数值进行校验。而现在它的唯一工作是将点击事件通知给对话框。收到通知后，对话框可以自行校验数值或将任务委派给各元素。这样一来，按钮不再与多个表单元素相关联，而仅依赖于对话框类。 你还可以为所有类型的对话框抽取通用接口，进一步削弱其依赖性。接口中将声明一个所有表单元素都能使用的通知方法，可用于将元素中发生的事件通知给对话框。这样一来，所有实现了该接口的对话框都能使用这个提交按钮了。 采用这种方式，中介者模式让你能在单个中介者对象中封装多个对象间的复杂关系网。类所拥有的依赖关系越少，就越易于修改、扩展或复用。","s":"解决方案","u":"/docs/design-patterns/mediator","h":"#解决方案","p":406},{"i":415,"t":"飞行器驾驶员之间不会通过相互沟通来决定下一架降落的飞机。所有沟通都通过控制塔台进行。 飞行器驾驶员们在靠近或离开空中管制区域时不会直接相互交流。但他们会与飞机跑道附近，塔台中的空管员通话。如果没有空管员，驾驶员就需要留意机场附近的所有飞机，并与数十位飞行员组成的委员会讨论降落顺序。那恐怕会让飞机坠毁的统计数据一飞冲天吧。 塔台无需管制飞行全程，只需在航站区加强管控即可，因为该区域的决策参与者数量对于飞行员来说实在太多了。","s":"真实世界类比","u":"/docs/design-patterns/mediator","h":"#真实世界类比","p":406},{"i":417,"t":"组件 (Component) 是各种包含业务逻辑的类。每个组件都有一个指向中介者的引用，该引用被声明为中介者接口类型。组件不知道中介者实际所属的类，因此你可通过将其连接到不同的中介者以使其能在其他程序中复用。 中介者 (Mediator) 接口声明了与组件交流的方法，但通常仅包括一个通知方法。组件可将任意上下文 (包括自己的对象) 作为该方法的参数，只有这样接收组件和发送者类之间才不会耦合。 具体中介者 (Concrete Mediator) 封装了多种组件间的关系。具体中介者通常会保存所有组件的引用并对其进行管理，甚至有时会对其生命周期进行管理。 组件并不知道其他组件的情况。如果组件内发生了重要事件，它只能通知中介者。中介者收到通知后能轻易地确定发送者，这或许已足以判断接下来需要触发的组件了。 对于组件来说，中介者看上去完全就是一个黑箱。发送者不知道最终会由谁来处理自己的请求，接收者也不知道最初是谁发出了请求。","s":"中介者模式结构","u":"/docs/design-patterns/mediator","h":"#中介者模式结构","p":406},{"i":419,"t":"在本例中，中介者模式可帮助你减少各种 UI 类 (按钮、复选框和文本标签) 之间的相互依赖关系。 UI 对话框类的结构 用户触发的元素不会直接与其他元素交流，即使看上去它们应该这样做。相反，元素只需让中介者知晓事件即可，并能在发出通知时同时传递任何上下文信息。 本例中的中介者是整个认证对话框。对话框知道具体元素应如何进行合作并促进它们的间接交流。当接收到事件通知后，对话框会确定负责处理事件的元素并据此重定向请求。 // 中介者接口声明了一个能让组件将各种事件通知给中介者的方法。中介者可对这 // 些事件做出响应并将执行工作传递给其他组件。 interface Mediator is method notify(sender: Component, event: string) // 具体中介者类可解开各组件之间相互交叉的连接关系并将其转移到中介者中。 class AuthenticationDialog implements Mediator is private field title: string private field loginOrRegisterChkBx: Checkbox private field loginUsername, loginPassword: Textbox private field registrationUsername, registrationPassword, registrationEmail: Textbox private field okBtn, cancelBtn: Button constructor AuthenticationDialog() is // 创建所有组件对象并将当前中介者传递给其构造函数以建立连接。 // 当组件中有事件发生时，它会通知中介者。中介者接收到通知后可自行处理， // 也可将请求传递给另一个组件。 method notify(sender, event) is if (sender == loginOrRegisterChkBx and event == \"check\") if (loginOrRegisterChkBx.checked) title = \"登录\" // 1. 显示登录表单组件。 // 2. 隐藏注册表单组件。 else title = \"注册\" // 1. 显示注册表单组件。 // 2. 隐藏登录表单组件。 if (sender == okBtn && event == \"click\") if (loginOrRegister.checked) // 尝试找到使用登录信息的用户。 if (!found) // 在登录字段上方显示错误信息。 else // 1. 使用注册字段中的数据创建用户账号。 // 2. 完成用户登录工作。 // …… // 组件会使用中介者接口与中介者进行交互。因此只需将它们与不同的中介者连接 // 起来，你就能在其他情境中使用这些组件了。 class Component is field dialog: Mediator constructor Component(dialog) is this.dialog = dialog method click() is dialog.notify(this, \"click\") method keypress() is dialog.notify(this, \"keypress\") // 具体组件之间无法进行交流。它们只有一个交流渠道，那就是向中介者发送通知。 class Button extends Component is // …… class Textbox extends Component is // …… class Checkbox extends Component is method check() is dialog.notify(this, \"check\") // ……","s":"伪代码","u":"/docs/design-patterns/mediator","h":"#伪代码","p":406},{"i":421,"t":"当一些对象和其他对象紧密耦合以致难以对其进行修改时，可使用中介者模式。 该模式让你将对象间的所有关系抽取成为一个单独的类，以使对于特定组件的修改工作独立于其他组件。 当组件因过于依赖其他组件而无法在不同应用中复用时，可使用中介者模式。 应用中介者模式后，每个组件不再知晓其他组件的情况。尽管这些组件无法直接交流，但它们仍可通过中介者对象进行间接交流。如果你希望在不同应用中复用一个组件，则需要为其提供一个新的中介者类。 如果为了能在不同情景下复用一些基本行为，导致你需要被迫创建大量组件子类时，可使用中介者模式。 由于所有组件间关系都被包含在中介者中，因此你无需修改组件就能方便地新建中介者类以定义新的组件合作方式。 实现方式 找到一组当前紧密耦合，且提供其独立性能带来更大好处的类 (例如更易于维护或更方便复用)。 声明中介者接口并描述中介者和各种组件之间所需的交流接口。在绝大多数情况下，一个接收组件通知的方法就足够了。如果你希望在不同情景下复用组件类，那么该接口将非常重要。只要组件使用通用接口与其中介者合作，你就能将该组件与不同实现中的中介者进行连接。 实现具体中介者类。该类可从自行保存其下所有组件的引用中受益。 你可以更进一步，让中介者负责组件对象的创建和销毁。此后，中介者可能会与工厂或外观类似。 组件必须保存对于中介者对象的引用。该连接通常在组件的构造函数中建立，该函数会将中介者对象作为参数传递。 修改组件代码，使其可调用中介者的通知方法，而非其他组件的方法。然后将调用其他组件的代码抽取到中介者类中，并在中介者接收到该组件通知时执行这些代码。","s":"中介者模式适合应用场景","u":"/docs/design-patterns/mediator","h":"#中介者模式适合应用场景","p":406},{"i":423,"t":"✔️ 单一职责原则。你可以将多个组件间的交流抽取到同一位置，使其更易于理解和维护。 ✔️ 开闭原则。你无需修改实际组件就能增加新的中介者。 ✔️ 你可以减轻应用中多个组件间的耦合情况。 ✔️ 你可以更方便地复用各个组件。 ❌ 一段时间后，中介者可能会演化成为上帝对象。","s":"中介者模式优缺点","u":"/docs/design-patterns/mediator","h":"#中介者模式优缺点","p":406},{"i":425,"t":"责任链模式、命令模式、中介者模式和观察者模式用于处理请求发送者和接收者之间的不同连接方式： 责任链按照顺序将请求动态传递给一系列的潜在接收者，直至其中一名接收者对请求进行处理。 命令在发送者和请求者之间建立单向连接。 中介者清除了发送者和请求者之间的直接连接，强制它们通过一个中介对象进行间接沟通。 观察者允许接收者动态地订阅或取消接收请求。 外观模式和中介者的职责类似：它们都尝试在大量紧密耦合的类中组织起合作。 外观为子系统中的所有对象定义了一个简单接口，但是它不提供任何新功能。子系统本身不会意识到外观的存在。子系统中的对象可以直接进行交流。 中介者将系统中组件的沟通行为中心化。各组件只知道中介者对象，无法直接相互交流。 中介者和观察者之间的区别往往很难记住。在大部分情况下，你可以使用其中一种模式，而有时可以同时使用。让我们来看看如何做到这一点。 中介者的主要目标是消除一系列系统组件之间的相互依赖。这些组件将依赖于同一个中介者对象。观察者的目标是在对象之间建立动态的单向连接，使得部分对象可作为其他对象的附属发挥作用。有一种流行的中介者模式实现方式依赖于观察者。中介者对象担当发布者的角色，其他组件则作为订阅者，可以订阅中介者的事件或取消订阅。当中介者以这种方式实现时，它可能看上去与观察者非常相似。当你感到疑惑时，记住可以采用其他方式来实现中介者。例如，你可永久性地将所有组件链接到同一个中介者对象。这种实现方式和观察者并不相同，但这仍是一种中介者模式。假设有一个程序，其所有的组件都变成了发布者，它们之间可以相互建立动态连接。这样程序中就没有中心化的中介者对象，而只有一些分布式的观察者。","s":"与其他模式的关系","u":"/docs/design-patterns/mediator","h":"#与其他模式的关系","p":406},{"i":427,"t":"亦称：快照、Snapshot、Memento","s":"备忘录模式","u":"/docs/design-patterns/memento","h":"","p":426},{"i":429,"t":"备忘录模式是一种行为设计模式，允许在不暴露对象实现细节的情况下保存和恢复对象之前的状态。","s":"意图","u":"/docs/design-patterns/memento","h":"#意图","p":426},{"i":431,"t":"假如你正在开发一款文字编辑器应用程序。除了简单的文字编辑功能外，编辑器中还要有设置文本格式和插入内嵌图片等功能。 后来，你决定让用户能撤销施加在文本上的任何操作。这项功能在过去几年里变得十分普遍，因此用户期待任何程序都有这项功能。你选择采用直接的方式来实现该功能：程序在执行任何操作前会记录所有的对象状态，并将其保存下来。当用户此后需要撤销某个操作时，程序将从历史记录中获取最近的快照，然后使用它来恢复所有对象的状态。 程序在执行操作前保存所有对象的状态快照，稍后可通过快照将对象恢复到之前的状态。 让我们来思考一下这些状态快照。首先，到底该如何生成一个快照呢？很可能你会需要遍历对象的所有成员变量并将其数值复制保存。但只有当对象对其内容没有严格访问权限限制的情况下，你才能使用该方式。不过很遗憾，绝大部分对象会使用私有成员变量来存储重要数据，这样别人就无法轻易查看其中的内容。 现在我们暂时忽略这个问题，假设对象都像嬉皮士一样：喜欢开放式的关系并会公开其所有状态。尽管这种方式能够解决当前问题，让你可随时生成对象的状态快照，但这种方式仍存在一些严重问题。未来你可能会添加或删除一些成员变量。这听上去很简单，但需要对负责复制受影响对象状态的类进行更改。 如何复制对象的私有状态？ 还有更多问题。让我们来考虑编辑器 (Editor) 状态的实际“快照”，它需要包含哪些数据？至少必须包含实际的文本、光标坐标和当前滚动条位置等。你需要收集这些数据并将其放入特定容器中，才能生成快照。 你很可能会将大量的容器对象存储在历史记录列表中。这样一来，容器最终大概率会成为同一个类的对象。这个类中几乎没有任何方法，但有许多与编辑器状态一一对应的成员变量。为了让其他对象能保存或读取快照，你很可能需要将快照的成员变量设为公有。无论这些状态是否私有，其都将暴露一切编辑器状态。其他类会对快照类的每个小改动产生依赖，除非这些改动仅存在于私有成员变量或方法中，而不会影响外部类。 我们似乎走进了一条死胡同：要么会暴露类的所有内部细节而使其过于脆弱；要么会限制对其状态的访问权限而无法生成快照。那么，我们还有其他方式来实现“撤销”功能吗？","s":"问题","u":"/docs/design-patterns/memento","h":"#问题","p":426},{"i":433,"t":"我们刚才遇到的所有问题都是封装“破损”造成的。一些对象试图超出其职责范围的工作。由于在执行某些行为时需要获取数据，所以它们侵入了其他对象的私有空间，而不是让这些对象来完成实际的工作。 备忘录模式将创建状态快照 (Snapshot) 的工作委派给实际状态的拥有者原发器 (Originator) 对象。这样其他对象就不再需要从“外部”复制编辑器状态了，编辑器类拥有其状态的完全访问权，因此可以自行生成快照。 模式建议将对象状态的副本存储在一个名为备忘录 (Memento) 的特殊对象中。除了创建备忘录的对象外，任何对象都不能访问备忘录的内容。其他对象必须使用受限接口与备忘录进行交互，它们可以获取快照的元数据 (创建时间和操作名称等)，但不能获取快照中原始对象的状态。 原发器拥有对备忘录的完全访问权限，负责人则只能访问元数据。 这种限制策略允许你将备忘录保存在通常被称为负责人 (Caretakers) 的对象中。由于负责人仅通过受限接口与备忘录互动，故其无法修改存储在备忘录内部的状态。同时，原发器拥有对备忘录所有成员的访问权限，从而能随时恢复其以前的状态。 在文字编辑器的示例中，我们可以创建一个独立的历史 (History) 类作为负责人。编辑器每次执行操作前，存储在负责人中的备忘录栈都会生长。你甚至可以在应用的 UI 中渲染该栈，为用户显示之前的操作历史。 当用户触发撤销操作时，历史类将从栈中取回最近的备忘录，并将其传递给编辑器以请求进行回滚。由于编辑器拥有对备忘录的完全访问权限，因此它可以使用从备忘录中获取的数值来替换自身的状态。","s":"解决方案","u":"/docs/design-patterns/memento","h":"#解决方案","p":426},{"i":436,"t":"该模式的经典实现方式依赖于许多流行编程语言 (例如 C++、C# 和 Java) 所支持的嵌套类。 原发器 (Originator) 类可以生成自身状态的快照，也可以在需要时通过快照恢复自身状态。 备忘录 (Memento) 是原发器状态快照的值对象 (value object)。通常做法是将备忘录设为不可变的，并通过构造函数一次性传递数据。 负责人 (Caretaker) 仅知道“何时”和“为何”捕捉原发器的状态，以及何时恢复状态。 负责人通过保存备忘录栈来记录原发器的历史状态。当原发器需要回溯历史状态时，负责人将从栈中获取最顶部的备忘录，并将其传递给原发器的恢复 (restoration) 方法。 在该实现方法中，备忘录类将被嵌套在原发器中。这样原发器就可访问备忘录的成员变量和方法，即使这些方法被声明为私有。另一方面，负责人对于备忘录的成员变量和方法的访问权限非常有限：它们只能在栈中保存备忘录，而不能修改其状态。","s":"基于嵌套类的实现","u":"/docs/design-patterns/memento","h":"#基于嵌套类的实现","p":426},{"i":438,"t":"另外一种实现方法适用于不支持嵌套类的编程语言 (没错，我说的就是 PHP)。 在没有嵌套类的情况下，你可以规定负责人仅可通过明确声明的中间接口与备忘录互动，该接口仅声明与备忘录元数据相关的方法，限制其对备忘录成员变量的直接访问权限。 另一方面，原发器可以直接与备忘录对象进行交互，访问备忘录类中声明的成员变量和方法。这种方式的缺点在于你需要将备忘录的所有成员变量声明为公有。","s":"基于中间接口的实现","u":"/docs/design-patterns/memento","h":"#基于中间接口的实现","p":426},{"i":440,"t":"如果你不想让其他类有任何机会通过备忘录来访问原发器的状态，那么还有另一种可用的实现方式。 这种实现方式允许存在多种不同类型的原发器和备忘录。每种原发器都和其相应的备忘录类进行交互。原发器和备忘录都不会将其状态暴露给其他类。 负责人此时被明确禁止修改存储在备忘录中的状态。但负责人类将独立于原发器，因为此时恢复方法被定义在了备忘录类中。 每个备忘录将与创建了自身的原发器连接。原发器会将自己及状态传递给备忘录的构造函数。由于这些类之间的紧密联系，只要原发器定义了合适的设置器 (setter)，备忘录就能恢复其状态。","s":"封装更加严格的实现","u":"/docs/design-patterns/memento","h":"#封装更加严格的实现","p":426},{"i":442,"t":"本例结合使用了命令模式与备忘录模式，可保存复杂文字编辑器的状态快照，并能在需要时从快照中恢复之前的状态。 保存文字编辑器状态的快照。 命令 (command) 对象将作为负责人，它们会在执行与命令相关的操作前获取编辑器的备忘录。当用户试图撤销最近的命令时，编辑器可以使用保存在命令中的备忘录来将自身回滚到之前的状态。 备忘录类没有声明任何公有的成员变量、获取器 (getter) 和设置器，因此没有对象可以修改其内容。备忘录与创建自己的编辑器相连接，这使得备忘录能够通过编辑器对象的设置器传递数据，恢复与其相连接的编辑器的状态。由于备忘录与特定的编辑器对象相连接，程序可以使用中心化的撤销栈实现对多个独立编辑器窗口的支持。 // 原发器中包含了一些可能会随时间变化的重要数据。它还定义了在备忘录中保存 // 自身状态的方法，以及从备忘录中恢复状态的方法。 class Editor is private field text, curX, curY, selectionWidth method setText(text) is this.text = text method setCursor(x, y) is this.curX = x this.curY = y method setSelectionWidth(width) is this.selectionWidth = width // 在备忘录中保存当前的状态。 method createSnapshot():Snapshot is // 备忘录是不可变的对象；因此原发器会将自身状态作为参数传递给备忘 // 录的构造函数。 return new Snapshot(this, text, curX, curY, selectionWidth) // 备忘录类保存有编辑器的过往状态。 class Snapshot is private field editor: Editor private field text, curX, curY, selectionWidth constructor Snapshot(editor, text, curX, curY, selectionWidth) is this.editor = editor this.text = text this.curX = x this.curY = y this.selectionWidth = selectionWidth // 在某一时刻，编辑器之前的状态可以使用备忘录对象来恢复。 method restore() is editor.setText(text) editor.setCursor(curX, curY) editor.setSelectionWidth(selectionWidth) // 命令对象可作为负责人。在这种情况下，命令会在修改原发器状态之前获取一个 // 备忘录。当需要撤销时，它会从备忘录中恢复原发器的状态。 class Command is private field backup: Snapshot method makeBackup() is backup = editor.createSnapshot() method undo() is if (backup != null) backup.restore() // ……","s":"伪代码","u":"/docs/design-patterns/memento","h":"#伪代码","p":426},{"i":444,"t":"当你需要创建对象状态快照来恢复其之前的状态时，可以使用备忘录模式。 备忘录模式允许你复制对象中的全部状态 (包括私有成员变量)，并将其独立于对象进行保存。尽管大部分人因为“撤销”这个用例才记得该模式，但其实它在处理事务 (比如需要在出现错误时回滚一个操作) 的过程中也必不可少。 当直接访问对象的成员变量、获取器或设置器将导致封装被突破时，可以使用该模式。 备忘录让对象自行负责创建其状态的快照。任何其他对象都不能读取快照，这有效地保障了数据的安全性。 实现方式 确定担任原发器角色的类。重要的是明确程序使用的一个原发器中心对象，还是多个较小的对象。 创建备忘录类。逐一声明对应每个原发器成员变量的备忘录成员变量。 将备忘录类设为不可变。备忘录只能通过构造函数一次性接收数据。该类中不能包含设置器。 如果你所使用的编程语言支持嵌套类，则可将备忘录嵌套在原发器中；如果不支持，那么你可从备忘录类中抽取一个空接口，然后让其他所有对象通过接口来引用备忘录。你可在该接口中添加一些元数据操作，但不能暴露原发器的状态。 在原发器中添加一个创建备忘录的方法。原发器必须通过备忘录构造函数的一个或多个实际参数来将自身状态传递给备忘录。该方法返回结果的类型必须是你在上一步中抽取的接口 (如果你已经抽取了)。实际上，创建备忘录的方法必须直接与备忘录类进行交互。 在原发器类中添加一个用于恢复自身状态的方法。该方法接受备忘录对象作为参数。如果你在之前的步骤中抽取了接口，那么可将接口作为参数的类型。在这种情况下，你需要将输入对象强制转换为备忘录，因为原发器需要拥有对该对象的完全访问权限。 无论负责人是命令对象、历史记录或其他完全不同的东西，它都必须要知道何时向原发器请求新的备忘录、如何存储备忘录以及何时使用特定备忘录来对原发器进行恢复。 负责人与原发器之间的连接可以移动到备忘录类中。在本例中，每个备忘录都必须与创建自己的原发器相连接。恢复方法也可以移动到备忘录类中，但只有当备忘录类嵌套在原发器中，或者原发器类提供了足够多的设置器并可对其状态进行重写时，这种方式才能实现。","s":"备忘录模式适合应用场景","u":"/docs/design-patterns/memento","h":"#备忘录模式适合应用场景","p":426},{"i":446,"t":"✔️ 你可以在不破坏对象封装情况的前提下创建对象状态快照。 ✔️ 你可以通过让负责人维护原发器状态历史记录来简化原发器代码。 ❌ 如果客户端过于频繁地创建备忘录，程序将消耗大量内存。 ❌ 负责人必须完整跟踪原发器的生命周期，这样才能销毁弃用的备忘录。 ❌ 绝大部分动态编程语言 (例如 PHP、Python 和 JavaScript) 不能确保备忘录中的状态不被修改。","s":"备忘录模式优缺点","u":"/docs/design-patterns/memento","h":"#备忘录模式优缺点","p":426},{"i":448,"t":"你可以同时使用命令模式和备忘录模式来实现“撤销”。在这种情况下，命令用于对目标对象执行各种不同的操作，备忘录用来保存一条命令执行前该对象的状态。 你可以同时使用备忘录和迭代器模式来获取当前迭代器的状态，并且在需要的时候进行回滚。 有时候原型模式可以作为备忘录的一个简化版本，其条件是你需要在历史记录中存储的对象的状态比较简单，不需要链接其他外部资源，或者链接可以方便地重建。","s":"与其他模式的关系","u":"/docs/design-patterns/memento","h":"#与其他模式的关系","p":426},{"i":450,"t":"亦称：事件订阅者、监听者、Event-Subscriber、Listener、Observer","s":"观察者模式","u":"/docs/design-patterns/observer","h":"","p":449},{"i":452,"t":"观察者模式是一种行为设计模式，允许你定义一种订阅机制，可在对象事件发生时通知多个“观察”该对象的其他对象。","s":"意图","u":"/docs/design-patterns/observer","h":"#意图","p":449},{"i":454,"t":"假如你有两种类型的对象：顾客 和 商店。顾客对某个特定品牌的产品非常感兴趣 (例如最新型号的 iPhone 手机)，而该产品很快将会在商店里出售。 顾客可以每天来商店看看产品是否到货。但如果商品尚未到货时，绝大多数来到商店的顾客都会空手而归。 前往商店和发送垃圾邮件 另一方面，每次新产品到货时，商店可以向所有顾客发送邮件 (可能会被视为垃圾邮件)。这样，部分顾客就无需反复前往商店了，但也可能会惹恼对新产品没有兴趣的其他顾客。 我们似乎遇到了一个矛盾：要么让顾客浪费时间检查产品是否到货，要么让商店浪费资源去通知没有需求的顾客。","s":"问题","u":"/docs/design-patterns/observer","h":"#问题","p":449},{"i":456,"t":"拥有一些值得关注的状态的对象通常被称为目标，由于它要将自身的状态改变通知给其他对象，我们也将其称为发布者 (publisher)。所有希望关注发布者状态变化的其他对象被称为订阅者 (subscribers)。 观察者模式建议你为发布者类添加订阅机制，让每个对象都能订阅或取消订阅发布者事件流。不要害怕！这并不像听上去那么复杂。实际上，该机制包括 1） 一个用于存储订阅者对象引用的列表成员变量；2） 几个用于添加或删除该列表中订阅者的公有方法。 订阅机制允许对象订阅事件通知。 现在，无论何时发生了重要的发布者事件，它都要遍历订阅者并调用其对象的特定通知方法。 实际应用中可能会有十几个不同的订阅者类跟踪着同一个发布者类的事件，你不会希望发布者与所有这些类相耦合的。此外如果他人会使用发布者类，那么你甚至可能会对其中的一些类一无所知。 因此，所有订阅者都必须实现同样的接口，发布者仅通过该接口与订阅者交互。接口中必须声明通知方法及其参数，这样发布者在发出通知时还能传递一些上下文数据。 发布者调用订阅者对象中的特定通知方法来通知订阅者。 如果你的应用中有多个不同类型的发布者，且希望订阅者可兼容所有发布者，那么你甚至可以进一步让所有发布者遵循同样的接口。该接口仅需描述几个订阅方法即可。这样订阅者就能在不与具体发布者类耦合的情况下通过接口观察发布者的状态。","s":"解决方案","u":"/docs/design-patterns/observer","h":"#解决方案","p":449},{"i":458,"t":"杂志和报纸订阅。 如果你订阅了一份杂志或报纸，那就不需要再去报摊查询新出版的刊物了。出版社 (即应用中的“发布者”) 会在刊物出版后 (甚至提前) 直接将最新一期寄送至你的邮箱中。 出版社负责维护订阅者列表，了解订阅者对哪些刊物感兴趣。当订阅者希望出版社停止寄送新一期的杂志时，他们可随时从该列表中退出。","s":"真实世界类比","u":"/docs/design-patterns/observer","h":"#真实世界类比","p":449},{"i":460,"t":"发布者 (Publisher) 会向其他对象发送值得关注的事件。事件会在发布者自身状态改变或执行特定行为后发生。发布者中包含一个允许新订阅者加入和当前订阅者离开列表的订阅构架。 当新事件发生时，发送者会遍历订阅列表并调用每个订阅者对象的通知方法。该方法是在订阅者接口中声明的。 订阅者 (Subscriber) 接口声明了通知接口。在绝大多数情况下，该接口仅包含一个 update 更新方法。该方法可以拥有多个参数，使发布者能在更新时传递事件的详细信息。 具体订阅者 (Concrete Subscribers) 可以执行一些操作来回应发布者的通知。所有具体订阅者类都实现了同样的接口，因此发布者不需要与具体类相耦合。 订阅者通常需要一些上下文信息来正确地处理更新。因此，发布者通常会将一些上下文数据作为通知方法的参数进行传递。发布者也可将自身作为参数进行传递，使订阅者直接获取所需的数据。 客户端 (Client) 会分别创建发布者和订阅者对象，然后为订阅者注册发布者更新。","s":"观察者模式结构","u":"/docs/design-patterns/observer","h":"#观察者模式结构","p":449},{"i":462,"t":"在本例中，观察者模式允许文本编辑器对象将自身的状态改变通知给其他服务对象。 将对象中发生的事件通知给其他对象。 订阅者列表是动态生成的：对象可在运行时根据程序需要开始或停止监听通知。 在本实现中，编辑器类自身并不维护订阅列表。它将工作委派给专门从事此工作的一个特殊帮手对象。你还可将该对象升级为中心化的事件分发器，允许任何对象成为发布者。 只要发布者通过同样的接口与所有订阅者进行交互，那么在程序中新增订阅者时就无需修改已有发布者类的代码。 // 发布者基类包含订阅管理代码和通知方法。 class EventManager is private field listeners: hash map of event types and listeners method subscribe(eventType, listener) is listeners.add(eventType, listener) method unsubscribe(eventType, listener) is listeners.remove(eventType, listener) method notify(eventType, data) is foreach (listener in listeners.of(eventType)) do listener.update(data) // 具体发布者包含一些订阅者感兴趣的实际业务逻辑。我们可以从发布者基类中扩 // 展出该类，但在实际情况下并不总能做到，因为具体发布者可能已经是子类了。 // 在这种情况下，你可用组合来修补订阅逻辑，就像我们在这里做的一样。 class Editor is public field events: EventManager private field file: File constructor Editor() is events = new EventManager() // 业务逻辑的方法可将变化通知给订阅者。 method openFile(path) is this.file = new File(path) events.notify(\"open\", file.name) method saveFile() is file.write() events.notify(\"save\", file.name) // …… // 这里是订阅者接口。如果你的编程语言支持函数类型，则可用一组函数来代替整 // 个订阅者的层次结构。 interface EventListener is method update(filename) // 具体订阅者会对其注册的发布者所发出的更新消息做出响应。 class LoggingListener implements EventListener is private field log: File private field message: string constructor LoggingListener(log_filename, message) is this.log = new File(log_filename) this.message = message method update(filename) is log.write(replace('%s',filename,message)) class EmailAlertsListener implements EventListener is private field email: string private field message: string constructor EmailAlertsListener(email, message) is this.email = email this.message = message method update(filename) is system.email(email, replace('%s',filename,message)) // 应用程序可在运行时配置发布者和订阅者。 class Application is method config() is editor = new Editor() logger = new LoggingListener( \"/path/to/log.txt\", \"有人打开了文件：%s\"); editor.events.subscribe(\"open\", logger) emailAlerts = new EmailAlertsListener( \"admin@example.com\", \"有人更改了文件：%s\") editor.events.subscribe(\"save\", emailAlerts)","s":"伪代码","u":"/docs/design-patterns/observer","h":"#伪代码","p":449},{"i":464,"t":"当一个对象状态的改变需要改变其他对象，或实际对象是事先未知的或动态变化的时，可使用观察者模式。 当你使用图形用户界面类时通常会遇到一个问题。比如，你创建了自定义按钮类并允许客户端在按钮中注入自定义代码，这样当用户按下按钮时就会触发这些代码。 观察者模式允许任何实现了订阅者接口的对象订阅发布者对象的事件通知。你可在按钮中添加订阅机制，允许客户端通过自定义订阅类注入自定义代码。 当应用中的一些对象必须观察其他对象时，可使用该模式。但仅能在有限时间内或特定情况下使用。 订阅列表是动态的，因此订阅者可随时加入或离开该列表。 实现方式 仔细检查你的业务逻辑，试着将其拆分为两个部分：独立于其他代码的核心功能将作为发布者；其他代码则将转化为一组订阅类。 声明订阅者接口。该接口至少应声明一个 update 方法。 声明发布者接口并定义一些接口来在列表中添加和删除订阅对象。记住发布者必须仅通过订阅者接口与它们进行交互。 确定存放实际订阅列表的位置并实现订阅方法。通常所有类型的发布者代码看上去都一样，因此将列表放置在直接扩展自发布者接口的抽象类中是显而易见的。具体发布者会扩展该类从而继承所有的订阅行为。但是，如果你需要在现有的类层次结构中应用该模式，则可以考虑使用组合的方式：将订阅逻辑放入一个独立的对象，然后让所有实际订阅者使用该对象。 创建具体发布者类。每次发布者发生了重要事件时都必须通知所有的订阅者。 在具体订阅者类中实现通知更新的方法。绝大部分订阅者需要一些与事件相关的上下文数据。这些数据可作为通知方法的参数来传递。但还有另一种选择。订阅者接收到通知后直接从通知中获取所有数据。在这种情况下，发布者必须通过更新方法将自身传递出去。另一种不太灵活的方式是通过构造函数将发布者与订阅者永久性地连接起来。 客户端必须生成所需的全部订阅者，并在相应的发布者处完成注册工作。","s":"观察者模式适合应用场景","u":"/docs/design-patterns/observer","h":"#观察者模式适合应用场景","p":449},{"i":466,"t":"✔️ 开闭原则。你无需修改发布者代码就能引入新的订阅者类 (如果是发布者接口则可轻松引入发布者类)。 ✔️ 你可以在运行时建立对象之间的联系。 ❌ 订阅者的通知顺序是随机的。","s":"观察者模式优缺点","u":"/docs/design-patterns/observer","h":"#观察者模式优缺点","p":449},{"i":468,"t":"责任链模式、命令模式、中介者模式和观察者模式用于处理请求发送者和接收者之间的不同连接方式： 责任链按照顺序将请求动态传递给一系列的潜在接收者，直至其中一名接收者对请求进行处理。 命令在发送者和请求者之间建立单向连接。 中介者清除了发送者和请求者之间的直接连接，强制它们通过一个中介对象进行间接沟通。 观察者允许接收者动态地订阅或取消接收请求。 中介者和观察者之间的区别往往很难记住。在大部分情况下，你可以使用其中一种模式，而有时可以同时使用。让我们来看看如何做到这一点。 中介者的主要目标是消除一系列系统组件之间的相互依赖。这些组件将依赖于同一个中介者对象。观察者的目标是在对象之间建立动态的单向连接，使得部分对象可作为其他对象的附属发挥作用。有一种流行的中介者模式实现方式依赖于观察者。中介者对象担当发布者的角色，其他组件则作为订阅者，可以订阅中介者的事件或取消订阅。当中介者以这种方式实现时，它可能看上去与观察者非常相似。当你感到疑惑时，记住可以采用其他方式来实现中介者。例如，你可永久性地将所有组件链接到同一个中介者对象。这种实现方式和观察者并不相同，但这仍是一种中介者模式。假设有一个程序，其所有的组件都变成了发布者，它们之间可以相互建立动态连接。这样程序中就没有中心化的中介者对象，而只有一些分布式的观察者。","s":"与其他模式的关系","u":"/docs/design-patterns/observer","h":"#与其他模式的关系","p":449},{"i":470,"t":"亦称：克隆、Clone、Prototype","s":"原型模式","u":"/docs/design-patterns/prototype","h":"","p":469},{"i":472,"t":"原型模式是一种创建型设计模式，使你能够复制已有对象，而又无需使代码依赖它们所属的类。","s":"意图","u":"/docs/design-patterns/prototype","h":"#意图","p":469},{"i":474,"t":"如果你有一个对象，并希望生成与其完全相同的一个复制品，你该如何实现呢？首先，你必须新建一个属于相同类的对象。然后，你必须遍历原始对象的所有成员变量，并将成员变量值复制到新对象中。 不错！但有个小问题。并非所有对象都能通过这种方式进行复制，因为有些对象可能拥有私有成员变量，它们在对象本身以外是不可见的。 “从外部”复制对象并非总是可行。 直接复制还有另外一个问题。因为你必须知道对象所属的类才能创建复制品，所以代码必须依赖该类。即使你可以接受额外的依赖性，那还有另外一个问题：有时你只知道对象所实现的接口，而不知道其所属的具体类，比如可向方法的某个参数传入实现了某个接口的任何对象。","s":"问题","u":"/docs/design-patterns/prototype","h":"#问题","p":469},{"i":476,"t":"原型模式将克隆过程委派给被克隆的实际对象。模式为所有支持克隆的对象声明了一个通用接口，该接口让你能够克隆对象，同时又无需将代码和对象所属类耦合。通常情况下，这样的接口中仅包含一个 克隆 方法。 所有的类对 克隆 方法的实现都非常相似。该方法会创建一个当前类的对象，然后将原始对象所有的成员变量值复制到新建的类中。你甚至可以复制私有成员变量，因为绝大部分编程语言都允许对象访问其同类对象的私有成员变量。 支持克隆的对象即为原型。当你的对象有几十个成员变量和几百种类型时，对其进行克隆甚至可以代替子类的构造。 预生成原型可以代替子类的构造。 其运作方式如下：创建一系列不同类型的对象并不同的方式对其进行配置。如果所需对象与预先配置的对象相同，那么你只需克隆原型即可，无需新建一个对象。","s":"解决方案","u":"/docs/design-patterns/prototype","h":"#解决方案","p":469},{"i":478,"t":"现实生活中，产品在得到大规模生产前会使用原型进行各种测试。但在这种情况下，原型只是一种被动的工具，不参与任何真正的生产活动。 一个细胞的分裂。 由于工业原型并不是真正意义上的自我复制，因此细胞有丝分裂 (还记得生物学知识吗？) 或许是更恰当的类比。有丝分裂会产生一对完全相同的细胞。原始细胞就是一个原型，它在复制体的生成过程中起到了推动作用。","s":"真实世界类比","u":"/docs/design-patterns/prototype","h":"#真实世界类比","p":469},{"i":481,"t":"原型 (Prototype) 接口将对克隆方法进行声明。在绝大多数情况下，其中只会有一个名为 clone 克隆的方法。 具体原型 (Concrete Prototype) 类将实现克隆方法。除了将原始对象的数据复制到克隆体中之外，该方法有时还需处理克隆过程中的极端情况，例如克隆关联对象和梳理递归依赖等等。 客户端 (Client) 可以复制实现了原型接口的任何对象。","s":"基本实现","u":"/docs/design-patterns/prototype","h":"#基本实现","p":469},{"i":483,"t":"原型注册表 (Prototype Registry) 提供了一种访问常用原型的简单方法，其中存储了一系列可供随时复制的预生成对象。最简单的注册表原型是一个 名称 → 原型 的哈希表。但如果需要使用名称以外的条件进行搜索，你可以创建更加完善的注册表版本。","s":"原型注册表实现","u":"/docs/design-patterns/prototype","h":"#原型注册表实现","p":469},{"i":485,"t":"在本例中，原型模式能让你生成完全相同的几何对象副本，同时无需代码与对象所属类耦合。 克隆一系列位于同一类层次结构中的对象。 所有形状类都遵循同一个提供克隆方法的接口。在复制自身成员变量值到结果对象前，子类可调用其父类的克隆方法。 // 基础原型。 abstract class Shape is field X: int field Y: int field color: string // 常规构造函数。 constructor Shape() is // …… // 原型构造函数。使用已有对象的数值来初始化一个新对象。 constructor Shape(source: Shape) is this() this.X = source.X this.Y = source.Y this.color = source.color // clone（克隆）操作会返回一个形状子类。 abstract method clone():Shape // 具体原型。克隆方法会创建一个新对象并将其传递给构造函数。直到构造函数运 // 行完成前，它都拥有指向新克隆对象的引用。因此，任何人都无法访问未完全生 // 成的克隆对象。这可以保持克隆结果的一致。 class Rectangle extends Shape is field width: int field height: int constructor Rectangle(source: Rectangle) is // 需要调用父构造函数来复制父类中定义的私有成员变量。 super(source) this.width = source.width this.height = source.height method clone():Shape is return new Rectangle(this) class Circle extends Shape is field radius: int constructor Circle(source: Circle) is super(source) this.radius = source.radius method clone():Shape is return new Circle(this) // 客户端代码中的某个位置。 class Application is field shapes: array of Shape constructor Application() is Circle circle = new Circle() circle.X = 10 circle.Y = 10 circle.radius = 20 shapes.add(circle) Circle anotherCircle = circle.clone() shapes.add(anotherCircle) // 变量 `anotherCircle（另一个圆）` 与 `circle（圆）` 对象的内 // 容完全一样。 Rectangle rectangle = new Rectangle() rectangle.width = 10 rectangle.height = 20 shapes.add(rectangle) method businessLogic() is // 原型是很强大的东西，因为它能在不知晓对象类型的情况下生成一个与 // 其完全相同的复制品。 Array shapesCopy = new Array of Shapes. // 例如，我们不知晓形状数组中元素的具体类型，只知道它们都是形状。 // 但在多态机制的帮助下，当我们在某个形状上调用 `clone（克隆）` // 方法时，程序会检查其所属的类并调用其中所定义的克隆方法。这样， // 我们将获得一个正确的复制品，而不是一组简单的形状对象。 foreach (s in shapes) do shapesCopy.add(s.clone()) // `shapesCopy（形状副本）` 数组中包含 `shape（形状）` 数组所有 // 子元素的复制品。","s":"伪代码","u":"/docs/design-patterns/prototype","h":"#伪代码","p":469},{"i":487,"t":"如果你需要复制一些对象，同时又希望代码独立于这些对象所属的具体类，可以使用原型模式。 这一点考量通常出现在代码需要处理第三方代码通过接口传递过来的对象时。即使不考虑代码耦合的情况，你的代码也不能依赖这些对象所属的具体类，因为你不知道它们的具体信息。 原型模式为客户端代码提供一个通用接口，客户端代码可通过这一接口与所有实现了克隆的对象进行交互，它也使得客户端代码与其所克隆的对象具体类独立开来。 如果子类的区别仅在于其对象的初始化方式，那么你可以使用该模式来减少子类的数量。别人创建这些子类的目的可能是为了创建特定类型的对象。 在原型模式中，你可以使用一系列预生成的、各种类型的对象作为原型。 客户端不必根据需求对子类进行实例化，只需找到合适的原型并对其进行克隆即可。 实现方式 创建原型接口，并在其中声明 克隆 方法。如果你已有类层次结构，则只需在其所有类中添加该方法即可。 原型类必须另行定义一个以该类对象为参数的构造函数。构造函数必须复制参数对象中的所有成员变量值到新建实体中。如果你需要修改子类，则必须调用父类构造函数，让父类复制其私有成员变量值。如果编程语言不支持方法重载，那么你可能需要定义一个特殊方法来复制对象数据。在构造函数中进行此类处理比较方便，因为它在调用 new 运算符后会马上返回结果对象。 克隆方法通常只有一行代码：使用 new 运算符调用原型版本的构造函数。注意，每个类都必须显式重写克隆方法并使用自身类名调用 new 运算符。否则，克隆方法可能会生成父类的对象。 你还可以创建一个中心化原型注册表，用于存储常用原型。你可以新建一个工厂类来实现注册表，或者在原型基类中添加一个获取原型的静态方法。该方法必须能够根据客户端代码设定的条件进行搜索。搜索条件可以是简单的字符串，或者是一组复杂的搜索参数。找到合适的原型后，注册表应对原型进行克隆，并将复制生成的对象返回给客户端。最后还要将对子类构造函数的直接调用替换为对原型注册表工厂方法的调用。","s":"原型模式适合应用场景","u":"/docs/design-patterns/prototype","h":"#原型模式适合应用场景","p":469},{"i":489,"t":"✔️ 你可以克隆对象，而无需与它们所属的具体类相耦合。 ✔️ 你可以克隆预生成原型，避免反复运行初始化代码。 ✔️ 你可以更方便地生成复杂对象。 ✔️ 你可以用继承以外的方式来处理复杂对象的不同配置。 ❌ 克隆包含循环引用的复杂对象可能会非常麻烦。","s":"原型模式优缺点","u":"/docs/design-patterns/prototype","h":"#原型模式优缺点","p":469},{"i":491,"t":"在许多设计工作的初期都会使用工厂方法模式 (较为简单，而且可以更方便地通过子类进行定制)，随后演化为使用抽象工厂模式、原型模式或生成器模式 (更灵活但更加复杂)。 抽象工厂模式通常基于一组工厂方法，但你也可以使用原型模式来生成这些类的方法。 原型可用于保存命令模式的历史记录。 大量使用组合模式和装饰模式的设计通常可从对于原型的使用中获益。你可以通过该模式来复制复杂结构，而非从零开始重新构造。 原型并不基于继承，因此没有继承的缺点。另一方面，原型需要对被复制对象进行复杂的初始化。工厂方法基于继承，但是它不需要初始化步骤。 有时候原型可以作为备忘录模式的一个简化版本，其条件是你需要在历史记录中存储的对象的状态比较简单，不需要链接其他外部资源，或者链接可以方便地重建。 抽象工厂、生成器和原型都可以用单例模式来实现。","s":"与其他模式的关系","u":"/docs/design-patterns/prototype","h":"#与其他模式的关系","p":469},{"i":493,"t":"亦称：Proxy","s":"代理模式","u":"/docs/design-patterns/proxy","h":"","p":492},{"i":495,"t":"代理模式是一种结构型设计模式，让你能够提供对象的替代品或其占位符。代理控制着对于原对象的访问，并允许在将请求提交给对象前后进行一些处理。","s":"意图","u":"/docs/design-patterns/proxy","h":"#意图","p":492},{"i":497,"t":"为什么要控制对于某个对象的访问呢？举个例子：有这样一个消耗大量系统资源的巨型对象，你只是偶尔需要使用它，并非总是需要。 数据库查询有可能会非常缓慢。 你可以实现延迟初始化：在实际有需要时再创建该对象。对象的所有客户端都要执行延迟初始代码。不幸的是，这很可能会带来很多重复代码。 在理想情况下，我们希望将代码直接放入对象的类中，但这并非总是能实现：比如类可能是第三方封闭库的一部分。","s":"问题","u":"/docs/design-patterns/proxy","h":"#问题","p":492},{"i":499,"t":"代理模式建议新建一个与原服务对象接口相同的代理类，然后更新应用以将代理对象传递给所有原始对象客户端。代理类接收到客户端请求后会创建实际的服务对象，并将所有工作委派给它。 代理将自己伪装成数据库对象，可在客户端或实际数据库对象不知情的情况下处理延迟初始化和缓存查询结果的工作。 这有什么好处呢？如果需要在类的主要业务逻辑前后执行一些工作，你无需修改类就能完成这项工作。由于代理实现的接口与原类相同，因此你可将其传递给任何一个使用实际服务对象的客户端。","s":"解决方案","u":"/docs/design-patterns/proxy","h":"#解决方案","p":492},{"i":501,"t":"信用卡和现金在支付过程中的用处相同。 信用卡是银行账户的代理，银行账户则是一大捆现金的代理。它们都实现了同样的接口，均可用于进行支付。消费者会非常满意，因为不必随身携带大量现金；商店老板同样会十分高兴，因为交易收入能以电子化的方式进入商店的银行账户中，无需担心存款时出现现金丢失或被抢劫的情况。","s":"真实世界类比","u":"/docs/design-patterns/proxy","h":"#真实世界类比","p":492},{"i":503,"t":"服务接口 (Service Interface) 声明了服务接口。代理必须遵循该接口才能伪装成服务对象。 服务 (Service) 类提供了一些实用的业务逻辑。 代理 (Proxy) 类包含一个指向服务对象的引用成员变量。代理完成其任务 (例如延迟初始化、记录日志、访问控制和缓存等) 后会将请求传递给服务对象。 通常情况下，代理会对其服务对象的整个生命周期进行管理。 客户端 (Client) 能通过同一接口与服务或代理进行交互，所以你可在一切需要服务对象的代码中使用代理。","s":"代理模式结构","u":"/docs/design-patterns/proxy","h":"#代理模式结构","p":492},{"i":505,"t":"本例演示如何使用代理模式在第三方腾讯视频 (TencentVideo，代码示例中记为 TV) 程序库中添加延迟初始化和缓存。 使用代理缓冲服务结果。 程序库提供了视频下载类。但是该类的效率非常低。如果客户端程序多次请求同一视频，程序库会反复下载该视频，而不会将首次下载的文件缓存下来复用。 代理类实现和原下载器相同的接口，并将所有工作委派给原下载器。不过，代理类会保存所有的文件下载记录，如果程序多次请求同一文件，它会返回缓存的文件。 // 远程服务接口。 interface ThirdPartyTVLib is method listVideos() method getVideoInfo(id) method downloadVideo(id) // 服务连接器的具体实现。该类的方法可以向腾讯视频请求信息。请求速度取决于 // 用户和腾讯视频的互联网连接情况。如果同时发送大量请求，即使所请求的信息 // 一模一样，程序的速度依然会减慢。 class ThirdPartyTVClass implements ThirdPartyTVLib is method listVideos() is // 向腾讯视频发送一个 API 请求。 method getVideoInfo(id) is // 获取某个视频的元数据。 method downloadVideo(id) is // 从腾讯视频下载一个视频文件。 // 为了节省网络带宽，我们可以将请求结果缓存下来并保存一段时间。但你可能无 // 法直接将这些代码放入服务类中。比如该类可能是第三方程序库的一部分或其签 // 名是 `final（最终）`。因此我们会在一个实现了服务类接口的新代理类中放入 // 缓存代码。当代理类接收到真实请求后，才会将其委派给服务对象。 class CachedTVClass implements ThirdPartyTVLib is private field service: ThirdPartyTVLib private field listCache, videoCache field needReset constructor CachedTVClass(service: ThirdPartyTVLib) is this.service = service method listVideos() is if (listCache == null || needReset) listCache = service.listVideos() return listCache method getVideoInfo(id) is if (videoCache == null || needReset) videoCache = service.getVideoInfo(id) return videoCache method downloadVideo(id) is if (!downloadExists(id) || needReset) service.downloadVideo(id) // 之前直接与服务对象交互的 GUI 类不需要改变，前提是它仅通过接口与服务对 // 象交互。我们可以安全地传递一个代理对象来代替真实服务对象，因为它们都实 // 现了相同的接口。 class TVManager is protected field service: ThirdPartyTVLib constructor TVManager(service: ThirdPartyTVLib) is this.service = service method renderVideoPage(id) is info = service.getVideoInfo(id) // 渲染视频页面。 method renderListPanel() is list = service.listVideos() // 渲染视频缩略图列表。 method reactOnUserInput() is renderVideoPage() renderListPanel() // 程序可在运行时对代理进行配置。 class Application is method init() is aTVService = new ThirdPartyTVClass() aTVProxy = new CachedTVClass(aTVService) manager = new TVManager(aTVProxy) manager.reactOnUserInput()","s":"伪代码","u":"/docs/design-patterns/proxy","h":"#伪代码","p":492},{"i":507,"t":"使用代理模式的方式多种多样，我们来看看最常见的几种。 延迟初始化 (虚拟代理)。如果你有一个偶尔使用的重量级服务对象，一直保持该对象运行会消耗系统资源时，可使用代理模式。 你无需在程序启动时就创建该对象，可将对象的初始化延迟到真正有需要的时候。 访问控制 (保护代理)。如果你只希望特定客户端使用服务对象，这里的对象可以是操作系统中非常重要的部分，而客户端则是各种已启动的程序 (包括恶意程序)，此时可使用代理模式。 代理可仅在客户端凭据满足要求时将请求传递给服务对象。 本地执行远程服务 (远程代理)。适用于服务对象位于远程服务器上的情形。 在这种情形中，代理通过网络传递客户端请求，负责处理所有与网络相关的复杂细节。 记录日志请求 (日志记录代理)。适用于当你需要保存对于服务对象的请求历史记录时。 代理可以在向服务传递请求前进行记录。 缓存请求结果 (缓存代理)。适用于需要缓存客户请求结果并对缓存生命周期进行管理时，特别是当返回结果的体积非常大时。 代理可对重复请求所需的相同结果进行缓存，还可使用请求参数作为索引缓存的键值。 智能引用。可在没有客户端使用某个重量级对象时立即销毁该对象。 代理会将所有获取了指向服务对象或其结果的客户端记录在案。代理会时不时地遍历各个客户端，检查它们是否仍在运行。如果相应的客户端列表为空，代理就会销毁该服务对象，释放底层系统资源。 代理还可以记录客户端是否修改了服务对象。其他客户端还可以复用未修改的对象。 实现方式 如果没有现成的服务接口，你就需要创建一个接口来实现代理和服务对象的可交换性。从服务类中抽取接口并非总是可行的，因为你需要对服务的所有客户端进行修改，让它们使用接口。备选计划是将代理作为服务类的子类，这样代理就能继承服务的所有接口了。 创建代理类，其中必须包含一个存储指向服务的引用的成员变量。通常情况下，代理负责创建服务并对其整个生命周期进行管理。在一些特殊情况下，客户端会通过构造函数将服务传递给代理。 根据需求实现代理方法。在大部分情况下，代理在完成一些任务后应将工作委派给服务对象。 可以考虑新建一个构建方法来判断客户端可获取的是代理还是实际服务。你可以在代理类中创建一个简单的静态方法，也可以创建一个完整的工厂方法。 可以考虑为服务对象实现延迟初始化。","s":"代理模式适合应用场景","u":"/docs/design-patterns/proxy","h":"#代理模式适合应用场景","p":492},{"i":509,"t":"✔️ 你可以在客户端毫无察觉的情况下控制服务对象。 ✔️ 如果客户端对服务对象的生命周期没有特殊要求，你可以对生命周期进行管理。 ✔️ 即使服务对象还未准备好或不存在，代理也可以正常工作。 ✔️ 开闭原则。你可以在不对服务或客户端做出修改的情况下创建新代理。 ❌ 代码可能会变得复杂，因为需要新建许多类。 ❌ 服务响应可能会延迟。","s":"代理模式优缺点","u":"/docs/design-patterns/proxy","h":"#代理模式优缺点","p":492},{"i":511,"t":"适配器模式能为被封装对象提供不同的接口，代理模式能为对象提供相同的接口，装饰模式则能为对象提供加强的接口。 外观模式与代理的相似之处在于它们都缓存了一个复杂实体并自行对其进行初始化。代理与其服务对象遵循同一接口，使得自己和服务对象可以互换，在这一点上它与外观不同。 装饰和代理有着相似的结构，但是其意图却非常不同。这两个模式的构建都基于组合原则，也就是说一个对象应该将部分工作委派给另一个对象。两者之间的不同之处在于代理通常自行管理其服务对象的生命周期，而装饰的生成则总是由客户端进行控制。","s":"与其他模式的关系","u":"/docs/design-patterns/proxy","h":"#与其他模式的关系","p":492},{"i":513,"t":"亦称：单件模式、Singleton","s":"单例模式","u":"/docs/design-patterns/singleton","h":"","p":512},{"i":515,"t":"单例模式是一种创建型设计模式，让你能够保证一个类只有一个实例，并提供一个访问该实例的全局节点。","s":"意图","u":"/docs/design-patterns/singleton","h":"#意图","p":512},{"i":517,"t":"单例模式同时解决了两个问题，所以违反了单一职责原则： 保证一个类只有一个实例。为什么会有人想要控制一个类所拥有的实例数量？最常见的原因是控制某些共享资源 (例如数据库或文件) 的访问权限。 它的运作方式是这样的：如果你创建了一个对象，同时过一会儿后你决定再创建一个新对象，此时你会获得之前已创建的对象，而不是一个新对象。 注意，普通构造函数无法实现上述行为，因为构造函数的设计决定了它必须总是返回一个新对象。 客户端甚至可能没有意识到它们一直都在使用同一个对象。 为该实例提供一个全局访问节点。还记得你 (好吧，其实是我自己) 用过的那些存储重要对象的全局变量吗？它们在使用上十分方便，但同时也非常不安全，因为任何代码都有可能覆盖掉那些变量的内容，从而引发程序崩溃。 和全局变量一样，单例模式也允许在程序的任何地方访问特定对象。但是它可以保护该实例不被其他代码覆盖。 还有一点：你不会希望解决同一个问题的代码分散在程序各处的。因此更好的方式是将其放在同一个类中，特别是当其他代码已经依赖这个类时更应该如此。 如今，单例模式已经变得非常流行，以至于人们会将只解决上文描述中任意一个问题的东西称为单例。","s":"问题","u":"/docs/design-patterns/singleton","h":"#问题","p":512},{"i":519,"t":"所有单例的实现都包含以下两个相同的步骤： 将默认构造函数设为私有，防止其他对象使用单例类的 new 运算符。 新建一个静态构建方法作为构造函数。该函数会“偷偷”调用私有构造函数来创建对象，并将其保存在一个静态成员变量中。此后所有对于该函数的调用都将返回这一缓存对象。 如果你的代码能够访问单例类，那它就能调用单例类的静态方法。无论何时调用该方法，它总是会返回相同的对象。","s":"解决方案","u":"/docs/design-patterns/singleton","h":"#解决方案","p":512},{"i":521,"t":"政府是单例模式的一个很好的示例。一个国家只有一个官方政府。不管组成政府的每个人的身份是什么，“某政府”这一称谓总是鉴别那些掌权者的全局访问节点。","s":"真实世界类比","u":"/docs/design-patterns/singleton","h":"#真实世界类比","p":512},{"i":523,"t":"单例 (Singleton) 类声明了一个名为 get­Instance 获取实例的静态方法来返回其所属类的一个相同实例。 单例的构造函数必须对客户端 (Client) 代码隐藏。调用 获取实例 方法必须是获取单例对象的唯一方式。","s":"单例模式结构","u":"/docs/design-patterns/singleton","h":"#单例模式结构","p":512},{"i":525,"t":"在本例中，数据库连接类即是一个单例。该类不提供公有构造函数，因此获取该对象的唯一方式是调用 获取实例 方法。该方法将缓存首次生成的对象，并为所有后续调用返回该对象。 // 数据库类会对 `getInstance（获取实例）` 方法进行定义以让客户端在程序各处 // 都能访问相同的数据库连接实例。 class Database is // 保存单例实例的成员变量必须被声明为静态类型。 private static field instance: Database // 单例的构造函数必须永远是私有类型，以防止使用 `new` 运算符直接调用构 // 造方法。 private constructor Database() is // 部分初始化代码（例如到数据库服务器的实际连接）。 // …… // 用于控制对单例实例的访问权限的静态方法。 public static method getInstance() is if (Database.instance == null) then acquireThreadLock() and then // 确保在该线程等待解锁时，其他线程没有初始化该实例。 if (Database.instance == null) then Database.instance = new Database() return Database.instance // 最后，任何单例都必须定义一些可在其实例上执行的业务逻辑。 public method query(sql) is // 比如应用的所有数据库查询请求都需要通过该方法进行。因此，你可以 // 在这里添加限流或缓冲逻辑。 // …… class Application is method main() is Database foo = Database.getInstance() foo.query(\"SELECT ……\") // …… Database bar = Database.getInstance() bar.query(\"SELECT ……\") // 变量 `bar` 和 `foo` 中将包含同一个对象。","s":"伪代码","u":"/docs/design-patterns/singleton","h":"#伪代码","p":512},{"i":527,"t":"如果程序中的某个类对于所有客户端只有一个可用的实例，可以使用单例模式。 单例模式禁止通过除特殊构建方法以外的任何方式来创建自身类的对象。该方法可以创建一个新对象，但如果该对象已经被创建，则返回已有的对象。 如果你需要更加严格地控制全局变量，可以使用单例模式。 单例模式与全局变量不同，它保证类只存在一个实例。除了单例类自己以外，无法通过任何方式替换缓存的实例。 请注意，你可以随时调整限制并设定生成单例实例的数量，只需修改 获取实例 方法，即 getInstance 中的代码即可实现。 实现方式 在类中添加一个私有静态成员变量用于保存单例实例。 声明一个公有静态构建方法用于获取单例实例。 在静态方法中实现“延迟初始化”。该方法会在首次被调用时创建一个新对象，并将其存储在静态成员变量中。此后该方法每次被调用时都返回该实例。 将类的构造函数设为私有。类的静态方法仍能调用构造函数，但是其他对象不能调用。 检查客户端代码，将对单例的构造函数的调用替换为对其静态构建方法的调用。","s":"单例模式适合应用场景","u":"/docs/design-patterns/singleton","h":"#单例模式适合应用场景","p":512},{"i":529,"t":"✔️ 你可以保证一个类只有一个实例。 ✔️ 你获得了一个指向该实例的全局访问节点。 ✔️ 仅在首次请求单例对象时对其进行初始化。 ❌ 违反了单一职责原则。该模式同时解决了两个问题。 ❌ 单例模式可能掩盖不良设计，比如程序各组件之间相互了解过多等。 ❌ 该模式在多线程环境下需要进行特殊处理，避免多个线程多次创建单例对象。 ❌ 单例的客户端代码单元测试可能会比较困难，因为许多测试框架以基于继承的方式创建模拟对象。由于单例类的构造函数是私有的，而且绝大部分语言无法重写静态方法，所以你需要想出仔细考虑模拟单例的方法。要么干脆不编写测试代码，或者不使用单例模式。","s":"单例模式优缺点","u":"/docs/design-patterns/singleton","h":"#单例模式优缺点","p":512},{"i":531,"t":"外观模式类通常可以转换为单例模式类，因为在大部分情况下一个外观对象就足够了。 如果你能将对象的所有共享状态简化为一个享元对象，那么享元模式就和单例类似了。但这两个模式有两个根本性的不同。 只会有一个单例实体，但是享元类可以有多个实体，各实体的内在状态也可以不同。 单例对象可以是可变的。享元对象是不可变的。 抽象工厂模式、生成器模式和原型模式都可以用单例来实现。","s":"与其他模式的关系","u":"/docs/design-patterns/singleton","h":"#与其他模式的关系","p":512},{"i":533,"t":"亦称：State","s":"状态模式","u":"/docs/design-patterns/state","h":"","p":532},{"i":535,"t":"状态模式是一种行为设计模式，让你能在一个对象的内部状态变化时改变其行为，使其看上去就像改变了自身所属的类一样。","s":"意图","u":"/docs/design-patterns/state","h":"#意图","p":532},{"i":537,"t":"状态模式与有限状态机的概念紧密相关。 有限状态机。 其主要思想是程序在任意时刻仅可处于几种有限的状态中。在任何一个特定状态中，程序的行为都不相同，且可瞬间从一个状态切换到另一个状态。不过，根据当前状态，程序可能会切换到另外一种状态，也可能会保持当前状态不变。这些数量有限且预先定义的状态切换规则被称为转移。 你还可将该方法应用在对象上。假如你有一个 文档 Document 类。文档可能会处于 草稿 Draft、审阅中 Moderation 和 已发布 Published 三种状态中的一种。文档的 publish 发布方法在不同状态下的行为略有不同： 处于 草稿 状态时，它会将文档转移到审阅中状态。 处于 审阅中 状态时，如果当前用户是管理员，它会公开发布文档。 处于 已发布 状态时，它不会进行任何操作。 文档对象的全部状态和转移。 状态机通常由众多条件运算符 (if 或 switch) 实现，可根据对象的当前状态选择相应的行为。“状态”通常只是对象中的一组成员变量值。即使你之前从未听说过有限状态机，你也很可能已经实现过状态模式。下面的代码应该能帮助你回忆起来。 class Document is field state: string // …… method publish() is switch (state) \"draft\": state = \"moderation\" break \"moderation\": if (currentUser.role == \"admin\") state = \"published\" break \"published\": // 什么也不做。 break // …… 当我们逐步在 文档 类中添加更多状态和依赖于状态的行为后，基于条件语句的状态机就会暴露其最大的弱点。为了能根据当前状态选择完成相应行为的方法，绝大部分方法中会包含复杂的条件语句。修改其转换逻辑可能会涉及到修改所有方法中的状态条件语句，导致代码的维护工作非常艰难。 这个问题会随着项目进行变得越发严重。我们很难在设计阶段预测到所有可能的状态和转换。随着时间推移，最初仅包含有限条件语句的简洁状态机可能会变成臃肿的一团乱麻。","s":"问题","u":"/docs/design-patterns/state","h":"#问题","p":532},{"i":539,"t":"状态模式建议为对象的所有可能状态新建一个类，然后将所有状态的对应行为抽取到这些类中。 原始对象被称为上下文 (context)，它并不会自行实现所有行为，而是会保存一个指向表示当前状态的状态对象的引用，且将所有与状态相关的工作委派给该对象。 文档将工作委派给一个状态对象。 如需将上下文转换为另外一种状态，则需将当前活动的状态对象替换为另外一个代表新状态的对象。采用这种方式是有前提的：所有状态类都必须遵循同样的接口，而且上下文必须仅通过接口与这些对象进行交互。 这个结构可能看上去与策略模式相似，但有一个关键性的不同——在状态模式中，特定状态知道其他所有状态的存在，且能触发从一个状态到另一个状态的转换；策略则几乎完全不知道其他策略的存在。","s":"解决方案","u":"/docs/design-patterns/state","h":"#解决方案","p":532},{"i":541,"t":"智能手机的按键和开关会根据设备当前状态完成不同行为： 当手机处于解锁状态时，按下按键将执行各种功能。 当手机处于锁定状态时，按下任何按键都将解锁屏幕。 当手机电量不足时，按下任何按键都将显示充电页面。","s":"真实世界类比","u":"/docs/design-patterns/state","h":"#真实世界类比","p":532},{"i":543,"t":"上下文 (Context) 保存了对于一个具体状态对象的引用，并会将所有与该状态相关的工作委派给它。上下文通过状态接口与状态对象交互，且会提供一个设置器用于传递新的状态对象。 状态 (State) 接口会声明特定于状态的方法。这些方法应能被其他所有具体状态所理解，因为你不希望某些状态所拥有的方法永远不会被调用。 具体状态 (Concrete States) 会自行实现特定于状态的方法。为了避免多个状态中包含相似代码，你可以提供一个封装有部分通用行为的中间抽象类。 状态对象可存储对于上下文对象的反向引用。状态可以通过该引用从上下文处获取所需信息，并且能触发状态转移。 上下文和具体状态都可以设置上下文的下个状态，并可通过替换连接到上下文的状态对象来完成实际的状态转换。","s":"状态模式结构","u":"/docs/design-patterns/state","h":"#状态模式结构","p":532},{"i":545,"t":"在本例中，状态模式将根据当前回放状态，让媒体播放器中的相同控件完成不同的行为。 使用状态对象更改对象行为的示例。 播放器的主要对象总是会连接到一个负责播放器绝大部分工作的状态对象中。部分操作会更换播放器当前的状态对象，以此改变播放器对于用户互动所作出的反应。 // 音频播放器（Audio­Player）类即为上下文。它还会维护指向状态类实例的引用， // 该状态类则用于表示音频播放器当前的状态。 class AudioPlayer is field state: State field UI, volume, playlist, currentSong constructor AudioPlayer() is this.state = new ReadyState(this) // 上下文会将处理用户输入的工作委派给状态对象。由于每个状态都以不 // 同的方式处理输入，其结果自然将依赖于当前所处的状态。 UI = new UserInterface() UI.lockButton.onClick(this.clickLock) UI.playButton.onClick(this.clickPlay) UI.nextButton.onClick(this.clickNext) UI.prevButton.onClick(this.clickPrevious) // 其他对象必须能切换音频播放器当前所处的状态。 method changeState(state: State) is this.state = state // UI 方法会将执行工作委派给当前状态。 method clickLock() is state.clickLock() method clickPlay() is state.clickPlay() method clickNext() is state.clickNext() method clickPrevious() is state.clickPrevious() // 状态可调用上下文的一些服务方法。 method startPlayback() is // …… method stopPlayback() is // …… method nextSong() is // …… method previousSong() is // …… method fastForward(time) is // …… method rewind(time) is // …… // 所有具体状态类都必须实现状态基类声明的方法，并提供反向引用指向与状态相 // 关的上下文对象。状态可使用反向引用将上下文转换为另一个状态。 abstract class State is protected field player: AudioPlayer // 上下文将自身传递给状态构造函数。这可帮助状态在需要时获取一些有用的 // 上下文数据。 constructor State(player) is this.player = player abstract method clickLock() abstract method clickPlay() abstract method clickNext() abstract method clickPrevious() // 具体状态会实现与上下文状态相关的多种行为。 class LockedState extends State is // 当你解锁一个锁定的播放器时，它可能处于两种状态之一。 method clickLock() is if (player.playing) player.changeState(new PlayingState(player)) else player.changeState(new ReadyState(player)) method clickPlay() is // 已锁定，什么也不做。 method clickNext() is // 已锁定，什么也不做。 method clickPrevious() is // 已锁定，什么也不做。 // 它们还可在上下文中触发状态转换。 class ReadyState extends State is method clickLock() is player.changeState(new LockedState(player)) method clickPlay() is player.startPlayback() player.changeState(new PlayingState(player)) method clickNext() is player.nextSong() method clickPrevious() is player.previousSong() class PlayingState extends State is method clickLock() is player.changeState(new LockedState(player)) method clickPlay() is player.stopPlayback() player.changeState(new ReadyState(player)) method clickNext() is if (event.doubleclick) player.nextSong() else player.fastForward(5) method clickPrevious() is if (event.doubleclick) player.previous() else player.rewind(5)","s":"伪代码","u":"/docs/design-patterns/state","h":"#伪代码","p":532},{"i":547,"t":"如果对象需要根据自身当前状态进行不同行为，同时状态的数量非常多且与状态相关的代码会频繁变更的话，可使用状态模式。 模式建议你将所有特定于状态的代码抽取到一组独立的类中。这样一来，你可以在独立于其他状态的情况下添加新状态或修改已有状态，从而减少维护成本。 如果某个类需要根据成员变量的当前值改变自身行为，从而需要使用大量的条件语句时，可使用该模式。 状态模式会将这些条件语句的分支抽取到相应状态类的方法中。同时，你还可以清除主要类中与特定状态相关的临时成员变量和帮手方法代码。 当相似状态和基于条件的状态机转换中存在许多重复代码时，可使用状态模式。 状态模式让你能够生成状态类层次结构，通过将公用代码抽取到抽象基类中来减少重复。 实现方式 确定哪些类是上下文。它可能是包含依赖于状态的代码的已有类；如果特定于状态的代码分散在多个类中，那么它可能是一个新的类。 声明状态接口。虽然你可能会需要完全复制上下文中声明的所有方法，但最好是仅把关注点放在那些可能包含特定于状态的行为的方法上。 为每个实际状态创建一个继承于状态接口的类。然后检查上下文中的方法并将与特定状态相关的所有代码抽取到新建的类中。在将代码移动到状态类的过程中，你可能会发现它依赖于上下文中的一些私有成员。你可以采用以下几种变通方式：- 将这些成员变量或方法设为公有。- 将需要抽取的上下文行为更改为上下文中的公有方法，然后在状态类中调用。这种方式简陋却便捷，你可以稍后再对其进行修补。- 将状态类嵌套在上下文类中。这种方式需要你所使用的编程语言支持嵌套类。 在上下文类中添加一个状态接口类型的引用成员变量，以及一个用于修改该成员变量值的公有设置器。 再次检查上下文中的方法，将空的条件语句替换为相应的状态对象方法。 为切换上下文状态，你需要创建某个状态类实例并将其传递给上下文。你可以在上下文、各种状态或客户端中完成这项工作。无论在何处完成这项工作，该类都将依赖于其所实例化的具体类。","s":"状态模式适合应用场景","u":"/docs/design-patterns/state","h":"#状态模式适合应用场景","p":532},{"i":549,"t":"✔️ 单一职责原则。将与特定状态相关的代码放在单独的类中。 ✔️ 开闭原则。无需修改已有状态类和上下文就能引入新状态。 ✔️ 通过消除臃肿的状态机条件语句简化上下文代码。 ❌ 如果状态机只有很少的几个状态，或者很少发生改变，那么应用该模式可能会显得小题大作。","s":"状态模式优缺点","u":"/docs/design-patterns/state","h":"#状态模式优缺点","p":532},{"i":551,"t":"桥接模式、状态模式和策略模式 (在某种程度上包括适配器模式) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。 状态可被视为策略的扩展。两者都基于组合机制：它们都通过将部分工作委派给“帮手”对象来改变其在不同情景下的行为。策略使得这些对象相互之间完全独立，它们不知道其他对象的存在。但状态模式没有限制具体状态之间的依赖，且允许它们自行改变在不同情景下的状态。","s":"与其他模式的关系","u":"/docs/design-patterns/state","h":"#与其他模式的关系","p":532},{"i":553,"t":"亦称：Strategy","s":"策略模式","u":"/docs/design-patterns/strategy","h":"","p":552},{"i":555,"t":"策略模式是一种行为设计模式，它能让你定义一系列算法，并将每种算法分别放入独立的类中，以使算法的对象能够相互替换。","s":"意图","u":"/docs/design-patterns/strategy","h":"#意图","p":552},{"i":557,"t":"一天，你打算为游客们创建一款导游程序。该程序的核心功能是提供美观的地图，以帮助用户在任何城市中快速定位。 用户期待的程序新功能是自动路线规划：他们希望输入地址后就能在地图上看到前往目的地的最快路线。 程序的首个版本只能规划公路路线。驾车旅行的人们对此非常满意。但很显然，并非所有人都会在度假时开车。因此你在下次更新时添加了规划步行路线的功能。此后，你又添加了规划公共交通路线的功能。 而这只是个开始。不久后，你又要为骑行者规划路线。又过了一段时间，你又要为游览城市中的所有景点规划路线。 导游代码将变得非常臃肿。 尽管从商业角度来看，这款应用非常成功，但其技术部分却让你非常头疼：每次添加新的路线规划算法后，导游应用中主要类的体积就会增加一倍。终于在某个时候，你觉得自己没法继续维护这堆代码了。 无论是修复简单缺陷还是微调街道权重，对某个算法进行任何修改都会影响整个类，从而增加在已有正常运行代码中引入错误的风险。 此外，团队合作将变得低效。如果你在应用成功发布后招募了团队成员，他们会抱怨在合并冲突的工作上花费了太多时间。在实现新功能的过程中，你的团队需要修改同一个巨大的类，这样他们所编写的代码相互之间就可能会出现冲突。","s":"问题","u":"/docs/design-patterns/strategy","h":"#问题","p":552},{"i":559,"t":"策略模式建议找出负责用许多不同方式完成特定任务的类，然后将其中的算法抽取到一组被称为策略的独立类中。 名为上下文的原始类必须包含一个成员变量来存储对于每种策略的引用。上下文并不执行任务，而是将工作委派给已连接的策略对象。 上下文不负责选择符合任务需要的算法——客户端会将所需策略传递给上下文。实际上，上下文并不十分了解策略，它会通过同样的通用接口与所有策略进行交互，而该接口只需暴露一个方法来触发所选策略中封装的算法即可。 因此，上下文可独立于具体策略。这样你就可在不修改上下文代码或其他策略的情况下添加新算法或修改已有算法了。 路线规划策略。 在导游应用中，每个路线规划算法都可被抽取到只有一个 build­Route 生成路线方法的独立类中。该方法接收起点和终点作为参数，并返回路线中途点的集合。 即使传递给每个路径规划类的参数一模一样，其所创建的路线也可能完全不同。主要导游类的主要工作是在地图上渲染一系列中途点，不会在意如何选择算法。该类中还有一个用于切换当前路径规划策略的方法，因此客户端 (例如用户界面中的按钮) 可用其他策略替换当前选择的路径规划行为。","s":"解决方案","u":"/docs/design-patterns/strategy","h":"#解决方案","p":552},{"i":561,"t":"各种前往机场的出行策略 假如你需要前往机场。你可以选择乘坐公共汽车、预约出租车或骑自行车。这些就是你的出行策略。你可以根据预算或时间等因素来选择其中一种策略。","s":"真实世界类比","u":"/docs/design-patterns/strategy","h":"#真实世界类比","p":552},{"i":563,"t":"上下文 (Context) 维护指向具体策略的引用，且仅通过策略接口与该对象进行交流。 策略 (Strategy) 接口是所有具体策略的通用接口，它声明了一个上下文用于执行策略的方法。 具体策略 (Concrete Strategies) 实现了上下文所用算法的各种不同变体。 当上下文需要运行算法时，它会在其已连接的策略对象上调用执行方法。上下文不清楚其所涉及的策略类型与算法的执行方式。 客户端 (Client) 会创建一个特定策略对象并将其传递给上下文。上下文则会提供一个设置器以便客户端在运行时替换相关联的策略。","s":"策略模式结构","u":"/docs/design-patterns/strategy","h":"#策略模式结构","p":552},{"i":565,"t":"在本例中，上下文使用了多个策略来执行不同的计算操作。 // 策略接口声明了某个算法各个不同版本间所共有的操作。上下文会使用该接口来 // 调用有具体策略定义的算法。 interface Strategy is method execute(a, b) // 具体策略会在遵循策略基础接口的情况下实现算法。该接口实现了它们在上下文 // 中的互换性。 class ConcreteStrategyAdd implements Strategy is method execute(a, b) is return a + b class ConcreteStrategySubtract implements Strategy is method execute(a, b) is return a - b class ConcreteStrategyMultiply implements Strategy is method execute(a, b) is return a * b // 上下文定义了客户端关注的接口。 class Context is // 上下文会维护指向某个策略对象的引用。上下文不知晓策略的具体类。上下 // 文必须通过策略接口来与所有策略进行交互。 private strategy: Strategy // 上下文通常会通过构造函数来接收策略对象，同时还提供设置器以便在运行 // 时切换策略。 method setStrategy(Strategy strategy) is this.strategy = strategy // 上下文会将一些工作委派给策略对象，而不是自行实现不同版本的算法。 method executeStrategy(int a, int b) is return strategy.execute(a, b) // 客户端代码会选择具体策略并将其传递给上下文。客户端必须知晓策略之间的差 // 异，才能做出正确的选择。 class ExampleApplication is method main() is 创建上下文对象。 读取第一个数。 读取最后一个数。 从用户输入中读取期望进行的行为。 if (action == addition) then context.setStrategy(new ConcreteStrategyAdd()) if (action == subtraction) then context.setStrategy(new ConcreteStrategySubtract()) if (action == multiplication) then context.setStrategy(new ConcreteStrategyMultiply()) result = context.executeStrategy(First number, Second number) 打印结果。","s":"伪代码","u":"/docs/design-patterns/strategy","h":"#伪代码","p":552},{"i":567,"t":"当你想使用对象中各种不同的算法变体，并希望能在运行时切换算法时，可使用策略模式。 策略模式让你能够将对象关联至可以不同方式执行特定子任务的不同子对象，从而以间接方式在运行时更改对象行为。 当你有许多仅在执行某些行为时略有不同的相似类时，可使用策略模式。 策略模式让你能将不同行为抽取到一个独立类层次结构中，并将原始类组合成同一个，从而减少重复代码。 如果算法在上下文的逻辑中不是特别重要，使用该模式能将类的业务逻辑与其算法实现细节隔离开来。 策略模式让你能将各种算法的代码、内部数据和依赖关系与其他代码隔离开来。不同客户端可通过一个简单接口执行算法，并能在运行时进行切换。 当类中使用了复杂条件运算符以在同一算法的不同变体中切换时，可使用该模式。 策略模式将所有继承自同样接口的算法抽取到独立类中，因此不再需要条件语句。原始对象并不实现所有算法的变体，而是将执行工作委派给其中的一个独立算法对象。 实现方式 从上下文类中找出修改频率较高的算法 (也可能是用于在运行时选择某个算法变体的复杂条件运算符)。 声明该算法所有变体的通用策略接口。 将算法逐一抽取到各自的类中，它们都必须实现策略接口。 在上下文类中添加一个成员变量用于保存对于策略对象的引用。然后提供设置器以修改该成员变量。上下文仅可通过策略接口同策略对象进行交互，如有需要还可定义一个接口来让策略访问其数据。 客户端必须将上下文类与相应策略进行关联，使上下文可以预期的方式完成其主要工作。","s":"策略模式适合应用场景","u":"/docs/design-patterns/strategy","h":"#策略模式适合应用场景","p":552},{"i":569,"t":"✔️ 你可以在运行时切换对象内的算法。 ✔️ 你可以将算法的实现和使用算法的代码隔离开来。 ✔️ 你可以使用组合来代替继承。 ✔️ 开闭原则。你无需对上下文进行修改就能够引入新的策略。 ❌ 如果你的算法极少发生改变，那么没有任何理由引入新的类和接口。使用该模式只会让程序过于复杂。 ❌ 客户端必须知晓策略间的不同——它需要选择合适的策略。 ❌ 许多现代编程语言支持函数类型功能，允许你在一组匿名函数中实现不同版本的算法。这样，你使用这些函数的方式就和使用策略对象时完全相同，无需借助额外的类和接口来保持代码简洁。","s":"策略模式优缺点","u":"/docs/design-patterns/strategy","h":"#策略模式优缺点","p":552},{"i":571,"t":"桥接模式、状态模式和策略模式 (在某种程度上包括适配器模式) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。 命令模式和策略看上去很像，因为两者都能通过某些行为来参数化对象。但是，它们的意图有非常大的不同。 你可以使用命令来将任何操作转换为对象。操作的参数将成为对象的成员变量。你可以通过转换来延迟操作的执行、将操作放入队列、保存历史命令或者向远程服务发送命令等。 另一方面，策略通常可用于描述完成某件事的不同方式，让你能够在同一个上下文类中切换算法。 装饰模式可让你更改对象的外表，策略则让你能够改变其本质。 模板方法模式基于继承机制：它允许你通过扩展子类中的部分内容来改变部分算法。策略基于组合机制：你可以通过对相应行为提供不同的策略来改变对象的部分行为。模板方法在类层次上运作，因此它是静态的。策略在对象层次上运作，因此允许在运行时切换行为。 状态可被视为策略的扩展。两者都基于组合机制：它们都通过将部分工作委派给“帮手”对象来改变其在不同情景下的行为。策略使得这些对象相互之间完全独立，它们不知道其他对象的存在。但状态模式没有限制具体状态之间的依赖，且允许它们自行改变在不同情景下的状态。","s":"与其他模式的关系","u":"/docs/design-patterns/strategy","h":"#与其他模式的关系","p":552},{"i":573,"t":"结构型模式介绍如何将对象和类组装成较大的结构，并同时保持结构的灵活和高效。","s":"结构型模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":575,"t":"让接口不兼容的对象能够相互合作。","s":"📄️ 适配器模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":577,"t":"可将一个大类或一系列紧密相关的类拆分为抽象和实现两个独立的层次结构，从而能在开发时分别使用。","s":"📄️ 桥接模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":579,"t":"你可以使用它将对象组合成树状结构，并且能像使用独立对象一样使用它们。","s":"📄️ 组合模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":581,"t":"允许你通过将对象放入包含行为的特殊封装对象中来为原对象绑定新的行为。","s":"📄️ 装饰模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":583,"t":"能为程序库、框架或其他复杂类提供一个简单的接口。","s":"📄️ 外观模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":585,"t":"摒弃了在每个对象中保存所有数据的方式，通过共享多个对象所共有的相同状态，让你能在有限的内存容量中载入更多对象。","s":"📄️ 享元模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":587,"t":"让你能够提供对象的替代品或其占位符。代理控制着对于原对象的访问，并允许在将请求提交给对象前后进行一些处理。","s":"📄️ 代理模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":589,"t":"亦称：Template Method","s":"模板方法模式","u":"/docs/design-patterns/template-method","h":"","p":588},{"i":591,"t":"模板方法模式是一种行为设计模式，它在超类中定义了一个算法的框架，允许子类在不修改结构的情况下重写算法的特定步骤。","s":"意图","u":"/docs/design-patterns/template-method","h":"#意图","p":588},{"i":593,"t":"假如你正在开发一款分析公司文档的数据挖掘程序。用户需要向程序输入各种格式 (PDF、DOC 或 CSV) 的文档，程序则会试图从这些文件中抽取有意义的数据，并以统一的格式将其返回给用户。 该程序的首个版本仅支持 DOC 文件。在接下来的一个版本中，程序能够支持 CSV 文件。一个月后，你“教会”了程序从 PDF 文件中抽取数据。 数据挖掘类中包含许多重复代码。 一段时间后，你发现这三个类中包含许多相似代码。尽管这些类处理不同数据格式的代码完全不同，但数据处理和分析的代码却几乎完全一样。如果能在保持算法结构完整的情况下去除重复代码，这难道不是一件很棒的事情吗？ 还有另一个与使用这些类的客户端代码相关的问题：客户端代码中包含许多条件语句，以根据不同的处理对象类型选择合适的处理过程。如果所有处理数据的类都拥有相同的接口或基类，那么你就可以去除客户端代码中的条件语句，转而使用多态机制来在处理对象上调用函数。","s":"问题","u":"/docs/design-patterns/template-method","h":"#问题","p":588},{"i":595,"t":"模板方法模式建议将算法分解为一系列步骤，然后将这些步骤改写为方法，最后在“模板方法”中依次调用这些方法。步骤可以是 抽象 的，也可以有一些默认的实现。为了能够使用算法，客户端需要自行提供子类并实现所有的抽象步骤。如有必要还需重写一些步骤 (但这一步中不包括模板方法自身)。 让我们考虑如何在数据挖掘应用中实现上述方案。我们可为图中的三个解析算法创建一个基类，该类将定义调用了一系列不同文档处理步骤的模板方法。 模板方法将算法分解为步骤，并允许子类重写这些步骤，而非重写实际的模板方法。 首先，我们将所有步骤声明为 抽象 类型，强制要求子类自行实现这些方法。在我们的例子中，子类中已有所有必要的实现，因此我们只需调整这些方法的签名，使之与超类的方法匹配即可。 现在，让我们看看如何去除重复代码。对于不同的数据格式，打开和关闭文件以及抽取和解析数据的代码都不同，因此无需修改这些方法。但分析原始数据和生成报告等其他步骤的实现方式非常相似，因此可将其提取到基类中，以让子类共享这些代码。 正如你所看到的那样，我们有两种类型的步骤： 抽象步骤必须由各个子类来实现 可选步骤已有一些默认实现，但仍可在需要时进行重写 还有另一种名为钩子的步骤。钩子是内容为空的可选步骤。即使不重写钩子，模板方法也能工作。钩子通常放置在算法重要步骤的前后，为子类提供额外的算法扩展点。","s":"解决方案","u":"/docs/design-patterns/template-method","h":"#解决方案","p":588},{"i":597,"t":"可对典型的建筑方案进行微调以更好地满足客户需求。 模板方法可用于建造大量房屋。标准房屋建造方案中可提供几个扩展点，允许潜在房屋业主调整成品房屋的部分细节。 每个建造步骤 (例如打地基、建造框架、建造墙壁和安装水电管线等) 都能进行微调，这使得成品房屋会略有不同。","s":"真实世界类比","u":"/docs/design-patterns/template-method","h":"#真实世界类比","p":588},{"i":599,"t":"抽象类 (Abstract­Class) 会声明作为算法步骤的方法，以及依次调用它们的实际模板方法。算法步骤可以被声明为 抽象 类型，也可以提供一些默认实现。 具体类 (Concrete­Class) 可以重写所有步骤，但不能重写模板方法自身。","s":"模板方法模式结构","u":"/docs/design-patterns/template-method","h":"#模板方法模式结构","p":588},{"i":601,"t":"本例中的模板方法模式为一款简单策略游戏中人工智能的不同分支提供“框架”。 一款简单游戏的 AI 类。 游戏中所有的种族都有几乎同类的单位和建筑。因此你可以在不同的种族上复用相同的 AI 结构，同时还需要具备重写一些细节的能力。通过这种方式，你可以重写半兽人的 AI 使其更富攻击性，也可以让人类侧重防守，还可以禁止怪物建造建筑。在游戏中新增种族需要创建新的 AI 子类，还需要重写 AI 基类中所声明的默认方法。 // 抽象类定义了一个模板方法，其中通常会包含某个由抽象原语操作调用组成的算 // 法框架。具体子类会实现这些操作，但是不会对模板方法做出修改。 class GameAI is // 模板方法定义了某个算法的框架。 method turn() is collectResources() buildStructures() buildUnits() attack() // 某些步骤可在基类中直接实现。 method collectResources() is foreach (s in this.builtStructures) do s.collect() // 某些可定义为抽象类型。 abstract method buildStructures() abstract method buildUnits() // 一个类可包含多个模板方法。 method attack() is enemy = closestEnemy() if (enemy == null) sendScouts(map.center) else sendWarriors(enemy.position) abstract method sendScouts(position) abstract method sendWarriors(position) // 具体类必须实现基类中的所有抽象操作，但是它们不能重写模板方法自身。 class OrcsAI extends GameAI is method buildStructures() is if (there are some resources) then // 建造农场，接着是谷仓，然后是要塞。 method buildUnits() is if (there are plenty of resources) then if (there are no scouts) // 建造苦工，将其加入侦查编组。 else // 建造兽族步兵，将其加入战士编组。 // …… method sendScouts(position) is if (scouts.length > 0) then // 将侦查编组送到指定位置。 method sendWarriors(position) is if (warriors.length > 5) then // 将战斗编组送到指定位置。 // 子类可以重写部分默认的操作。 class MonstersAI extends GameAI is method collectResources() is // 怪物不会采集资源。 method buildStructures() is // 怪物不会建造建筑。 method buildUnits() is // 怪物不会建造单位。","s":"伪代码","u":"/docs/design-patterns/template-method","h":"#伪代码","p":588},{"i":603,"t":"当你只希望客户端扩展某个特定算法步骤，而不是整个算法或其结构时，可使用模板方法模式。 模板方法将整个算法转换为一系列独立的步骤，以便子类能对其进行扩展，同时还可让超类中所定义的结构保持完整。 当多个类的算法除一些细微不同之外几乎完全一样时，你可使用该模式。但其后果就是，只要算法发生变化，你就可能需要修改所有的类。 在将算法转换为模板方法时，你可将相似的实现步骤提取到超类中以去除重复代码。子类间各不同的代码可继续保留在子类中。 实现方式 分析目标算法，确定能否将其分解为多个步骤。从所有子类的角度出发，考虑哪些步骤能够通用，哪些步骤各不相同。 创建抽象基类并声明一个模板方法和代表算法步骤的一系列抽象方法。在模板方法中根据算法结构依次调用相应步骤。可用 final 最终修饰模板方法以防止子类对其进行重写。 虽然可将所有步骤全都设为抽象类型，但默认实现可能会给部分步骤带来好处，因为子类无需实现那些方法。 可考虑在算法的关键步骤之间添加钩子。 为每个算法变体新建一个具体子类，它必须实现所有的抽象步骤，也可以重写部分可选步骤。","s":"模板方法模式适合应用场景","u":"/docs/design-patterns/template-method","h":"#模板方法模式适合应用场景","p":588},{"i":605,"t":"✔️ 你可仅允许客户端重写一个大型算法中的特定部分，使得算法其他部分修改对其所造成的影响减小。 ✔️ 你可将重复代码提取到一个超类中。 ❌ 部分客户端可能会受到算法框架的限制。 ❌ 通过子类抑制默认步骤实现可能会导致违反里氏替换原则。 ❌ 模板方法中的步骤越多，其维护工作就可能会越困难。","s":"模板方法模式优缺点","u":"/docs/design-patterns/template-method","h":"#模板方法模式优缺点","p":588},{"i":607,"t":"工厂方法模式是模板方法模式的一种特殊形式。同时，工厂方法可以作为一个大型模板方法中的一个步骤。 模板方法基于继承机制：它允许你通过扩展子类中的部分内容来改变部分算法。策略模式基于组合机制：你可以通过对相应行为提供不同的策略来改变对象的部分行为。模板方法在类层次上运作，因此它是静态的。策略在对象层次上运作，因此允许在运行时切换行为。","s":"与其他模式的关系","u":"/docs/design-patterns/template-method","h":"#与其他模式的关系","p":588},{"i":609,"t":"亦称：Visitor","s":"访问者模式","u":"/docs/design-patterns/visitor","h":"","p":608},{"i":611,"t":"访问者模式是一种行为设计模式，它能将算法与其所作用的对象隔离开来。","s":"意图","u":"/docs/design-patterns/visitor","h":"#意图","p":608},{"i":613,"t":"假如你的团队开发了一款能够使用巨型图像中地理信息的应用程序。图像中的每个节点既能代表复杂实体 (例如一座城市)，也能代表更精细的对象 (例如工业区和旅游景点等)。如果节点代表的真实对象之间存在公路，那么这些节点就会相互连接。在程序内部，每个节点的类型都由其所属的类来表示，每个特定的节点则是一个对象。 将图像导出为 XML。 一段时间后，你接到了实现将图像导出到 XML 文件中的任务。这些工作最初看上去非常简单。你计划为每个节点类添加导出函数，然后递归执行图像中每个节点的导出函数。解决方案简单且优雅：使用多态机制可以让导出方法的调用代码不会和具体的节点类相耦合。 但你不太走运，系统架构师拒绝批准对已有节点类进行修改。他认为这些代码已经是产品了，不想冒险对其进行修改，因为修改可能会引入潜在的缺陷。 所有节点的类中都必须添加导出至 XML 文件的方法，但如果在修改代码的过程中引入了任何缺陷，那么整个程序都会面临风险。 此外，他还质疑在节点类中包含导出 XML 文件的代码是否有意义。这些类的主要工作是处理地理数据。导出 XML 文件的代码放在这里并不合适。 还有另一个原因，那就是在此项任务完成后，营销部门很有可能会要求程序提供导出其他类型文件的功能，或者提出其他奇怪的要求。这样你很可能会被迫再次修改这些重要但脆弱的类。","s":"问题","u":"/docs/design-patterns/visitor","h":"#问题","p":608},{"i":615,"t":"访问者模式建议将新行为放入一个名为访问者的独立类中，而不是试图将其整合到已有类中。现在，需要执行操作的原始对象将作为参数被传递给访问者中的方法，让方法能访问对象所包含的一切必要数据。 如果现在该操作能在不同类的对象上执行会怎么样呢？比如在我们的示例中，各节点类导出 XML 文件的实际实现很可能会稍有不同。因此，访问者类可以定义一组 (而不是一个) 方法，且每个方法可接收不同类型的参数，如下所示： class ExportVisitor implements Visitor is method doForCity(City c) { …… } method doForIndustry(Industry f) { …… } method doForSightSeeing(SightSeeing ss) { …… } // …… 但我们究竟应该如何调用这些方法 (尤其是在处理整个图像方面) 呢？这些方法的签名各不相同，因此我们不能使用多态机制。为了可以挑选出能够处理特定对象的访问者方法，我们需要对它的类进行检查。这是不是听上去像个噩梦呢？ foreach (Node node in graph) if (node instanceof City) exportVisitor.doForCity((City) node) if (node instanceof Industry) exportVisitor.doForIndustry((Industry) node) // …… } 你可能会问，我们为什么不使用方法重载呢？就是使用相同的方法名称，但它们的参数不同。不幸的是，即使我们的编程语言 (例如 Java 和 C#) 支持重载也不行。由于我们无法提前知晓节点对象所属的类，所以重载机制无法执行正确的方法。方法会将 节点 基类作为输入参数的默认类型。 但是，访问者模式可以解决这个问题。它使用了一种名为双分派的技巧，不使用累赘的条件语句也可下执行正确的方法。与其让客户端来选择调用正确版本的方法，不如将选择权委派给作为参数传递给访问者的对象。由于该对象知晓其自身的类，因此能更自然地在访问者中选出正确的方法。它们会“接收”一个访问者并告诉其应执行的访问者方法。 // 客户端代码 foreach (Node node in graph) node.accept(exportVisitor) // 城市 class City is method accept(Visitor v) is v.doForCity(this) // …… // 工业区 class Industry is method accept(Visitor v) is v.doForIndustry(this) // …… 我承认最终还是修改了节点类，但毕竟改动很小，且使得我们能够在后续进一步添加行为时无需再次修改代码。 现在，如果我们抽取出所有访问者的通用接口，所有已有的节点都能与我们在程序中引入的任何访问者交互。如果需要引入与节点相关的某个行为，你只需要实现一个新的访问者类即可。","s":"解决方案","u":"/docs/design-patterns/visitor","h":"#解决方案","p":608},{"i":617,"t":"优秀的保险代理人总能为不同类型的团体提供不同的保单。 假如有这样一位非常希望赢得新客户的资深保险代理人。他可以拜访街区中的每栋楼，尝试向每个路人推销保险。所以，根据大楼内组织类型的不同，他可以提供专门的保单： 如果建筑是居民楼，他会推销医疗保险。 如果建筑是银行，他会推销失窃保险。 如果建筑是咖啡厅，他会推销火灾和洪水保险。","s":"真实世界类比","u":"/docs/design-patterns/visitor","h":"#真实世界类比","p":608},{"i":619,"t":"访问者 (Visitor) 接口声明了一系列以对象结构的具体元素为参数的访问者方法。如果编程语言支持重载，这些方法的名称可以是相同的，但是其参数一定是不同的。 具体访问者 (Concrete Visitor) 会为不同的具体元素类实现相同行为的几个不同版本。 元素 (Element) 接口声明了一个方法来“接收”访问者。该方法必须有一个参数被声明为访问者接口类型。 具体元素 (Concrete Element) 必须实现接收方法。该方法的目的是根据当前元素类将其调用重定向到相应访问者的方法。请注意，即使元素基类实现了该方法，所有子类都必须对其进行重写并调用访问者对象中的合适方法。 客户端 (Client) 通常会作为集合或其他复杂对象 (例如一个组合树) 的代表。客户端通常不知晓所有的具体元素类，因为它们会通过抽象接口与集合中的对象进行交互。","s":"访问者模式结构","u":"/docs/design-patterns/visitor","h":"#访问者模式结构","p":608},{"i":621,"t":"在本例中，访问者模式为几何图像层次结构添加了对于 XML 文件导出功能的支持。 通过访问者对象将各种类型的对象导出为 XML 格式文件。 // 元素接口声明了一个 `accept（接收）` 方法，它会将访问者基础接口作为一个参 // 数。 interface Shape is method move(x, y) method draw() method accept(v: Visitor) // 每个具体元素类都必须以特定方式实现 `accept` 方法，使其能调用相应元素类的 // 访问者方法。 class Dot implements Shape is // …… // 注意我们正在调用的 `visitDot（访问点）` 方法与当前类的名称相匹配。 // 这样我们能让访问者知晓与其交互的元素类。 method accept(v: Visitor) is v.visitDot(this) class Circle implements Shape is // …… method accept(v: Visitor) is v.visitCircle(this) class Rectangle implements Shape is // …… method accept(v: Visitor) is v.visitRectangle(this) class CompoundShape implements Shape is // …… method accept(v: Visitor) is v.visitCompoundShape(this) // 访问者接口声明了一组与元素类对应的访问方法。访问方法的签名能让访问者准 // 确辨别出与其交互的元素所属的类。 interface Visitor is method visitDot(d: Dot) method visitCircle(c: Circle) method visitRectangle(r: Rectangle) method visitCompoundShape(cs: CompoundShape) // 具体访问者实现了同一算法的多个版本，而且该算法能与所有具体类进行交互。 // // 访问者模式在复杂对象结构（例如组合树）上使用时能发挥最大作用。在这种情 // 况下，它可以存储算法的一些中间状态，并同时在结构中的不同对象上执行访问 // 者方法。这可能会非常有帮助。 class XMLExportVisitor implements Visitor is method visitDot(d: Dot) is // 导出点（dot）的 ID 和中心坐标。 method visitCircle(c: Circle) is // 导出圆（circle）的 ID、中心坐标和半径。 method visitRectangle(r: Rectangle) is // 导出长方形（rectangle）的 ID、左上角坐标、宽和长。 method visitCompoundShape(cs: CompoundShape) is // 导出图形（shape）的 ID 和其子项目的 ID 列表。 // 客户端代码可在不知晓具体类的情况下在一组元素上运行访问者操作。“接收”操 // 作会将调用定位到访问者对象的相应操作上。 class Application is field allShapes: array of Shapes method export() is exportVisitor = new XMLExportVisitor() foreach (shape in allShapes) do shape.accept(exportVisitor)","s":"伪代码","u":"/docs/design-patterns/visitor","h":"#伪代码","p":608},{"i":623,"t":"如果你需要对一个复杂对象结构 (例如对象树) 中的所有元素执行某些操作，可使用访问者模式。 访问者模式通过在访问者对象中为多个目标类提供相同操作的变体，让你能在属于不同类的一组对象上执行同一操作。 可使用访问者模式来清理辅助行为的业务逻辑。 该模式会将所有非主要的行为抽取到一组访问者类中，使得程序的主要类能更专注于主要的工作。 当某个行为仅在类层次结构中的一些类中有意义，而在其他类中没有意义时，可使用该模式。 你可将该行为抽取到单独的访问者类中，只需实现接收相关类的对象作为参数的访问者方法并将其他方法留空即可。 实现方式 在访问者接口中声明一组“访问”方法，分别对应程序中的每个具体元素类。 声明元素接口。如果程序中已有元素类层次接口，可在层次结构基类中添加抽象的“接收”方法。该方法必须接受访问者对象作为参数。 在所有具体元素类中实现接收方法。这些方法必须将调用重定向到当前元素对应的访问者对象中的访问者方法上。 元素类只能通过访问者接口与访问者进行交互。不过访问者必须知晓所有的具体元素类，因为这些类在访问者方法中都被作为参数类型引用。 为每个无法在元素层次结构中实现的行为创建一个具体访问者类并实现所有的访问者方法。你可能会遇到访问者需要访问元素类的部分私有成员变量的情况。在这种情况下，你要么将这些变量或方法设为公有，这将破坏元素的封装；要么将访问者类嵌入到元素类中。后一种方式只有在支持嵌套类的编程语言中才可能实现。 客户端必须创建访问者对象并通过“接收”方法将其传递给元素。","s":"访问者模式适合应用场景","u":"/docs/design-patterns/visitor","h":"#访问者模式适合应用场景","p":608},{"i":625,"t":"✔️ 开闭原则。你可以引入在不同类对象上执行的新行为，且无需对这些类做出修改。 ✔️ 单一职责原则。可将同一行为的不同版本移到同一个类中。 ✔️ 访问者对象可以在与各种对象交互时收集一些有用的信息。当你想要遍历一些复杂的对象结构 (例如对象树)，并在结构中的每个对象上应用访问者时，这些信息可能会有所帮助。 ❌ 每次在元素层次结构中添加或移除一个类时，你都要更新所有的访问者。 ❌ 在访问者同某个元素进行交互时，它们可能没有访问元素私有成员变量和方法的必要权限。","s":"访问者模式优缺点","u":"/docs/design-patterns/visitor","h":"#访问者模式优缺点","p":608},{"i":627,"t":"你可以将访问者模式视为命令模式的加强版本，其对象可对不同类的多种对象执行操作。 你可以使用访问者对整个组合模式树执行操作。 可以同时使用访问者和迭代器模式来遍历复杂数据结构，并对其中的元素执行所需操作，即使这些元素所属的类完全不同。","s":"与其他模式的关系","u":"/docs/design-patterns/visitor","h":"#与其他模式的关系","p":608},{"i":629,"t":"You have just learned the basics of Docusaurus and made some changes to the initial template. Docusaurus has much more to offer! Take a look at versioning and i18n.","s":"Congratulations!","u":"/docs/docusaurus-mdx/docusaurus-tutorial/congratulations","h":"","p":628},{"i":631,"t":"Read the official documentation Modify your site configuration with docusaurus.config.ts Add navbar and footer items with themeConfig Add a custom Design and Layout Add a search bar Find inspirations in the Docusaurus showcase Get involved in the Docusaurus Community","s":"What's next?","u":"/docs/docusaurus-mdx/docusaurus-tutorial/congratulations","h":"#whats-next","p":628},{"i":633,"t":"Docusaurus creates a page for each blog post, but also a blog index page, a tag system, an RSS feed...","s":"Create a Blog Post","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-blog-post","h":"","p":632},{"i":635,"t":"Create a file at blog/2021-02-28-greetings.md: blog/2021-02-28-greetings.md --- slug: greetings title: Greetings! authors: - name: Joel Marcey title: Co-creator of Docusaurus 1 url: https://github.com/JoelMarcey image_url: https://github.com/JoelMarcey.png - name: Sébastien Lorber title: Docusaurus maintainer url: https://sebastienlorber.com image_url: https://github.com/slorber.png tags: [greetings] --- Congratulations, you have made your first post! Feel free to play around and edit this post as much you like. A new blog post is now available at http://localhost:3000/blog/greetings.","s":"Create your first Post","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-blog-post","h":"#create-your-first-post","p":632},{"i":637,"t":"Documents are groups of pages connected through: a sidebar previous/next navigation versioning","s":"Create a Document","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-document","h":"","p":636},{"i":639,"t":"Create a Markdown file at docs/hello.md: docs/hello.md # Hello This is my **first Docusaurus document**! A new document is now available at http://localhost:3000/docs/hello.","s":"Create your first Doc","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-document","h":"#create-your-first-doc","p":636},{"i":641,"t":"Docusaurus automatically creates a sidebar from the docs folder. Add metadata to customize the sidebar label and position: docs/hello.md --- sidebar_label: 'Hi!' sidebar_position: 3 --- # Hello This is my **first Docusaurus document**! It is also possible to create your sidebar explicitly in sidebars.js: sidebars.js export default { tutorialSidebar: [ 'intro', // highlight-next-line 'hello', { type: 'category', label: 'Tutorial', items: ['tutorial-basics/create-a-document'], }, ], };","s":"Configure the Sidebar","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-document","h":"#configure-the-sidebar","p":636},{"i":643,"t":"Add Markdown or React files to src/pages to create a standalone page: src/pages/index.js → localhost:3000/ src/pages/foo.md → localhost:3000/foo src/pages/foo/bar.js → localhost:3000/foo/bar","s":"Create a Page","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-page","h":"","p":642},{"i":645,"t":"Create a file at src/pages/my-react-page.js: src/pages/my-react-page.js import React from 'react'; import Layout from '@theme/Layout'; export default function MyReactPage() { return ( <Layout> <h1>My React page</h1> <p>This is a React page</p> </Layout> ); } A new page is now available at http://localhost:3000/my-react-page.","s":"Create your first React Page","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-page","h":"#create-your-first-react-page","p":642},{"i":647,"t":"Create a file at src/pages/my-markdown-page.md: src/pages/my-markdown-page.md # My Markdown page This is a Markdown page A new page is now available at http://localhost:3000/my-markdown-page.","s":"Create your first Markdown Page","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-page","h":"#create-your-first-markdown-page","p":642},{"i":649,"t":"Docusaurus is a static-site-generator (also called Jamstack). It builds your site as simple static HTML, JavaScript and CSS files.","s":"Deploy your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/deploy-your-site","h":"","p":648},{"i":651,"t":"Build your site for production: npm run build The static files are generated in the build folder.","s":"Build your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/deploy-your-site","h":"#build-your-site","p":648},{"i":652,"t":"Test your production build locally: npm run serve The build folder is now served at http://localhost:3000/. You can now deploy the build folder almost anywhere easily, for free or very small cost (read the Deployment Guide).","s":"Deploy your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/deploy-your-site","h":"#deploy-your-site-1","p":648},{"i":654,"t":"Let's discover Docusaurus in less than 5 minutes.","s":"Tutorial Intro","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"","p":653},{"i":656,"t":"Get started by creating a new site. Or try Docusaurus immediately with docusaurus.new.","s":"Getting Started","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"#getting-started","p":653},{"i":658,"t":"Node.js version 18.0 or above: When installing Node.js, you are recommended to check all checkboxes related to dependencies.","s":"What you'll need","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"#what-youll-need","p":653},{"i":660,"t":"Generate a new Docusaurus site using the classic template. The classic template will automatically be added to your project after you run the command: npm init docusaurus@latest my-website classic You can type this command into Command Prompt, Powershell, Terminal, or any other integrated terminal of your code editor. The command also installs all necessary dependencies you need to run Docusaurus.","s":"Generate a new site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"#generate-a-new-site","p":653},{"i":662,"t":"Run the development server: cd my-website npm run start The cd command changes the directory you're working with. In order to work with your newly created Docusaurus site, you'll need to navigate the terminal there. The npm run start command builds your website locally and serves it through a development server, ready for you to view at http://localhost:3000/. Open docs/intro.md (this page) and edit some lines: the site reloads automatically and displays your changes.","s":"Start your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"#start-your-site","p":653},{"i":664,"t":"Docusaurus can manage multiple versions of your docs.","s":"Manage Docs Versions","u":"/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions","h":"","p":663},{"i":666,"t":"Release a version 1.0 of your project: npm run docusaurus docs:version 1.0 The docs folder is copied into versioned_docs/version-1.0 and versions.json is created. Your docs now have 2 versions: 1.0 at http://localhost:3000/docs/ for the version 1.0 docs current at http://localhost:3000/docs/next/ for the upcoming, unreleased docs","s":"Create a docs version","u":"/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions","h":"#create-a-docs-version","p":663},{"i":668,"t":"To navigate seamlessly across versions, add a version dropdown. Modify the docusaurus.config.ts file: docusaurus.config.ts export default { themeConfig: { navbar: { items: [ { type: 'docsVersionDropdown', }, ], }, }, }; The docs version dropdown appears in your navbar:","s":"Add a Version Dropdown","u":"/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions","h":"#add-a-version-dropdown","p":663},{"i":670,"t":"It is possible to edit versioned docs in their respective folder: versioned_docs/version-1.0/hello.md updates http://localhost:3000/docs/hello docs/hello.md updates http://localhost:3000/docs/next/hello","s":"Update an existing version","u":"/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions","h":"#update-an-existing-version","p":663},{"i":672,"t":"Docusaurus supports Markdown and a few additional features.","s":"Markdown Features","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"","p":671},{"i":674,"t":"Markdown documents have metadata at the top called Front Matter: my-doc.md --- id: my-doc-id title: My document title description: My document description slug: /my-custom-url --- ## Markdown heading Markdown text with [links](./hello.md)","s":"Front Matter","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#front-matter","p":671},{"i":676,"t":"Regular Markdown links are supported, using url paths or relative file paths. Let's see how to [Create a page](/create-a-page). Let's see how to [Create a page](./create-a-page.md). Result: Let's see how to Create a page.","s":"Links","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#links","p":671},{"i":678,"t":"Regular Markdown images are supported. You can use absolute paths to reference images in the static directory (static/img/docusaurus.png): ![Docusaurus logo](/img/docusaurus.png) You can reference images relative to the current file as well. This is particularly useful to colocate images close to the Markdown files using them: ![Docusaurus logo](./img/docusaurus.png)","s":"Images","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#images","p":671},{"i":680,"t":"Markdown code blocks are supported with Syntax highlighting. src/components/HelloDocusaurus.js function HelloDocusaurus() { return ( <h1>Hello, Docusaurus!</h1> ) } src/components/HelloDocusaurus.js function HelloDocusaurus() { return <h1>Hello, Docusaurus!</h1>; }","s":"Code Blocks","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#code-blocks","p":671},{"i":682,"t":"Docusaurus has a special syntax to create admonitions and callouts: My tip Use this awesome feature option Take care This action is dangerous My tip Use this awesome feature option Take care This action is dangerous","s":"Admonitions","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#admonitions","p":671},{"i":684,"t":"MDX can make your documentation more interactive and allows using any React components inside Markdown: export const Highlight = ({children, color}) => ( <span style={{ backgroundColor: color, borderRadius: '20px', color: '#fff', padding: '10px', cursor: 'pointer', }} onClick={() => { alert(`You clicked the color ${color} with label ${children}`) }}> {children} </span> ); This is <Highlight color=\"#25c2a0\">Docusaurus green</Highlight> ! This is <Highlight color=\"#1877F2\">Facebook blue</Highlight> ! This is Docusaurus green ! This is Facebook blue !","s":"MDX and React Components","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#mdx-and-react-components","p":671},{"i":686,"t":"Let's translate docs/intro.md to French.","s":"Translate your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"","p":685},{"i":688,"t":"Modify docusaurus.config.ts to add support for the fr locale: docusaurus.config.ts export default { i18n: { defaultLocale: 'en', locales: ['en', 'fr'], }, };","s":"Configure i18n","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#configure-i18n","p":685},{"i":690,"t":"Copy the docs/intro.md file to the i18n/fr folder: mkdir -p i18n/fr/docusaurus-plugin-content-docs/current/ cp docs/intro.md i18n/fr/docusaurus-plugin-content-docs/current/intro.md Translate i18n/fr/docusaurus-plugin-content-docs/current/intro.md in French.","s":"Translate a doc","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#translate-a-doc","p":685},{"i":692,"t":"Start your site on the French locale: npm run start -- --locale fr Your localized site is accessible at http://localhost:3000/fr/ and the Getting Started page is translated. 警告 In development, you can only use one locale at a time.","s":"Start your localized site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#start-your-localized-site","p":685},{"i":694,"t":"To navigate seamlessly across languages, add a locale dropdown. Modify the docusaurus.config.ts file: docusaurus.config.ts export default { themeConfig: { navbar: { items: [ { type: 'localeDropdown', }, ], }, }, }; The locale dropdown now appears in your navbar:","s":"Add a Locale Dropdown","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#add-a-locale-dropdown","p":685},{"i":696,"t":"Build your site for a specific locale: npm run build -- --locale fr Or build your site to include all the locales at once: npm run build","s":"Build your localized site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#build-your-localized-site","p":685},{"i":699,"t":"Build optimized websites quickly, focus on your content using react and powered by MDX. ⚡️ Docusaurus will help you ship a beautiful documentation site in no time. 💸 Building a custom tech stack is expensive. Instead, focus on your content and just write Markdown files. 💥 Ready for more? Use advanced features like versioning, i18n, search and theme customizations. 💅 Check the best Docusaurus sites for inspiration and read some testimonials. 🧐 Docusaurus is a static-site generator. It builds a single-page application with fast client-side navigation, leveraging the full power of React to make your site interactive. It provides out-of-the-box documentation features but can be used to create any kind of site (personal website, product, blog, marketing landing pages, etc).","s":"What is Docusaurus?","u":"/docs/docusaurus-mdx/intro","h":"#what-is-docusaurus","p":697},{"i":701,"t":"MDX lets you use JSX in your markdown content. You can import components, such as interactive charts or alerts, and embed them within your content. This makes writing long-form content with components a blast. ❤️ Powerful: MDX blends markdown and JSX syntax to fit perfectly in JSX-based projects 💻 Everything is a component: Use existing components in your MDX and import other MDX files as components 🔧 Customizable: Decide which component is rendered for each markdown construct ({h1: MyHeading}) 📚 Markdown-based: The simplicity and elegance of markdown remains, you use JSX only when you want to 🔥 Blazingly blazing fast: MDX has no runtime, all compilation occurs during the build stage","s":"What is MDX?","u":"/docs/docusaurus-mdx/intro","h":"#what-is-mdx","p":697},{"i":703,"t":"In addition to the basic Markdown syntax, we have a special admonitions syntax by wrapping text with a set of 3 colons, followed by a label denoting its type. Example: :::note Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: :::tip Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: :::info Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: :::warning Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: :::danger Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: 备注 Some content with Markdown syntax. Check this api. 提示 Some content with Markdown syntax. Check this api. 信息 Some content with Markdown syntax. Check this api. 注意 Some content with Markdown syntax. Check this api. 危险 Some content with Markdown syntax. Check this api.","s":"Admonitions","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"","p":702},{"i":705,"t":"If you use Prettier to format your Markdown files, Prettier might auto-format your code to invalid admonition syntax. To avoid this problem, add empty lines around the starting and ending directives. This is also why the examples we show here all have empty lines around the content. <!-- Prettier doesn't change this --> :::note Hello world ::: <!-- Prettier changes this --> :::note Hello world ::: <!-- to this --> ::: note Hello world:::","s":"Usage with Prettier","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#usage-with-prettier","p":702},{"i":707,"t":"You may also specify an optional title. :::note[Your Title **with** some _Markdown_ `syntax`!] Some **content** with some _Markdown_ `syntax`. ::: Your Title with some Markdown syntax! Some content with some Markdown syntax.","s":"Specifying title","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#specifying-title","p":702},{"i":709,"t":"Admonitions can be nested. Use more colons : for each parent admonition level. :::::info[Parent] Parent content ::::danger[Child] Child content :::tip[Deep Child] Deep child content ::: :::: ::::: Parent Parent content Child Child content Deep Child Deep child content","s":"Nested admonitions","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#nested-admonitions","p":702},{"i":711,"t":"You can use MDX inside admonitions too! import Tabs from '@theme/Tabs'; import TabItem from '@theme/TabItem'; :::tip[Use tabs in admonitions] <Tabs> <TabItem value=\"apple\" label=\"Apple\">This is an apple 🍎</TabItem> <TabItem value=\"orange\" label=\"Orange\">This is an orange 🍊</TabItem> <TabItem value=\"banana\" label=\"Banana\">This is a banana 🍌</TabItem> </Tabs> ::: Use tabs in admonitions Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌","s":"Admonitions with MDX","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#admonitions-with-mdx","p":702},{"i":713,"t":"Outside of Markdown, you can use the @theme/Admonition component to get the same output. MyReactPage.jsx import Admonition from '@theme/Admonition'; export default function MyReactPage() { return ( <div> <Admonition type=\"info\"> <p>Some information</p> </Admonition> </div> ); } The types that are accepted are the same as above: note, tip, danger, info, warning. Optionally, you can specify an icon by passing a JSX element or a string, or a title: MyReactPage.jsx <Admonition type=\"tip\" icon=\"💡\" title=\"Did you know...\"> Use plugins to introduce shorter syntax for the most commonly used JSX elements in your project. </Admonition> 💡Did you know... Use plugins to introduce shorter syntax for the most commonly used JSX elements in your project.","s":"Usage in JSX","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#usage-in-jsx","p":702},{"i":715,"t":"There are two kinds of customizations possible with admonitions: parsing and rendering.","s":"Customizing admonitions","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#customizing-admonitions","p":702},{"i":717,"t":"You can customize how each individual admonition type is rendered through swizzling. You can often achieve your goal through a simple wrapper. For example, in the follow example, we swap out the icon for info admonitions only. src/theme/Admonition.js import React from 'react'; import Admonition from '@theme-original/Admonition'; import MyCustomNoteIcon from '@site/static/img/info.svg'; export default function AdmonitionWrapper(props) { if (props.type !== 'info') { return <Admonition title=\"My Custom Admonition Title\" {...props} />; } return <Admonition icon={<MyCustomNoteIcon />} {...props} />; }","s":"Customizing rendering behavior","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#customizing-rendering-behavior","p":702},{"i":719,"t":"Admonitions are implemented with a Remark plugin. The plugin is designed to be configurable. To customize the Remark plugin for a specific content plugin (docs, blog, pages), pass the options through the admonitions key. docusaurus.config.ts export default { presets: [ [ '@docusaurus/preset-classic', { docs: { admonitions: { keywords: ['note', 'tip', 'info', 'warning', 'danger'], extendDefaults: true, }, }, }, ], ], }; The plugin accepts the following options: keywords: An array of keywords that can be used as the type for the admonition. extendDefaults: Should the provided options (such as keywords) be merged into the existing defaults. Defaults to true. The keyword will be passed as the type prop of the Admonition component.","s":"Customizing parsing behavior","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#customizing-parsing-behavior","p":702},{"i":721,"t":"Sometimes you want to link to assets (e.g. docx files, images...) directly from Markdown files, and it is convenient to co-locate the asset next to the Markdown file using it. Let's imagine the following file structure: # Your doc /website/docs/myFeature.mdx # Some assets you want to use /website/docs/assets/docusaurus-asset-example-banner.png /website/docs/assets/docusaurus-asset-example.docx","s":"Assets","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"","p":720},{"i":723,"t":"You can display images in three different ways: Markdown syntax, CJS require, or ES imports syntax. Markdown syntax CommonJS require Import statement Display images using simple Markdown syntax: ![Example banner](./assets/docusaurus-asset-example-banner.png) Display images using inline CommonJS require in JSX image tag: <img src={require('./assets/docusaurus-asset-example-banner.png').default} alt=\"Example banner\" /> Display images using ES import syntax and JSX image tag: import myImageUrl from '../assets/docusaurus-asset-example-banner.png'; <img src={myImageUrl} alt=\"Example banner\" />; All of the above result in displaying the image: 备注 If you are using @docusaurus/plugin-ideal-image, you need to use the dedicated image component, as documented.","s":"Images","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#images","p":720},{"i":725,"t":"In the same way, you can link to existing assets by require'ing them and using the returned URL in videos, a anchor links, etc. # My Markdown page <a target=\"\\_blank\" href={require('../assets/docusaurus-asset-example.docx').default}> Download this docx </a> or [Download this docx using Markdown](../assets/docusaurus-asset-example.docx) Download this docx Download this docx using Markdown Markdown links are always file paths If you use the Markdown image or link syntax, all asset paths will be resolved as file paths by Docusaurus and automatically converted to require() calls. You don't need to use require() in Markdown unless you use the JSX syntax, which you do have to handle yourself.","s":"Files","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#files","p":720},{"i":727,"t":"Docusaurus supports inlining SVGs out of the box. import DocusaurusSvg from './docusaurus.svg'; <DocusaurusSvg />; This can be useful if you want to alter the part of the SVG image via CSS. For example, you can change one of the SVG colors based on the current theme. import DocusaurusSvg from './docusaurus.svg'; <DocusaurusSvg className=\"themedDocusaurus\" />; [data-theme='light'] .themedDocusaurus [fill='#FFFF50'] { fill: greenyellow; } [data-theme='dark'] .themedDocusaurus [fill='#FFFF50'] { fill: seagreen; }","s":"Inline SVGs","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#inline-svgs","p":720},{"i":729,"t":"Docusaurus supports themed images: the ThemedImage component (included in the themes) allows you to switch the image source based on the current theme. import ThemedImage from '@theme/ThemedImage'; <ThemedImage alt=\"Docusaurus themed image\" sources={{ light: useBaseUrl('/img/docusaurus_light.svg'), dark: useBaseUrl('/img/docusaurus_dark.svg'), }} />;","s":"Themed Images","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#themed-images","p":720},{"i":731,"t":"GitHub uses its own image theming approach with path fragments, which you can easily implement yourself. To toggle the visibility of an image using the path fragment (for GitHub, it's #gh-dark-mode-only and #gh-light-mode-only), add the following to your custom CSS (you can also use your own suffix if you don't want to be coupled to GitHub): src/css/custom.css [data-theme='light'] img[src$='#gh-dark-mode-only'], [data-theme='dark'] img[src$='#gh-light-mode-only'] { display: none; } ![Docusaurus themed image](/img/docusaurus_keytar.svg#gh-light-mode-only)![Docusaurus themed image](/img/docusaurus_speed.svg#gh-dark-mode-only)","s":"GitHub-style themed images","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#github-style-themed-images","p":720},{"i":733,"t":"If a Markdown link or image has an absolute path, the path will be seen as a file path and will be resolved from the static directories. For example, if you have configured static directories to be ['public', 'static'], then for the following image: my-doc.md ![An image from the static](/img/docusaurus.png) Docusaurus will try to look for it in both static/img/docusaurus.png and public/img/docusaurus.png. The link will then be converted to a require() call instead of staying as a URL. This is desirable in two regards: You don't have to worry about the base URL, which Docusaurus will take care of when serving the asset; The image enters Webpack's build pipeline and its name will be appended by a hash, which enables browsers to aggressively cache the image and improves your site's performance. If you intend to write URLs, you can use the pathname:// protocol to disable automatic asset linking. ![banner](pathname:///img/docusaurus-asset-example-banner.png) This link will be generated as <img src=\"/img/docusaurus-asset-example-banner.png\" alt=\"banner\" />, without any processing or file existence checking.","s":"Static assets","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#static-assets","p":720},{"i":735,"t":"Code blocks within documentation are super-powered 💪.","s":"Code blocks","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"","p":734},{"i":737,"t":"You can add a title to the code block by adding a title key after the language (leave a space between them). ```jsx title=\"/src/components/HelloCodeTitle.js\" function HelloCodeTitle(props) { return <h1>Hello, {props.name}</h1>; } ``` /src/components/HelloCodeTitle.js function HelloCodeTitle(props) { return <h1>Hello, {props.name}</h1>; }","s":"Code title","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#code-title","p":734},{"i":739,"t":"Code blocks are text blocks wrapped around by strings of 3 backticks. You may check out this reference for the specifications of MDX. ```js console.log('Every repo must come with a mascot.'); ``` Use the matching language meta string for your code block, and Docusaurus will pick up syntax highlighting automatically, powered by Prism React Renderer. console.log('Every repo must come with a mascot.');","s":"Syntax highlighting","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#syntax-highlighting","p":734},{"i":741,"t":"By default, the Prism syntax highlighting theme we use is Palenight. You can change this to another theme by passing theme field in prism as themeConfig in your docusaurus.config.ts. For example, if you prefer to use the dracula highlighting theme: docusaurus.config.ts import {themes as prismThemes} from 'prism-react-renderer'; export default { themeConfig: { prism: { // highlight-next-line theme: prismThemes.dracula, }, }, }; Because a Prism theme is just a JS object, you can also write your own theme if you are not satisfied with the default. Docusaurus enhances the github and vsDark themes to provide richer highlight, and you can check our implementations for the light and dark code block themes.","s":"Theming","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#theming","p":734},{"i":743,"t":"By default, Docusaurus comes with a subset of commonly used languages. 注意 Some popular languages like Java, C#, or PHP are not enabled by default. To add syntax highlighting for any of the other Prism-supported languages, define it in an array of additional languages. 备注 Each additional language has to be a valid Prism component name. For example, Prism would map the language cs to csharp, but only prism-csharp.js exists as a component, so you need to use additionalLanguages: ['csharp']. You can look into node_modules/prismjs/components to find all components (languages) available. For example, if you want to add highlighting for the PowerShell language: docusaurus.config.ts export default { // ... themeConfig: { prism: { // highlight-next-line additionalLanguages: ['powershell'], }, // ... }, }; After adding additionalLanguages, restart Docusaurus. If you want to add highlighting for languages not yet supported by Prism, you can swizzle prism-include-languages: npm Yarn pnpm npm run swizzle @docusaurus/theme-classic prism-include-languages yarn swizzle @docusaurus/theme-classic prism-include-languages pnpm run swizzle @docusaurus/theme-classic prism-include-languages It will produce prism-include-languages.js in your src/theme folder. You can add highlighting support for custom languages by editing prism-include-languages.js: src/theme/prism-include-languages.js const prismIncludeLanguages = (Prism) => { // ... additionalLanguages.forEach((lang) => { require(`prismjs/components/prism-${lang}`); }); // highlight-next-line require('/path/to/your/prism-language-definition'); // ... }; You can refer to Prism's official language definitions when you are writing your own language definitions. When adding a custom language definition, you do not need to add the language to the additionalLanguages config array, since Docusaurus only looks up the additionalLanguages strings in languages that Prism provides. Adding the language import in prism-include-languages.js is sufficient.","s":"Supported Languages","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#supported-languages","p":734},{"i":746,"t":"You can use comments with highlight-next-line, highlight-start, and highlight-end to select which lines are highlighted. ```js function HighlightSomeText(highlight) { if (highlight) { // highlight-next-line return 'This text is highlighted!'; } return 'Nothing highlighted'; } function HighlightMoreText(highlight) { // highlight-start if (highlight) { return 'This range is highlighted!'; } // highlight-end return 'Nothing highlighted'; } ``` function HighlightSomeText(highlight) { if (highlight) { // highlight-next-line return 'This text is highlighted!'; } return 'Nothing highlighted'; } function HighlightMoreText(highlight) { if (highlight) { return 'This range is highlighted!'; } return 'Nothing highlighted'; } Supported commenting syntax: Style Syntax C-style /* ... */ and // ... JSX-style {/* ... */} Bash-style # ... HTML-style <!-- ... --> We will do our best to infer which set of comment styles to use based on the language, and default to allowing all comment styles. If there's a comment style that is not currently supported, we are open to adding them! Pull requests welcome. Note that different comment styles have no semantic difference, only their content does. You can set your own background color for highlighted code line in your src/css/custom.css which will better fit to your selected syntax highlighting theme. The color given below works for the default highlighting theme (Palenight), so if you are using another theme, you will have to tweak the color accordingly. /src/css/custom.css :root { --docusaurus-highlighted-code-line-bg: rgb(72, 77, 91); } /* If you have a different syntax highlighting theme for dark mode. */ [data-theme='dark'] { /* Color which works with dark mode syntax highlighting theme */ --docusaurus-highlighted-code-line-bg: rgb(100, 100, 100); } If you also need to style the highlighted code line in some other way, you can target on theme-code-block-highlighted-line CSS class.","s":"Highlighting with comments","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#highlighting-with-comments","p":734},{"i":748,"t":"You can also specify highlighted line ranges within the language meta string (leave a space after the language). To highlight multiple lines, separate the line numbers by commas or use the range syntax to select a chunk of lines. This feature uses the parse-number-range library and you can find more syntax on their project details. ```jsx {1,4-6,11} import React from 'react'; function MyComponent(props) { if (props.isBar) { return <div>Bar</div>; } return <div>Foo</div>; } export default MyComponent; ``` import React from 'react'; function MyComponent(props) { if (props.isBar) { return <div>Bar</div>; } return <div>Foo</div>; } export default MyComponent; prefer comments Prefer highlighting with comments where you can. By inlining highlight in the code, you don't have to manually count the lines if your code block becomes long. If you add/remove lines, you also don't have to offset your line ranges. - ```jsx {3} + ```jsx {4} function HighlightSomeText(highlight) { if (highlight) { + console.log('Highlighted text found'); return 'This text is highlighted!'; } return 'Nothing highlighted'; } ``` Below, we will introduce how the magic comment system can be extended to define custom directives and their functionalities. The magic comments would only be parsed if a highlight metastring is not present.","s":"Highlighting with metadata string","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#highlighting-with-metadata-string","p":734},{"i":750,"t":"// highlight-next-line and // highlight-start etc. are called \"magic comments\", because they will be parsed and removed, and their purposes are to add metadata to the next line, or the section that the pair of start- and end-comments enclose. You can declare custom magic comments through theme config. For example, you can register another magic comment that adds a code-block-error-line class name: docusaurus.config.ts src/css/custom.css myDoc.md export default { themeConfig: { prism: { magicComments: [ // Remember to extend the default highlight class name as well! { className: 'theme-code-block-highlighted-line', line: 'highlight', block: {start: 'highlight-start', end: 'highlight-end'}, }, { className: 'code-block-red-line', line: 'highlight-red', block: {start: 'highlight-red-start', end: 'highlight-red-end'}, }, ], }, }, }; .code-block-error-line { background-color: #ff000020; display: block; margin: 0 calc(-1 * var(--ifm-pre-padding)); padding: 0 var(--ifm-pre-padding); border-left: 3px solid #ff000080; } In JavaScript, trying to access properties on `null` will error. ```js const name = null; // highlight-red console.log(name.toUpperCase()); // Uncaught TypeError: Cannot read properties of null (reading 'toUpperCase') ``` In JavaScript, trying to access properties on null will error. const name = null; console.log(name.toUpperCase()); // Uncaught TypeError: Cannot read properties of null (reading 'toUpperCase') If you use number ranges in metastring (the {1,3-4} syntax), Docusaurus will apply the first magicComments entry's class name. This, by default, is theme-code-block-highlighted-line, but if you change the magicComments config and use a different entry as the first one, the meaning of the metastring range will change as well. You can disable the default line highlighting comments with magicComments: []. If there's no magic comment config, but Docusaurus encounters a code block containing a metastring range, it will error because there will be no class name to apply—the highlighting class name, after all, is just a magic comment entry. Every magic comment entry will contain three keys: className (required), line, which applies to the directly next line, or block (containing start and end), which applies to the entire block enclosed by the two comments. Using CSS to target the class can already do a lot, but you can unlock the full potential of this feature through swizzling. npm Yarn pnpm npm run swizzle @docusaurus/theme-classic CodeBlock/Line yarn swizzle @docusaurus/theme-classic CodeBlock/Line pnpm run swizzle @docusaurus/theme-classic CodeBlock/Line The Line component will receive the list of class names, based on which you can conditionally render different markup.","s":"Custom magic comments","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#custom-magic-comments","p":734},{"i":752,"t":"You can enable line numbering for your code block by using showLineNumbers key within the language meta string (don't forget to add space directly before the key). ```jsx {1,4-6,11} showLineNumbers import React from 'react'; function MyComponent(props) { if (props.isBar) { return <div>Bar</div>; } return <div>Foo</div>; } export default MyComponent; ``` import React from 'react'; function MyComponent(props) { if (props.isBar) { return <div>Bar</div>; } return <div>Foo</div>; } export default MyComponent;","s":"Line numbering","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#line-numbering","p":734},{"i":754,"t":"(Powered by React Live) You can create an interactive coding editor with the @docusaurus/theme-live-codeblock plugin. First, add the plugin to your package. npm Yarn pnpm npm install --save @docusaurus/theme-live-codeblock yarn add @docusaurus/theme-live-codeblock pnpm add @docusaurus/theme-live-codeblock You will also need to add the plugin to your docusaurus.config.ts. export default { // ... themes: ['@docusaurus/theme-live-codeblock'], // ... }; To use the plugin, create a code block with live attached to the language meta string. ```jsx live function Clock(props) { const [date, setDate] = useState(new Date()); useEffect(() => { const timerID = setInterval(() => tick(), 1000); return function cleanup() { clearInterval(timerID); }; }); function tick() { setDate(new Date()); } return ( <div> <h2>It is {date.toLocaleTimeString()}.</h2> </div> ); } ``` The code block will be rendered as an interactive editor. Changes to the code will reflect on the result panel live. function Clock(props) { const [date, setDate] = useState(new Date()); useEffect(() => { const timerID = setInterval(() => tick(), 1000); return function cleanup() { clearInterval(timerID); }; }); function tick() { setDate(new Date()); } return ( <div> <h2>It is {date.toLocaleTimeString()}.</h2> </div> ); }","s":"Interactive code editor","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#interactive-code-editor","p":734},{"i":756,"t":"react-live and imports It is not possible to import components directly from the react-live code editor, you have to define available imports upfront. By default, all React imports are available. If you need more imports available, swizzle the react-live scope: npm Yarn pnpm npm run swizzle @docusaurus/theme-live-codeblock ReactLiveScope -- --eject yarn swizzle @docusaurus/theme-live-codeblock ReactLiveScope --eject pnpm run swizzle @docusaurus/theme-live-codeblock ReactLiveScope --eject src/theme/ReactLiveScope/index.js import React from 'react'; const ButtonExample = (props) => ( <button {...props} style={{ backgroundColor: 'white', color: 'black', border: 'solid red', borderRadius: 20, padding: 10, cursor: 'pointer', ...props.style, }} /> ); // Add react-live imports you need here const ReactLiveScope = { React, ...React, // highlight-next-line ButtonExample, }; export default ReactLiveScope; The ButtonExample component is now available to use: function MyPlayground(props) { return ( <div> <ButtonExample onClick={() => alert('hey!')}>Click me</ButtonExample> </div> ); }","s":"Imports","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#imports","p":734},{"i":758,"t":"The noInline option should be used to avoid errors when your code spans multiple components or variables. ```jsx live noInline const project = 'Docusaurus'; const Greeting = () => <p>Hello {project}!</p>; render(<Greeting />); ``` Unlike an ordinary interactive code block, when using noInline React Live won't wrap your code in an inline function to render it. You will need to explicitly call render() at the end of your code to display the output. const project = \"Docusaurus\"; const Greeting = () => ( <p>Hello {project}!</p> ); render( <Greeting /> );","s":"Imperative Rendering (noInline)","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#imperative-rendering-noinline","p":734},{"i":760,"t":"Code block in Markdown always preserves its content as plain text, meaning you can't do something like: type EditUrlFunction = (params: { // This doesn't turn into a link (for good reason!) version: <a href=\"/docs/versioning\">Version</a>; versionDocsDirPath: string; docPath: string; permalink: string; locale: string; }) => string | undefined; If you want to embed HTML markup such as anchor links or bold type, you can use the <pre> tag, <code> tag, or <CodeBlock> component. <pre> <b>Input: </b>1 2 3 4{'\\n'} <b>Output: </b>\"366300745\"{'\\n'} </pre> Input: 1 2 3 4 Output: \"366300745\" MDX is whitespace insensitive MDX is in line with JSX behavior: line break characters, even when inside <pre>, are turned into spaces. You have to explicitly write the new line character for it to be printed out. 注意 Syntax highlighting only works on plain strings. Docusaurus will not attempt to parse code block content containing JSX children.","s":"Using JSX markup in code blocks","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#using-jsx-markup","p":734},{"i":762,"t":"With MDX, you can easily create interactive components within your documentation, for example, to display code in multiple programming languages and switch between them using a tabs component. Instead of implementing a dedicated component for multi-language support code blocks, we've implemented a general-purpose <Tabs> component in the classic theme so that you can use it for other non-code scenarios as well. The following example is how you can have multi-language code tabs in your docs. Note that the empty lines above and below each language block are intentional. This is a current limitation of MDX: you have to leave empty lines around Markdown syntax for the MDX parser to know that it's Markdown syntax and not JSX. import Tabs from '@theme/Tabs'; import TabItem from '@theme/TabItem'; <Tabs> <TabItem value=\"js\" label=\"JavaScript\"> ```js function helloWorld() { console.log('Hello, world!'); } ``` </TabItem> <TabItem value=\"py\" label=\"Python\"> ```py def hello_world(): print(\"Hello, world!\") ``` </TabItem> <TabItem value=\"java\" label=\"Java\"> ```java class HelloWorld { public static void main(String args[]) { System.out.println(\"Hello, World\"); } } ``` </TabItem> </Tabs> And you will get the following: JavaScript Python Java function helloWorld() { console.log('Hello, world!'); } def hello_world(): print(\"Hello, world!\") class HelloWorld { public static void main(String args[]) { System.out.println(\"Hello, World\"); } } If you have multiple of these multi-language code tabs, and you want to sync the selection across the tab instances, refer to the Syncing tab choices section.","s":"Multi-language support code blocks","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#multi-language-support-code-blocks","p":734},{"i":764,"t":"Displaying CLI commands in both npm and Yarn is a very common need, for example: npm Yarn pnpm npm install @docusaurus/remark-plugin-npm2yarn yarn add @docusaurus/remark-plugin-npm2yarn pnpm add @docusaurus/remark-plugin-npm2yarn Docusaurus provides such a utility out of the box, freeing you from using the Tabs component every time. To enable this feature, first install the @docusaurus/remark-plugin-npm2yarn package as above, and then in docusaurus.config.ts, for the plugins where you need this feature (doc, blog, pages, etc.), register it in the remarkPlugins option. (See docs configuration for more details on configuration format) docusaurus.config.ts export default { // ... presets: [ [ '@docusaurus/preset-classic', { docs: { remarkPlugins: [[require('@docusaurus/remark-plugin-npm2yarn'), {sync: true}]], }, pages: { // highlight-next-line remarkPlugins: [require('@docusaurus/remark-plugin-npm2yarn')], }, blog: { remarkPlugins: [[require('@docusaurus/remark-plugin-npm2yarn'), {converters: ['pnpm']}]], // ... }, }, ], ], }; And then use it by adding the npm2yarn key to the code block: ```bash npm2yarn npm install @docusaurus/remark-plugin-npm2yarn ``` Configuration​ Option Type Default Description sync boolean false Whether to sync the selected converter across all code blocks. converters array 'yarn', 'pnpm' The list of converters to use. The order of the converters is important, as the first converter will be used as the default choice.","s":"Docusaurus npm2yarn remark plugin","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#npm2yarn-remark-plugin","p":734},{"i":766,"t":"Outside of Markdown, you can use the @theme/CodeBlock component to get the same output. import CodeBlock from '@theme/CodeBlock'; export default function MyReactPage() { return ( <div> <CodeBlock language=\"jsx\" title=\"/src/components/HelloCodeTitle.js\" showLineNumbers> {`function HelloCodeTitle(props) { return <h1>Hello, {props.name}</h1>; }`} </CodeBlock> </div> ); } /src/components/HelloCodeTitle.js function HelloCodeTitle(props) { return <h1>Hello, {props.name}</h1>; } The props accepted are language, title and showLineNumbers, in the same way as you write Markdown code blocks. Although discouraged, you can also pass in a metastring prop like metastring='{1-2} title=\"/src/components/HelloCodeTitle.js\" showLineNumbers', which is how Markdown code blocks are handled under the hood. However, we recommend you use comments for highlighting lines. As previously stated, syntax highlighting is only applied when the children is a simple string.","s":"Usage in JSX","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#usage-in-jsx","p":734},{"i":768,"t":"信息 Mermaid is default installed and enabled on this site. Diagrams can be rendered using Mermaid in a code block.","s":"Diagrams with Mermaid","u":"/docs/docusaurus-mdx/mdx-features/diagrams","h":"","p":767},{"i":770,"t":"Add a code block with language mermaid: Example Mermaid diagram ```mermaid graph TD; A-->B; A-->C; B-->D; C-->D; ``` See the Mermaid syntax documentation for more information on the Mermaid syntax.","s":"Usage","u":"/docs/docusaurus-mdx/mdx-features/diagrams","h":"#usage","p":767},{"i":772,"t":"Options in mermaid.options will be passed directly to mermaid.initialize. You can set themes for both light and dark mode. docusaurus.config.ts export default { themeConfig: { mermaid: { theme: {light: 'neutral', dark: 'forest'}, options: { maxTextSize: 50, }, }, }, }; See the Mermaid config documentation and the Mermaid config types for the available config options.","s":"Mermaid Config","u":"/docs/docusaurus-mdx/mdx-features/diagrams","h":"#configuration","p":767},{"i":775,"t":"Docusaurus automatically sets useful page metadata in <html>, <head> and <body> for you. It is possible to add extra metadata (or override existing ones) with the <head> tag in Markdown files: markdown-features-head-metadata.mdx --- id: head-metadata title: Head Metadata --- <head> <html className=\"some-extra-html-class\" /> <body className=\"other-extra-body-class\" /> <title>Head Metadata customized title!</title> <meta charSet=\"utf-8\" /> <meta name=\"twitter:card\" content=\"summary\" /> <link rel=\"canonical\" href=\"https://docusaurus.io/docs/mdx-features/head-metadata\" /> </head> # Head Metadata My text This <head> declaration has been added to the current Markdown doc as a demo. Open your browser DevTools and check how this page's metadata has been affected. 备注 This feature is built on top of the Docusaurus <Head> component. Refer to react-helmet for exhaustive documentation. You don't need this for regular SEO Content plugins (e.g. docs and blog) provide front matter options like description, keywords, and image, which will be automatically applied to both description and og:description, while you would have to manually declare two metadata tags when using the <head> tag.","s":"Customizing head metadata","u":"/docs/docusaurus-mdx/mdx-features/head-metadata","h":"#customizing-head-metadata","p":773},{"i":777,"t":"The Markdown pages' description metadata may be used in more places than the head metadata. For example, the docs plugin's generated category index uses the description metadata for the doc cards. By default, the description is the first content-ful line, with some efforts to convert it to plain text. For example, the following file... # Title Main content... May contain some [links](./file.mdx) or **emphasis**. ...will have the default description \"Main content... May contain some links or emphasis\". However, it's not designed to be fully functional. Where it fails to produce reasonable descriptions, you can explicitly provide one through front matter: --- description: This description will override the default. --- # Title Main content... May contain some [links](./file.mdx) or **emphasis**.","s":"Markdown page description","u":"/docs/docusaurus-mdx/mdx-features/head-metadata","h":"#markdown-page-description","p":773},{"i":779,"t":"Docusaurus uses Markdown as its main content authoring format. Learn Markdown You can learn Markdown in 10 minutes. Docusaurus uses modern tooling to help you create interactive documentation. The MDX compiler transforms Markdown files to React components, and allows you to use JSX in your Markdown content. This enables you to easily interleave React components within your content, and create delightful learning experiences. Use the MDX Playground The MDX playground is your new best friend! It is a very helpful debugging tool that shows how the MDX compiler transforms Markdown to React. Options: select the right format (MDX or CommonMark) and the following plugins Docusaurus uses: remark-gfm, remark-directive, rehype-raw.","s":"Markdown Features","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"","p":778},{"i":781,"t":"Docusaurus compiles both .md and .mdx files to React components using the MDX compiler, but the syntax can be interpreted differently depending on your settings. The MDX compiler supports 2 formats: The MDX format: a powerful parser allowing the usage of JSX The CommonMark format: a standard-compliant Markdown parser that does not allow the usage of JSX By default, Docusaurus v3 uses the MDX format for all files (including .md files) for historical reasons. We changed this by setting siteConfig.markdown.format: 'detect'. what is siteConfig.markdown.format: 'detect' The appropriate format will be selected automatically, based on file extensions: .md files will use the CommonMark format .mdx files will use the MDX format","s":"MDX vs. CommonMark","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#mdx-vs-commonmark","p":778},{"i":783,"t":"Markdown is a syntax that enables you to write formatted content in a readable syntax. ### My Doc Section Hello world message with some **bold** text, some _italic_ text, and a [link](/) ![img alt](/img/docusaurus.png) My Doc Section Hello world message with some bold text, some italic text and a link Markdown is declarative Some may assume a 1-1 correlation between Markdown and HTML, e.g., ![Preview](/img/docusaurus.png) will always become <img src=\"/img/docusaurus.png\" alt=\"Preview\" />, as-is. However, that is not the case. The Markdown syntax ![message](url) only declaratively tells Docusaurus that an image needs to be inserted here, but we may do other things like transforming a file path to URL path, so the generated markup may differ from the output of other Markdown renderers, or a naïve hand-transcription to the equivalent JSX/HTML code. In general, you should only assume the semantics of the markup (``` fences become code blocks; > becomes quotes, etc.), but not the actual compiled output.","s":"Standard features","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#standard-features","p":778},{"i":785,"t":"Hello world message with some bold text, some italic text and a link","s":"My Doc Section","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"","p":778},{"i":787,"t":"Front matter is used to add metadata to your Markdown file. All content plugins have their own front matter schema, and use the front matter to enrich the default metadata inferred from the content or other configuration. Front matter is provided at the very top of the file, enclosed by three dashes ---. The content is parsed as YAML. --- title: My Doc Title more_data: - Can be provided - as: objects or: arrays --- 信息 The API documentation of each official plugin lists the supported attributes: Docs front matter Blog front matter Pages front matter","s":"Front matter","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#front-matter","p":778},{"i":789,"t":"Markdown quotes are beautifully styled: > Easy to maintain open source documentation websites. > > — Docusaurus Easy to maintain open source documentation websites. — Docusaurus","s":"Quotes","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#quotes","p":778},{"i":791,"t":"Markdown can embed HTML elements, and details HTML elements are beautifully styled: ### Details element example <details> <summary>Toggle me!</summary> <div> <div>This is the detailed content</div> <br/> <details> <summary> Nested toggle! Some surprise inside... </summary> <div>😲😲😲😲😲</div> </details> </div> </details> Details element example Toggle me! This is the detailed content Nested toggle! Some surprise inside... 😲😲😲😲😲","s":"Details","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#details","p":778},{"i":793,"t":"Toggle me! This is the detailed content Nested toggle! Some surprise inside... 😲😲😲😲😲","s":"Details element example","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"","p":778},{"i":795,"t":"There are two ways of adding a link to another page: through a URL path and a file path. - [URL path to another document](./installation) - [file path to another document](./installation.mdx) URL paths are unprocessed by Docusaurus, and you can see them as directly rendering to <a href=\"./installation\">, i.e. it will be resolved according to the page's URL location, rather than its file-system location. If you want to reference another Markdown file included by the same plugin, you could use the relative path of the document you want to link to. Docusaurus' Markdown loader will convert the file path to the target file's URL path (and hence remove the .md extension). For example, if you are in docs/folder/doc1.md and you want to reference docs/folder/doc2.md, docs/folder/subfolder/doc3.md and docs/otherFolder/doc4.md: docs/folder/doc1.md I am referencing a [document](doc2.mdx). Reference to another [document in a subfolder](subfolder/doc3.mdx). [Relative document](../otherFolder/doc4.mdx) referencing works as well. Relative file paths are resolved against the current file's directory. Absolute file paths, on the other hand, are resolved relative to the content root, usually docs/, blog/, or localized ones like i18n/zh-Hans/plugin-content-docs/current. Absolute file paths can also be relative to the site directory. However, beware that links that begin with /docs/ or /blog/ are not portable as you would need to manually update them if you create new doc versions or localize them. You can write [links](/otherFolder/doc4.mdx) relative to the content root (`/docs/`). You can also write [links](/docs/otherFolder/doc4.mdx) relative to the site directory, but it's not recommended. Using relative file paths (with .md extensions) instead of relative URL links provides the following benefits: Links will keep working on the GitHub interface and many Markdown editors You can customize the files' slugs without having to update all the links Moving files around the folders can be tracked by your editor, and some editors may automatically update file links A versioned doc will link to another doc of the exact same version Relative URL links are very likely to break if you update the trailingSlash config 注意 Markdown file references only work when the source and target files are processed by the same plugin instance. This is a technical limitation of our Markdown processing architecture and will be fixed in the future. If you are linking files between plugins (e.g. linking to a doc page from a blog post), you have to use URL links.","s":"Markdown links","u":"/docs/docusaurus-mdx/mdx-features/links","h":"","p":794},{"i":797,"t":"信息 Math render KaTeX is default installed and enabled on this site. Mathematical equations can be rendered using KaTeX.","s":"Math Equations","u":"/docs/docusaurus-mdx/mdx-features/math-equations","h":"","p":796},{"i":799,"t":"Please read KaTeX documentation for more details.","s":"Usage","u":"/docs/docusaurus-mdx/mdx-features/math-equations","h":"#usage","p":796},{"i":801,"t":"Write inline math equations by wrapping LaTeX equations between $: Let $f\\colon[a,b]\\to\\R$ be Riemann integrable. Let $F\\colon[a,b]\\to\\R$ be $F(x)=\\int_{a}^{x} f(t)\\,dt$. Then $F$ is continuous, and at all $x$ such that $f$ is continuous at $x$, $F$ is differentiable at $x$ with $F'(x)=f(x)$. Let f ⁣:[a,b]→Rf\\colon[a,b] \\to \\Rf:[a,b]→R be Riemann integrable. Let F ⁣:[a,b]→RF\\colon[a,b]\\to\\RF:[a,b]→R be F(x)=∫axf(t) dtF(x)= \\int_{a}^{x} f(t)\\,dtF(x)=∫ax​f(t)dt. Then FFF is continuous, and at all xxx such that fff is continuous at xxx, FFF is differentiable at xxx with F′(x)=f(x)F'(x)=f(x)F′(x)=f(x).","s":"Inline","u":"/docs/docusaurus-mdx/mdx-features/math-equations","h":"#inline","p":796},{"i":803,"t":"For equation block or display mode, use line breaks and $$: $$ I = \\int_0^{2\\pi} \\sin(x)\\,dx $$ I=∫02πsin⁡(x) dxI = \\int_0^{2\\pi} \\sin(x)\\,dxI=∫02π​sin(x)dx","s":"Blocks","u":"/docs/docusaurus-mdx/mdx-features/math-equations","h":"#blocks","p":796},{"i":805,"t":"Sometimes, you may want to extend or tweak your Markdown syntax. For example: How do I embed youtube videos using the image syntax (![](https://youtu.be/yKNxeF4KMsY))? How do I style links that are on their own lines differently, e.g., as a social card? How do I make every page start with a copyright notice? And the answer is: create an MDX plugin! MDX has a built-in plugin system that can be used to customize how the Markdown files will be parsed and transformed to JSX. There are three typical use-cases of MDX plugins: Using existing remark plugins or rehype plugins; Creating remark/rehype plugins to transform the elements generated by existing MDX syntax; Creating remark/rehype plugins to introduce new syntaxes to MDX. If you play with the MDX playground, you would notice that the MDX transpilation has two intermediate steps: Markdown AST (MDAST), and Hypertext AST (HAST), before arriving at the final JSX output. MDX plugins also come in two forms: Remark: processes the Markdown AST. Rehype: processes the Hypertext AST. 提示 Use plugins to introduce shorter syntax for the most commonly used JSX elements in your project. The admonition syntax that we offer is also generated by a Remark plugin, and you could do the same for your own use case.","s":"MDX Plugins","u":"/docs/docusaurus-mdx/mdx-features/plugins","h":"","p":804},{"i":807,"t":"Docusaurus injects some default Remark plugins during Markdown processing. These plugins would: Generate the table of contents; Add anchor links to each heading; Transform images and links to require() calls. … These are all typical use-cases of Remark plugins, which can also be a source of inspiration if you want to implement your own plugin.","s":"Default plugins","u":"/docs/docusaurus-mdx/mdx-features/plugins","h":"#default-plugins","p":804},{"i":809,"t":"An MDX plugin is usually an npm package, so you install them like other npm packages using npm. Take the math plugins as an example. npm Yarn pnpm npm install --save remark-math@6 rehype-katex@7 yarn add remark-math@6 rehype-katex@7 pnpm add remark-math@6 rehype-katex@7 How are remark-math and rehype-katex different? In case you are wondering how Remark and Rehype are different, here is a good example. remark-math operates on the Markdown AST, where it sees text like $...$, and all it does is transform that to the JSX <span class=\"math math-inline\">...</span> without doing too much with the content. This decouples the extraction of math formulae from their rendering, which means you can swap KaTeX\\KaTeXKATE​X out with other math renderers, like MathJax (with rehype-mathjax), just by replacing the Rehype plugin. Next, the rehype-katex operates on the Hypertext AST where everything has been converted to HTML-like tags already. It traverses all the elements with math class and uses KaTeX\\KaTeXKATE​X to parse and render the content to actual HTML. 注意 Many official Remark/Rehype plugins are ES Modules only, a JavaScript module system, which Docusaurus supports. We recommend using an ES Modules config file to make it easier to import such packages. Next, import your plugins and add them to the plugin options through plugin or preset config in docusaurus.config.ts: docusaurus.config.ts import remarkMath from 'remark-math'; import rehypeKatex from 'rehype-katex'; export default { presets: [ [ '@docusaurus/preset-classic', { docs: { path: 'docs', remarkPlugins: [remarkMath], rehypePlugins: [rehypeKatex], }, }, ], ], };","s":"Installing plugins","u":"/docs/docusaurus-mdx/mdx-features/plugins","h":"#installing-plugins","p":804},{"i":811,"t":"Docusaurus has built-in support for MDX, which allows you to write JSX within your Markdown files and render them as React components. Check out the MDX docs to see what fancy stuff you can do with MDX. Debugging MDX The MDX format is quite strict, and you may get compilation errors. Use the MDX playground to debug them and make sure your syntax is valid.","s":"MDX and React","u":"/docs/docusaurus-mdx/mdx-features/react","h":"","p":810},{"i":813,"t":"To define any custom component within an MDX file, you have to export it: only paragraphs that start with export will be parsed as components instead of prose. export const Highlight = ({children, color}) => ( <span style={{ backgroundColor: color, borderRadius: '2px', color: '#fff', padding: '0.2rem', }}> {children} </span> ); <Highlight color=\"#25c2a0\">Docusaurus green</Highlight> and <Highlight color=\"#1877F2\">Facebook blue</Highlight> are my favorite colors. I can write **Markdown** alongside my _JSX_! Notice how it renders both the markup from your React component and the Markdown syntax: Docusaurus green and Facebook blue are my favorite colors. I can write Markdown alongside my JSX! MDX is JSX Since all doc files are parsed using MDX, anything that looks like HTML is actually JSX. Therefore, if you need to inline-style a component, follow JSX flavor and provide style objects. /* Instead of this: */ <span style=\"background-color: red\">Foo</span> /* Use this: */ <span style={{backgroundColor: 'red'}}>Foo</span>","s":"Exporting components","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#exporting-components","p":810},{"i":815,"t":"You can also import your own components defined in other files or third-party components installed via npm. <!-- Docusaurus theme component --> import TOCInline from '@theme/TOCInline'; <!-- External component --> import Button from '@mui/material/Button'; <!-- Custom component --> import BrowserWindow from '@site/src/components/BrowserWindow'; 提示 The @site alias points to your website's directory, usually where the docusaurus.config.ts file is. Using an alias instead of relative paths ('../../src/components/BrowserWindow') saves you from updating import paths when moving files around, or when versioning docs and translating. While declaring components within Markdown is very convenient for simple cases, it becomes hard to maintain because of limited editor support, risks of parsing errors, and low reusability. Use a separate .js file when your component involves complex JS logic: src/components/Highlight.js import React from 'react'; export default function Highlight({children, color}) { return ( <span style={{ backgroundColor: color, borderRadius: '2px', color: '#fff', padding: '0.2rem', }}> {children} </span> ); } markdown-file.mdx import Highlight from '@site/src/components/Highlight'; <Highlight color=\"#25c2a0\">Docusaurus green</Highlight> 提示 If you use the same component across a lot of files, you don't need to import it everywhere—consider adding it to the global scope. See below","s":"Importing components","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#importing-components","p":810},{"i":817,"t":"Apart from importing a component and exporting a component, a third way to use a component in MDX is to register it to the global scope, which will make it automatically available in every MDX file, without any import statements. For example, given this MDX file: - a - list! And some <Highlight>custom markup</Highlight>... It will be compiled to a React component containing ul, li, p, and Highlight elements. Highlight is not a native html element: you need to provide your own React component implementation for it. In Docusaurus, the MDX component scope is provided by the @theme/MDXComponents file. It's not a React component, per se, unlike most other exports under the @theme/ alias: it is a record from tag names like Highlight to their React component implementations. If you swizzle this component, you will find all tags that have been implemented, and you can further customize our implementation by swizzling the respective sub-component, like @theme/MDXComponents/Code (which is used to render Markdown code blocks). If you want to register extra tag names (like the <Highlight> tag above), you should consider wrapping @theme/MDXComponents by swizzling, so you don't have to maintain all the existing mappings. Since the swizzle CLI doesn't allow wrapping non-component files yet, you should manually create the wrapper: src/theme/MDXComponents.js import React from 'react'; // Import the original mapper import MDXComponents from '@theme-original/MDXComponents'; // highlight-next-line import Highlight from '@site/src/components/Highlight'; export default { // Re-use the default mapping ...MDXComponents, // Map the \"<Highlight>\" tag to our Highlight component // `Highlight` will receive all props that were passed to `<Highlight>` in MDX // highlight-next-line Highlight, }; And now, you can freely use <Highlight> in every page, without writing the import statement: I can conveniently use <Highlight color=\"#25c2a0\">Docusaurus green</Highlight> everywhere! I can conveniently use Docusaurus green everywhere! 注意 We use upper-case tag names like Highlight on purpose. From MDX v3+ onward (Docusaurus v3+), lower-case tag names are always rendered as native html elements, and will not use any component mapping you provide. 注意 This feature is powered by an MDXProvider. If you are importing Markdown in a React page, you have to supply this provider yourself through the MDXContent theme component. src/pages/index.js import React from 'react'; import FeatureDisplay from './_featureDisplay.mdx'; // highlight-next-line import MDXContent from '@theme/MDXContent'; export default function LandingPage() { return ( <div> <MDXContent> <FeatureDisplay /> </MDXContent> </div> ); } If you don't wrap your imported MDX with MDXContent, the global scope will not be available.","s":"MDX component scope","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#mdx-component-scope","p":810},{"i":819,"t":"Docusaurus v3 is using MDX v3. The MDX syntax is mostly compatible with CommonMark, but is much stricter because your .mdx files can use JSX and are compiled into real React components (check the playground). Some valid CommonMark features won't work with MDX (more info), notably: Indented code blocks: use triple backticks instead Autolinks (<http://localhost:3000>): use regular link syntax instead ([http://localhost:3000](http://localhost:3000)) HTML syntax (<p style=\"color: red;\">): use JSX instead (<p style={{color: 'red'}}>) Unescaped { and <: escape them with \\ instead (\\{ and \\<) Experimental CommonMark support Docusaurus v3 makes it possible to opt-in for a less strict, standard CommonMark support with the following options: The format: md front matter The .md file extension combined with the siteConfig.markdown.format: \"detect\" configuration This feature is experimental and currently has a few limitations.","s":"Markdown and JSX interoperability","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#markdown-and-jsx-interoperability","p":810},{"i":821,"t":"You can not only import a file containing a component definition, but also import any code file as raw text, and then insert it in a code block, thanks to Webpack raw-loader. In order to use raw-loader, you first need to install it in your project: npm Yarn pnpm npm install --save raw-loader yarn add raw-loader pnpm add raw-loader Now you can import code snippets from another file as it is: myMarkdownFile.mdx import CodeBlock from '@theme/CodeBlock'; import MyComponentSource from '!!raw-loader!./_myReactComponent'; <CodeBlock language=\"jsx\">{MyComponentSource}</CodeBlock> /** * Copyright (c) Facebook, Inc. and its affiliates. * * This source code is licensed under the MIT license found in the * LICENSE file in the root directory of this source tree. */ import React, {useState} from 'react'; export default function MyComponent() { const [bool, setBool] = useState(false); return ( <div> <p>MyComponent rendered !</p> <p>bool={bool ? 'true' : 'false'}</p> <p> <button onClick={() => setBool((b) => !b)}>toggle bool</button> </p> </div> ); } See using code blocks in JSX for more details of the <CodeBlock> component. 备注 You have to use <CodeBlock> rather than the Markdown triple-backtick ```, because the latter will ship out any of its content as-is, but you want to interpolate the imported text here. 注意 This feature is experimental and might be subject to breaking API changes in the future.","s":"Importing code snippets","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#importing-code-snippets","p":810},{"i":823,"t":"You can use Markdown files as components and import them elsewhere, either in Markdown files or in React pages. By convention, using the _ filename prefix will not create any doc page and means the Markdown file is a \"partial\", to be imported by other files. _markdown-partial-example.mdx <span>Hello {props.name}</span> This is text some content from `_markdown-partial-example.mdx`. someOtherDoc.mdx import PartialExample from './_markdown-partial-example.mdx'; <PartialExample name=\"Sebastien\" /> Hello Sebastien This is text some content from _markdown-partial-example.md. This way, you can reuse content among multiple pages and avoid duplicating materials. 注意 Currently, the table of contents does not contain the imported Markdown headings. This is a technical limitation that we are trying to solve (issue).","s":"Importing Markdown","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#importing-markdown","p":810},{"i":825,"t":"Within the MDX page, the following variables are available as globals: frontMatter: the front matter as a record of string keys and values; toc: the table of contents, as a tree of headings. See also Inline TOC for a more concrete use-case. contentTitle: the Markdown title, which is the first h1 heading in the Markdown text. It's undefined if there isn't one (e.g. title specified in the front matter). import TOCInline from '@theme/TOCInline'; import CodeBlock from '@theme/CodeBlock'; The table of contents for this page, serialized: <CodeBlock className=\"language-json\">{JSON.stringify(toc, null, 2)}</CodeBlock> The front matter of this page: <ul> {Object.entries(frontMatter).map(([key, value]) => <li key={key}><b>{key}</b>: {value}</li>)} </ul> <p>The title of this page is: <b>{contentTitle}</b></p> The table of contents for this page, serialized: [ { \"value\": \"Exporting components\", \"id\": \"exporting-components\", \"level\": 3 }, { \"value\": \"Importing components\", \"id\": \"importing-components\", \"level\": 3 }, { \"value\": \"MDX component scope\", \"id\": \"mdx-component-scope\", \"level\": 3 }, { \"value\": \"Markdown and JSX interoperability\", \"id\": \"markdown-and-jsx-interoperability\", \"level\": 3 }, { \"value\": \"Importing code snippets\", \"id\": \"importing-code-snippets\", \"level\": 2 }, { \"value\": \"Importing Markdown\", \"id\": \"importing-markdown\", \"level\": 2 }, { \"value\": \"Available exports\", \"id\": \"available-exports\", \"level\": 2 } ] The front matter of this page: description: Using the power of React in Docusaurus Markdown documents, thanks to MDX The title of this page is: MDX and React","s":"Available exports","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#available-exports","p":810},{"i":827,"t":"信息 Tag <Tabs> and <TabItems> are default installed and enabled. Docusaurus provides the <Tabs> component that you can use in Markdown thanks to MDX: <Tabs> <TabItem value=\"apple\" label=\"Apple\" default> This is an apple 🍎 </TabItem> <TabItem value=\"orange\" label=\"Orange\"> This is an orange 🍊 </TabItem> <TabItem value=\"banana\" label=\"Banana\"> This is a banana 🍌 </TabItem> </Tabs> Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌 It is also possible to provide values and defaultValue props to Tabs: <Tabs defaultValue=\"apple\" values={[ {label: 'Apple', value: 'apple'}, {label: 'Orange', value: 'orange'}, {label: 'Banana', value: 'banana'}, ]}> <TabItem value=\"apple\">This is an apple 🍎</TabItem> <TabItem value=\"orange\">This is an orange 🍊</TabItem> <TabItem value=\"banana\">This is a banana 🍌</TabItem> </Tabs> Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌 Tabs props take precedence over the TabItem props: <Tabs defaultValue=\"apple\" values={[ {label: 'Apple 1', value: 'apple'}, {label: 'Orange 1', value: 'orange'}, {label: 'Banana 1', value: 'banana'}, ]}> <TabItem value=\"apple\" label=\"Apple 2\"> This is an apple 🍎 </TabItem> <TabItem value=\"orange\" label=\"Orange 2\"> This is an orange 🍊 </TabItem> <TabItem value=\"banana\" label=\"Banana 2\" default> This is a banana 🍌 </TabItem> </Tabs> Apple 1 Orange 1 Banana 1 This is an apple 🍎 This is an orange 🍊 This is a banana 🍌 提示 By default, all tabs are rendered eagerly during the build process, and search engines can index hidden tabs. It is possible to only render the default tab with <Tabs lazy />.","s":"Tabs and TabItem","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"","p":826},{"i":829,"t":"The first tab is displayed by default, and to override this behavior, you can specify a default tab by adding default to one of the tab items. You can also set the defaultValue prop of the Tabs component to the label value of your choice. For example, in the example above, either setting default for the value=\"apple\" tab or setting defaultValue=\"apple\" for the tabs forces the \"Apple\" tab to be open by default. Docusaurus will throw an error if a defaultValue is provided for the Tabs but it refers to a non-existing value. If you want none of the tabs to be shown by default, use defaultValue={null}.","s":"Displaying a default tab","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#displaying-a-default-tab","p":826},{"i":831,"t":"You may want choices of the same kind of tabs to sync with each other. For example, you might want to provide different instructions for users on Windows vs users on macOS, and you want to change all OS-specific instructions tabs in one click. To achieve that, you can give all related tabs the same groupId prop. Note that doing this will persist the choice in localStorage and all <Tab> instances with the same groupId will update automatically when the value of one of them is changed. Note that group IDs are globally namespaced. // highlight-next-line <Tabs groupId=\"operating-systems\"> <TabItem value=\"win\" label=\"Windows\">Use Ctrl + C to copy.</TabItem> <TabItem value=\"mac\" label=\"macOS\">Use Command + C to copy.</TabItem> </Tabs> // highlight-next-line <Tabs groupId=\"operating-systems\"> <TabItem value=\"win\" label=\"Windows\">Use Ctrl + V to paste.</TabItem> <TabItem value=\"mac\" label=\"macOS\">Use Command + V to paste.</TabItem> </Tabs> Windows macOS Use Ctrl + C to copy. Use Command + C to copy. Windows macOS Use Ctrl + V to paste. Use Command + V to paste. For all tab groups that have the same groupId, the possible values do not need to be the same. If one tab group is chosen a value that does not exist in another tab group with the same groupId, the tab group with the missing value won't change its tab. You can see that from the following example. Try to select Linux, and the above tab groups don't change. <Tabs groupId=\"operating-systems\"> <TabItem value=\"win\" label=\"Windows\"> I am Windows. </TabItem> <TabItem value=\"mac\" label=\"macOS\"> I am macOS. </TabItem> <TabItem value=\"linux\" label=\"Linux\"> I am Linux. </TabItem> </Tabs> Windows macOS Linux I am Windows. I am macOS. I am Linux. Tab choices with different group IDs will not interfere with each other: // highlight-next-line <Tabs groupId=\"operating-systems\"> <TabItem value=\"win\" label=\"Windows\">Windows in windows.</TabItem> <TabItem value=\"mac\" label=\"macOS\">macOS is macOS.</TabItem> </Tabs> // highlight-next-line <Tabs groupId=\"non-mac-operating-systems\"> <TabItem value=\"win\" label=\"Windows\">Windows is windows.</TabItem> <TabItem value=\"unix\" label=\"Unix\">Unix is unix.</TabItem> </Tabs> Windows macOS Windows in windows. macOS is macOS. Windows Unix Windows is windows. Unix is unix.","s":"Syncing tab choices","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#syncing-tab-choices","p":826},{"i":833,"t":"You might want to customize the appearance of a certain set of tabs. You can pass the string in className prop, and the specified CSS class will be added to the Tabs component: // highlight-next-line <Tabs className=\"unique-tabs\"> <TabItem value=\"Apple\">This is an apple 🍎</TabItem> <TabItem value=\"Orange\">This is an orange 🍊</TabItem> <TabItem value=\"Banana\">This is a banana 🍌</TabItem> </Tabs> Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌","s":"Customizing tabs","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#customizing-tabs","p":826},{"i":835,"t":"You can also customize each tab heading independently by using the attributes field. The extra props can be passed to the headings either through the values prop in Tabs, or props of each TabItem—in the same way as you declare label. some-doc.mdx import styles from './markdown-features-tabs-styles.module.css'; <Tabs> <TabItem value=\"apple\" label=\"Apple\" attributes={{className: styles.red}}> This is an apple 🍎 </TabItem> <TabItem value=\"orange\" label=\"Orange\" attributes={{className: styles.orange}}> This is an orange 🍊 </TabItem> <TabItem value=\"banana\" label=\"Banana\" attributes={{className: styles.yellow}}> This is a banana 🍌 </TabItem> </Tabs> styles.module.css .red { color: red; } .red[aria-selected='true'] { border-bottom-color: red; } .orange { color: orange; } .orange[aria-selected='true'] { border-bottom-color: orange; } .yellow { color: yellow; } .yellow[aria-selected='true'] { border-bottom-color: yellow; } Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌 提示 className would be merged with other default class names. You may also use a custom data-value field ({'data-value': 'apple'}) paired with CSS attribute selectors: styles.module.css li[role='tab'][data-value='apple'] { color: red; }","s":"Customizing tab headings","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#customizing-tab-headings","p":826},{"i":837,"t":"It is possible to persist the selected tab into the url search parameters. This enables you to share a link to a page which pre-selects the tab - linking from your Android app to documentation with the Android tabs pre-selected. This feature does not provide an anchor link - the browser will not scroll to the tab. Use the queryString prop to enable this feature and define the search param name to use. // highlight-next-line <Tabs queryString=\"current-os\"> <TabItem value=\"android\" label=\"Android\"> Android </TabItem> <TabItem value=\"ios\" label=\"iOS\"> iOS </TabItem> </Tabs> Android iOS Android iOS As soon as a tab is clicked, a search parameter is added at the end of the url: ?current-os=android or ?current-os=ios. 提示 queryString can be used together with groupId. For convenience, when the queryString prop is true, the groupId value will be used as a fallback. // highlight-next-line <Tabs groupId=\"current-os\" queryString> <TabItem value=\"android\" label=\"Android\"> Android </TabItem> <TabItem value=\"ios\" label=\"iOS\"> iOS </TabItem> </Tabs> Android iOS Android iOS When the page loads, the tab query string choice will be restored in priority over the groupId choice (using localStorage).","s":"Query string","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#query-string","p":826},{"i":840,"t":"You can use regular Markdown headings. ## Level 2 title ### Level 3 title #### Level 4 title Each Markdown heading will appear as a table of contents entry.","s":"Markdown headings","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#markdown-headings","p":838},{"i":842,"t":"Each heading has an ID that can be automatically generated or explicitly specified. Heading IDs allow you to link to a specific document heading in Markdown or JSX: [link](#heading-id) <Link to=\"#heading-id\">link</Link> By default, Docusaurus will generate heading IDs for you, based on the heading text. For example, ### Hello World will have ID hello-world. Generated IDs have some limitations: The ID might not look good You might want to change or translate the text without updating the existing ID A special Markdown syntax lets you set an explicit heading id: ### Hello World {#my-explicit-id} 提示 Use the write-heading-ids CLI command to add explicit IDs to all your Markdown documents. Avoid colliding IDs Generated heading IDs will be guaranteed to be unique on each page, but if you use custom IDs, make sure each one appears exactly once on each page, or there will be two DOM elements with the same ID, which is invalid HTML semantics, and will lead to one heading being unlinkable.","s":"Heading IDs","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#heading-ids","p":838},{"i":844,"t":"Each Markdown document displays a table of contents on the top-right corner. By default, this table only shows h2 and h3 headings, which should be sufficient for an overview of the page structure. In case you need to change the range of headings displayed, you can customize the minimum and maximum heading level — either per page or globally. To set the heading level for a particular page, use the toc_min_heading_level and toc_max_heading_level front matter. myDoc.md --- # Display h2 to h5 headings toc_min_heading_level: 2 toc_max_heading_level: 5 --- To set the heading level for all pages, use the themeConfig.tableOfContents option. docusaurus.config.ts export default { themeConfig: { tableOfContents: { minHeadingLevel: 2, maxHeadingLevel: 5, }, }, }; If you've set the options globally, you can still override them locally via front matter. 备注 The themeConfig option would apply to all TOC on the site, including inline TOC, but front matter options only affect the top-right TOC. You need to use the minHeadingLevel and maxHeadingLevel props to customize each <TOCInline /> component.","s":"Table of contents heading level","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#table-of-contents-heading-level","p":838},{"i":846,"t":"It is also possible to display an inline table of contents directly inside a Markdown document, thanks to MDX. The toc variable is available in any MDX document and contains all the headings of an MDX document. By default, only h2 and h3 headings are displayed in the TOC. You can change which heading levels are visible by setting minHeadingLevel or maxHeadingLevel for individual TOCInline components. import TOCInline from '@theme/TOCInline'; <TOCInline toc={toc} /> Markdown headings Heading IDs Table of contents heading level Inline table of contents Customizing table of contents generation Example Section 1 Example Subsection 1 a Example Subsection 1 b Example Subsection 1 c Example Section 2 Example Subsection 2 a Example Subsection 2 b Example Subsection 2 c Example Section 3 Example Subsection 3 a Example Subsection 3 b Example Subsection 3 c The toc global is just a list of heading items: declare const toc: { value: string; id: string; level: number; }[]; Note that the toc global is a flat array, so you can easily cut out unwanted nodes or insert extra nodes, and create a new TOC tree. import TOCInline from '@theme/TOCInline'; <TOCInline // Only show h2 and h4 headings toc={toc.filter((node) => node.level === 2 || node.level === 4)} minHeadingLevel={2} // Show h4 headings in addition to the default h2 and h3 headings maxHeadingLevel={4} /> Markdown headings Table of contents heading level Inline table of contents Customizing table of contents generation Example Section 1 Example subsubsection 1 a I Example subsubsection 1 a II Example subsubsection 1 a III Example subsubsection 1 b I Example subsubsection 1 b II Example subsubsection 1 b III Example subsubsection 1 c I Example subsubsection 1 c II Example subsubsection 1 c III Example Section 2 Example subsubsection 2 a I Example subsubsection 2 a II Example subsubsection 2 a III Example subsubsection 2 b I Example subsubsection 2 b II Example subsubsection 2 b III Example subsubsection 2 c I Example subsubsection 2 c II Example subsubsection 2 c III Example Section 3 Example subsubsection 3 a I Example subsubsection 3 a II Example subsubsection 3 a III Example subsubsection 3 b I Example subsubsection 3 b II Example subsubsection 3 b III Example subsubsection 3 c I Example subsubsection 3 c II Example subsubsection 3 c III","s":"Inline table of contents","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#inline-table-of-contents","p":838},{"i":848,"t":"The table-of-contents is generated by parsing the Markdown source with a Remark plugin. There are known edge-cases where it generates false-positives and false-negatives. Markdown headings within hideable areas will still show up in the TOC. For example, headings within Tabs and details will not be excluded. Non-Markdown headings will not show up in the TOC. This can be used to your advantage to tackle the aforementioned issue. <details> <summary>Some details containing headings</summary> <h2 id=\"#heading-id\">I'm a heading that will not show up in the TOC</h2> Some content... </details> The ability to ergonomically insert extra headings or ignore certain headings is a work-in-progress. If this feature is important to you, please report your use-case in this issue. 注意 Below is just some dummy content to have more table of contents items available on the current page.","s":"Customizing table of contents generation","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#customizing-table-of-contents-generation","p":838},{"i":850,"t":"Lorem ipsum","s":"Example Section 1","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-section-1","p":838},{"i":852,"t":"Lorem ipsum Example subsubsection 1 a I​ Example subsubsection 1 a II​ Example subsubsection 1 a III​","s":"Example Subsection 1 a","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-1-a","p":838},{"i":854,"t":"Lorem ipsum Example subsubsection 1 b I​ Example subsubsection 1 b II​ Example subsubsection 1 b III​","s":"Example Subsection 1 b","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-1-b","p":838},{"i":856,"t":"Lorem ipsum Example subsubsection 1 c I​ Example subsubsection 1 c II​ Example subsubsection 1 c III​","s":"Example Subsection 1 c","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-1-c","p":838},{"i":858,"t":"Lorem ipsum","s":"Example Section 2","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-section-2","p":838},{"i":860,"t":"Lorem ipsum Example subsubsection 2 a I​ Example subsubsection 2 a II​ Example subsubsection 2 a III​","s":"Example Subsection 2 a","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-2-a","p":838},{"i":862,"t":"Lorem ipsum Example subsubsection 2 b I​ Example subsubsection 2 b II​ Example subsubsection 2 b III​","s":"Example Subsection 2 b","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-2-b","p":838},{"i":864,"t":"Lorem ipsum Example subsubsection 2 c I​ Example subsubsection 2 c II​ Example subsubsection 2 c III​","s":"Example Subsection 2 c","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-2-c","p":838},{"i":866,"t":"Lorem ipsum","s":"Example Section 3","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-section-3","p":838},{"i":868,"t":"Lorem ipsum Example subsubsection 3 a I​ Example subsubsection 3 a II​ Example subsubsection 3 a III​","s":"Example Subsection 3 a","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-3-a","p":838},{"i":870,"t":"Lorem ipsum Example subsubsection 3 b I​ Example subsubsection 3 b II​ Example subsubsection 3 b III​","s":"Example Subsection 3 b","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-3-b","p":838},{"i":872,"t":"Lorem ipsum Example subsubsection 3 c I​ Example subsubsection 3 c II​ Example subsubsection 3 c III​","s":"Example Subsection 3 c","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-3-c","p":838},{"i":874,"t":"Provides the Blog feature and is the default blog plugin for Docusaurus. some features production only The feed feature works by extracting the build output, and is only active in production.","s":"📦 plugin-content-blog","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"","p":873},{"i":876,"t":"npm Yarn pnpm npm install --save @docusaurus/plugin-content-blog yarn add @docusaurus/plugin-content-blog pnpm add @docusaurus/plugin-content-blog 提示 If you use the preset @docusaurus/preset-classic, you don't need to install this plugin as a dependency. You can configure this plugin through the preset options.","s":"Installation","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#installation","p":873},{"i":878,"t":"Accepted fields: Name Type Default Description path string 'blog' Path to the blog content directory on the file system, relative to site dir. editUrl string | EditUrlFn undefined Base URL to edit your site. The final URL is computed by editUrl + relativePostPath. Using a function allows more nuanced control for each file. Omitting this variable entirely will disable edit links. editLocalizedFiles boolean false The edit URL will target the localized file, instead of the original unlocalized file. Ignored when editUrl is a function. blogTitle string 'Blog' Blog page title for better SEO. blogDescription string 'Blog' Blog page meta description for better SEO. blogSidebarCount number | 'ALL' 5 Number of blog post elements to show in the blog sidebar. 'ALL' to show all blog posts; 0 to disable. blogSidebarTitle string 'Recent posts' Title of the blog sidebar. routeBasePath string 'blog' URL route for the blog section of your site. DO NOT include a trailing slash. Use / to put the blog at root path. tagsBasePath string 'tags' URL route for the tags section of your blog. Will be appended to routeBasePath. DO NOT include a trailing slash. archiveBasePath string | null 'archive' URL route for the archive section of your blog. Will be appended to routeBasePath. DO NOT include a trailing slash. Use null to disable generation of archive. include string[] ['**/*.{md,mdx}'] Array of glob patterns matching Markdown files to be built, relative to the content path. exclude string[] See example configuration Array of glob patterns matching Markdown files to be excluded. Serves as refinement based on the include option. postsPerPage number | 'ALL' 10 Number of posts to show per page in the listing page. Use 'ALL' to display all posts on one listing page. blogListComponent string '@theme/BlogListPage' Root component of the blog listing page. blogPostComponent string '@theme/BlogPostPage' Root component of each blog post page. blogTagsListComponent string '@theme/BlogTagsListPage' Root component of the tags list page. blogTagsPostsComponent string '@theme/BlogTagsPostsPage' Root component of the \"posts containing tag\" page. blogArchiveComponent string '@theme/BlogArchivePage' Root component of the blog archive page. remarkPlugins any[] [] Remark plugins passed to MDX. rehypePlugins any[] [] Rehype plugins passed to MDX. beforeDefaultRemarkPlugins any[] [] Custom Remark plugins passed to MDX before the default Docusaurus Remark plugins. beforeDefaultRehypePlugins any[] [] Custom Rehype plugins passed to MDX before the default Docusaurus Rehype plugins. truncateMarker RegExp /<!--\\s*truncate\\s*-->/ | \\{\\/\\*\\s*truncate\\s*\\*\\/\\}/ Truncate marker marking where the summary ends. showReadingTime boolean true Show estimated reading time for the blog post. readingTime ReadingTimeFn The default reading time A callback to customize the reading time number displayed. authorsMapPath string 'authors.yml' Path to the authors map file, relative to the blog content directory. feedOptions See below {type: ['rss', 'atom']} Blog feed. feedOptions.type FeedType | FeedType[] | 'all' | null Required Type of feed to be generated. Use null to disable generation. feedOptions.createFeedItems CreateFeedItemsFn | undefined undefined An optional function which can be used to transform and / or filter the items in the feed. feedOptions.limit number | null | false 20 Limits the feed to the specified number of posts, false or null for all entries. Defaults to 20. feedOptions.title string siteConfig.title Title of the feed. feedOptions.description string `${siteConfig.title} Blog` Description of the feed. feedOptions.copyright string undefined Copyright message. feedOptions.language string (See documentation for possible values) undefined Language metadata of the feed. sortPosts 'descending' | 'ascending' 'descending' Governs the direction of blog post sorting.","s":"Configuration","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#configuration","p":873},{"i":880,"t":"EditUrlFn​ type EditUrlFunction = (params: { blogDirPath: string; blogPath: string; permalink: string; locale: string; }) => string | undefined; ReadingTimeFn​ type ReadingTimeOptions = { wordsPerMinute: number; wordBound: (char: string) => boolean; }; type ReadingTimeCalculator = (params: { content: string; frontMatter?: BlogPostFrontMatter & Record<string, unknown>; options?: ReadingTimeOptions; }) => number; type ReadingTimeFn = (params: { content: string; frontMatter: BlogPostFrontMatter & Record<string, unknown>; defaultReadingTime: ReadingTimeCalculator; }) => number | undefined; FeedType​ type FeedType = 'rss' | 'atom' | 'json'; CreateFeedItemsFn​ type CreateFeedItemsFn = (params: { blogPosts: BlogPost[]; siteConfig: DocusaurusConfig; outDir: string; defaultCreateFeedItemsFn: CreateFeedItemsFn; }) => Promise<BlogFeedItem[]>;","s":"Types","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#types","p":873},{"i":882,"t":"You can configure this plugin through preset options or plugin options. 提示 Most Docusaurus users configure this plugin through the preset options. JavaScript // Preset Options: blog // Plugin Options: @docusaurus/plugin-content-blog const config = { path: 'blog', // Simple use-case: string editUrl // editUrl: 'https://github.com/facebook/docusaurus/edit/main/website/', // Advanced use-case: functional editUrl editUrl: ({locale, blogDirPath, blogPath, permalink}) => `https://github.com/facebook/docusaurus/edit/main/website/${blogDirPath}/${blogPath}`, editLocalizedFiles: false, blogTitle: 'Blog title', blogDescription: 'Blog', blogSidebarCount: 5, blogSidebarTitle: 'All our posts', routeBasePath: 'blog', include: ['**/*.{md,mdx}'], exclude: [ '**/_*.{js,jsx,ts,tsx,md,mdx}', '**/_*/**', '**/*.test.{js,jsx,ts,tsx}', '**/__tests__/**', ], postsPerPage: 10, blogListComponent: '@theme/BlogListPage', blogPostComponent: '@theme/BlogPostPage', blogTagsListComponent: '@theme/BlogTagsListPage', blogTagsPostsComponent: '@theme/BlogTagsPostsPage', remarkPlugins: [require('./my-remark-plugin')], rehypePlugins: [], beforeDefaultRemarkPlugins: [], beforeDefaultRehypePlugins: [], truncateMarker: /<!--\\s*(truncate)\\s*-->/, showReadingTime: true, feedOptions: { type: '', title: '', description: '', copyright: '', language: undefined, createFeedItems: async (params) => { const {blogPosts, defaultCreateFeedItems, ...rest} = params; return defaultCreateFeedItems({ // keep only the 10 most recent blog posts in the feed blogPosts: blogPosts.filter((item, index) => index < 10), ...rest, }); }, }, };","s":"Example configuration","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#ex-config","p":873},{"i":884,"t":"Markdown documents can use the following Markdown front matter metadata fields, enclosed by a line --- on either side. Accepted fields: Name Type Default Description authors Authors undefined List of blog post authors (or unique author). Read the authors guide for more explanations. Prefer authors over the author_* front matter fields, even for single author blog posts. author string undefined ⚠️ Prefer using authors. The blog post author's name. author_url string undefined ⚠️ Prefer using authors. The URL that the author's name will be linked to. This could be a GitHub, Twitter, Facebook profile URL, etc. author_image_url string undefined ⚠️ Prefer using authors. The URL to the author's thumbnail image. author_title string undefined ⚠️ Prefer using authors. A description of the author. title string Markdown title The blog post title. date string File name or file creation time The blog post creation date. If not specified, this can be extracted from the file or folder name, e.g, 2021-04-15-blog-post.mdx, 2021-04-15-blog-post/index.mdx, 2021/04/15/blog-post.mdx. Otherwise, it is the Markdown file creation time. tags Tag[] undefined A list of strings or objects of two string fields label and permalink to tag to your post. draft boolean false Draft blog posts will only be available during development. unlisted boolean false Unlisted blog posts will be available in both development and production. They will be \"hidden\" in production, not indexed, excluded from sitemaps, and can only be accessed by users having a direct link. hide_table_of_contents boolean false Whether to hide the table of contents to the right. toc_min_heading_level number 2 The minimum heading level shown in the table of contents. Must be between 2 and 6 and lower or equal to the max value. toc_max_heading_level number 3 The max heading level shown in the table of contents. Must be between 2 and 6. keywords string[] undefined Keywords meta tag, which will become the <meta name=\"keywords\" content=\"keyword1,keyword2,...\"/> in <head>, used by search engines. description string The first line of Markdown content The description of your document, which will become the <meta name=\"description\" content=\"...\"/> and <meta property=\"og:description\" content=\"...\"/> in <head>, used by search engines. image string undefined Cover or thumbnail image that will be used when displaying the link to your post. slug string File path Allows to customize the blog post URL (/<routeBasePath>/<slug>). Support multiple patterns: slug: my-blog-post, slug: /my/path/to/blog/post, slug: /. type Tag = string | {label: string; permalink: string}; // An author key references an author from the global plugin authors.yml file type AuthorKey = string; type Author = { key?: AuthorKey; name: string; title?: string; url?: string; image_url?: string; }; // The front matter authors field allows various possible shapes type Authors = AuthorKey | Author | (AuthorKey | Author)[]; Example: --- title: Welcome Docusaurus authors: - slorber - yangshun - name: Joel Marcey title: Co-creator of Docusaurus 1 url: https://github.com/JoelMarcey image_url: https://github.com/JoelMarcey.png tags: [hello, docusaurus-v2] description: This is my first post on Docusaurus. image: https://i.imgur.com/mErPwqL.png hide_table_of_contents: false --- A Markdown blog post","s":"Markdown front matter","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#markdown-front-matter","p":873},{"i":886,"t":"Read the i18n introduction first.","s":"i18n","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#i18n","p":873},{"i":888,"t":"Base path: website/i18n/[locale]/docusaurus-plugin-content-blog Multi-instance path: website/i18n/[locale]/docusaurus-plugin-content-blog-[pluginId] JSON files: extracted with docusaurus write-translations Markdown files: website/i18n/[locale]/docusaurus-plugin-content-blog","s":"Translation files location","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#translation-files-location","p":873},{"i":890,"t":"website/i18n/[locale]/docusaurus-plugin-content-blog │ │ # translations for website/blog ├── authors.yml ├── first-blog-post.md ├── second-blog-post.md │ │ # translations for the plugin options that will be rendered └── options.json","s":"Example file-system structure","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#example-file-system-structure","p":873},{"i":892,"t":"Provides the docs functionality and is the default docs plugin for Docusaurus.","s":"📦 plugin-content-docs","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"","p":891},{"i":894,"t":"npm Yarn pnpm npm install --save @docusaurus/plugin-content-docs yarn add @docusaurus/plugin-content-docs pnpm add @docusaurus/plugin-content-docs 提示 If you use the preset @docusaurus/preset-classic, you don't need to install this plugin as a dependency. You can configure this plugin through the preset options.","s":"Installation","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#installation","p":891},{"i":896,"t":"Accepted fields: Name Type Default Description path string 'docs' Path to the docs content directory on the file system, relative to site directory. editUrl string | EditUrlFunction undefined Base URL to edit your site. The final URL is computed by editUrl + relativeDocPath. Using a function allows more nuanced control for each file. Omitting this variable entirely will disable edit links. editLocalizedFiles boolean false The edit URL will target the localized file, instead of the original unlocalized file. Ignored when editUrl is a function. editCurrentVersion boolean false The edit URL will always target the current version doc instead of older versions. Ignored when editUrl is a function. routeBasePath string 'docs' URL route for the docs section of your site. DO NOT include a trailing slash. Use / for shipping docs without base path. tagsBasePath string 'tags' URL route for the tags list page of your site. It is prepended to the routeBasePath. include string[] ['**/*.{md,mdx}'] Array of glob patterns matching Markdown files to be built, relative to the content path. exclude string[] See example configuration Array of glob patterns matching Markdown files to be excluded. Serves as refinement based on the include option. sidebarPath false | string undefined Path to sidebar configuration. Use false to disable sidebars, or undefined to create a fully autogenerated sidebar. sidebarCollapsible boolean true Whether sidebar categories are collapsible by default. See also Collapsible categories sidebarCollapsed boolean true Whether sidebar categories are collapsed by default. See also Expanded categories by default sidebarItemsGenerator SidebarGenerator Omitted Function used to replace the sidebar items of type 'autogenerated' with real sidebar items (docs, categories, links...). See also Customize the sidebar items generator numberPrefixParser boolean | PrefixParser Omitted Custom parsing logic to extract number prefixes from file names. Use false to disable this behavior and leave the docs untouched, and true to use the default parser. See also Using number prefixes docsRootComponent string '@theme/DocsRoot' Parent component of all the docs plugin pages (including all versions). Stays mounted when navigation between docs pages and versions. docVersionRootComponent string '@theme/DocVersionLayout' Parent component of all docs pages of an individual version (doc pages with sidebars, tags pages). Stays mounted when navigation between pages of that specific version. docRootComponent string '@theme/DocPage' Parent component of all doc pages with sidebars (regular docs pages, category generated index pages). Stays mounted when navigation between such pages. docItemComponent string '@theme/DocItem' Main doc container, with TOC, pagination, etc. docTagsListComponent string '@theme/DocTagsListPage' Root component of the tags list page docTagDocListComponent string '@theme/DocTagDocListPage' Root component of the \"docs containing tag X\" page. docCategoryGeneratedIndexComponent string '@theme/DocCategoryGeneratedIndexPage' Root component of the generated category index page. remarkPlugins any[] [] Remark plugins passed to MDX. rehypePlugins any[] [] Rehype plugins passed to MDX. beforeDefaultRemarkPlugins any[] [] Custom Remark plugins passed to MDX before the default Docusaurus Remark plugins. beforeDefaultRehypePlugins any[] [] Custom Rehype plugins passed to MDX before the default Docusaurus Rehype plugins. showLastUpdateAuthor boolean false Whether to display the author who last updated the doc. showLastUpdateTime boolean false Whether to display the last date the doc was updated. breadcrumbs boolean true Enable or disable the breadcrumbs on doc pages. disableVersioning boolean false Explicitly disable versioning even when multiple versions exist. This will make the site only include the current version. Will error if includeCurrentVersion: false and disableVersioning: true. includeCurrentVersion boolean true Include the current version of your docs. lastVersion string First version in versions.json The version navigated to in priority and displayed by default for docs navbar items. onlyIncludeVersions string[] All versions available Only include a subset of all available versions. versions VersionsConfig {} Independent customization of each version's properties.","s":"Configuration","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#configuration","p":891},{"i":898,"t":"EditUrlFunction​ type EditUrlFunction = (params: { version: string; versionDocsDirPath: string; docPath: string; permalink: string; locale: string; }) => string | undefined; PrefixParser​ type PrefixParser = (filename: string) => { filename: string; numberPrefix?: number; }; SidebarGenerator​ type SidebarGenerator = (generatorArgs: { /** The sidebar item with type \"autogenerated\" to be transformed. */ item: {type: 'autogenerated'; dirName: string}; /** Useful metadata for the version this sidebar belongs to. */ version: {contentPath: string; versionName: string}; /** All the docs of that version (unfiltered). */ docs: { id: string; title: string; frontMatter: DocFrontMatter & Record<string, unknown>; source: string; sourceDirName: string; sidebarPosition?: number | undefined; }[]; /** Number prefix parser configured for this plugin. */ numberPrefixParser: PrefixParser; /** The default category index matcher which you can override. */ isCategoryIndex: CategoryIndexMatcher; /** * key is the path relative to the doc content directory, value is the * category metadata file's content. */ categoriesMetadata: {[filePath: string]: CategoryMetadata}; /** * Useful to re-use/enhance the default sidebar generation logic from * Docusaurus. */ defaultSidebarItemsGenerator: SidebarGenerator; // Returns an array of sidebar items — same as what you can declare in // sidebars.js, except for shorthands. See https://docusaurus.io/docs/sidebar/items }) => Promise<SidebarItem[]>; type CategoryIndexMatcher = (param: { /** The file name, without extension */ fileName: string; /** * The list of directories, from lowest level to highest. * If there's no dir name, directories is ['.'] */ directories: string[]; /** The extension, with a leading dot */ extension: string; }) => boolean; VersionsConfig​ type VersionConfig = { /** * The base path of the version, will be appended to `baseUrl` + * `routeBasePath`. */ path?: string; /** The label of the version to be used in badges, dropdowns, etc. */ label?: string; /** The banner to show at the top of a doc of that version. */ banner?: 'none' | 'unreleased' | 'unmaintained'; /** Show a badge with the version label at the top of each doc. */ badge?: boolean; /** Prevents search engines from indexing this version */ noIndex?: boolean; /** Add a custom class name to the <html> element of each doc */ className?: string; }; type VersionsConfig = {[versionName: string]: VersionConfig};","s":"Types","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#types","p":891},{"i":900,"t":"You can configure this plugin through preset options or plugin options. 提示 Most Docusaurus users configure this plugin through the preset options. JavaScript // Preset Options: docs // Plugin Options: @docusaurus/plugin-content-docs const config = { path: 'docs', breadcrumbs: true, // Simple use-case: string editUrl // editUrl: 'https://github.com/facebook/docusaurus/edit/main/website/', // Advanced use-case: functional editUrl editUrl: ({versionDocsDirPath, docPath}) => `https://github.com/facebook/docusaurus/edit/main/website/${versionDocsDirPath}/${docPath}`, editLocalizedFiles: false, editCurrentVersion: false, routeBasePath: 'docs', include: ['**/*.md', '**/*.mdx'], exclude: [ '**/_*.{js,jsx,ts,tsx,md,mdx}', '**/_*/**', '**/*.test.{js,jsx,ts,tsx}', '**/__tests__/**', ], sidebarPath: 'sidebars.js', async sidebarItemsGenerator({ defaultSidebarItemsGenerator, numberPrefixParser, item, version, docs, isCategoryIndex, }) { // Use the provided data to generate a custom sidebar slice return [ {type: 'doc', id: 'intro'}, { type: 'category', label: 'Tutorials', items: [ {type: 'doc', id: 'tutorial1'}, {type: 'doc', id: 'tutorial2'}, ], }, ]; }, numberPrefixParser(filename) { // Implement your own logic to extract a potential number prefix const numberPrefix = findNumberPrefix(filename); // Prefix found: return it with the cleaned filename if (numberPrefix) { return { numberPrefix, filename: filename.replace(prefix, ''), }; } // No number prefix found return {numberPrefix: undefined, filename}; }, docLayoutComponent: '@theme/DocPage', docItemComponent: '@theme/DocItem', remarkPlugins: [require('./my-remark-plugin')], rehypePlugins: [], beforeDefaultRemarkPlugins: [], beforeDefaultRehypePlugins: [], showLastUpdateAuthor: false, showLastUpdateTime: false, disableVersioning: false, includeCurrentVersion: true, lastVersion: undefined, versions: { current: { label: 'Android SDK v2.0.0 (WIP)', path: 'android-2.0.0', banner: 'none', }, '1.0.0': { label: 'Android SDK v1.0.0', path: 'android-1.0.0', banner: 'unmaintained', }, }, onlyIncludeVersions: ['current', '1.0.0', '2.0.0'], };","s":"Example configuration","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#ex-config","p":891},{"i":902,"t":"Markdown documents can use the following Markdown front matter metadata fields, enclosed by a line --- on either side. Accepted fields: Name Type Default Description id string file path (including folders, without the extension) A unique document ID. title string Markdown title or id The text title of your document. Used for the page metadata and as a fallback value in multiple places (sidebar, next/previous buttons...). Automatically added at the top of your doc if it does not contain any Markdown title. pagination_label string sidebar_label or title The text used in the document next/previous buttons for this document. sidebar_label string title The text shown in the document sidebar for this document. sidebar_position number Default ordering Controls the position of a doc inside the generated sidebar slice when using autogenerated sidebar items. See also Autogenerated sidebar metadata. sidebar_class_name string undefined Gives the corresponding sidebar label a special class name when using autogenerated sidebars. sidebar_custom_props object undefined Assign custom props to the sidebar item referencing this doc displayed_sidebar string undefined Force the display of a given sidebar when browsing the current document. Read the multiple sidebars guide for details. hide_title boolean false Whether to hide the title at the top of the doc. It only hides a title declared through the front matter, and have no effect on a Markdown title at the top of your document. hide_table_of_contents boolean false Whether to hide the table of contents to the right. toc_min_heading_level number 2 The minimum heading level shown in the table of contents. Must be between 2 and 6 and lower or equal to the max value. toc_max_heading_level number 3 The max heading level shown in the table of contents. Must be between 2 and 6. pagination_next string | null Next doc in the sidebar The ID of the documentation you want the \"Next\" pagination to link to. Use null to disable showing \"Next\" for this page. pagination_prev string | null Previous doc in the sidebar The ID of the documentation you want the \"Previous\" pagination to link to. Use null to disable showing \"Previous\" for this page. parse_number_prefixes boolean numberPrefixParser plugin option Whether number prefix parsing is disabled on this doc. See also Using number prefixes. custom_edit_url string | null Computed using the editUrl plugin option The URL for editing this document. Use null to disable showing \"Edit this page\" for this page. keywords string[] undefined Keywords meta tag for the document page, for search engines. description string The first line of Markdown content The description of your document, which will become the <meta name=\"description\" content=\"...\"/> and <meta property=\"og:description\" content=\"...\"/> in <head>, used by search engines. image string undefined Cover or thumbnail image that will be used when displaying the link to your post. slug string File path Allows to customize the document URL (/<routeBasePath>/<slug>). Support multiple patterns: slug: my-doc, slug: /my/path/myDoc, slug: /. tags Tag[] undefined A list of strings or objects of two string fields label and permalink to tag to your docs. draft boolean false Draft documents will only be available during development. unlisted boolean false Unlisted documents will be available in both development and production. They will be \"hidden\" in production, not indexed, excluded from sitemaps, and can only be accessed by users having a direct link. last_update FileChange undefined Allows overriding the last updated author and/or date. Date can be any parsable date string. type Tag = string | {label: string; permalink: string}; type FileChange = {date: string; author: string}; Example: --- id: doc-markdown title: Docs Markdown Features hide_title: false hide_table_of_contents: false sidebar_label: Markdown sidebar_position: 3 pagination_label: Markdown features custom_edit_url: https://github.com/facebook/docusaurus/edit/main/docs/api-doc-markdown.md description: How do I find you when I cannot solve this problem keywords: - docs - docusaurus image: https://i.imgur.com/mErPwqL.png slug: /myDoc last_update: date: 1/1/2000 author: custom author name --- # Markdown Features My Document Markdown content","s":"Markdown front matter","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#markdown-front-matter","p":891},{"i":904,"t":"Read the i18n introduction first.","s":"i18n","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#i18n","p":891},{"i":906,"t":"Base path: website/i18n/[locale]/docusaurus-plugin-content-docs Multi-instance path: website/i18n/[locale]/docusaurus-plugin-content-docs-[pluginId] JSON files: extracted with docusaurus write-translations Markdown files: website/i18n/[locale]/docusaurus-plugin-content-docs/[versionName]","s":"Translation files location","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#translation-files-location","p":891},{"i":908,"t":"website/i18n/[locale]/docusaurus-plugin-content-docs │ │ # translations for website/docs ├── current │ ├── api │ │ └── config.md │ └── getting-started.md ├── current.json │ │ # translations for website/versioned_docs/version-1.0.0 ├── version-1.0.0 │ ├── api │ │ └── config.md │ └── getting-started.md └── version-1.0.0.json","s":"Example file-system structure","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#example-file-system-structure","p":891},{"i":910,"t":"The functionalities of the most three contents blog, docs and pages are provided by docusaurus. These contents plugins are responsible for loading your site's content, and creating pages for your theme to render. plugin-content-docs plugin-content-blog plugin-content-pages","s":"Plugin Contents","u":"/docs/docusaurus-mdx/plugin-contents/intro","h":"","p":909},{"i":912,"t":"Front matter is used to add metadata to your Markdown file. All content plugins have their own front matter schema, and use the front matter to enrich the default metadata inferred from the content or other configuration. Front matter is provided at the very top of the file, enclosed by three dashes ---. The content is parsed as YAML. --- title: My Doc Title more_data: - Can be provided - as: objects or: arrays --- The API documentation of each official plugin lists the supported attributes.","s":"Front Matter","u":"/docs/docusaurus-mdx/plugin-contents/intro","h":"#front-matter","p":909},{"i":914,"t":"The default pages plugin for Docusaurus. The classic template ships with this plugin with default configurations. This plugin provides creating pages functionality.","s":"📦 plugin-content-pages","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"","p":913},{"i":916,"t":"npm Yarn pnpm npm install --save @docusaurus/plugin-content-pages yarn add @docusaurus/plugin-content-pages pnpm add @docusaurus/plugin-content-pages 提示 If you use the preset @docusaurus/preset-classic, you don't need to install this plugin as a dependency. You can configure this plugin through the preset options.","s":"Installation","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#installation","p":913},{"i":918,"t":"Accepted fields: Name Type Default Description path string 'src/pages' Path to data on filesystem relative to site dir. Components in this directory will be automatically converted to pages. routeBasePath string '/' URL route for the pages section of your site. DO NOT include a trailing slash. include string[] ['**/*.{js,jsx,ts,tsx,md,mdx}'] Matching files will be included and processed. exclude string[] See example configuration No route will be created for matching files. mdxPageComponent string '@theme/MDXPage' Component used by each MDX page. remarkPlugins [] any[] Remark plugins passed to MDX. rehypePlugins [] any[] Rehype plugins passed to MDX. beforeDefaultRemarkPlugins any[] [] Custom Remark plugins passed to MDX before the default Docusaurus Remark plugins. beforeDefaultRehypePlugins any[] [] Custom Rehype plugins passed to MDX before the default Docusaurus Rehype plugins.","s":"Configuration","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#configuration","p":913},{"i":920,"t":"You can configure this plugin through preset options or plugin options. 提示 Most Docusaurus users configure this plugin through the preset options. JavaScript // Preset Options: pages // Plugin Options: @docusaurus/plugin-content-pages const config = { path: 'src/pages', routeBasePath: '', include: ['**/*.{js,jsx,ts,tsx,md,mdx}'], exclude: [ '**/_*.{js,jsx,ts,tsx,md,mdx}', '**/_*/**', '**/*.test.{js,jsx,ts,tsx}', '**/__tests__/**', ], mdxPageComponent: '@theme/MDXPage', remarkPlugins: [require('./my-remark-plugin')], rehypePlugins: [], beforeDefaultRemarkPlugins: [], beforeDefaultRehypePlugins: [], };","s":"Example configuration","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#ex-config","p":913},{"i":922,"t":"Markdown pages can use the following Markdown front matter metadata fields, enclosed by a line --- on either side. Accepted fields: Name Type Default Description title string Markdown title The blog post title. description string The first line of Markdown content The description of your page, which will become the <meta name=\"description\" content=\"...\"/> and <meta property=\"og:description\" content=\"...\"/> in <head>, used by search engines. keywords string[] undefined Keywords meta tag, which will become the <meta name=\"keywords\" content=\"keyword1,keyword2,...\"/> in <head>, used by search engines. image string undefined Cover or thumbnail image that will be used when displaying the link to your post. wrapperClassName string Class name to be added to the wrapper element to allow targeting specific page content. hide_table_of_contents boolean false Whether to hide the table of contents to the right. draft boolean false Draft pages will only be available during development. unlisted boolean false Unlisted pages will be available in both development and production. They will be \"hidden\" in production, not indexed, excluded from sitemaps, and can only be accessed by users having a direct link. Example: --- title: Markdown Page description: Markdown page SEO description wrapperClassName: markdown-page hide_table_of_contents: false draft: true --- Markdown page content","s":"Markdown front matter","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#markdown-front-matter","p":913},{"i":924,"t":"Read the i18n introduction first.","s":"i18n","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#i18n","p":913},{"i":926,"t":"Base path: website/i18n/[locale]/docusaurus-plugin-content-pages Multi-instance path: website/i18n/[locale]/docusaurus-plugin-content-pages-[pluginId] JSON files: extracted with docusaurus write-translations Markdown files: website/i18n/[locale]/docusaurus-plugin-content-pages","s":"Translation files location","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#translation-files-location","p":913},{"i":928,"t":"website/i18n/[locale]/docusaurus-plugin-content-pages │ │ # translations for website/src/pages ├── first-markdown-page.md └── second-markdown-page.md","s":"Example file-system structure","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#example-file-system-structure","p":913},{"i":930,"t":"在实际中，采集的数据往往不完整、不一致，并可能包含许多错误。数据预处理 (Data Preprocessing) 是一种数据挖掘技术，对原始数据进行处理以便进一步分析。 本文介绍分类数据 (Categorical Data) 的处理。","s":"分类数据的预处理","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"","p":929},{"i":932,"t":"在处理分类数据时，需要区分定类 (nominal) 特征和定序 (ordinal) 特征。 定类特征：不同类别，相互间比较没有意义。如姓名，性别，水果等。 定序特征：不同类别，相互间可以比较排序。如非常满意/一般满意/不满意，小型/中型/大型等。和数字特征不同，两者之差一般没有意义。 以下的 df 变量代表了 T 恤的一些特征： >>> import pandas as pd >>> df = pd.DataFrame([ ... ['green', 'M', 10.1, 'class1'], ... ['red', 'L', 13.5, 'class2'], ... ['blue', 'XL', 15.3, 'class1']]) >>> df.columns = ['color', 'size', 'price', 'classlabel'] >>> df color size price classlabel 0 green M 10.1 class1 1 red L 13.5 class2 2 blue XL 15.3 class1 其中包括定类特征 color（颜色）、定序特征 size（尺码） 和数字特征 price（价格）。最后一列为分类类别 label。","s":"定类和定序","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#nominal-and-ordinal","p":929},{"i":934,"t":"为了确保学习算法能够识别定序特征，需要手动将分类字符串映射 (Mapping) 为整型。 如上例的 T 恤尺码，假设已知排序 XL>L>MXL > L > MXL>L>M，可以进行如下转换： >>> size_mapping = { ... 'XL': 3, ... 'L': 2, ... 'M': 1} >>> df['size'] = df['size'].map(size_mapping) >>> df color size price classlabel 0 green 1 10.1 class1 1 red 2 13.5 class2 2 blue 3 15.3 class1 对于反向转换，创建反向词典然后进行 map 即可： >>> inv_size_mapping = {v: k for k, v in size_mapping.items()} >>> df['size'].map(inv_size_mapping) 0 M 1 L 2 XL Name: size, dtype: object","s":"定序特征的映射","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#mapping-of-ordinal-features","p":929},{"i":936,"t":"许多机器学习库要求类标签编码 (Encoding) 为整数值；虽然 scikit-learn 已默认集成了此处理机制，但是建议养成手动转换的习惯。 类标签的数字大小没有任何意义，因此可以直接使用枚举进行标签转换： >>> import numpy as np >>> class_mapping = {label:idx for idx,label in ... enumerate(np.unique(df['classlabel']))} >>> class_mapping {'class1': 0, 'class2': 1} 将类标签编码为整数： >>> df['classlabel'] = df['classlabel'].map(class_mapping) >>> df color size price classlabel 0 green 1 10.1 0 1 red 2 13.5 1 2 blue 3 15.3 0 反向转换： >>> inv_class_mapping = {v: k for k, v in class_mapping.items()} >>> df['classlabel'] = df['classlabel'].map(inv_class_mapping) >>> df color size price classlabel 0 green 1 10.1 class1 1 red 2 13.5 class2 2 blue 3 15.3 class1 通过 sklearn.preprocessing.LabelEncoder 可以更简便地将类标签编码为整数： >>> from sklearn.preprocessing import LabelEncoder >>> class_le = LabelEncoder() >>> y = class_le.fit_transform(df['classlabel'].values) >>> y array([0, 1, 0]) 反向转换： >>> class_le.inverse_transform(y) array(['class1', 'class2', 'class1'], dtype=object)","s":"类标签的编码","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#encoding-of-class-labels","p":929},{"i":939,"t":"在介绍独热编码 (One-Hot Encoding) 之前，先说明一下为什么不用之前章节的编码方式。 如果按照之前的方式进行编码： >>> X = df[['color', 'size', 'price']].values >>> color_le = LabelEncoder() >>> X[:, 0] = color_le.fit_transform(X[:, 0]) >>> X array([[1, 1, 10.1], [2, 2, 13.5], [0, 3, 15.3]], dtype=object) 编码结果为： blue = 0 green = 1 red = 2 如果把上述数据提供给分类器，则会发生处理分类数据的最常见错误之一：虽然我们知道 0、1、2 这些数字不代表大小，但是算法并不知道。因此算法在学习过程中，会默认将其关联起来，即假定 red > green > blue。这样处理后，算法仍然能产生一定的结果，但其性能会受影响。 独热编码的思想为为每一个值创建一个新的特征。对于上述的例子，可以把颜色特征转换为三个新的特征：blue、green 和 red，然后使用二进制值标记。对于 blue 样本而言，编码为 blue=1, green=0, red=0。","s":"独热编码的原理","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#onehot-encoding-principle","p":929},{"i":941,"t":"使用 sklearn.preprocessing.OneHotEncoder 对特征 color 进行编码，返回一个稀疏矩阵： >>> from sklearn.preprocessing import OneHotEncoder >>> ohe = OneHotEncoder(categorical_features=[0]) >>> ohe.fit_transform(X).toarray() array([[ 0. , 1. , 0. , 1. , 10.1], [ 0. , 0. , 1. , 2. , 13.5], [ 1. , 0. , 0. , 3. , 15.3]]) 另一个更方便的独热编码方法是 pandas 中的 get_dummies 方法，转换 DataFrame 的指定字符串列，其他列保持不变： >>> pd.get_dummies(df[['price', 'color', 'size']]) price size color_blue color_green color_red 0 10.1 1 0 1 0 1 13.5 2 0 0 1 2 15.3 3 1 0 0","s":"独热编码的实现","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#onehot-encoding-implementation","p":929},{"i":943,"t":"当使用热门的编码数据集时，必须记住它引入了多重共线性，即某个变量可以由其他变量线性预测得到 (如上面的矩阵，若已知 blue、green、red 中的任意两个，可以得到最后一个)。这会对某些操作 (如矩阵求逆) 造成影响。 为了减少变量之间的相关性，我们可以简单地从独热编码数组中删除一个特征列。 sklearn.preprocessing.OneHotEncoder 不提供特征列删除方法，需要转换为 numpy 数组后进行切片： >>> ohe = OneHotEncoder(categorical_features=[0]) >>> ohe.fit_transform(X).toarray()[:, 1:] array([[ 1. , 0. , 1. , 10.1], [ 0. , 1. , 2. , 13.5], [ 0. , 0. , 3. , 15.3]]) pandas 中的 get_dummies 提供参数 drop_first，可以很方便地删除首个特征列： >>> pd.get_dummies(df[['price', 'color', 'size']], ... drop_first=True) price size color_green color_red 0 10.1 1 1 0 1 13.5 2 0 1 2 15.3 3 0 0","s":"独热编码的相关性","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#onehot-encoding-correlation","p":929},{"i":945,"t":"特征缩放 (Feature Scaling) 是将不同特征的值量化到同一区间的方法，也是预处理中容易忽视的关键步骤之一。除了极少数算法 (如决策树和随机森林) 之外，大部分机器学习和优化算法采用特征缩放后会表现更优。 特征缩放方法可分为包含归一化 (Normalization) 和标准化 (Standardization)。不同领域对这两个术语的定义可能不同，本文只对常用的定义进行介绍。","s":"特征缩放","u":"/docs/machine-learning/data-preprocessing/feature-scaling","h":"","p":944},{"i":947,"t":"一般来说，归一化是指将特征重新缩放到 [0，1][0，1][0，1] 的范围，属于极值缩放 (Min-Max Scaling) 的一种情况。其数学表达如下： xnorm(i)=x(i)−xminxmax−xmin\\begin{align} x_{norm}^{(i)} = \\cfrac {x^{(i)} - x_{min}} {x_{max} - x_{min}} \\end{align}xnorm(i)​=xmax​−xmin​x(i)−xmin​​​​ 其中，x(i)x^{(i)}x(i) 和 xnorm(i)x_{norm}^{(i)}xnorm(i)​ 分别表示第 iii 个样本归一化前后的特征值，xmaxx_{max}xmax​ 和 xminx_{min}xmin​ 分别表示该特征的最大值和最小值。 在 scikit-learn 中，可通过 sklearn.preprocessing.MinMaxScaler 实现： >>> from sklearn.preprocessing import MinMaxScaler >>> mms = MinMaxScaler() >>> X_train_norm = mms.fit_transform(X_train) >>> X_test_norm = mms.transform(X_test)","s":"归一化","u":"/docs/machine-learning/data-preprocessing/feature-scaling","h":"#normalization","p":944},{"i":949,"t":"标准化是将对特征缩放为服从正态分布，即平均值为 0、方差为 1。与归一化相比，标准化更适用于大部分学习算法。 以梯度下降法为例，如下左子图 (标准化前的收敛) 和右子图 (标准化后的收敛)： 其数学表达如下： xstd(i)=x(i)−μxσx\\begin{align} x_{std}^{(i)} = \\cfrac {x^{(i)} - \\mu_x} {\\sigma_x} \\end{align}xstd(i)​=σx​x(i)−μx​​​​ 其中，x(i)x^{(i)}x(i) 和 xstd(i)x_{std}^{(i)}xstd(i)​ 分别表示第 iii 个样本标准化前后的特征值，μx\\mu_xμx​ 和 σx\\sigma_xσx​ 分别表示该特征的平均值和标准差。 在 scikit-learn 中，可通过 sklearn.preprocessing.StandardScaler 实现： >>> from sklearn.preprocessing import StandardScaler >>> stdsc = StandardScaler() >>> X_train_std = stdsc.fit_transform(X_train) >>> X_test_std = stdsc.transform(X_test)","s":"标准化","u":"/docs/machine-learning/data-preprocessing/feature-scaling","h":"#standardization","p":944},{"i":951,"t":"评估指标 (Evaluation Metrics) 除了准确率 (Accuracy) 之外，还有其他的一些指标，如精确率 (Precision)、召回率 (Recall) 和 F1 分数 (F1 Score) 等。它们是混淆矩阵中的评估指标。","s":"混淆矩阵","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"","p":950},{"i":953,"t":"在介绍不同评分指标的评估指标之前，先介绍混淆矩阵 (Confusion Matrix)： TP (True Positives)：预测为正、实际为正的样本数 FN (False Negatives)：预测为负、实际为正的样本数 FP (False Positives)：预测为正、实际为负的样本数 TN (True Negatives)：预测为负、实际为负的样本数 混淆矩阵的形式为 True/False + Positive/Negative (Positive/Negative 是对于预测的类标签而言)。","s":"混淆矩阵的概念","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#confusion-matrix-concept","p":950},{"i":955,"t":"以 wdbc 数据集为例进行说明。先进行导入及预处理： import pandas as pd from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.svm import SVC from sklearn.pipeline import make_pipeline df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.iloc[:, 2:] y = df.iloc[:, 1] le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, stratify=y, random_state=1 ) pipe_svc = make_pipeline(StandardScaler(), SVC(random_state=1)) 通过 sklearn.metrics.confusion_matrix 计算混淆矩阵： from sklearn.metrics import confusion_matrix pipe_svc.fit(X_train, y_train) y_pred = pipe_svc.predict(X_test) confmat = confusion_matrix(y_true=y_test, y_pred=y_pred) print(confmat) 上面的函数打印出了 pipe_svc 在测试集上的混淆矩阵： 需要注意的是，scikit-learn 的混淆矩阵排列方式为 [[TN，FP]，[FN，TP]]。 [[71 1] [ 2 40]] 为了更直观地说明，通过 matplotlib 绘图如下： import matplotlib.pyplot as plt fig, ax = plt.subplots(figsize=(2.5, 2.5)) ax.matshow(confmat, cmap=plt.cm.Blues, alpha=0.3) for i in range(confmat.shape[0]): for j in range(confmat.shape[1]): ax.text(x=j, y=i, s=confmat[i, j], va=\"center\", ha=\"center\") plt.xlabel(\"predicted label\") plt.ylabel(\"true label\") plt.show() 这个数据集的类标签为病情恶性或者良性，通过 LabelEncoder 进行分类标签编码，恶性为 1 (正)，良性为 0 (负)。 左上：TN，预测为良性且预测正确的样本数。 右上：FP，预测为恶性且预测错误 (实际上为良性) 的样本数。 左下：FN，预测为良性且预测错误 (实际上为恶性) 的样本数。 右下：TP，预测为恶性且预测正确的样本数。 虽然大部分情况下比较关注分类正确 (TN + TP) 的表现。但是对于一些实际问题而言，FP 和 FN 是不一样的。以上述的 wdbc 数据而言，如果把良性病情预测恶性 (FP)，患者很有可能再后续再进行复查；但是如果把恶性病情预测成良性 (FN)，可能会让患者掉以轻心以拖延治疗，相比 FP 而言会带来更严重的后果。这也是需要制定不同评估指标的原因。 为了便于记忆，FP 也称 false alarm，可以理解为报警铃的误报；FN 也称 miss，应该报警但是实际没有报警。","s":"混淆矩阵的 scikit-learn 演示","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#confusion-matrix-using-sklearn","p":950},{"i":957,"t":"下图来自 Wikipedia - Confusion matrix： 下面介绍其中一些重要的评估指标，其中 P=TP+FNP = TP + FNP=TP+FN 表示实际为正的样本数，N=TN+FPN = TN + FPN=TN+FP 表示实际为负的样本数。","s":"评估指标介绍","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#evaluation-metrics-introduction","p":950},{"i":959,"t":"ACC (Accuracy) 代表准确率，ERR (Error) 代表错误率： ACC=TP+TNP+N=TP+TNTP+TN+FP+FNERR=FP+FNP+N=FP+FNTP+TN+FP+FN=1−ACC\\begin{align} ACC & = \\frac {TP + TN} {P + N} = \\frac {TP + TN} {TP + TN + FP + FN} \\\\ ERR & = \\frac {FP + FN} {P + N} = \\frac {FP + FN} {TP + TN + FP + FN} = 1 - ACC \\end{align}ACCERR​=P+NTP+TN​=TP+TN+FP+FNTP+TN​=P+NFP+FN​=TP+TN+FP+FNFP+FN​=1−ACC​​ scikit-learn 实现如下： from sklearn.metrics import accuracy_score accuracy = accuracy_score(y_true=y_test, y_pred=y_pred)","s":"准确率","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#accuracy","p":950},{"i":961,"t":"召回率 (Recall) 即 TPR (True Positive Rate)，表示实际为正的样本中正确预测的概率，也称敏感度 (Sensitivity) 或命中率 (Hit Rate)： Recall=TPR=TPP=TPTP+FN\\begin{align} Recall = TPR = \\frac {TP} {P} = \\frac {TP} {TP + FN} \\end{align}Recall=TPR=PTP​=TP+FNTP​​​ scikit-learn 实现如下： from sklearn.metrics import recall_score recall = recall_score(y_true=y_test, y_pred=y_pred)","s":"召回率","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#recall","p":950},{"i":963,"t":"精准率 (Precision) 即 PPV (Positive Predictive Value)，表示预测为正的样本中正确预测的概率： Precision=PPV=TPTP+FP\\begin{align} Precision = PPV = \\frac {TP} {TP + FP} \\end{align}Precision=PPV=TP+FPTP​​​ scikit-learn 实现如下： from sklearn.metrics import precision_score precision = precision_score(y_true=y_test, y_pred=y_pred)","s":"精准率","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#precision","p":950},{"i":965,"t":"F1 分数 (F1 Score) 是召回率和精准率的调和平均值： F1=21Recall+1Precision=2Recall×PrecisionRecall+Precision\\begin{align} F_1 = \\cfrac 2 {\\cfrac 1 {Recall} + \\cfrac 1 {Precision}} = 2 \\frac {Recall \\times Precision} {Recall + Precision} \\end{align}F1​=Recall1​+Precision1​2​=2Recall+PrecisionRecall×Precision​​​ scikit-learn 实现如下： from sklearn.metrics import f1_score f1 = f1_score(y_true=y_test, y_pred=y_pred)","s":"F1 分数","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#f1-score","p":950},{"i":967,"t":"马修斯相关系数 (Matthews Correlation Coefficient，MCC) 对多个指标进行综合打分： MCC=TP×TN−FP×FN(TP+FP)(TP+FN)(TN+FP)(TN+FN)\\begin{align} MCC = \\frac {TP \\times TN - FP \\times FN} {\\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}} \\end{align}MCC=(TP+FP)(TP+FN)(TN+FP)(TN+FN)​TP×TN−FP×FN​​​ scikit-learn 实现如下： from sklearn.metrics import matthews_corrcoef mcc = matthews_corrcoef(y_true=y_test, y_pred=y_pred)","s":"马修斯相关系数","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#matthews-correlation-coefficient","p":950},{"i":969,"t":"需要注意的是，scikit-learn 中大多数算法默认使用 accuracy_score 作为评估指标。另外，其中正类认为是的标签为 1 的类。 通过 sklearn.metrics.make_scorer 可以替换评估指标和正类的类标签： from sklearn.metrics import make_scorer, f1_score scorer = make_scorer(f1_score, pos_label=0) gs = GridSearchCV(estimator=pipe_svc, param_grid=param_grid, scoring=scorer, cv=10) gs = gs.fit(X_train, y_train) print(gs.best_score_) # Output: 0.986202145696 >>> print(gs.best_params_) # Output: {'svc__C': 10.0, 'svc__gamma': 0.01, 'svc__kernel': 'rbf'} 有关评估指标的更多内容，请参见 Wikipedia - Confusion matrix 和 sklearn.metrics。","s":"替换 scikit-learn 的评估指标","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#replace-evaluation-metrics-in-sklearn","p":950},{"i":971,"t":"在信号检测理论中，接收者操作特征 (Receiver Operating Characteristic，ROC) 曲线是是一种坐标图式的分析工具，通过计算 ROC 的曲线下面积 (Area Under Curve，AUC) 可以对分类模型进行评估。ROC 分析的是二分分类模型。 ROC 曲线通过绘制采用不同分类阈值时的 TPR (True Positive Rate) 与 FPR (False Positive Rate) 来选择模型。它展示了在不同分类阈值下，模型的性能表现。ROC 曲线的对角线可以被解释为随机猜测 (如丢硬币、正反面出现概率预测均是 50%)，并且落在对角线上方的分类模型优于随机猜测，落在对角线下方的分类模型比随机猜测更差。 AUC 是 ROC 曲线下的面积，即 ROC 曲线和横轴之间的面积。AUC 值的范围在 0 到 1 之间，其中 0.5 表示模型的预测性能等于随机猜测，而 1 表示完美分类器。AUC 值越接近 1，表示模型的性能越好。 下文将实现分类器的 ROC 曲线绘制，该分类器仅使用 wdbc 数据集中的两个特征来预测肿瘤是良性还是恶性。","s":"ROC 和 AUC","u":"/docs/machine-learning/evaluation-metrics/roc-and-auc","h":"","p":970},{"i":973,"t":"import pandas as pd import numpy as np import matplotlib.pyplot as plt from sklearn.model_selection import StratifiedKFold from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA from sklearn.linear_model import LogisticRegression from sklearn.pipeline import make_pipeline df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.loc[:, 2:].values y = df.loc[:, 1].values le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.20, stratify=y, random_state=1 )","s":"数据导入和预处理","u":"/docs/machine-learning/evaluation-metrics/roc-and-auc","h":"#data-loading-and-preprocessing","p":970},{"i":975,"t":"使用逻辑回归 pipeline，并采用折叠数为 3 的 StratifiedKFold，如下代码： from sklearn.metrics import roc_curve, auc from scipy import interp pipe_lr = make_pipeline( StandardScaler(), PCA(n_components=2), LogisticRegression(penalty=\"l2\", random_state=1, C=100.0), ) X_train2 = X_train[:, [4, 14]] cv = list(StratifiedKFold(n_splits=3, random_state=1).split(X_train, y_train)) fig = plt.figure(figsize=(7, 5)) mean_tpr = 0.0 mean_fpr = np.linspace(0, 1, 100) all_tpr = [] for i, (train, test) in enumerate(cv): probas = pipe_lr.fit(X_train2[train], y_train[train]).predict_proba(X_train2[test]) fpr, tpr, thresholds = roc_curve(y_train[test], probas[:, 1], pos_label=1) mean_tpr += interp(mean_fpr, fpr, tpr) mean_tpr[0] = 0.0 roc_auc = auc(fpr, tpr) plt.plot(fpr, tpr, label=\"ROC fold {} (area = {:.2f}\".format(i + 1, roc_auc)) plt.plot([0, 1], [0, 1], linestyle=\"--\", color=(0.6, 0.6, 0.6), label=\"random guessing\") mean_tpr /= len(cv) mean_tpr[-1] = 1.0 mean_auc = auc(mean_fpr, mean_tpr) plt.plot( mean_fpr, mean_tpr, \"k--\", label=\"mean ROC (area = {:.2f}\".format(mean_auc), lw=2 ) 上面的代码通过从 SciPy 导入的 interp 函数插入了三次折叠的平均 ROC 曲线，并通过 auc 函数计算曲线下面积。 三次绘制的 ROC 曲线表明不同折叠之间存在一定程度的变化，并且 ROC AUC 的平均值 (0.76) 落在完美预测 (1.0) 和随机猜测 (0.5) 之间： 如果只需要用到 ROC AUC 分数，也可以直接导入 sklearn.metrics.roc_auc_score 函数。ROC AUC 分数可以对样本数量不平均的二分分类模型进行评估。","s":"ROC 曲线的 scikit-learn 实现","u":"/docs/machine-learning/evaluation-metrics/roc-and-auc","h":"#roc-plotting-in-sklearn","p":970},{"i":977,"t":"线性判别分析 (Linear Discriminant Analysis，LDA) 作为一种特征提取技术，可以提高计算效率，防止由于维数灾难而导致的过拟合。LDA 与 PCA 类似，不同之处在于 PCA 的目标是找到数据集中最大方差的正交分量轴，而 LDA 的目标是找到优化类可分性的特征子空间。 LDA 和 PCA 都是线性变换技术，可用于减少数据集中的维数。区别在于 LDA 是监督算法，而 PCA 是无监督算法。 LDA 旨在找到对应最多投影的线性判别，如下图所示，其中圆形和十字分别表示两类的正态分布样本： xxx 轴 (LD1) 所示的线性判别可以很好地分类；而尽管 yyy 轴 (LD2) 所示的线性判别拥有更大的投影方差，但是无法捕获任何分类信息。 LDA 中假设数据是正态分布的。此外，我们假设类的协方差矩阵相同，并且特征之间互不相关。","s":"线性判别分析","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"","p":976},{"i":979,"t":"LDA 的算法流程的简单介绍如下： 对输入的 ddd 维数据集 X\\boldsymbol XX 进行标准化。 计算每个类的 ddd 维均值向量，构造类内散布矩阵 SW\\boldsymbol S_WSW​ 和类间散布矩阵 SB\\boldsymbol S_BSB​。 计算矩阵 SW−1SB\\boldsymbol S_W^{-1} \\boldsymbol S_BSW−1​SB​ 的特征向量和特征值。 对特征值进行降序排序，对相应的特征向量进行排序。 提取 kkk 个最大特征值对应的特征向量，其中 kkk (k≤dk \\le dk≤d) 是新特征子空间的维数。 使用提取的 kkk 个特征向量构造投影矩阵 W\\boldsymbol WW。 使用投影矩阵 W\\boldsymbol WW 对 X\\boldsymbol XX 进行变换，得到新的 kkk 维特征子空间。 LDA 与 PCA 非常相似，通过将矩阵分解成特征值和特征向量，然后通过投影矩阵得到新的低维特征空间。其不同点在于 LDA 将类标签考虑在内 (步骤 2)。","s":"算法思想","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#algorithm-principle","p":976},{"i":981,"t":"导入 Wine 数据集，第 1 列为其分类标签，第 2~14 列为特征。分割数据集为 70% 的训练集和 30% 的测试集： import pandas as pd from sklearn.model_selection import train_test_split df_wine = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data\", header=None, ) X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=0, stratify=y ) 对训练集和测试集进行标准化： from sklearn.preprocessing import StandardScaler sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test)","s":"数据导入和标准化","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#data-load-and-standardization","p":976},{"i":984,"t":"计算均值向量，后面将用它来构造类内散布矩阵和类间散布矩阵。在第 iii 类样本的均值向量为 mi\\boldsymbol m_imi​中，存储了该类样本特征的平均值 μm\\mu_mμm​： mi=1ni∑x∈Dicxm\\begin{align} \\boldsymbol m_i = \\frac 1 {n_i} \\sum_{x \\in D_i}^c \\boldsymbol x_m \\end{align}mi​=ni​1​x∈Di​∑c​xm​​​ 得到三个均值向量： mi=[μi,alcoholμi,malic acid⋮μi,proline]\\begin{align} \\boldsymbol m_i = \\begin{bmatrix} \\mu_{i,alcohol} \\\\ \\mu_{i,malic \\ acid} \\\\ \\vdots \\\\ \\mu_{i,proline} \\end{bmatrix} \\end{align}mi​=​μi,alcohol​μi,malic acid​⋮μi,proline​​​​​ np.set_printoptions(precision=4) mean_vecs = [] for label in range(1, 4): mean_vecs.append(np.mean(X_train_std[y_train == label], axis=0)) print(\"MV {}: {}\\n\".format(label, mean_vecs[label - 1])) # Output: # MV 1: [ 0.9066 -0.3497 0.3201 -0.7189 0.5056 0.8807 0.9589 -0.5516 0.5416 # 0.2338 0.5897 0.6563 1.2075] # MV 2: [-0.8749 -0.2848 -0.3735 0.3157 -0.3848 -0.0433 0.0635 -0.0946 0.0703 # -0.8286 0.3144 0.3608 -0.7253] # MV 3: [ 0.1992 0.866 0.1682 0.4148 -0.0451 -1.0286 -1.2876 0.8287 -0.7795 # 0.9649 -1.209 -1.3622 -0.4013]","s":"均值向量","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#mean-vector","p":976},{"i":986,"t":"类内散布矩阵 SW\\boldsymbol S_WSW​ 的计算如下，其中 Si\\boldsymbol S_iSi​ 为第 iii 类的散布矩阵。 SW=∑i=1cSiSi:=1niSi=1ni∑x∈Dic(x−mi)(x−mi)T=Σi\\begin{align} \\boldsymbol S_W & = \\sum_{i=1}^c \\boldsymbol S_i \\\\ \\boldsymbol S_i & := \\frac 1 {n_i} \\boldsymbol S_i = \\frac 1 {n_i} \\sum_{x \\in D_i}^c (\\boldsymbol x - \\boldsymbol m_i) (\\boldsymbol x - \\boldsymbol m_i)^T = \\boldsymbol \\Sigma_i \\end{align}SW​Si​​=i=1∑c​Si​:=ni​1​Si​=ni​1​x∈Di​∑c​(x−mi​)(x−mi​)T=Σi​​​ 由于 LDA 假设是训练集中的类别标签是均匀分布的，这里将散列矩阵 Si\\boldsymbol S_iSi​ 缩放至 1ni\\frac 1 {n_i}ni​1​，缩放后恰好为协方差矩阵。 d = 13 # number of features S_W = np.zeros((d, d)) for label, mv in zip(range(1, 4), mean_vecs): class_scatter = np.cov(X_train_std[y_train == label].T) S_W += class_scatter print(\"Scaled within-class scatter matrix: {}x{}\".format(S_W.shape[0], S_W.shape[1])) # Output: Scaled within-class scatter matrix: 13x13","s":"类内散布矩阵","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#intra-class-scatter-matrix","p":976},{"i":988,"t":"类间散布矩阵 SB\\boldsymbol S_BSB​ 的计算如下，其中 m\\boldsymbol mm 为所有样本的均值向量： SB=∑i=1cni(mi−m)(mi−m)T\\begin{align} \\boldsymbol S_B = \\sum_{i=1}^cn_i (\\boldsymbol m_i - \\boldsymbol m) (\\boldsymbol m_i - \\boldsymbol m)^T \\end{align}SB​=i=1∑c​ni​(mi​−m)(mi​−m)T​​ mean_overall = np.mean(X_train_std, axis=0) d = 13 # number of features S_B = np.zeros((d, d)) for i, mean_vec in enumerate(mean_vecs): n = X_train[y_train == i + 1, :].shape[0] mean_vec = mean_vec.reshape(d, 1) # make column vector mean_overall = mean_overall.reshape(d, 1) S_B += n * (mean_vec - mean_overall).dot((mean_vec - mean_overall).T) print(\"Between-class scatter matrix: {}x{}\".format(S_B.shape[0], S_B.shape[1])) # Output: Between-class scatter matrix: 13x13","s":"类间散布矩阵","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#inter-class-scatter-matrix","p":976},{"i":990,"t":"计算矩阵 SW−1SB\\boldsymbol S_W^{-1} \\boldsymbol S_BSW−1​SB​ 的特征值和特征向量，按照特征值降序对相应的特征向量进行排序： eigen_vals, eigen_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B)) eigen_pairs = [ (np.abs(eigen_vals[i]), eigen_vecs[:, i]) for i in range(len(eigen_vals)) ] eigen_pairs.sort(key=lambda k: k[0], reverse=True) 在 LDA 中，线性判别式的数目至多为 c−1c-1c−1，其中 ccc 为类标签的数量。","s":"特征值和特征向量","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#eigenvalues-and-eigenvectors","p":976},{"i":992,"t":"为了衡量线性判别式 (特征向量) 捕获多少类别鉴别信息，对不同的线性判别式的辨别能力 (discriminability) 进行绘图： import matplotlib.pyplot as plt tot = sum(eigen_vals.real) discr = [(i / tot) for i in sorted(eigen_vals.real, reverse=True)] cum_discr = np.cumsum(discr) plt.bar( range(1, 14), discr, alpha=0.5, align=\"center\", label='individual \"discriminability\"', ) plt.step(range(1, 14), cum_discr, where=\"mid\", label='cumulative \"discriminability\"') plt.ylabel('\"discriminability\" ratio') plt.xlabel(\"Linear Discriminants\") plt.ylim([-0.1, 1.1]) plt.legend(loc=\"best\") plt.show()","s":"线性判别式的辨别能力","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#discrimination-ability-of-linear-discriminant","p":976},{"i":994,"t":"使用投影矩阵转换原始数据集： x′=xW↓X′=XW\\begin{align} \\boldsymbol x' & = \\boldsymbol x \\boldsymbol W \\\\ & \\downarrow \\\\ \\boldsymbol X' & = \\boldsymbol X \\boldsymbol W \\end{align}x′X′​=xW↓=XW​​ w = np.hstack( (eigen_pairs[0][1][:, np.newaxis].real, eigen_pairs[1][1][:, np.newaxis].real) ) X_train_lda = X_train_std.dot(w) colors = [\"r\", \"b\", \"g\"] markers = [\"s\", \"x\", \"o\"] for l, c, m in zip(np.unique(y_train), colors, markers): plt.scatter( X_train_lda[y_train == l, 0], X_train_lda[y_train == l, 1] * (-1), c=c, label=l, marker=m, ) plt.xlabel(\"LD 1\") plt.ylabel(\"LD 2\") plt.legend(loc=\"lower right\") plt.show() 代码绘图结果如下，类别在新的特征子空间中线性可分：","s":"特征提取","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#feature-extraction","p":976},{"i":996,"t":"边界绘图函数 plot_decision_regions 见之前的文章。 通过 sklearn.discriminant_analysis.LinearDiscriminantAnalysis 将测试集和训练集降至二维，然后使用逻辑回归对降维后的测试集进行线性分类： from sklearn.linear_model import LogisticRegression from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA lda = LDA(n_components=2) lr = LogisticRegression() X_train_lda = lda.fit_transform(X_train_std, y_train) X_test_lda = lda.transform(X_test_std) lr.fit(X_train_lda, y_train) plot_decision_regions(X_train_lda, y_train, classifier=lr) plt.xlabel(\"LD 1\") plt.ylabel(\"LD 2\") plt.legend(loc=\"lower left\") plt.show() 在降维空间绘制已通过训练得到的决策边界，观察是否能够进行很好地分类： plot_decision_regions(X_test_lda, y_test, classifier=lr) plt.xlabel(\"LD 1\") plt.ylabel(\"LD 2\") plt.legend(loc=\"lower left\") plt.show() 可以看到逻辑回归在新的二维子空间上表现很好，在测试数据集上只有很少样本分类错误。","s":"Scikit-learn 实现","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#sklearn-implementation","p":976},{"i":998,"t":"与特征选择类似，我们可以使用特征提取 (Feature Extraction) 来减少数据集中特征的数量。其区别在于，特征选择保留原始特征，而特征提取则将数据转换或投影到新的特征空间。本文介绍主成分分析 (Principal Component Analysis，PCA)，它是一种无监督的线性变换技术，主要特点是特征提取和降维。","s":"主成分分析","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"","p":997},{"i":1000,"t":"PCA 广泛应用于不同领域，帮助我们根据特征之间的相关性来识别数据中的模式。其原理是找到高维数据中最大方差的方向，并将其投影到与原始维数相同或更少维数的新的正交空间上。 新的子空间的正交轴 (即主成分) 可以被解释为在新的特征轴彼此正交的约束下的最大方差的方向，如下图所示： 在上图中，x1x_1x1​ 和 x2x_2x2​ 是原始特征轴，PC1 和 PC2 是数据集的第一主成分和第二主成分。 PCA 构造了一个维度变换矩阵 W\\boldsymbol WW，将高维空间向量 x\\boldsymbol xx 映射到低维空间向量 z\\boldsymbol zz： x=[x1,x2,⋯ ,xd],x∈Rd↓xW,W∈Rd×kz=[z1,z2,⋯ ,zk],z∈Rk\\begin{align} \\boldsymbol x & = [x_1, x_2, \\cdots, x_d], x \\in R^d \\\\ & \\downarrow \\boldsymbol x \\boldsymbol W, \\boldsymbol W \\in R^{d \\times k} \\\\ \\boldsymbol z & = [z_1, z_2, \\cdots, z_k], z \\in R^k \\end{align}xz​=[x1​,x2​,⋯,xd​],x∈Rd↓xW,W∈Rd×k=[z1​,z2​,⋯,zk​],z∈Rk​​ 维度变换后，第一主成分将具有最大的方差，第二主成分将具有第二大的方差，以此类推。这些主成分必须均不相关 (即使输入特征之间有相关性)，数学表示为主成分向量之间两两正交。 需要注意的是，PCA 方向对数据缩放非常敏感。举例来说，假设一个特征在 [-100,100] 之间平均分布，另外一个特征在 [-1,1] 之间平均分布，PCA 会认为前一个特征重要得多。因此在运用 PCA 时，需要使用标准化将输入特征缩放到相同的尺度。 PCA 的算法流程的简单介绍如下： 对输入的 ddd 维数据集 X\\boldsymbol XX 进行标准化。 构造协方差矩阵。 计算协方差矩阵的特征向量和特征值。 对特征值进行降序排序，对相应的特征向量进行排序。 提取 kkk 个最大特征值对应的特征向量，其中 kkk (k≤dk \\le dk≤d) 是新特征子空间的维数。 使用提取的 kkk 个特征向量构造投影矩阵 W\\boldsymbol WW。 使用投影矩阵 W\\boldsymbol WW 对 X\\boldsymbol XX 进行变换，得到新的 kkk 维特征子空间。","s":"算法思想","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#algorithm-principle","p":997},{"i":1002,"t":"导入 Wine 数据集，第 1 列为其分类标签，第 2~14 列为特征。分割数据集为 70% 的训练集和 30% 的测试集： import pandas as pd from sklearn.model_selection import train_test_split df_wine = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data\", header=None, ) X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=0, stratify=y ) 对训练集和测试集进行标准化： from sklearn.preprocessing import StandardScaler sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test)","s":"数据导入和标准化","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#data-load-and-standardization","p":997},{"i":1004,"t":"接下来引入协方差矩阵。对于 nnn 的两个特征向量 (机器学习中通常用列向量表示) xj\\boldsymbol x_jxj​ 和 xk\\boldsymbol x_kxk​，其协方差如下： σjk=σkj=1n∑i=1n(xj(i)−μj)(xk(i)−μk)\\begin{align} \\sigma_{jk} = \\sigma_{kj} = {\\frac 1 n} \\sum_{i=1}^n (x_j^{(i)} - \\mu_j)(x_k^{(i)} - \\mu_k) \\end{align}σjk​=σkj​=n1​i=1∑n​(xj(i)​−μj​)(xk(i)​−μk​)​​ 其中 μj\\mu_jμj​ 和 μk\\mu_kμk​ 分别代表 xj\\boldsymbol x_jxj​ 和 xk\\boldsymbol x_kxk​ 平均值。对于 PCA 的样本，在标准化后这两个平均值都为 0。 协方差 σjk\\sigma_{jk}σjk​ 可以表示 xj\\boldsymbol x_jxj​ 和 xk\\boldsymbol x_kxk​ 的相关程度： 若 σjk\\sigma_{jk}σjk​ 大于 0，表明这两个特征正相关，即一个特征随另外一个特征的变大而变大。 若 σjk\\sigma_{jk}σjk​ 大于 0，表明这两个特征负相关，即一个特征随另外一个特征的变大而变小。 若 σjk\\sigma_{jk}σjk​ 等于 0，表明这两个特征不相关，即一个特征变化不受另外一个特征的变化影响。此时这两个特征向量两两正交。 接下来构建协方差矩阵 Σ\\boldsymbol \\SigmaΣ(这是大写的希腊字母 Sigma，不要与求和符号 ∑\\sum∑ 混淆)。以 3 个特征为例，其协方差矩阵如下： Σ=[σ12σ12σ13σ21σ22σ23σ31σ32σ32]\\begin{align} \\boldsymbol \\Sigma = \\begin{bmatrix} \\sigma_1^2 & \\sigma_{12} & \\sigma_{13} \\\\ \\sigma_{21} & \\sigma_2^2 & \\sigma_{23} \\\\ \\sigma_{31} & \\sigma_{32} & \\sigma_3^2 \\end{bmatrix} \\end{align}Σ=​σ12​σ21​σ31​​σ12​σ22​σ32​​σ13​σ23​σ32​​​​​ 协方差矩阵 Σ\\boldsymbol \\SigmaΣ 是实对称矩阵，矩阵对角线为特征的方差，其余为特征之间的协方差。Σ\\boldsymbol \\SigmaΣ 的特征向量表示主成分 (即具有最大方差的方向)，对应的特征值为主成分的大小。 Wine 数据集有 13 个特征，我们将从 13×13 维协方差矩阵中获得 13 个特征向量和特征值。","s":"协方差矩阵的构造","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#construct-covariance-matrix","p":997},{"i":1006,"t":"求解矩阵的特征值 λ\\lambdaλ 和特征向量 v\\boldsymbol vv，使其满足条件： Σv=λv\\begin{align} {\\boldsymbol \\Sigma} {\\boldsymbol v} = \\lambda {\\boldsymbol v} \\end{align}Σv=λv​​ 矩阵特征值和特征向量的数学计算较为繁琐，这里不作过多介绍。 使用 numpy 内置的 linalg.eig 函数可以方便地计算特征值和特征向量： import numpy as np cov_mat = np.cov(X_train_std.T) eigen_vals, eigen_vecs = np.linalg.eig(cov_mat) 上面通过 numpy.cov 创建协方差矩阵，然后通过 numpy.linalg.eig 对其进行特征分解，产生由 13 个特征值组成的向量 eigen_vals 和 13 个特征向量 (列向量) 组成的矩阵 eigen_vecs。","s":"特征值和特征向量","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#eigenvalues-and-eigenvectors","p":997},{"i":1008,"t":"把 ddd 维空间压缩到 kkk 维空间，需要从中挑选包含信息最多 (方差最大) 的 kkk 个特征向量 (主成分)。特征值反映了特征向量的大小，需要降序排序特征值，然后提取前 kkk 个特征值对应的特征向量。 在提取特征之前，为了观察特征的方差之间的差异，这里先对特征值的解释方差占比 (explained variance ratio) 进行绘图： import matplotlib.pyplot as plt tot = sum(eigen_vals) var_exp = [(i / tot) for i in sorted(eigen_vals, reverse=True)] cum_var_exp = np.cumsum(var_exp) plt.bar( range(1, 14), var_exp, alpha=0.5, align=\"center\", label=\"individual explained variance\", ) plt.step(range(1, 14), cum_var_exp, where=\"mid\", label=\"cumulative explained variance\") plt.ylabel(\"Explained variance ratio\") plt.xlabel(\"Principal component index\") plt.legend(loc=\"best\") plt.show() 可以看到，第一主成分大约占了方差的 40%，第二主成分大约占了总方差的 20%，这两个特征值解释了接近 60% 的数据集方差。 需要注意的是，整个过程中没有使用 y_train。PCA 属于无监督学习，在分析和提取主成分的过程中从来不使用类的标签。","s":"解释方差占比","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#explained-variance-ratio","p":997},{"i":1010,"t":"本节以 Wine 数据集进行演示特征提取的最后几个步骤： 提取 kkk 个最大特征值对应的特征向量，其中 kkk (k≤dk \\le dk≤d) 是新特征子空间的维数。 使用提取的 kkk 个特征向量构造投影矩阵 W\\boldsymbol WW， 使用投影矩阵 W\\boldsymbol WW 对 X\\boldsymbol XX 进行变换，得到新的 kkk 维特征子空间。 简单来说，就是按照特征值降序将特征向量进行排序，从特征向量中构造投影矩阵，并使用投影矩阵将数据转换到低维子空间。 特征向量排序： # Make a list of (eigenvalue, eigenvector) tuples eigen_pairs = [ (np.abs(eigen_vals[i]), eigen_vecs[:, i]) for i in range(len(eigen_vals)) ] # Sort the (eigenvalue, eigenvector) tuples from high to low eigen_pairs.sort(key=lambda k: k[0], reverse=True) 以两个主成分为例，构造投影矩阵： 注意，为了后面的绘制二维散点图，因此这里只挑选了两个主成分。实际中应该根据效率性能的平衡来确定主成分的个数。 w = np.hstack((eigen_pairs[0][1][:, np.newaxis], eigen_pairs[1][1][:, np.newaxis])) 使用投影矩阵转换原始数据集： x′=xW↓X′=XW\\begin{align} \\boldsymbol x' & = \\boldsymbol x \\boldsymbol W \\\\ & \\downarrow \\\\ \\boldsymbol X' & = \\boldsymbol X \\boldsymbol W \\end{align}x′X′​=xW↓=XW​​ 其中 X\\boldsymbol XX 为原始数据集，x\\boldsymbol xx 为其中的单个样本；X‘\\boldsymbol X‘X‘ 为变换后的数据集， x’\\boldsymbol x’x’ 为其中的单个样本。 X_train_pca = X_train_std.dot(w) 原始的 Wine 数据集有 13 维，通过特征矩阵 W∈R13×2\\boldsymbol W \\in R^{13 \\times 2}W∈R13×2 后降为 2 维，对降维后的数据集进行绘图： colors = [\"r\", \"b\", \"g\"] markers = [\"s\", \"x\", \"o\"] for l, c, m in zip(np.unique(y_train), colors, markers): plt.scatter( X_train_pca[y_train == l, 0], X_train_pca[y_train == l, 1], c=c, label=l, marker=m, ) plt.xlabel(\"PC 1\") plt.ylabel(\"PC 2\") plt.legend(loc=\"lower left\") plt.show() 从下图可以看到，数据沿着 xxx 轴 (第一主成分) 比沿着 yyy 轴 (第二主成分) 更加分散，与上节中第一主成分的方差较大相吻合。另外，降维后的分类数据仍保留其特征，可以用线性分类器进行分类。 需要再次强调，PCA 是一种无监督的技术，在整个 PCA 过程中不使用任何类标签信息。","s":"特征提取","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#feature-extraction","p":997},{"i":1012,"t":"边界绘图函数 plot_decision_regions 见之前的文章。 通过 sklearn.decomposition.PCA 将测试集和训练集降至二维，然后使用逻辑回归对降维后的测试集进行线性分类： from sklearn.linear_model import LogisticRegression from sklearn.decomposition import PCA pca = PCA(n_components=2) lr = LogisticRegression() X_train_pca = pca.fit_transform(X_train_std) X_test_pca = pca.transform(X_test_std) lr.fit(X_train_pca, y_train) plot_decision_regions(X_train_pca, y_train, classifier=lr) plt.xlabel(\"PC 1\") plt.ylabel(\"PC 2\") plt.legend(loc=\"lower left\") plt.show() 在降维空间绘制已通过训练得到的决策边界，观察是否能够进行很好地分类： plot_decision_regions(X_test_pca, y_test, classifier=lr) plt.xlabel(\"PC1\") plt.ylabel(\"PC2\") plt.legend(loc=\"lower left\") plt.show() 可以看到逻辑回归在新的二维子空间上表现很好，在测试数据集上只有很少样本分类错误。 关于数据集的解释方差占比，可以设置 PCA 的参数 n_components 为 None，对测试集进行变换后通过 explained_variance_ratio_ 属性得到： pca = PCA(n_components=None) X_train_pca = pca.fit_transform(X_train_std) print(pca.explained_variance_ratio_)","s":"Scikit-learn 实现","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#sklearn-implementation","p":997},{"i":1014,"t":"避免过拟合的方法中，有一种称为特征选择 (Feature Selection)，即选择最重要的特征、同时舍弃不重要的特征。本文以 Wine 数据集为例，使用随机森林演示了特征重要性评估和选择方法。","s":"特征的重要性","u":"/docs/machine-learning/feature-selection/feature-importance","h":"","p":1013},{"i":1016,"t":"Wine 数据集是对意大利同一地区种植的葡萄酒进行化学分析的结果，但起源于三种不同的品种。 第一列为其分类标签 (即葡萄酒产地)，其余 13 列为特征。 import pandas as pd df_wine = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data\", header=None, ) df_wine.columns = [ \"Class label\", \"Alcohol\", \"Malic acid\", \"Ash\", \"Alcalinity of ash\", \"Magnesium\", \"Total phenols\", \"Flavanoids\", \"Nonflavanoid phenols\", \"Proanthocyanins\", \"Color intensity\", \"Hue\", \"OD280/OD315 of diluted wines\", \"Proline\", ] print(df_wine.head()) 按分类标签分割数据集为 70% 的训练数据集和 30% 的测试数据集： from sklearn.model_selection import train_test_split X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=0, stratify=y )","s":"Wine 数据集","u":"/docs/machine-learning/feature-selection/feature-importance","h":"#wine-dataset","p":1013},{"i":1018,"t":"scikit-learn 中的 sklearn.ensemble.RandomForestClassifier 已经集成了特征的重要性排序，实现如下： from sklearn.ensemble import RandomForestClassifier feat_labels = df_wine.columns[1:] forest = RandomForestClassifier(n_estimators=500, random_state=1) forest.fit(X_train, y_train) importances = forest.feature_importances_ indices = np.argsort(importances)[::-1] for f in range(X_train.shape[1]): print(\"{:2d}) {:30}{:f} \".format(f + 1, feat_labels[f], importances[f])) 特征的重要性排序如下： 1) Proline 0.179927 2) Color intensity 0.153158 3) Flavanoids 0.146123 4) Alcohol 0.138224 5) OD280/OD315 of diluted wines 0.114818 6) Hue 0.077525 7) Total phenols 0.058236 8) Malic acid 0.030856 9) Alcalinity of ash 0.030000 10) Proanthocyanins 0.025713 11) Magnesium 0.025135 12) Nonflavanoid phenols 0.011548 13) Ash 0.008738 对特征重要性进行绘图： import matplotlib.pyplot as plt plt.title(\"Feature Importance\") plt.bar(range(X_train.shape[1]), importances[indices], align=\"center\") plt.xticks(range(X_train.shape[1]), feat_labels, rotation=90) plt.xlim([-1, X_train.shape[1]]) plt.tight_layout() plt.show() 需要提到的是，scikit-learn 还实现了一个 SelectFromModel 对象，它在模型拟合之后根据用户指定的阈值选择特征，并且可以将不同估计器 (Estimator) 与其连接。 以随机森林为例，以使用以下代码将特征阈值设置为 0.1，可以筛选出最重要的五个特征： from sklearn.feature_selection import SelectFromModel sfm = SelectFromModel(forest, threshold=0.1, prefit=True) X_selected = sfm.transform(X_train) print(\"Number of samples that meet this criterion:\", X_selected.shape[0]) for f in range(X_selected.shape[1]): print( \"{:2d}) {:30}{:f} \".format( f + 1, feat_labels[indices[f]], importances[indices[f]] ) ) 输出如下： Number of samples that meet this criterion: 124 1) Proline 0.179927 2) Color intensity 0.153158 3) Flavanoids 0.146123 4) Alcohol 0.138224 5) OD280/OD315 of diluted wines 0.114818","s":"特征重要性的 Scikit-learn 实现","u":"/docs/machine-learning/feature-selection/feature-importance","h":"#feature-importance-using-sklearn","p":1013},{"i":1021,"t":"我应该用自顶向下的方法还是自底向上的方法学习机器学习相关知识？ 自顶向下 自顶向下学习方法从整体或高层次的概念、理论或问题开始，然后逐步细化、深入和扩展。它强调整体观念和宏观理解，并通过逐渐分解、归纳和推演形成更具体的细节。 自底向上 相比之下，自底向上学习方法从具体的细节、实例或基本要素开始，然后逐步组合、归纳和抽象形成更高层次的概念、理论或问题。它强调逐步建立对细节的理解和掌握，并通过将细节逐步整合和推广来形成整体认知。","s":"如何学习","u":"/docs/machine-learning/ml-basics/how-to-learn","h":"","p":1020},{"i":1023,"t":"您需要快速熟悉或者重温机器学习中使用先决知识，例如： 数学 线性代数 概率与统计 数值优化 微积分 Python 编程基础 在开始学习机器学习所需的数学基础知识时，您需要使用自底向上的方法。数学知识和 Python 基础是一套系统性的知识，因此自底向上更合适。 学到什么程度合适？每个算法的原理和数学建模是不一样的，不是说数学知识掌握 100 分才能进行机器学习。建议同步进行。","s":"先决知识：自底向上","u":"/docs/machine-learning/ml-basics/how-to-learn","h":"#how-to-learn-prerequisite","p":1020},{"i":1025,"t":"假设您需要开始学习机器学习，从高级概念开始，然后逐步深入。 如果您自学，那么在学习机器学习时使用自顶向下的方法更有意义，否则你可能会在不重要的概念上浪费很多时间。 例如，您可能想运行一个基于 CNN 的图像识别，这样您就可以建立一定程度的好奇心，例如 CNN 是如何工作的？如果你有一个已完成的 demo，你就会更有动力去寻找答案。正如在编程中，我们从 hello world 开始学习而不是从汇编开始学习一样。 因此，我建议在学习先决条件 (数学、Python) 时使用自底向上的方法。然后在学习机器学习本身时，使用自顶向下的方法。这两个步骤可以同步进行。","s":"机器学习知识：自顶向下","u":"/docs/machine-learning/ml-basics/how-to-learn","h":"#how-to-learn-ml","p":1020},{"i":1027,"t":"进入 21 世纪，你所考虑的不应该是“我没有学习资料”：学习资料网上随处可见，而且未来会越来越多。 这是我建议的学习方法： 对于初学者：遵循“自顶向下”的方法，首先学习 python，然后按照在线教程或者进行编码。在小型数据集上构建您的第一个机器学习模型。 对于中级开发人员：遵循“自底向上”的方法，阅读官方文档、机器学习书籍，并尝试解决 kaggle 数据集上的一些问题。选择您感兴趣的一个或一些类别，并了解该算法为何有效，了解其数学原理。 对于高级开发人员：我认为高级开发人员不太需要阅读本文；如果实在有什么建议，建议多读论文和代码，多问“为什么”和“怎么做”。","s":"在哪里学习","u":"/docs/machine-learning/ml-basics/how-to-learn","h":"#where-to-learn","p":1020},{"i":1030,"t":"信息 在这个网站中，python 默认为 python3，因为 python2 不再维护。 近年来，Python 已成为世界上最流行的编程语言之一。它用于从机器学习到构建网站和软件测试的各个方面。它可供开发人员和非开发人员使用。 在后面的文章中，我们假设您了解 python 的基本知识并且在您的计算机上安装了 python。我们建议您使用 Anaconda 安装，这样您就不需要再安装 python。 如果你确实想只安装 Python，请参阅下面的链接： Python Source Releases for Linux Python Releases for Windows Python Releases for macOS 对于那些刚接触 Python 的人，请查看 Python 教程。","s":"什么是 Python？","u":"/docs/machine-learning/ml-basics/python-environment-installation","h":"#what-is-python","p":1028},{"i":1032,"t":"信息 在这个网站中，Anaconda 是 python3 版本的 Anaconda3。 Anaconda 是用于科学计算 (数据科学、机器学习应用、大规模数据处理、预测分析等) 的 Python 和 R 编程语言的发行版，旨在简化包管理和部署。该发行版包括适用于 Windows、Linux 和 macOS 的数据科学包。 您可以从 Anaconda Archive 下载 Anaconda 并按照以下指南进行安装。 在 Linux 上安装 Anaconda 在 Windows 上安装 Anaconda 在 macOS 上安装 Anaconda 如果您想了解 Anaconda 中包含哪些软件包，请查看此链接。","s":"什么是 Anaconda？","u":"/docs/machine-learning/ml-basics/python-environment-installation","h":"#what-is-anaconda","p":1028},{"i":1034,"t":"Jupyter Notebook 和 Jupyter Lab 都是交互式计算环境，使用户能够在基于 Web 的界面中处理代码、数据和多媒体内容。与传统的 Jupyter Notebook 相比，Jupyter Lab 提供了增强的现代化界面以及附加的特性和功能。 在 Anaconda 中，Jupyter Notebook 和 Jupyter Lab 默认已经安装。 启动 Jupyter Lab： jupyter lab 或者启动 Jupyter Notebook： jupyter notebook","s":"什么是 Jupyter？","u":"/docs/machine-learning/ml-basics/python-environment-installation","h":"#what-is-jupyter","p":1028},{"i":1036,"t":"本文介绍机器学习的三大类型：监督式学习、非监督式学习和强化学习。 机器学习在近 30 多年已发展为一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、计算复杂性理论等多门学科。机器学习理论主要是设计和分析一些让计算机可以自动“学习”的算法。机器学习算法是一类从数据中自动分析获得规律，并利用规律对未知数据进行预测的算法。机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA 序列测序、语音和手写识别、战略游戏和机器人等领域。","s":"机器学习三大类型","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"","p":1035},{"i":1038,"t":"监督式学习，是一个机器学习中的方法，可以由训练资料中学到或建立一个模式，并依此模式推测新的实例。训练资料是由输入物件 (通常是向量) 和预期输出所组成。函数的输出可以是一个连续的值 (称为回归分析)，或是预测一个分类标签 (称为分类)。","s":"监督式学习 (Supervised Learning)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#supervised-learning","p":1035},{"i":1040,"t":"在分类中，函数的输出是一个分类标签。常见的例子有垃圾邮件识别和手写数字识别。","s":"分类 (Classification)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#classification","p":1035},{"i":1042,"t":"在回归中，函数的输出可以是一个连续的值，通常是一个数学函数。例如，对于某一职位，员工薪水和工龄之间的关系。","s":"回归 (Regression)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#regression","p":1035},{"i":1044,"t":"另一种类型的机器学习是强化学习。在强化学习中，目标是开发一种基于与环境交互来改善其性能的代理。由于存在反馈机制，因此可以认为强化学习和监督式学习相关。然而，在强化学习中，这种反馈不是正确标签，而是强调如何基于环境而行动，以取得最大化的预期利益。 一个普遍的例子是象棋引擎。在这里，代理根据棋盘状态 (环境) 决定一系列动作，反馈可以在游戏结束时定义为胜或负。","s":"强化学习 (Reinforcement Learning)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#reinforcement-learning","p":1035},{"i":1046,"t":"在无监督学习中，我们处理的是未标记的数据或未知结构的数据。使用无监督的学习技术，我们能够探索我们的数据的结构，以提取有意义的信息。常见的非监督式学习方法有聚类分析和降维。","s":"非监督式学习 (Unsupervised Learning)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#unsupervised-learning","p":1035},{"i":1048,"t":"聚类是一种探索性数据分析技术，能够在不知道输入对象的任何先验知识的情况下，将其分成不同的集群。每个集群包含一定程度相似的对象，但是与其他集群中的对象不相似。例如营销人员将客户分类成不同的客户群。","s":"聚类 (Clustering)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#clustering","p":1035},{"i":1050,"t":"通常，我们正在处理高维度的数据，这对于有限的存储空间和机器学习算法的计算性能是很大的挑战。降维是指在某些限定条件下，降低随机变量的维度，得到一组“不相关”的主变量，同时保留大部分有效信息。","s":"降维 (Dimensionality Reduction)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#dimensionality-reduction","p":1035},{"i":1052,"t":"机器学习主要包括预处理、训练、评估和预测阶段。本文演示了如何使用 scikit-learn 进行分类。","s":"入门：基于 Iris 数据集","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"","p":1051},{"i":1054,"t":"原始数据很少呈现为学习算法的最佳性能所需的形式和形状。因此，数据的预处理是任何机器学习应用程序中最关键的步骤之一。以鸢尾花数据集为例，我们可以将原始数据看作一系列花图，从中我们可以提取有意义的特征，如花的颜色，花萼和花瓣的长度和宽度。 许多机器学习算法还要求能够将所有特征在同一数量级，这通常通过归一化或者正态分布等特征变换方法来实现。部分特征可能是高度相关的，特征可能存在冗余。在这种情况下，降维可以减少所需的存储空间，并且算法可以学习得更快。 为了确定机器学习算法是否不仅在训练集上表现良好的同时，能很好地预测到新的数据，我们将数据集随机分为相互独立的训练集和测试集。训练集用于训练和优化我们的机器学习模型，测试集用于最终评估最终模型。 在开始加载数据之前，按照常用约定导入这些库： import pandas as pd import numpy as np import matplotlib.pyplot as plt","s":"预处理","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#preprocessing","p":1051},{"i":1056,"t":"您可以在此处下载 iris.csv。 names = [\"sepal-length\", \"sepal-width\", \"petal-length\", \"petal-width\", \"class\"] dataset = read_csv(\"iris.csv\", names=names)","s":"加载数据","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#load-data","p":1051},{"i":1058,"t":"打印 dataset 的形状： print(dataset.shape) # (150, 5) 打印 dataset 的前几行 (head() 默认打印 5 行)： print(dataset.head()) # sepal-length sepal-width petal-length petal-width class # 0 5.1 3.5 1.4 0.2 Iris-setosa # 1 4.9 3.0 1.4 0.2 Iris-setosa # 3 4.6 3.1 1.5 0.2 Iris-setosa # 2 4.7 3.2 1.3 0.2 Iris-setosa # 4 5.0 3.6 1.4 0.2 Iris-setosa 打印 dataset 的 class 和每个 class 的数量： print(dataset.groupby(\"class\").size()) # class # Iris-setosa 50 # Iris-versicolor 50 # Iris-virginica 50 # dtype: int64 打印 dataset 的统计数据： print(dataset.describe()) # sepal-length sepal-width petal-length petal-width # count 150.000000 150.000000 150.000000 150.000000 # mean 5.843333 3.054000 3.758667 1.198667 # std 0.828066 0.433594 1.764420 0.763161 # min 4.300000 2.000000 1.000000 0.100000 # 25% 5.100000 2.800000 1.600000 0.300000 # 50% 5.800000 3.000000 4.350000 1.300000 # 75% 6.400000 3.300000 5.100000 1.800000 # max 7.900000 4.400000 6.900000 2.500000","s":"探索性数据分析","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#exploratory-data-analysis","p":1051},{"i":1060,"t":"有些文章将 train-test-split 作为数据预处理过程，有些文章认为这是一个训练过程。 在我看来，它是数据预处理和训练之间的桥梁。 将原始数据随机分成 80% 的训练集和 20% 的测试集： from sklearn.model_selection import train_test_split array = dataset.values X = array[:, 0:4] y = array[:, 4] X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.20, shuffle=True, random_state=1 ) 备注 random_state 是用于分割的随机种子。设置后，将在不同的计算机上生成相同的训练数据集和测试数据集，以便重现结果。 print(X_train.shape, X_test.shape, y_train.shape, y_test.shape) # (120, 4) (30, 4) (120,) (30,)","s":"测试集训练集划分","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#test-train-split","p":1051},{"i":1062,"t":"目前已有许多不同的机器学习算法，用于解决不同的问题任务。每个分类算法都有其固有的偏差，在实践中，比较几个不同的算法然后从中选出最优算法，对于训练和选择最佳性能模型至关重要。一个常用的算法度量指标是分类准确率，即正确分类数据的比重。 另外，我们可以使用不同的交叉验证技术，其中将训练数据集进一步分为训练和验证子集，以估计模型的泛化性能。 最后，算法的默认参数对于实际问题往往不会具有最佳表现。因此，我们可以使用超参数优化技术，通过调节算法参数，我们可以提高算法的性能。 在训练之前，我们需要知道我们面临什么样的问题：这是一个多类分类监督问题。我们可以使用 DecisionTreeClassifier 分类器。 from sklearn.tree import DecisionTreeClassifier tree_model = DecisionTreeClassifier() tree_model.fit(X_train, Y_train)","s":"训练","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#training","p":1051},{"i":1064,"t":"在选择了模型并使用训练集进行训练之后，我们可以使用测试集来来估计泛化误差。 如果我们对其性能感到满意，可以使用这个模型来预测新的未来数据。 需要注意的是，训练的参数 (如特征缩放和降维) 仅从训练数据集中获得，在测试数据上测量的性能可能是过拟合的。 进行评估： print(f\"Score of tree_model: {tree_model.score(X_validation, Y_validation)}\") # Score of tree_model: 0.9666666666666667 对新的未知数据进行分类： print( f\"Prediction of [6.0, 3.1, 5.1, 1.9]: {tree_model.predict([[6.0, 3.1, 5.1, 1.9]])[0]}\" ) # Prediction of [6.0, 3.1, 5.1, 1.9]: Iris-virginica","s":"评估和预测","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#evaluation-and-prediction","p":1051},{"i":1066,"t":"欠拟合 (Underfitting) 和过拟合 (Overfitting) 是机器学习中的重要概念和常见问题。本文就这两个概念进行简单说明。","s":"欠拟合和过拟合","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"","p":1065},{"i":1068,"t":"机器学习的目的，是利用已知数据 (训练数据) 训练出机器学习的模型，然后将该模型应用到未知数据 (测试数据) 中。 从已知数据归纳总结，然后对未知数据的预测称为泛化 (Generalize)。 泛化能力好的机器学习模型，在使用训练数据进行训练后，对没有见过的数据可以进行准确预测。反之，泛化能力差的模型不能对未知数据进行准确预测。","s":"泛化","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"#generalization","p":1065},{"i":1070,"t":"过拟合和欠拟合都会导致模型没有良好的泛化能力。 以二维数据的二分分类为例，如下图： 左子图：对已知数据欠缺拟合，存在高偏差 (high bias) 右子图：对已知数据过度拟合，存在高方差 (high variance) 中间子图：对已知数据良好拟合，可以概括出已知数据的特征","s":"拟合","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"#fitting","p":1065},{"i":1072,"t":"欠拟合的模型存在高偏差，对于已知数据和未知数据都表现不佳。 在机器学习中一般较少讨论欠拟合。一般而言，增加模型复杂度即可解决欠拟合问题。","s":"欠拟合","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"#underfitting","p":1065},{"i":1074,"t":"过拟合的模型存在高方差，对已知数据表现良好，但是对未知数据表现不佳。 过拟合表示对已知数据进行了过度解读，包括其中的噪音和细节，导致训练出来的模型不能很好地适用于未知数据。 样本数量少、噪音数据多、模型参数过多和复杂度过高等原因，都会导致过拟合。","s":"过拟合","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"#overfitting","p":1065},{"i":1076,"t":"网格搜索 (Grid Search) 是一种通过遍历给定的超参数组合来优化模型表现的方法。 机器学习算法中有两类参数：一类是从训练集中学习到的参数，比如逻辑回归中的权重参数和偏差参数，另一类是超参数 (Hyperparameter)，也就是需要人工设定的参数，比如正则项系数或者决策树的深度。 网格搜索通过寻找最佳的超参数组合，可以进一步帮助提高模型的性能。","s":"网格搜索","u":"/docs/machine-learning/model-selection/grid-search","h":"","p":1075},{"i":1078,"t":"网格搜索的思想非常简单，属于暴力 (Brute Force) 算法：穷尽每个超参数的组合来评估对应的模型性能，然后挑选模型性能的超参数。","s":"算法思想","u":"/docs/machine-learning/model-selection/grid-search","h":"#algorithm-principle","p":1075},{"i":1080,"t":"import pandas as pd from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.iloc[:, 2:] y = df.iloc[:, 1] le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, stratify=y, random_state=1 )","s":"数据导入和预处理","u":"/docs/machine-learning/model-selection/grid-search","h":"#data-load-and-preprocessing","p":1075},{"i":1082,"t":"创建管道对象： from sklearn.preprocessing import StandardScaler from sklearn.svm import SVC from sklearn.pipeline import make_pipeline pipe_svc = make_pipeline(StandardScaler(), SVC(random_state=1)) 通过网格搜索所有超参数组合 (下面是 8 + 64 = 72 个) 中的准确率最高的一个： from sklearn.model_selection import GridSearchCV param_range = [0.0001, 0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0] param_grid = [ {\"svc__C\": param_range, \"svc__kernel\": [\"linear\"]}, {\"svc__C\": param_range, \"svc__gamma\": param_range, \"svc__kernel\": [\"rbf\"]}, ] gs = GridSearchCV(estimator=pipe_svc, param_grid=param_grid, scoring=\"accuracy\", cv=10) gs.fit(X_train, y_train) 网格搜索得到的最优模型的准确率、参数、以及模型调用如下： print(gs.best_score_) # Output: 0.984615384615 print(gs.best_params_) # Output: {'svc__C': 100.0, 'svc__gamma': 0.001, 'svc__kernel': 'rbf'} clf = gs.best_estimator_ clf.fit(X_train, y_train) print(\"Test accuracy: {:.3f}\".format(clf.score(X_test, y_test))) # Output: Test accuracy: 0.974","s":"基于 Scikit-learn 的网格搜索","u":"/docs/machine-learning/model-selection/grid-search","h":"#grid-search-using-sklearn","p":1075},{"i":1084,"t":"Holdout 验证 (Holdout Validation) 是一种广泛使用的模型验证方法，将数据集划分为不同的集合，一部分用于训练，另一部分用于测试。","s":"Holdout 验证","u":"/docs/machine-learning/model-selection/holdout","h":"","p":1083},{"i":1086,"t":"对于评估机器学习模型的泛化性能，一种经典和普遍的方法是 holdout 交叉验证。holdout 方法将初始数据集分成单独的训练集 (Training Set) 和测试集 (Test Set)，前者用于模型训练，后者用于评估模型的泛化性能。在典型的机器学习程序中，人们会对超参数进行不断调整和比较，以进一步提高对不可见数据进行预测的性能。这个过程被称为模型选择 (Model Selection)，尝试将超参数调整至最优。 但是，如果在模型选择过程中重复使用相同的测试集，那么这个测试集就不是真正意义上的测试集。真正的测试集应该是不可见的。如果一直尝试对测试集拟合，这个测试集实际上就是训练集的一部分。 尽管如此，许多人仍然将数据集分为测试集和训练集，然后按照测试集的表现来进行模型选择。这不是一个良好的机器学习方法。","s":"数据集划分：训练集和测试集","u":"/docs/machine-learning/model-selection/holdout","h":"#数据集划分训练集和测试集","p":1083},{"i":1088,"t":"一种更好的模型选择方法是将数据分成三部分：训练集、验证集 (Validation Set) 和测试集。训练集用于拟合不同的模型，然后根据模型在验证集上的表现来进行模型选择。在整个训练过程中，测试集是不可见的，不会对测试集过拟合。 下图说明了保持交叉验证的概念，使用训练集和验证集进行反复训练并将超参数调整至较优水平，再使用测试集来评估模型的泛化性能： Holdout 方法的缺点是算法评估对数据划分比较敏感，对于不同的数据划分比例和不同的分布，评估结果可能会有较大差异。","s":"数据集划分：训练集、验证集和测试集","u":"/docs/machine-learning/model-selection/holdout","h":"#数据集划分训练集验证集和测试集","p":1083},{"i":1090,"t":"K 折交叉验证 (K-Fold Cross-Validation) 是一种模型选择 (Model Selection) 方法，将初始样本分为 K 个折叠 (Fold)，一个折叠作为数据集、其余 K-1 个折叠作为训练集，反复重复上述步骤 K 次并将得到的结果综合起来，得到最终的评估结果。K 折交叉验证在一定程度上解决了 holdout 只划分数据一次的缺点。","s":"K 折交叉验证","u":"/docs/machine-learning/model-selection/k-fold-cross-validation","h":"","p":1089},{"i":1092,"t":"K 折交叉验证的步骤是，随机地将训练数据集分成 K 次折叠。其中 K-1 次折叠用于模型训练、另外一个折叠用于性能评估，上述步骤重复 K 次 (每次抽取不同的折叠)，获得 K 个模型的性能评估结果。 K 折交叉验证可以得到令人满意的泛化性能的最优超参数值，具有更高的准确率和鲁棒性。K 折交叉验证表现好的原因在于其拥有更多的训练样本，且每个训练样本都恰好验证一次，这样可以产生较低的方差。 下图说明了详细的 K 折交叉验证 (K = 10) 的流程，其中 test fold 实际上发挥的是验证集的作用： 根据以往研究人员的经验，超参数 K 一般推荐采用 10。如果 K 太小，方差会较高，如果 K 太大，模型的训练时间会变长。对于大型数据集，可以适当降低 K 的值 (如 K = 5)。 一种特殊的 K 折交叉验证为留一验证 (Leave-One-Out Cross-Validation，LOOCV)，K = n (n 为数据集的样本数量)，每折只有一个样本，可以用于处理小数据集。","s":"K 折交叉验证原理","u":"/docs/machine-learning/model-selection/k-fold-cross-validation","h":"#kfold-cross-validation-principle","p":1089},{"i":1094,"t":"分层 K 折交叉验证 (Stratified K-Fold Cross-Validation) 是对 K 折交叉验证的改进，分层的意思是每一个折叠中的分类比例都与原始数据集相同，能更好地适用于不同分类的样本数差异较大的情况。下面基于 scikit-learn 中的进行说明。 先做好交叉验证之前的前提工作，其中 pipe_lr 是管道对象，封装了标准化、PCA 和逻辑回归： import pandas as pd from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA from sklearn.linear_model import LogisticRegression from sklearn.pipeline import make_pipeline df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.loc[:, 2:].values y = df.loc[:, 1].values le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.20, stratify=y, random_state=1 ) pipe_lr = make_pipeline( StandardScaler(), PCA(n_components=2), LogisticRegression(random_state=1) ) 使用 sklearn.model_selection.StratifiedKFold 进行 K 折分层交叉验证： import numpy as np from sklearn.model_selection import StratifiedKFold kfold = StratifiedKFold(n_splits=10, random_state=1).split(X_train, y_train) scores = [] for k, (train, test) in enumerate(kfold): pipe_lr.fit(X_train[train], y_train[train]) score = pipe_lr.score(X_train[test], y_train[test]) scores.append(score) print('Fold: {:2d}, Class dist.: {}, Acc: {:.3f}'.format(k + 1, np.bincount(y_train[train]), score) 将样本分为 n_splits=10 个折叠，在每一次循环中使用管道对象 pipe_lr 对测试集进行训练，然后观察训练后的模型在验证集上的准确率。运行结果如下： Fold: 1, Class dist.: [256 153], Acc: 0.935 Fold: 2, Class dist.: [256 153], Acc: 0.935 Fold: 3, Class dist.: [256 153], Acc: 0.957 Fold: 4, Class dist.: [256 153], Acc: 0.957 Fold: 5, Class dist.: [256 153], Acc: 0.935 Fold: 6, Class dist.: [257 153], Acc: 0.956 Fold: 7, Class dist.: [257 153], Acc: 0.978 Fold: 8, Class dist.: [257 153], Acc: 0.933 Fold: 9, Class dist.: [257 153], Acc: 0.956 Fold: 10, Class dist.: [257 153], Acc: 0.956 计算 10 次训练的准确率的平均值和方差： print(\"CV accuracy: {:.3f} +/- {:.3f}\".format(np.mean(scores), np.std(scores))) # Output: CV accuracy: 0.950 +/- 0.014 上面是通过具体实现流程说明交叉验证的工作流程，也可以通过 sklearn.model_selection.cross_val_score 实现模型评估： scores = cross_val_score(estimator=pipe_lr, X=X_train, y=y_train, cv=10, n_jobs=1) print(\"CV accuracy scores: {}\".format(scores)) print(\"CV accuracy: {:.3f} +/- {:.3f}\".format(np.mean(scores), np.std(scores))) 其中 cv 为折叠数量，n_jobs 是代码运行使用 CPU 核心的数量，结果如下： CV accuracy scores: [ 0.93478261 0.93478261 0.95652174 0.95652174 0.93478261 0.95555556 0.97777778 0.93333333 0.95555556 0.95555556] CV accuracy: 0.950 +/- 0.014 结果与之前一致，采用 cross_val_score 可以非常便捷地对交叉验证模型进行评估。","s":"分层 K 折交叉验证的 scikit-learn 实现","u":"/docs/machine-learning/model-selection/k-fold-cross-validation","h":"#stratified-kfold-cross-validation-using-sklearn","p":1089},{"i":1096,"t":"嵌套交叉验证 (Nested Cross-Validation) 算法具有更稳定的性能，在训练集上的结果相对于测试集几乎是无偏的。 其思想是先使用 K 折交叉验证将数据分为训练折叠和测试折叠，然后在训练折叠内部使用 K 折交叉验证后用于测试折叠，以选择最优模型。如下为 5×2 折叠交叉验证的示意图： 基于 SVM 的 5×2 折叠交叉验证，实现如下： gs = GridSearchCV(estimator=pipe_svc, param_grid=param_grid, scoring=\"accuracy\", cv=2) scores = cross_val_score(gs, X_train, y_train, scoring=\"accuracy\", cv=5) print(\"CV accuracy: {:.3f} +/- {:.3f}\".format(np.mean(scores), np.std(scores))) # Output: CV accuracy: 0.974 +/- 0.015 基于决策树的 5×2 折叠交叉验证，实现如下： from sklearn.tree import DecisionTreeClassifier gs = GridSearchCV( estimator=DecisionTreeClassifier(om_state=0), param_grid=[{\"max_depth\": [1, 2, 3, 4, 5, 6, 7, None]}], scoring=\"accuracy\", cv=2, ) scores = cross_val_score(gs, X_train, y_train, scoring=\"accuracy\", cv=5) print(\"CV accuracy: %.3f +/- %.3f\" % (np.mean(scores), np.std(scores))) # Output: CV accuracy: 0.934 +/- 0.016 可以看到，基于 SVM 模型的嵌套交叉验证相比于基于决策树的交叉验证更优。","s":"嵌套交叉验证","u":"/docs/machine-learning/model-selection/k-fold-cross-validation","h":"#nested-cross-validation","p":1089},{"i":1098,"t":"绘制模型的学习曲线 (Learning Curve) 和验证曲线 (Validation Curve) 是常用的调试手段，能够从中直观看到模型在测试集和验证集上的表现，以及判断是否有过拟合或欠拟合问题。","s":"学习曲线和验证曲线","u":"/docs/machine-learning/model-selection/learning-and-validation-curve","h":"","p":1097},{"i":1100,"t":"通过曲线可以容易看出模型是否存在高偏差或高偏差，以及判断否能够通过增加样本数目解决这些问题。 常见的学习曲线如下图所示： 左上子图：学习曲线和验证曲线都很差，高偏差、欠拟合。 右上子图：学习曲线很好但验证曲线很差，高方差、过拟合 右下子图：在拥有一定数量样本的情况下，具有良好的方差 - 偏差权衡 (bias-variance tradeoff) 和拟合程度。","s":"方差 - 偏差权衡","u":"/docs/machine-learning/model-selection/learning-and-validation-curve","h":"#variance-bias-tradeoff","p":1097},{"i":1102,"t":"绘制学习曲线时，自变量为样本数，因变量为评价指标。 读取 wdbc 数据集，并将其分为 80% 的训练集和 20% 的测试集： import pandas as pd from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA from sklearn.linear_model import LogisticRegression from sklearn.pipeline import make_pipeline df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.loc[:, 2:].values y = df.loc[:, 1].values le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.20, stratify=y, random_state=1 ) 使用 sklearn.model_selection.learning_curve 生成学习曲线的值，然后通过 pyplot 绘制模型对于训练集和验证集的准确率： pipe_lr：scikit-learn 管道对象 train_sizes：测试集为数据集 X_train 的比例 (这里为 10%、20%、…、100%) cv：分层交叉验证的折叠数 K n_jobs：使用的 CPU 核心数 train_scores 和 test_scores：共有 len(train_sizes) 行，每行有 cv 个交叉验证的分数，因此均值标准差都是按行计算 axis=1 plt.fill_between：通过标准差绘制数据的离散程度 import numpy as np import matplotlib.pyplot as plt from sklearn.model_selection import learning_curve pipe_lr = make_pipeline(StandardScaler(), LogisticRegression(random_state=1)) train_sizes, train_scores, test_scores = learning_curve( estimator=pipe_lr, X=X_train, y=y_train, train_sizes=np.linspace(0.1, 1.0, 10), cv=10, n_jobs=1, ) train_mean = np.mean(train_scores, axis=1) train_std = np.std(train_scores, axis=1) test_mean = np.mean(test_scores, axis=1) test_std = np.std(test_scores, axis=1) plt.plot( train_sizes, train_mean, color=\"blue\", marker=\"o\", markersize=5, label=\"training accuracy\", ) plt.fill_between( train_sizes, train_mean + train_std, train_mean - train_std, alpha=0.15, color=\"blue\", ) plt.plot( train_sizes, test_mean, color=\"green\", linestyle=\"--\", marker=\"s\", markersize=5, label=\"validation accuracy\", ) plt.fill_between( train_sizes, test_mean + test_std, test_mean - test_std, alpha=0.15, color=\"green\" ) plt.grid() plt.xlabel(\"Number of training samples\") plt.ylabel(\"Accuracy\") plt.legend(loc=\"lower right\") plt.ylim([0.8, 1.03]) plt.show() 得到模型的准确率随样本数变化的曲线： 若训练集的样本数小于 250，训练集的准确率很高，但是测试集的准确率相对较低，模型存在过拟合问题。若训练集的样本数大于 250，则模型在训练集和验证集上的表现都非常好。","s":"学习曲线","u":"/docs/machine-learning/model-selection/learning-and-validation-curve","h":"#learning-curve","p":1097},{"i":1104,"t":"和学习曲线不同，验证曲线的因变量往往是模型的参数值，如逻辑回归中的参数 C。 使用 sklearn.model_selection.validation_curve 生成学习曲线的值，然后通过 pyplot 绘制模型对于训练集和验证集的准确率： pipe_lr：scikit-learn 管道对象 logisticregression__C：逻辑回归的超参数 C，正则化系数的倒数 param_range：超参数的取值范围 from sklearn.model_selection import validation_curve param_range = [0.001, 0.01, 0.1, 1.0, 10.0, 100.0] train_scores, test_scores = validation_curve( estimator=pipe_lr, X=X_train, y=y_train, param_name=\"logisticregression__C\", param_range=param_range, cv=10, ) train_mean = np.mean(train_scores, axis=1) train_std = np.std(train_scores, axis=1) test_mean = np.mean(test_scores, axis=1) test_std = np.std(test_scores, axis=1) plt.plot( param_range, train_mean, color=\"blue\", marker=\"o\", markersize=5, label=\"training accuracy\", ) plt.fill_between( param_range, train_mean + train_std, train_mean - train_std, alpha=0.15, color=\"blue\", ) plt.plot( param_range, test_mean, color=\"green\", linestyle=\"--\", marker=\"s\", markersize=5, label=\"validation accuracy\", ) plt.fill_between( param_range, test_mean + test_std, test_mean - test_std, alpha=0.15, color=\"green\" ) plt.grid() plt.xscale(\"log\") plt.legend(loc=\"lower right\") plt.xlabel(\"Parameter C\") plt.ylabel(\"Accuracy\") plt.ylim([0.8, 1.03]) plt.show() 得到模型的准确率随逻辑回归参数 C 变化的曲线： 在正则化强度较大 (C 小于 0.01) 时，模型有一定程度的欠拟合 (高偏差)，但在正则化强度较小 (C 大于 10) 时，模型又会出现过拟合 (高方差)。超参数 C 的取值在 0.01 和 0.1 之间时，模型性能最优。","s":"验证曲线","u":"/docs/machine-learning/model-selection/learning-and-validation-curve","h":"#validation-curve","p":1097},{"i":1106,"t":"本文介绍了基于梯度下降法 (Gradient Descent，GD) 的自适应线性神经元 (Adaptive Linear Neuron，Adaline)，以及对应的算法实现。","s":"Adaline 和梯度下降法","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"","p":1105},{"i":1108,"t":"Adaline 是 1960 年由 Bernard Widrow 和 Tedd Hoff 提出的，被认为是对 Rosenblatt 感知器的改进。Adaline 算法定义了最小化成本函数的核心概念，为之后一些更先进的机器学习算法 (如逻辑回归和支持向量机) 奠定了基础。 Adaline 规则和 Rosenblatt 感知器的不同之处在于在调整权重的激活函数不同，前者采用线性函数，后者采用单位阶跃函数。在 Adaline 中，ϕ(wTx)=wTx\\phi(w^T x)= w^T xϕ(wTx)=wTx。 Adaline 在使用线性激活函数更新权重之外，采用单位阶跃的量化器来预测类标签，如下图所示：","s":"Adaline 原理","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#adaline-principle","p":1105},{"i":1110,"t":"定义在学习过程中需要优化的目标函数，是监督式学习的关键步骤。目标函数通常是需要最小化的成本函数。对于 Adaline，我们定义权重的成本函数 JJJ 为预测类标签和实际类标签之间的方差总和 (Sum of Squared Errors，SSE)。 J(w)=12Σi(y(i)−ϕ(z(i)))2\\begin{align} J(w) = {\\frac 1 2} \\Sigma_i(y^{(i)} - \\phi(z^{(i)}))^2 \\end{align}J(w)=21​Σi​(y(i)−ϕ(z(i)))2​​ 线性激活函数的优点是，成本函数可微并且是凸函数 (局部最小值为全局最小值)。 ∂J(w)∂wj=12Σi(y(i)−ϕ(z(i)))2∂z∂z∂wj=−Σi(y(i)−ϕ(z(i)))xj(i)\\begin{align} {\\frac {\\partial J(w)} {\\partial w_j}} &= {\\frac 1 2} {\\frac {\\Sigma_i(y^{(i)} - \\phi(z^{(i)}))^2} {\\partial z}} {\\frac {\\partial z} {\\partial w_j}} \\\\ &= -{\\Sigma_i(y^{(i)} - \\phi(z^{(i)}))} x_j^{(i)} \\end{align}∂wj​∂J(w)​​=21​∂zΣi​(y(i)−ϕ(z(i)))2​∂wj​∂z​=−Σi​(y(i)−ϕ(z(i)))xj(i)​​​ 这里采用一种称为梯度下降的算法来找出最小化成本函数对应的权重，以便对 Iris 数据子集的样本进行分类。如下图所示，可以将梯度下降类比成下山的过程，直到达到局部最小值。每次训练相当于在斜坡上行走一步，其中步长由学习率和斜率决定： 梯度下降法的思想是，如果函数在某点可微且有定义，那么函数在该点沿着梯度相反的方向下降最快，下降系数用学习率 η\\etaη 表示： Δwj=−ηΔJ(w)\\begin{align} \\Delta w_j = -\\eta \\Delta J(w) \\end{align}Δwj​=−ηΔJ(w)​​ 每次训练后，权重更新为： wj:=wj+Δwj=wj−ηΔJ(w)\\begin{align} w_j := w_j + \\Delta w_j = w_j - \\eta \\Delta J(w) \\end{align}wj​:=wj​+Δwj​=wj​−ηΔJ(w)​​ 权重的每次更新是基于训练集中的所有样本 (而并非单个样本)，因此这种最原始的梯度下降法也被称为批量梯度下降法 (Batch Gradient Descent，BGD)。","s":"批量梯度下降法","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#batch-gradient-descent","p":1105},{"i":1112,"t":"下面代码中，采用了面向对象的方法，定义 Adaline 为 Python 类。 import numpy as np class AdalineGD(object): def __init__(self, eta=0.01, n_iter=50, random_state=1): self.eta = eta self.n_iter = n_iter self.random_state = random_state def fit(self, X, y): rgen = np.random.RandomState(self.random_state) self.w_ = rgen.normal(loc=0.0, scale=0.01, size=1 + X.shape[1]) self.cost_ = [] for i in range(self.n_iter): net_input = self.net_input(X) output = self.activation(net_input) errors = y - output self.w_[1:] += self.eta * X.T.dot(errors) self.w_[0] += self.eta * errors.sum() cost = (errors**2).sum() / 2.0 self.cost_.append(cost) return self def net_input(self, X): return np.dot(X, self.w_[1:]) + self.w_[0] def activation(self, X): return X def predict(self, X): return np.where(self.activation(X) >= 0.0, 1, -1) 对算法训练过程进行绘图： import pandas as pd import matplotlib.pyplot as plt df = pd.read_csv( \"https://archive.ics.uci.edu/ml/achine-learning-databases/iris/iris.data\", header=None, ) X = df.iloc[:100, [0, 2]].values y = df.iloc[:100, 4].values y = np.where(y == \"Iris-setosa\", -1, 1) fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(8, 4)) ada1 = AdalineGD(n_iter=10, eta=0.01).fit(X, y) ax[0].plot(range(1, len(ada1.cost_) + 1), np.log10(ada1.cost_), marker=\"o\") ax[0].set_xlabel(\"Epochs\") ax[0].set_ylabel(\"log(Sum-squared-error)\") ax[0].set_title(\"Adaline - Learning rate 0.01\") ada2 = AdalineGD(n_iter=10, eta=0.0001).fit(X, y) ax[1].plot(range(1, len(ada2.cost_) + 1), ada2.cost_, marker=\"o\") ax[1].set_xlabel(\"Epochs\") ax[1].set_ylabel(\"Sum-squared-error\") ax[1].set_title(\"Adaline - Learning rate 0.0001\") plt.tight_layout() plt.show() 从上图中的左子图可以观察到，如果学习率太大，由于每次训练都越过了局部最小值，成本函数得不到最小化，反而错误会在学习过程中一直增加。右子图中，成本函数能够逐渐降低，但由于选择了非常小的学习率 η=0.0001\\eta = 0.0001η=0.0001 ，以至于算法需要很长时间才能收敛。 下图中的左子图说明了成本函数随权重的调整而最小化，右子图说明了学习率太大所带来的问题： 许多机器学习算法需要某些方法才能实现最佳性能，梯度下降法是从特征缩放 (feature scaling) 中受益的许多算法之一。这里我们将使用一种称为标准化 (standardization) 的特征缩放方法，能够将数据变换成服从标准正态分布 (平均值为 0，标准差为 1)。 例如，对第 jjj 个特征，只需要对每个训练样本减去样本均值 μj\\mu_jμj​ ，并除以标准差 σj\\sigma_jσj​ ： xj′=xj−μjσj\\begin{align} x_j^{'} = {\\frac {x_j - \\mu_j} {\\sigma_j}} \\end{align}xj′​=σj​xj​−μj​​​​ 标准化可以通过 NumPy 的方法轻松实现： X_std = np.copy(X) X_std[:, 0] = (X[:, 0] - X[:, 0].mean()) / X[:, 0].std() X_std[:, 1] = (X[:, 1] - X[:, 1].mean()) / X[:, 1].std() 标准化后，再次使用 Adaline 进行训练，可以看到在学习率 η=0.01\\eta = 0.01η=0.01 上可以收敛： ada = AdalineGD(n_iter=15, eta=0.01) ada.fit(X_std, y) plot_decision_regions(X_std, y, classifier=ada) plt.title(\"Adaline - Gradient Descent\") plt.xlabel(\"sepal length [standardized]\") plt.ylabel(\"petal length [standardized]\") plt.legend(loc=\"upper left\") plt.tight_layout() plt.show() plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker=\"o\") plt.xlabel(\"Epochs\") plt.ylabel(\"Sum-squared-error\") plt.tight_layout() plt.show() 上图显示成本函数 SSE 随着训练次数的增加而逐渐变小，样本正确分类时，成本函数得到最小化，但并不为 0。","s":"基于批量梯度下降法的 Adaline 实现","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#adaline-implementation-based-on-batch-gradient-descent","p":1105},{"i":1114,"t":"批量梯度下降法在每次训练时，都需要使用到所有样本。假设有一个百万数量级的数据集 (这在机器学习中并不罕见)，使用批量梯度下降法会带来极大的计算成本，其权重的更新如下： Δw=ηΣi(y(i)−ϕ(z(i)))x(i)\\begin{align} \\Delta w = \\eta {\\Sigma_i(y^{(i)} - \\phi(z^{(i)}))} x^{(i)} \\end{align}Δw=ηΣi​(y(i)−ϕ(z(i)))x(i)​​ 一种流行替代方法是随机梯度下降法 (Stochastic Gradient Descent，SGD)，有时也称为迭代 (Iterative) 梯度下降法或在线 (On-line) 梯度下降法，每次使用单个训练样本对权重进行更新： Δw=η(y(i)−ϕ(z(i)))x(i)\\begin{align} \\Delta w = \\eta (y^{(i)} - \\phi(z^{(i)})) x^{(i)} \\end{align}Δw=η(y(i)−ϕ(z(i)))x(i)​​ 相对于批量梯度下下降法，随机梯度下降法的权重的更新频率更快，通常收敛也会更快。由于单个样本有很大的随机性 (即噪音较大)，每次迭代方向并不是都朝着局部最优解方向，算法准确率会相对下降一些。但随着训练次数增加，通常能够收敛到局部最优解附近。采用随机梯度下降法时，在每个训练时期都需要对样本进行洗牌，以获得随机样本。 在随机梯度下降法的实现中，固定学习率 η\\etaη 经常被随着时间的推移而减少的自适应学习率来代替，如 num1niter+num2{\\frac {num1} {n_{iter} + num2}}niter​+num2num1​, 其中 num1num1num1 和 num2num2num2 是常数。 随机梯度下降法的另一个优点是在线学习 (On-line Learning)。每当获取新的样本数据之后，都可以对模型进行训练。这能够适用于持续输入大量数据 (如网络应用中的用户数据) 的情况，另外每次训练后可以丢弃样本以防止数据累积造成的空间不足。 小批量梯度下降法 (Mini-batch Gradient Descent，MBGD) 是批量梯度下降法和随机梯度下降法思想的融合，每次训练采用小批量的样本 (例如样本总数为 1000，每次训练采用其中随机 10 个)，可以克制 BGD 训练较慢和 SGD 噪音较大的问题。","s":"随机梯度下降法","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#stochastic-gradient-descent","p":1105},{"i":1116,"t":"对上节的代码进行调整，添加权重的在线学习函数 partial_fit、训练样本洗牌函数 _shuffle、权重初始化函数 _initialize_weights 和权重调节函数 _update_weights，实现基于随机梯度下降的 Adaline。 import numpy as np class AdalineSGD(object): def __init__(self, eta=0.01, n_iter=10, shuffle=True, random_state=None): self.eta = eta self.n_iter = n_iter self.w_initialized = False self.shuffle = shuffle self.random_state = random_state def fit(self, X, y): self._initialize_weights(X.shape[1]) self.cost_ = [] for i in range(self.n_iter): if self.shuffle: X, y = self._shuffle(X, y) cost = [] for xi, target in zip(X, y): cost.append(self._update_weights(xi, target)) avg_cost = sum(cost) / len(y) self.cost_.append(avg_cost) return self def partial_fit(self, X, y): if not self.w_initialized: self._initialize_weights(X.shape[1]) if y.ravel().shape[0] > 1: for xi, target in zip(X, y): self._update_weights(xi, target) else: self._update_weights(X, y) return self def _shuffle(self, X, y): r = self.rgen.permutation(len(y)) return X[r], y[r] def _initialize_weights(self, m): \"\"\"Initialize weights to small random numbers\"\"\" self.rgen = np.random.RandomState(self.random_state) self.w_ = self.rgen.normal(loc=0.0, scale=0.01, size=1 + m) self.w_initialized = True def _update_weights(self, xi, target): output = self.activation(self.net_input(xi)) error = target - output self.w_[1:] += self.eta * xi.dot(error) self.w_[0] += self.eta * error cost = 0.5 * error**2 return cost def net_input(self, X): return np.dot(X, self.w_[1:]) + self.w_[0] def activation(self, X): return X def predict(self, X): return np.where(self.activation(self.net_input(X)) >= 0.0, 1, -1) 对算法训练过程进行绘图： ada = AdalineSGD(n_iter=15, eta=0.01, random_state=1) ada.fit(X_std, y) plot_decision_regions(X_std, y, classifier=ada) plt.title(\"Adaline - Stochastic Gradient Descent\") plt.xlabel(\"sepal length [standardized]\") plt.ylabel(\"petal length [standardized]\") plt.legend(loc=\"upper left\") plt.tight_layout() plt.show() plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker=\"o\") plt.xlabel(\"Epochs\") plt.ylabel(\"Average Cost\") plt.tight_layout() plt.show() 从上图可以看到，随机梯度下降法每次使用单个样本训练，成本函数 SSE 也可以快速收敛。对于在线学习的场景，对单个样本调用 ada.partial_fit(X_std[0, :], y[0]) 即可对训练模型进行更新。","s":"基于随机梯度下降法的 Adaline 实现","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#adaline-implementation-based-on-stochastic-gradient-descent","p":1105},{"i":1118,"t":"Scikit-learn 的名字源于 SciKit (SciPy Toolkit)，即 SciPy 的第三方扩展工具包。经过历年的发展，Scikit-learn 已成为最流行的机器学习库之一。本文以 Iris 数据集的分类为例，对其进行简介。 如官方网站所介绍，以下是 scikit-learn 的特征： 简单高效的数据挖掘和数据分析工具 可供任何人使用，可在任何环境中重复使用 基于 NumPy，SciPy，以及 matplotlib 开放源码，可用作商业用途 (需遵循 BSD 许可证) 关于 scikit-learn 的安装，请参照这份文档。","s":"Scikit-learn 简介：使用感知器","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"","p":1117},{"i":1120,"t":"从 scikit-learn 加载 Iris 数据集，其中第三列表示花瓣长度 petal length，第四列表示花瓣宽度 petal width。这些类已经转换为整数标签，其中 0 = 山鸢尾 Iris-Setosa，1 = 变色鸢尾 Iris-Versicolor，2 = 维吉尼亚鸢尾 Iris-Verginica。 from sklearn import datasets import numpy as np iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target print(\"Class labels:\", np.unique(y)) # output: Class labels: [0 1 2]","s":"数据导入","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#load-data","p":1117},{"i":1122,"t":"通过函数 sklearn.model_selection.train_test_split 将 150 个数据集分为 70% 的训练集和 30% 的测试集： from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) 这里 stratify=y 表示按照标签值将数据集划分，划分后训练集和测试集的标签具有相同的比例，可以用 np.bincount 打印其中每类标签的个数： print(\"Labels counts in y:\", np.bincount(y)) # output: Labels counts in y: [50 50 50] print( \"Labels counts in y_train:\", np.bincount(y_train) ) # output: Labels counts in y_train: [35 35 35] print( \"Labels counts in y_test:\", np.bincount(y_test) ) # output: Labels counts in y_test: [15 15 15] 通过函数 sklearn.preprocessing.StandardScaler 对特征进行标准化： from sklearn.preprocessing import StandardScaler sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test)","s":"预处理","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#preprocessing","p":1117},{"i":1124,"t":"使用神经元模型 sklearn.linear_model.Perceptron，对训练集进行训练 fit： from sklearn.linear_model import Perceptron ppn = Perceptron(max_iter=40, eta0=0.1, random_state=0) ppn.fit(X_train_std, y_train)","s":"模型训练","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#model-training","p":1117},{"i":1126,"t":"训练完成后，对测试集进行预测 predict，并打印出其中错误预测的样本数量： y_pred = ppn.predict(X_test_std) print( \"Misclassified samples: %d\" % (y_test != y_pred).sum() ) # output: Misclassified samples: 3 训练准确率可以通过 sklearn.metrics.accuracy_score 得到： from sklearn.metrics import accuracy_score print(\"Accuracy: %.2f\" % accuracy_score(y_test, y_pred)) # output: Accuracy: 0.93 scikit-learn 中的每种分类函数都有计算准确率的方法 score，执行时会计算 accuracy_score 并返回，输出结果相同： print(\"Accuracy: %.2f\" % ppn.score(X_test_std, y_test)) # output: Accuracy: 0.93","s":"模型评估","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#model-evaluation","p":1117},{"i":1128,"t":"对算法训练过程进行绘图： from matplotlib.colors import ListedColormap import matplotlib.pyplot as plt def plot_decision_regions(X, y, classifier, test_idx=None, resolution=0.02): markers = (\"s\", \"x\", \"o\", \"^\", \"v\") colors = (\"red\", \"blue\", \"lightgreen\", \"gray\", \"cyan\") cmap = ListedColormap(colors[: len(np.unique(y))]) x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1 x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1 xx1, xx2 = np.meshgrid( np.arange(x1_min, x1_max, resolution), np.arange(x2_min, x2_max, resolution) ) Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T) Z = Z.reshape(xx1.shape) plt.contourf(xx1, xx2, Z, alpha=0.3, cmap=cmap) plt.xlim(xx1.min(), xx1.max()) plt.ylim(xx2.min(), xx2.max()) for idx, cl in enumerate(np.unique(y)): plt.scatter( x=X[y == cl, 0], y=X[y == cl, 1], alpha=0.8, c=colors[idx], marker=markers[idx], label=cl, edgecolor=\"black\", ) if test_idx: X_test, y_test = X[test_idx, :], y[test_idx] plt.scatter( X_test[:, 0], X_test[:, 1], c=\"\", edgecolor=\"black\", alpha=1.0, linewidth=1, marker=\"o\", s=100, label=\"test set\", ) X_combined_std = np.vstack((X_train_std, X_test_std)) y_combined = np.hstack((y_train, y_test)) plot_decision_regions( X=X_combined_std, y=y_combined, classifier=ppn, test_idx=range(105, 150) ) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show() 绘制边界如下，其中测试集用黑色圆圈标出：","s":"绘制分类边界","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#plot-decistion-boundary","p":1117},{"i":1130,"t":"逻辑回归 (Logistic Regression) 是一种非常容易实现的分类模型，对于线性可分的情况有很好的表现。与之前文章中的感知器和 Adaline 类似，本文中的逻辑回归也是二元分类的线性模型。","s":"逻辑回归","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"","p":1129},{"i":1132,"t":"为了解释逻辑回归模型背后的思想，先介绍一个概念：比值比 (Odds ratio，OR)。 比值比的数学表示为 p1−p\\cfrac p {1-p}1−pp​，其中 ppp 为某事件可能发生的几率。 在此基础上，定义 logit 函数，即比值比的对数 (计算机科学中 log⁡\\loglog 表示自然对数)： logit(p)=log⁡p1−plogit(p) = \\log {\\cfrac p {1-p}}logit(p)=log1−pp​ logit 的作用是将范围为 (0,1)(0,1)(0,1) 的变量，映射到整个实数集。 对于给定的 xxx： y=1y=1y=1 的概率 p(y=1∣x)p(y=1 | x)p(y=1∣x) 在 (0,1)(0,1)(0,1) 之间。 基于神经元模型，输出的概率是由净输入 z=∑i=0mwixi=wTxz = \\sum_{i=0}^m w_i x_i = w^T xz=∑i=0m​wi​xi​=wTx 得到的。 基于以上逻辑，建立 p(y=1∣x)→zp(y=1 \\mid x) \\rightarrow zp(y=1∣x)→z 的 logit 映射： logit(p(y=1∣x))=z\\begin{align} logit(p(y=1 \\mid x)) = z \\end{align}logit(p(y=1∣x))=z​​ 因此，logit 的反函数即为 z→p(y=1∣x)z \\rightarrow p(y=1 \\mid x)z→p(y=1∣x) 的映射： ϕ(z)=11+e−z=p(y=1∣x)\\begin{align} \\phi (z) = \\cfrac 1 {1+e^{-z}} = p(y=1 \\mid x) \\end{align}ϕ(z)=1+e−z1​=p(y=1∣x)​​ 这里 ϕ(z)=11+e−z\\phi (z) = \\cfrac 1 {1+e^{-z}}ϕ(z)=1+e−z1​ 称为 logistic sigmoid 函数，通常简称为 sigmoid 函数。(sigmoid 意为 S-shaped，即 S 形状的曲线。) import matplotlib.pyplot as plt import numpy as np def sigmoid(z): return 1.0 / (1.0 + np.exp(-z)) z = np.arange(-7, 7, 0.1) phi_z = sigmoid(z) plt.plot(z, phi_z) plt.axvline(0.0, color=\"k\") plt.ylim(-0.1, 1.1) plt.xlabel(\"z\") plt.ylabel(\"$\\phi (z)$\") plt.yticks([0.0, 0.5, 1.0]) ax = plt.gca() ax.yaxis.grid(True) plt.show()","s":"算法思想","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#idea-of-algorithm","p":1129},{"i":1134,"t":"Adaline 和逻辑回归的差异，如下图所示： Adaline： 激活函数：线性函数 ϕ(z)=z\\phi (z) = zϕ(z)=z 阈值函数：阶跃函数 y^={1if ϕ(z)≥00otherwise\\hat y = \\begin{cases} 1 & if \\ \\phi (z) \\ge 0 \\\\[2ex] 0 & otherwise \\end{cases}y^​=⎩⎨⎧​10​if ϕ(z)≥0otherwise​ 逻辑回归： 激活函数：sigmoid 函数 ϕ(z)=11+e−z\\phi (z) = \\cfrac 1 {1+e^{-z}}ϕ(z)=1+e−z1​ 阈值函数：阶跃函数 y^={1if ϕ(z)≥0.50otherwise\\hat y = \\begin{cases} 1 & if \\ \\phi (z) \\ge 0.5 \\\\[2ex] 0 & otherwise \\end{cases}y^​=⎩⎨⎧​10​if ϕ(z)≥0.5otherwise​ 需要注意的是，逻辑回归中的条件 ϕ(z)≥0.5\\phi (z) \\ge 0.5ϕ(z)≥0.5，等价于 z≥0z \\ge 0z≥0。","s":"算法模型","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#algorithm-model","p":1129},{"i":1136,"t":"定义损失函数 (Loss Function) 和成本函数 (Cost Function)，以训练权重参数 www。 损失函数用于单个样本，代表预测输出 y^(i)\\hat y^{(i)}y^​(i) 和实际输出 y(i)y^{(i)}y(i) 之间的误差。 L(y^(i),y(i))=−[y(i)log⁡(y^(i))+(1−y(i))log⁡(1−y^(i))]={−log⁡(y^(i))if y(i)=1−log⁡(1−y^(i))if y(i)=0\\begin{align} L(\\hat y^{(i)}, y^{(i)}) & = -[y^{(i)} \\log (\\hat y^{(i)}) + (1 - y^{(i)}) \\log (1 - \\hat y^{(i)})] \\\\ & = \\begin{cases} -\\log (\\hat y^{(i)}) & \\text{if} \\ y^{(i)} = 1 \\\\[2ex] -\\log (1 - \\hat y^{(i)}) & \\text{if} \\ y^{(i)} = 0\\end{cases} \\end{align}L(y^​(i),y(i))​=−[y(i)log(y^​(i))+(1−y(i))log(1−y^​(i))]=⎩⎨⎧​−log(y^​(i))−log(1−y^​(i))​if y(i)=1if y(i)=0​​​ 当 y(i)=1y^{(i)} = 1y(i)=1 时，最小化 LLL 等价于 y^(i)\\hat y^{(i)}y^​(i) 接近于 1。 当 y(i)=0y^{(i)} = 0y(i)=0 时，最小化 LLL 等价于 y^(i)\\hat y^{(i)}y^​(i) 接近于 0。 成本函数是整个训练集的损失函数的平均值。最小化成本函数，可以得到最优的参数 www。 J(w)=1m∑i=1mL(y^(i),y(i))=−1m∑i=1m[y(i)log⁡(y^(i))+(1−y(i))log⁡(1−y^(i))]\\begin{align} J(w) & = {\\frac 1 m} \\sum _{i=1}^m L(\\hat y^{(i)}, y^{(i)}) \\\\ & = -{\\frac 1 m} \\sum _{i=1}^m [y^{(i)} \\log (\\hat y^{(i)}) + (1 - y^{(i)}) \\log (1 - \\hat y^{(i)})] \\end{align}J(w)​=m1​i=1∑m​L(y^​(i),y(i))=−m1​i=1∑m​[y(i)log(y^​(i))+(1−y(i))log(1−y^​(i))]​​","s":"损失函数和成本函数","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#loss-function-and-cost-function","p":1129},{"i":1138,"t":"逻辑回归的实现如下，使用梯度下降法进行参数训练： import numpy as np class LogisticRegressionGD(object): def __init__(self, eta=0.05, n_iter=100, random_state=1): self.eta = eta self.n_iter = n_iter self.random_state = random_state def fit(self, X, y): rgen = np.random.RandomState(self.random_state) self.w_ = rgen.normal(loc=0.0, scale=0.01, size=1 + X.shape[1]) self.cost_ = [] for i in range(self.n_iter): net_input = self.net_input(X) output = self.activation(net_input) errors = y - output self.w_[1:] += self.eta * X.T.dot(errors) self.w_[0] += self.eta * errors.sum() cost = -(y.dot(np.log(output)) + ((1 - y).dot(np.log(1 - output)))) / X.shape[0] self.cost_.append(cost) return self def net_input(self, X): return np.dot(X, self.w_[1:]) + self.w_[0] def activation(self, z): return 1.0 / (1.0 + np.exp(-np.clip(z, -250, 250))) def predict(self, X): return np.where(self.net_input(X) >= 0.0, 1, 0)","s":"Python 实现","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#python-implementation","p":1129},{"i":1140,"t":"以 Iris-setosa (标签 0) and Iris-versicolor (标签 1) 为例，采用逻辑回归分类，绘制决策边界如下， import matplotlib.pyplot as plt from plot_decision_regions import plot_decision_regions from sklearn import datasets from sklearn.model_selection import train_test_split iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=1, stratify=y) X_train_01_subset = X_train[(y_train == 0) | (y_train == 1)] y_train_01_subset = y_train[(y_train == 0) | (y_train == 1)] lrgd = LogisticRegressionGD(eta=0.05,n_iter=1000,random_state=1) lrgd.fit(X_train_01_subset,y_train_01_subset) plot_decision_regions(X=X_train_01_subset,y=y_train_01_subset,classifier=lrgd) plt.xlabel('petal length [standardized]') plt.ylabel('petal width [standardized]') plt.legend(loc='upper left') plt.show()","s":"绘制图像","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#plotting","p":1129},{"i":1142,"t":"本文介绍了逻辑回归 (Logistic Regression) 相关的数学知识，重点在于参数和变量的向量化。","s":"逻辑回归的向量化","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"","p":1141},{"i":1144,"t":"二元分类，是将示例归类为两个类别中的一类。 例如，有 1000 张 64 x 64 像素的图片，已知其中哪些是猫、哪些不是。在这个基础上，给一张新的 64 x 64 像素的图片，需要判断是不是猫。 这种基础的图像识别问题，可以归为二元分类。","s":"二元分类","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#binary-classification","p":1141},{"i":1146,"t":"训练样本数和测试样本数 m=mtrain=1000mtest=1\\begin{align} m = m_{train} & = 1000 \\\\ m_{test} & = 1 \\end{align}m=mtrain​mtest​​=1000=1​​ 单个样本的特征数 n=nx=64×64×3\\begin{align} n = n_x = 64 \\times 64 \\times 3 \\end{align}n=nx​=64×64×3​​ 单个样本的输入和输出 x(i)=[x1(i)x2(i)⋮xn(i)]∈Rn,y(i)∈{0,1}⊂R1\\begin{align} x^{(i)} = \\begin{bmatrix} x^{(i)}_1 \\\\x^{(i)}_2 \\\\ \\vdots \\\\ x^{(i)}_n \\end{bmatrix} \\in R^{n}, \\quad y^{(i)} \\in \\{0,1\\} \\subset R^1 \\end{align}x(i)=​x1(i)​x2(i)​⋮xn(i)​​​∈Rn,y(i)∈{0,1}⊂R1​​ 总样本的输入和输出 X=[x(1)x(2)⋯x(m)]∈Rn×mY=[y(1)y(2)⋯y(m)]∈R1×m\\begin{align} X & = \\begin{bmatrix} x^{(1)} & x^{(2)} & \\cdots & x^{(m)} \\end{bmatrix} \\in R^{n \\times m} \\\\ Y & = \\begin{bmatrix} y^{(1)} & y^{(2)} & \\cdots & y^{(m)} \\end{bmatrix} \\in R^{1 \\times m} \\end{align}XY​=[x(1)​x(2)​⋯​x(m)​]∈Rn×m=[y(1)​y(2)​⋯​y(m)​]∈R1×m​​","s":"数学建模","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#modeling-in-math","p":1141},{"i":1148,"t":"逻辑回归是一种学习算法，适用于输出为 0 或 1 的情况。逻辑回归的目标是最小化其预测输出 y^\\hat yy^​ 和实际输出 yyy 的误差。 Given x, y^=P(y=1∣x),where 0≤y^≤1\\begin{align} Given \\ x, \\ \\hat y = P(y =1 \\mid x), \\quad where \\ 0 \\leq \\hat y \\leq 1 \\end{align}Given x, y^​=P(y=1∣x),where 0≤y^​≤1​​ 对于单个样本，逻辑回归使用的参数如下： 输入：x∈Rnx \\in R^nx∈Rn 实际输出：y∈0,1y \\in {0,1}y∈0,1 权重：w∈Rnw \\in R^nw∈Rn 阈值/偏置：b∈R1b \\in R^1b∈R1 净输入/加权输入：z=wTx+bz = w^T x + bz=wTx+b 预测输出：y^=σ(z)=σ(wTx+b)\\hat y = \\sigma (z) = \\sigma (w^T x + b)y^​=σ(z)=σ(wTx+b) 将输入 zzz 映射到输出 y^\\hat yy^​ 的函数称为激活函数 (Activation Function)。这里激活函数使用 Sigmoid 函数σ(z)\\sigma (z)σ(z)，可以将输出映射到 [0,1][0,1][0,1] 的范围内： σ(z)=11+e−z\\begin{align} \\sigma (z) = \\frac 1 {1 + e^{-z}} \\end{align}σ(z)=1+e−z1​​​ 如果 zzz 很大，那么 y^\\hat yy^​ 接近于 1；反之则接近于 0。","s":"逻辑回归","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#logistic-regression","p":1141},{"i":1150,"t":"定义损失函数 (Loss Function) 和成本函数 (Cost Function)，以训练参数 www 和 bbb。 损失函数用于单个样本，代表预测输出 y^(i)\\hat y^{(i)}y^​(i) 和实际输出 y(i)y^{(i)}y(i) 之间的误差。 L(y^(i),y(i))=−[y(i)log⁡(y^(i))+(1−y(i))log⁡(1−y^(i))]\\begin{align} L(\\hat y^{(i)}, y^{(i)}) = -[y^{(i)} \\log (\\hat y^{(i)}) + (1 - y^{(i)}) \\log (1 - \\hat y^{(i)})] \\end{align}L(y^​(i),y(i))=−[y(i)log(y^​(i))+(1−y(i))log(1−y^​(i))]​​ 若 y(i)=1y^{(i)} = 1y(i)=1，则 L(y^(i)，y(i))=−log⁡(y^(i))L (\\hat y^{(i)}，y^{(i)}) = -\\log (\\hat y^{(i)})L(y^​(i)，y(i))=−log(y^​(i))，最小化 LLL 等价于 y^(i)\\hat y^{(i)}y^​(i) 接近于 1。 若 y(i)=0y^{(i)} = 0y(i)=0，则 L(y^(i)，y(i))=−log⁡(1−y^(i))L (\\hat y^{(i)}，y^{(i)}) = -\\log (1 - \\hat y^{(i)})L(y^​(i)，y(i))=−log(1−y^​(i))，最小化 LLL 等价于 y^(i)\\hat y^{(i)}y^​(i) 接近于 0。 成本函数是整个训练集的损失函数的平均值。最小化成本函数，可以得到最优的参数 www 和 bbb。 J(w,b)=1m∑i=1mL(y^(i),y(i))=−1m∑i=1m[y(i)log⁡(y^(i))+(1−y(i))log⁡(1−y^(i))]\\begin{align} J(w, b) & = {\\frac 1 m} \\sum _{i=1}^m L(\\hat y^{(i)}, y^{(i)}) \\\\ & = -{\\frac 1 m} \\sum _{i=1}^m [y^{(i)} \\log (\\hat y^{(i)}) + (1 - y^{(i)}) \\log (1 - \\hat y^{(i)})] \\end{align}J(w,b)​=m1​i=1∑m​L(y^​(i),y(i))=−m1​i=1∑m​[y(i)log(y^​(i))+(1−y(i))log(1−y^​(i))]​​","s":"函数定义","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#function-definition","p":1141},{"i":1152,"t":"梯度下降法的定义为，如果实值函数 F(x)F(x)F(x) 在点 aaa 处可微且有定义，那么函数 F(x)F(x)F(x) 在点 aaa 沿着梯度相反的方向下降最快。这里使用梯度下降法最小化成本函数 J(w，b)J(w，b)J(w，b)，以得到最优的参数 www 和 bbb，其中 α\\alphaα 为学习率 (learning rate)。 wj:=wj−α∂J∂wj,where j=1,2,⋯ ,nb:=b−α∂J∂b\\begin{align} w_j & := w_j - \\alpha \\frac {\\partial J} {\\partial w_j}, \\quad where \\ j = 1,2,\\cdots,n \\\\ b & := b - \\alpha \\frac {\\partial J} {\\partial b} \\end{align}wj​b​:=wj​−α∂wj​∂J​,where j=1,2,⋯,n:=b−α∂b∂J​​​ 记 a(i)=y^(i)=σ(z(i))a^{(i)} = \\hat y^{(i)} = \\sigma (z^{(i)})a(i)=y^​(i)=σ(z(i))： {∂J∂L=1m∂L∂a(i)=−y(i)a(i)+1−y(i)1−a(i)∂a(i)∂z(i)=e−z(i)(1+e−z(i))2=a(i)(1−a(i))⇒∂J∂z(i)=∂J∂L∂L∂a(i)∂a(i)∂z(i)=1m(a(i)−y(i))\\left \\lbrace \\begin{align} \\frac {\\partial J} {\\partial L} & = \\frac 1 m \\\\ \\frac {\\partial L} {\\partial a^{(i)}} & = - {\\frac {y^{(i)}} {a^{(i)}}} + {\\frac {1 - y^{(i)}} {1 - a^{(i)}}} \\\\ \\frac {\\partial a^{(i)}} {\\partial z^{(i)}} & = \\frac {e^{-z^{(i)}}} {(1 + e^{-z^{(i)}})^2} = a^{(i)}(1 - a^{(i)}) \\\\ \\end{align} \\right . \\\\ \\Rightarrow \\frac {\\partial J} {\\partial z^{(i)}} = {\\frac {\\partial J} {\\partial L}} {\\frac {\\partial L} {\\partial a^{(i)}}} {\\frac {\\partial a^{(i)}} {\\partial z^{(i)}}} = {\\frac 1 m} (a^{(i)} - y^{(i)})⎩⎨⎧​∂L∂J​∂a(i)∂L​∂z(i)∂a(i)​​=m1​=−a(i)y(i)​+1−a(i)1−y(i)​=(1+e−z(i))2e−z(i)​=a(i)(1−a(i))​​⇒∂z(i)∂J​=∂L∂J​∂a(i)∂L​∂z(i)∂a(i)​=m1​(a(i)−y(i)) 由于 z(i)=w1x1(i)+w2x2(i)+⋯+wnxn(i)+bz^{(i)} = w_1 x^{(i)} _1 + w_2 x^{(i)} _2 + \\cdots + w_n x^{(i)} _n + bz(i)=w1​x1(i)​+w2​x2(i)​+⋯+wn​xn(i)​+b，因此有： ∂J∂wj=∑i=1m∂J∂z(i)∂z(i)∂wj=∑i=1mxj(i)∂J∂z(i)∂J∂b=∑i=1m∂J∂z(i)∂z(i)∂b=∑i=1m∂J∂z(i)\\begin{align} \\frac {\\partial J} {\\partial w_j} & = \\sum_{i=1}^m {\\frac {\\partial J} {\\partial z^{(i)}}} {\\frac {\\partial z^{(i)}} {\\partial w_j}} = \\sum_{i=1}^m x_j^{(i)} {\\frac {\\partial J} {\\partial z^{(i)}}} \\\\ \\frac {\\partial J} {\\partial b} & = \\sum_{i=1}^m {\\frac {\\partial J} {\\partial z^{(i)}}} {\\frac {\\partial z^{(i)}} {\\partial b}} = \\sum_{i=1}^m {\\frac {\\partial J} {\\partial z^{(i)}}} \\end{align}∂wj​∂J​∂b∂J​​=i=1∑m​∂z(i)∂J​∂wj​∂z(i)​=i=1∑m​xj(i)​∂z(i)∂J​=i=1∑m​∂z(i)∂J​∂b∂z(i)​=i=1∑m​∂z(i)∂J​​​","s":"梯度下降法","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#梯度下降法","p":1141},{"i":1154,"t":"以 z=wTx+bz = w^T x + bz=wTx+b 为例，原始输入输出为： z(1)=w1x1(1)+w2x2(1)+⋯+wnxn(1)+bz(2)=w1x1(2)+w2x2(2)+⋯+wnxn(2)+b⋮z(m)=w1x1(m)+w2x2(m)+⋯+wnxn(m)+b\\begin{align} z^{(1)} & = w_1 x^{(1)}_1 + w_2 x^{(1)}_2 + \\cdots + w_n x^{(1)}_n + b \\\\ z^{(2)} & = w_1 x^{(2)}_1 + w_2 x^{(2)}_2 + \\cdots + w_n x^{(2)}_n + b \\\\ & \\vdots \\\\ z^{(m)} & = w_1 x^{(m)}_1 + w_2 x^{(m)}_2 + \\cdots + w_n x^{(m)}_n + b \\end{align}z(1)z(2)z(m)​=w1​x1(1)​+w2​x2(1)​+⋯+wn​xn(1)​+b=w1​x1(2)​+w2​x2(2)​+⋯+wn​xn(2)​+b⋮=w1​x1(m)​+w2​x2(m)​+⋯+wn​xn(m)​+b​​ 向量化之后为： [z(1)z(2)⋮z(m)]T=[w1w2⋮wn]T[x1(1)x1(2)⋯x1(m)x2(1)x2(2)⋯x2(m)⋮⋮⋱⋮xn(1)xn(2)⋯xn(m)]+[bb⋮b]T⇓Z=WTX+B\\begin{align} {\\begin{bmatrix} z^{(1)} \\\\ z^{(2)} \\\\ \\vdots \\\\ z^{(m)} \\end{bmatrix}}^T & = {\\begin{bmatrix} w_1 \\\\ w_2 \\\\ \\vdots \\\\ w_n \\end{bmatrix}}^T \\begin{bmatrix} x^{(1)}_1 & x^{(2)}_1 & \\cdots & x^{(m)}_1 \\\\ x^{(1)}_2 & x^{(2)}_2 & \\cdots & x^{(m)}_2 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ x^{(1)}_n & x^{(2)}_n & \\cdots & x^{(m)}_n \\end{bmatrix} + {\\begin{bmatrix} b \\\\ b \\\\ \\vdots \\\\ b \\end{bmatrix}}^T \\\\ & \\Downarrow \\\\ Z & = W^T X + B \\end{align}​z(1)z(2)⋮z(m)​​TZ​=​w1​w2​⋮wn​​​T​x1(1)​x2(1)​⋮xn(1)​​x1(2)​x2(2)​⋮xn(2)​​⋯⋯⋱⋯​x1(m)​x2(m)​⋮xn(m)​​​+​bb⋮b​​T⇓=WTX+B​​ 向量化之后，对整个训练样本进行单次训练，描述如下： Z=WTX+BA=σ(Z)dZ=∂J∂Z=1m(A−Y)dW=∂J∂W=X⋅[dZ]Tdb=∑i=1mdZiW:=W−α⋅dWb:=b−α⋅db\\begin{align} Z & = W^T X + B \\\\ A & = \\sigma (Z) \\\\ dZ & = \\frac {\\partial J} {\\partial Z} = {\\frac 1 m} (A - Y) \\\\ dW & = \\frac {\\partial J} {\\partial W} = X \\cdot [dZ]^T \\\\ db & = \\sum_{i=1}^m dZ_i \\\\ W & := W - \\alpha \\cdot dW \\\\ b & := b - \\alpha \\cdot db \\end{align}ZAdZdWdbWb​=WTX+B=σ(Z)=∂Z∂J​=m1​(A−Y)=∂W∂J​=X⋅[dZ]T=i=1∑m​dZi​:=W−α⋅dW:=b−α⋅db​​ 以上可以使用 Python Numpy 进行实现。","s":"向量化","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#向量化","p":1141},{"i":1156,"t":"本文介绍了 MCP 神经元和感知器，以及对应的算法实现。","s":"MCP 神经元和感知器","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","h":"","p":1155},{"i":1158,"t":"Warren McCullock 和 Walter Pitts 通过研究大脑，于 1943 年提出了第一个人工智能模型：MCP 神经元。神经元是涉及化学和电信号处理和传输的大脑中相互联系的神经细胞，如下图所示： MCP 神经元为具有二进制输出的简单逻辑门。多个信号从树突传入细胞体中，如果累积输入信号超过一定阈值，则从轴突传出输出信号。 Frank Rosenblatt 于 1957 年发表了基于 MCP 神经元模型的感知器学习规则，提出了一种自动学习最佳权重系数的算法，然后与输入特征相乘，从而决定是否触发神经元。这种算法可以用于监督式学习中的分类。 感知器采用输入向量 xxx 和权重向量 www，净输入 zzz 为这二者的线性组合 (z=w1x1+…+wmxmz = w_1 x_1 + \\ldots + w_m x_mz=w1​x1​+…+wm​xm​)： w=[w1w2⋮wm],x=[x1x2⋮xm]w = \\begin{bmatrix} w_1 \\\\ w_2 \\\\ \\vdots \\\\ w_m \\\\ \\end{bmatrix}, x = \\begin{bmatrix} x_1 \\\\ x_2 \\\\ \\vdots \\\\ x_m \\\\ \\end{bmatrix}w=​w1​w2​⋮wm​​​,x=​x1​x2​⋮xm​​​ 激活函数采用阶跃函数 ϕ(z)\\phi(z)ϕ(z), θ\\thetaθ 为神经元的触发阈值： ϕ(z)={1,if z≥θ−1,if z<θ\\phi(z) = \\begin{cases} 1, &\\text{if } z \\geq \\theta \\\\[2ex] -1, &\\text{if } z \\lt \\theta \\end{cases}ϕ(z)=⎩⎨⎧​1,−1,​if z≥θif z<θ​ 通过设定 x0=1x_0 = 1x0​=1 和 w0=−θw_0 = -\\thetaw0​=−θ，将 θ\\thetaθ 集成到 zzz 中，可以让上式更整齐： z=w0x0+w1x1+w2x2+…+wmxm=wTxz = w_0 x_0 + w_1 x_1 + w_2 x_2 + \\ldots + w_m x_m = w^T xz=w0​x0​+w1​x1​+w2​x2​+…+wm​xm​=wTxϕ(z)={1,if z≥0−1,if z<0\\phi(z) = \\begin{cases} 1, &\\text{if } z \\geq 0 \\\\[2ex] -1, &\\text{if } z \\lt 0 \\end{cases}ϕ(z)=⎩⎨⎧​1,−1,​if z≥0if z<0​ 下图为通过 z=wTxz = w^T xz=wTx 得到 1 或 -1 的激活函数 (左子图)，以及其用于区分两个线性可分的类 (右子图)： MCP 神经元和 Rosenblatt 阈值感知器模型的思想为简化模拟大脑单个神经元的工作原理，即输入是否达到触发条件。 Rosenblatt 感知器规则非常简单： 将权重初始化为 0 或较小的随机数。 对于每个训练样本 x(i)x^{(i)}x(i)，执行以下步骤： 计算输出值 y^\\hat yy^​。 更新权重。 权重 wjw_jwj​ 的更新可以表示为： wj:=wj+Δwjw_j := w_j + \\Delta w_jwj​:=wj​+Δwj​ 用于更新权重向量中的第 jjj 个权重 Δwj\\Delta w_jΔwj​ 可由感知器学习规则计算得到： Δwj=η(y(i)−y^(i))xj(i)\\Delta w_j = \\eta (y^{(i)} - \\hat y^{(i)}) x_j^{(i)}Δwj​=η(y(i)−y^​(i))xj(i)​ 其中 η\\etaη 是学习率 (介于 0 和 1 之间)，y(i)y^{(i)}y(i) 是第 iii 次训练的实际类标签，y^(i)\\hat y^{(i)}y^​(i) 是第 iii 次训练的预测类标签。需要注意，权重向量中的所有权重的更新是同时的，更新权重之后才会更新下一次的 y^(i)\\hat y^{(i)}y^​(i)。 例如，二维数据的权重更新如下： Δw0=η(y(i)−output(i))Δw1=η(y(i)−output(i))x1(i)Δw2=η(y(i)−output(i))x2(i)\\begin{align} \\Delta w_0 &= \\eta (y^{(i)} - \\text{output}^{(i)}) \\\\ \\Delta w_1 &= \\eta (y^{(i)} - \\text{output}^{(i)}) x_1^{(i)} \\\\ \\Delta w_2 &= \\eta (y^{(i)} - \\text{output}^{(i)}) x_2^{(i)} \\end{align}Δw0​Δw1​Δw2​​=η(y(i)−output(i))=η(y(i)−output(i))x1(i)​=η(y(i)−output(i))x2(i)​​​ 在感知器预测正确类标签的情况下，权重保持不变： Δwj=η(−1(i)−−1(i))xj(i)=0Δwj=η(1(i)−1(i))xj(i)=0\\begin{align} \\Delta w_j &= \\eta (-1^{(i)} - -1^{(i)}) x_j^{(i)} = 0 \\\\ \\Delta w_j &= \\eta (1^{(i)} - 1^{(i)}) x_j^{(i)} = 0 \\end{align}Δwj​Δwj​​=η(−1(i)−−1(i))xj(i)​=0=η(1(i)−1(i))xj(i)​=0​​ 在感知器预测错误类标签的情况下，权重朝正确类标签的方向更新： 2Δwj=η(1(i)−−1(i))xj(i)=η(2)xj(i)Δwj=η(−1(i)−1(i))xj(i)=η(−2)xj(i)\\begin{align}{2} \\Delta w_j &= \\eta (1^{(i)} - -1^{(i)}) x_j^{(i)} = \\eta (2) x_j^{(i)} \\\\ \\Delta w_j &= \\eta (-1^{(i)} - 1^{(i)}) x_j^{(i)} = \\eta (-2) x_j^{(i)} \\end{align}2Δwj​Δwj​​=η(1(i)−−1(i))xj(i)​=η(2)xj(i)​=η(−1(i)−1(i))xj(i)​=η(−2)xj(i)​​​ 为了更好地理解上述表达式中乘数因子 xj(i)x_j^{(i)}xj(i)​ 的作用，这里按照以下条件来举例说明： y(i)=1,y^(i)=−1,η=1y^{(i)} = 1, \\hat y^{(i)} = -1, \\eta = 1y(i)=1,y^​(i)=−1,η=1 如果有样本 xj(i)=0.5x_j^{(i)} = 0.5xj(i)​=0.5，但是被错误分类为 -1，对应的 Δwj\\Delta w_jΔwj​ 为： Δwj(i)=1×(1−(−1))×0.5=1\\Delta w_j^{(i)} = 1 \\times (1 - (-1)) \\times 0.5 = 1Δwj(i)​=1×(1−(−1))×0.5=1 如果有另外一个样本为 xj(i)=2x_j^{(i)} = 2xj(i)​=2，但是被错误分类为 -1，会产生更大的 Δwj\\Delta w_jΔwj​，以便下次能正确分类： Δwj(i)=1×(1−(−1))×2=4\\Delta w_j^{(i)} = 1 \\times (1 - (-1)) \\times 2 = 4Δwj(i)​=1×(1−(−1))×2=4 注意，感知器只有在类线性可分且学习率足够小才能收敛。如果类之间不是线性可分的，需要设置最大训练次数或者设置可容忍的错误分类数量，否则感知器会一直更新权重： 下图简单描述了感知器的原理： 在输入阶段，感知器接收样本 xxx 的输入并和权重 www 来计算净输入，然后将净输入传递到激活函数 (这里采用单位阶跃函数)，该函数生成输出预测类标签 -1 或 +1。在学习阶段，该输出用于计算预测误差并更新权重。","s":"MCP 神经元和感知器原理","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","h":"#mcp-neuron-and-perceptron-priciple","p":1155},{"i":1160,"t":"下面代码中，采用了面向对象的方法，定义感知器为 Python 类。 import numpy as np class Perceptron(object): def __init__(self, eta=0.01, n_iter=50, random_state=1): self.eta = eta self.n_iter = n_iter self.random_state = random_state def fit(self, X, y): rgen = np.random.RandomState(self.random_state) self.w_ = rgen.normal(loc=0.0, scale=0.01, size=1 + X.shape[1]) self.errors_ = [] for _ in range(self.n_iter): errors = 0 for xi, target in zip(X, y): errors += int(self.predict(xi) != target) update = self.eta * (target - self.predict(xi)) self.w_[1:] += update * xi self.w_[0] += update self.errors_.append(errors) return self def net_input(self, X): return np.dot(X, self.w_[1:]) + self.w_[0] def predict(self, X): return np.where(self.net_input(X) >= 0.0, 1, -1) 通过上述实现，可以通过指定学习速率 eta 和训练次数 n_iter 来初始化感知器对象。fit 方法可以初始化一个全 0 权重向量 self.w_，包含权重 w0w_0w0​ ~ wmw_mwm​ 。 在权重初始化后，使用感知器的学习规则更新权重。fit 传入已知样本和对应标签，用于训练阶段得到算法参数；predict 用于预测任何样本 (通常使用未知样本以观察算法性能) 的对应标签，用于验证阶段。 另外，这里定义了错误分类的样本数目 self.errors_，以观察算法在每次训练后的表现。","s":"Rosenblatt 感知器的 Python 实现","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","h":"#python-implementation-of-perceptron","p":1155},{"i":1162,"t":"加载 Iris 数据集​ Iris 数据集可以看做矩阵 R150×4R^{150 \\times 4}R150×4，具有 150 个样本，4 个特征 (花萼长度 sepal length、花萼宽度 sepal width、花瓣长度 petal length、花瓣宽度 petal width)，可分成 3 个分类 (山鸢尾 Setosa、变色鸢尾 Versicolor、维吉尼亚鸢尾 Verginica)。 从 UCI Machine Learning Repository 读取 Iris 数据集，并打印最后五行： import pandas as pd df = pd.read_csv( \"https://archive.ics.uci.edu/ml/achine-learning-databases/iris/iris.data\", header=None, ) df.tail() Iris 数据子集绘图​ 为了简单演示训练流程，我们只挑选 Sepal Length 和 Petal Length 这两个特征，另外只挑选 Setosa 和 Versicolor 这两类。 我们提取前 100 个样本的类标签 (依次对应 50 个 Setosa 和 50 个 Versicolor)，并将类标签转换为整数类标签 -1 (Setosa) 和 1 (Versicolor)，用 pandas.DataFrame 表示。然后提取这 100 个样本的第一个特征列 Sepal Length 和第三个特征列 Petal Length，将它们分配给特征矩阵 X 并通过二维散点图可视化： import pandas as pd import matplotlib.pyplot as plt df = pd.read_csv( \"https://archive.ics.uci.edu/ml/achine-learning-databases/iris/iris.data\", header=None, ) X = df.iloc[:100, [0, 2]].values y = df.iloc[:100, 4].values y = np.where(y == \"Iris-setosa\", -1, 1) plt.scatter(X[:50, 0], X[:50, 1], color=\"red\", marker=\"o\", label=\"setosa\") plt.scatter(X[50:100, 0], X[50:100, 1], color=\"blue\", marker=\"x\", label=\"versicolor\") plt.xlabel(\"sepal length [cm]\") plt.ylabel(\"petal length [cm]\") plt.legend(loc=\"upper left\") plt.tight_layout() plt.show() 感知器模型训练​ 接下来在提取的 Iris 数据子集上训练我们的感知器算法，同时，我们将绘制每次训练后的分类错误以检查算法是否收敛，并找到分离两个花类的决策边界： ppn = Perceptron(eta=0.1, n_iter=10) ppn.fit(X, y) plt.plot(range(1, len(ppn.errors_) + 1), ppn.errors_, marker=\"o\") plt.xlabel(\"Epochs\") plt.ylabel(\"Number of updates\") plt.tight_layout() plt.show() 从上图可以观察到在六次训练后，样本错误分类数目为 0，算法得到收敛。 决策边界绘图​ 定义决策边界绘图函数如下： from matplotlib.colors import ListedColormap def plot_decision_regions(X, y, classifier, resolution=0.02): # setup marker generator and color map markers = (\"s\", \"x\", \"o\", \"^\", \"v\") colors = (\"red\", \"blue\", \"lightgreen\", \"gray\", \"cyan\") cmap = ListedColormap(colors[: len(np.unique(y))]) # plot the decision surface x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1 x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1 xx1, xx2 = np.meshgrid( np.arange(x1_min, x1_max, resolution), np.arange(x2_min, x2_max, resolution) ) Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T) Z = Z.reshape(xx1.shape) plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap) plt.xlim(xx1.min(), xx1.max()) plt.ylim(xx2.min(), xx2.max()) # plot class samples for idx, cl in enumerate(np.unique(y)): plt.scatter( x=X[y == cl, 0], y=X[y == cl, 1], alpha=0.8, c=cmap(idx), edgecolor=\"black\", marker=markers[idx], label=cl, ) 对上一节中的样本进行绘图： plot_decision_regions(X, y, classifier=ppn) plt.xlabel(\"sepal length [cm]\") plt.ylabel(\"petal length [cm]\") plt.legend(loc=\"upper left\") plt.tight_layout() plt.show() 通过学习，感知器生成了将 Iris 训练子集完全分类的决策边界。 备注 虽然本例中感知器能够完全分类两种花卉，但收敛仍是感知器最重要的问题之一。如果两个类线性可分，感知器算法就能够收敛。然而对于无法线性可分的类，除非我们手动设置最大训练次数，否则权重永远不会停止更新。","s":"基于 Iris 数据集的感知器模型训练","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","h":"#perceptron-model-training-based-on-iris-dataset","p":1155},{"i":1164,"t":"信息 NumPy 是用于 Python 中多维数组计算的软件库。 本文部分内容翻译自斯坦福大学文档 CS231n - Python NumPy Tutorial。","s":"NumPy 快速入门","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"","p":1163},{"i":1166,"t":"NumPy 是 Python 中科学计算的基础包。它是一个 Python 库，提供多维数组对象、各种派生对象 (例如数组和矩阵) 以及各种用于快速数组操作的例程，包括数学、逻辑、形状操作、排序、选择、I/O、离散傅里叶变换、基本线性代数、基本统计运算、随机模拟等等。 NumPy 包的核心是 ndarray 对象。它封装了同构数据类型的 n 维数组，许多操作在编译代码中执行以提高性能。NumPy 数组和标准 Python 序列之间有几个重要的区别： 与 Python 列表 (可以动态增长) 不同，NumPy 数组在创建时大小是固定的。更改 ndarray 的大小将创建一个新数组并删除原始数组。 NumPy 数组中的元素都必须具有相同的数据类型，因此在内存中的大小也相同。例外：可以拥有 (Python，包括 NumPy) 对象的数组，从而允许不同大小元素的数组。 NumPy 数组有助于对大量数据进行高级数学和其他类型的运算。通常，与使用 Python 的内置序列相比，此类操作的执行效率更高，并且代码更少。 越来越多的基于 Python 的科学和数学包正在使用 NumPy 数组；尽管这些通常支持 Python 序列输入，但它们在处理之前将此类输入转换为 NumPy 数组，并且通常输出 NumPy 数组。换句话说，为了有效地使用当今大部分 (甚至是大多数) 基于 Python 的科学/数学软件，仅仅知道如何使用 Python 的内置序列类型是不够的 - 还需要知道如何使用 NumPy 数组。 关于序列大小和速度的问题在科学计算中尤为重要。作为一个简单的示例，考虑将一维序列中的每个元素与相同长度的另一个序列中的相应元素相乘的情况。如果数据存储在两个 Python 列表 a 和 b 中，我们可以迭代每个元素： c = [] for i in range(len(a)): c.append(a[i] * b[i]) 这会产生正确的答案，但如果 a 和 b 各自包含数百万个数字，我们将为 Python 中的循环效率低下付出代价。我们可以通过编写 C 语言更快地完成相同的任务 (为了清楚起见，我们忽略了变量声明和初始化、内存分配等) for (i = 0; i < rows; i++) { c[i] = a[i]*b[i]; } 这节省了解释 Python 代码和操作 Python 对象所涉及的所有开销，但代价是牺牲了从 Python 编码中获得的好处。此外，所需的编码工作随着数据维度的增加而增加。例如，在二维数组的情况下，C 代码 (如前所述) 扩展为 for (i = 0; i < rows; i++) { for (j = 0; j < columns; j++) { c[i][j] = a[i][j]*b[i][j]; } } NumPy 为我们提供了两全其美的功能：当涉及 ndarray 时，逐元素操作是“默认模式”，但逐元素操作可以通过预编译的 C 代码快速执行。在 NumPy 中可以用 c = a * b 执行前面示例的操作，速度接近 C 语言，同时代码简单，符合我们基于 Python 的期望。","s":"什么是 NumPy","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#what-is-numpy","p":1163},{"i":1168,"t":"矢量化的代码没有任何显式循环、索引等 - 当然，这些事情实际上是在优化的预编译 C 代码中被处理了。矢量化代码具有许多优点，其中包括： 矢量化代码更简洁，更容易阅读 更少的代码行通常意味着更少的错误 代码更类似于标准数学符号 (通常更容易正确编码数学结构) 矢量化会产生更多符合 Python 风格的代码；如果没有矢量化，我们的代码将充斥着低效且难以阅读的 for 循环","s":"为什么 NumPy 很快？","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#why-numpy-fast","p":1163},{"i":1170,"t":"Numpy 是 Python 中科学计算的核心库。它提供了一个高性能的多维数组对象，以及使用这些数组的工具。","s":"使用 Numpy","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#use-numpy","p":1163},{"i":1172,"t":"Numpy 的核心功能是 ndarray (即 n-dimensional array，多维数组) 数据结构。这是一个表示多维度、同质并且固定大小的数组对象。维数是数组的秩 rank；数组的形状 shape 是一个整数元组，表示沿着每个维度的数组大小。 我们可以从嵌套的 Python 列表初始化 Numpy 数组，并使用方括号来访问元素： import numpy as np a = np.array([1, 2, 3]) # Create a rank 1 array print type(a) # Prints \"<type 'numpy.ndarray'>\" print a.shape # Prints \"(3,)\" print a[0], a[1], a[2] # Prints \"1 2 3\" a[0] = 5 # Change an element of the array print a # Prints \"[5, 2, 3]\" b = np.array([[1,2,3],[4,5,6]]) # Create a rank 2 array print b.shape # Prints \"(2, 3)\" print b[0, 0], b[0, 1], b[1, 0] # Prints \"1 2 4\" Numpy 还提供许多创建数组的函数： import numpy as np a = np.zeros((2,2)) # Create an array of all zeros print a # Prints \"[[ 0. 0.] # [ 0. 0.]]\" b = np.ones((1,2)) # Create an array of all ones print b # Prints \"[[ 1. 1.]]\" c = np.full((2,2), 7) # Create a constant array print c # Prints \"[[ 7. 7.] # [ 7. 7.]]\" d = np.eye(2) # Create a 2x2 identity matrix print d # Prints \"[[ 1. 0.] # [ 0. 1.]]\" e = np.random.random((2,2)) # Create an array filled with random values print e # Might print \"[[ 0.91940167 0.08143941] # [ 0.68744134 0.87236687]]\" 你可以在这份文档中阅读关于数组创建的其他方法。","s":"数组","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#arrays","p":1163},{"i":1174,"t":"Numpy 提供了多种索引到数组的方法。 切片：与 Python 列表类似，可以对 Numpy 数组进行切片。由于数组可能是多维的，因此必须为数组的每个维度指定一个切片： import numpy as np # Create the following rank 2 array with shape (3, 4) # [[ 1 2 3 4] # [ 5 6 7 8] # [ 9 10 11 12]] a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]]) # Use slicing to pull out the subarray consisting of the first 2 rows # and columns 1 and 2; b is the following array of shape (2, 2): # [[2 3] # [6 7]] b = a[:2, 1:3] # A slice of an array is a view into the same data, so modifying it # will modify the original array. print a[0, 1] # Prints \"2\" b[0, 0] = 77 # b[0, 0] is the same piece of data as a[0, 1] print a[0, 1] # Prints \"77\" 你还可以将整数索引与片段索引进行混合。但是，这样做会产生比原始数组更低的数组： import numpy as np # Create the following rank 2 array with shape (3, 4) # [[ 1 2 3 4] # [ 5 6 7 8] # [ 9 10 11 12]] a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]]) # Two ways of accessing the data in the middle row of the array. # Mixing integer indexing with slices yields an array of lower rank, # while using only slices yields an array of the same rank as the # original array: row_r1 = a[1, :] # Rank 1 view of the second row of a row_r2 = a[1:2, :] # Rank 2 view of the second row of a print row_r1, row_r1.shape # Prints \"[5 6 7 8] (4,)\" print row_r2, row_r2.shape # Prints \"[[5 6 7 8]] (1, 4)\" # We can make the same distinction when accessing columns of an array: col_r1 = a[:, 1] col_r2 = a[:, 1:2] print col_r1, col_r1.shape # Prints \"[ 2 6 10] (3,)\" print col_r2, col_r2.shape # Prints \"[[ 2] # [ 6] # [10]] (3, 1)\" 整数数组索引：当你使用切片索引到 Numpy 数组时，生成的数组视图将始终是原始数组的子数组。相反，整数数组索引允许你使用另一个数组的数据来构造任意数组。例如： import numpy as np a = np.array([[1,2], [3, 4], [5, 6]]) # An example of integer array indexing. # The returned array will have shape (3,) and print a[[0, 1, 2], [0, 1, 0]] # Prints \"[1 4 5]\" # The above example of integer array indexing is equivalent to this: print np.array([a[0, 0], a[1, 1], a[2, 0]]) # Prints \"[1 4 5]\" # When using integer array indexing, you can reuse the same # element from the source array: print a[[0, 0], [1, 1]] # Prints \"[2 2]\" # Equivalent to the previous integer array indexing example print np.array([a[0, 1], a[0, 1]]) # Prints \"[2 2]\" 一个有用的整数数组索引技巧，是从矩阵的每一行中选择一个元素： import numpy as np # Create a new array from which we will select elements a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]]) print a # prints \"array([[ 1, 2, 3], # [ 4, 5, 6], # [ 7, 8, 9], # [10, 11, 12]])\" # Create an array of indices b = np.array([0, 2, 0, 1]) # Select one element from each row of a using the indices in b print a[np.arange(4), b] # Prints \"[ 1 6 7 11]\" # Mutate one element from each row of a using the indices in b a[np.arange(4), b] += 10 print a # prints \"array([[11, 2, 3], # [ 4, 5, 16], # [17, 8, 9], # [10, 21, 12]]) 布尔数组索引：布尔数组索引可以让你选择数组的任意元素。通常，这种类型的索引用于选择满足某些条件的数组的元素。例如： import numpy as np a = np.array([[1,2], [3, 4], [5, 6]]) bool_idx = (a > 2) # Find the elements of a that are bigger than 2; # this returns a numpy array of Booleans of the same # shape as a, where each slot of bool_idx tells # whether that element of a is > 2. print bool_idx # Prints \"[[False False] # [ True True] # [ True True]]\" # We use boolean array indexing to construct a rank 1 array # consisting of the elements of a corresponding to the True values # of bool_idx print a[bool_idx] # Prints \"[3 4 5 6]\" # We can do all of the above in a single concise statement: print a[a > 2] # Prints \"[3 4 5 6]\" 为了简洁起见，我们省略了很多有关 Numpy 数组索引的细节；如果你想了解更多，请阅读这份文档。","s":"数组索引","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#array-indexing","p":1163},{"i":1176,"t":"每个 Numpy 数组都是相同类型元素的网格。Numpy 提供了大量可用于构造数组的数值数据类型。创建数组时，Numpy 会尝试猜测数据类型，但构造数组的函数通常还包含一个可选参数来显式指定数据类型。下面是一个例子： import numpy as np x = np.array([1, 2]) # Let numpy choose the datatype print(x.dtype) # Prints \"int64\" x = np.array([1.0, 2.0]) # Let numpy choose the datatype print(x.dtype) # Prints \"float64\" x = np.array([1, 2], dtype=np.int64) # Force a particular datatype print(x.dtype) # Prints \"int64\" 你可以在这份文档中查看 Numpy 支持的数据类型。","s":"数据类型","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#datatypes","p":1163},{"i":1178,"t":"基本的数学函数在数组上按元素运算，并且可以作为运算符重载和 numpy 模块中的函数使用： import numpy as np x = np.array([[1,2],[3,4]], dtype=np.float64) y = np.array([[5,6],[7,8]], dtype=np.float64) # Elementwise sum; both produce the array # [[ 6.0 8.0] # [10.0 12.0]] print x + y print np.add(x, y) # Elementwise difference; both produce the array # [[-4.0 -4.0] # [-4.0 -4.0]] print x - y print np.subtract(x, y) # Elementwise product; both produce the array # [[ 5.0 12.0] # [21.0 32.0]] print x * y print np.multiply(x, y) # Elementwise division; both produce the array # [[ 0.2 0.33333333] # [ 0.42857143 0.5 ]] print x / y print np.divide(x, y) # Elementwise square root; produces the array # [[ 1. 1.41421356] # [ 1.73205081 2. ]] print np.sqrt(x) 请注意，* 是元素乘法，而不是矩阵乘法。如需使用矩阵乘法，请使用函数 dot。dot 可用作 Numpy 模块中的函数，也可用作数组对象的实例方法： import numpy as np x = np.array([[1,2],[3,4]]) y = np.array([[5,6],[7,8]]) v = np.array([9,10]) w = np.array([11, 12]) # Inner product of vectors; both produce 219 print v.dot(w) print np.dot(v, w) # Matrix / vector product; both produce the rank 1 array [29 67] print x.dot(v) print np.dot(x, v) # Matrix / matrix product; both produce the rank 2 array # [[19 22] # [43 50]] print x.dot(y) print np.dot(x, y) Numpy 提供了许多有用的矩阵计算函数；其中最重要的函数之一是 sum： import numpy as np x = np.array([[1,2],[3,4]]) print np.sum(x) # Compute sum of all elements; prints \"10\" print np.sum(x, axis=0) # Compute sum of each column; prints \"[4 6]\" print np.sum(x, axis=1) # Compute sum of each row; prints \"[3 7]\" 你可以在这份文档中找到 numpy 提供的数学函数完整列表。 除了使用数组计算数学函数之外，我们经常需要重新整形或以其他方式处理数组中的数据。这种类型的操作的最简单的例子是转置矩阵；要转置矩阵，只需使用数组对象的 T 属性： import numpy as np x = np.array([[1,2], [3,4]]) print x # Prints \"[[1 2] # [3 4]]\" print x.T # Prints \"[[1 3] # [2 4]]\" # Note that taking the transpose of a rank 1 array does nothing: v = np.array([1,2,3]) print v # Prints \"[1 2 3]\" print v.T # Prints \"[1 2 3]\" Numpy 提供了更多的功能来操作数组；你可以在这份文档中看到完整列表。","s":"数组计算","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#array-math","p":1163},{"i":1180,"t":"广播是一种强大的机制，允许 Numpy 在执行算术运算时使用不同形状的数组。通常我们有一个更小的数组和一个更大的数组，我们想要使用较小的数组多次来对较大的数组执行一些操作。 例如，假设我们要为矩阵的每一行添加一个常量向量。我们可以这样做： import numpy as np # We will add the vector v to each row of the matrix x, # storing the result in the matrix y x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]]) v = np.array([1, 0, 1]) y = np.empty_like(x) # Create an empty matrix with the same shape as x # Add the vector v to each row of the matrix x with an explicit loop for i in range(4): y[i, :] = x[i, :] + v # Now y is the following # [[ 2 2 4] # [ 5 5 7] # [ 8 8 10] # [11 11 13]] print y 这种方法是可以的；然而，当矩阵 x 非常大时，Python 循环可能会运行很长时间。实际上，将向量 v 添加到矩阵 x 的每一行，等价于通过创建垂直堆叠 v 的矩阵 vv，然后执行 x 和 vv 的元素求和。我们可以这样实现这个方法： import numpy as np # We will add the vector v to each row of the matrix x, # storing the result in the matrix y x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]]) v = np.array([1, 0, 1]) vv = np.tile(v, (4, 1)) # Stack 4 copies of v on top of each other print vv # Prints \"[[1 0 1] # [1 0 1] # [1 0 1] # [1 0 1]]\" y = x + vv # Add x and vv elementwise print y # Prints \"[[ 2 2 4 # [ 5 5 7] # [ 8 8 10] # [11 11 13]]\" Numpy 广播允许我们在不创建 v 的多个副本的情况下执行这个计算。以上情况下，我们可以使用广播： import numpy as np # We will add the vector v to each row of the matrix x, # storing the result in the matrix y x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]]) v = np.array([1, 0, 1]) y = x + v # Add v to each row of x using broadcasting print y # Prints \"[[ 2 2 4] # [ 5 5 7] # [ 8 8 10] # [11 11 13]]\" 即使 x 具有形状 (4, 3) 且 v 具有形状 (3,)，行 y = x + v 可以正常执行；工作原理是由于广播，v 仿佛有形状 (4, 3)，其中每行都是 v 的副本，然后按元素进行求和。 两个数组间的广播遵循以下规则： 如果阵列不具有相同的秩，则对较小秩的阵列进行预处理，直到两个形状都具有相同的长度。 如果两个数组在某一维度的大小相等，或者其中一个数组在该维度的大小为 1，则称两个数组在这个维度上兼容。 如果两个数组在所有维度上都兼容，则可以进行广播。 广播后，每个数组形状等同于较大的数组形状。 如果在某一维度，其中一个数组大小等于 1 并且另一个数组大小大于 1，则前者沿着此维度复制自身。 如果感到困惑，请尝试阅读这份文档或这份说明。 支持广播的函数被称为通用函数。你可以在这份文档中找到所有通用函数的列表。 以下是广播的一些应用： import numpy as np # Compute outer product of vectors v = np.array([1,2,3]) # v has shape (3,) w = np.array([4,5]) # w has shape (2,) # To compute an outer product, we first reshape v to be a column # vector of shape (3, 1); we can then broadcast it against w to yield # an output of shape (3, 2), which is the outer product of v and w: # [[ 4 5] # [ 8 10] # [12 15]] print np.reshape(v, (3, 1)) * w # Add a vector to each row of a matrix x = np.array([[1,2,3], [4,5,6]]) # x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3), # giving the following matrix: # [[2 4 6] # [5 7 9]] print x + v # Add a vector to each column of a matrix # x has shape (2, 3) and w has shape (2,). # If we transpose x then it has shape (3, 2) and can be broadcast # against w to yield a result of shape (3, 2); transposing this result # yields the final result of shape (2, 3) which is the matrix x with # the vector w added to each column. Gives the following matrix: # [[ 5 6 7] # [ 9 10 11]] print (x.T + w).T # Another solution is to reshape w to be a column vector of shape (2, 1); # we can then broadcast it directly against x to produce the same # output. print x + np.reshape(w, (2, 1)) # Multiply a matrix by a constant: # x has shape (2, 3). NumPy treats scalars as arrays of shape (); # these can be broadcast together to shape (2, 3), producing the # following array: # [[ 2 4 6] # [ 8 10 12]] print x * 2 广播通常会使你的代码更加简洁快捷，因此你应尽可能地使用它。","s":"广播","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#broadcasting","p":1163},{"i":1182,"t":"这个简短的概述已经涉及到大部分 Numpy 的重要功能，但仍有许多地方未涉及。查看 Numpy 参考文档以了解更多关于 Numpy 的信息。","s":"Numpy 文档","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#numpy-documentation","p":1163},{"i":1184,"t":"Numpy 提供了一个高性能的多维数组和基本的工具来计算和操纵这些数组。Scipy 建立在此基础之上，并提供了大量功能，可以运行在 Numpy 数组上，并且可用于不同类型的科学和工程应用。 熟悉 Scipy 的最佳方法是浏览这份文档。","s":"Scipy","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#scipy","p":1163},{"i":1186,"t":"Scipy 提供了一些基本功能来处理图像。例如，它具有从磁盘读取图像到 Numpy 数组，将 Numpy 数组写入磁盘作为图像并调整图像大小的功能。下面的示例中展示了这些功能： from scipy.misc import imread, imsave, imresize # Read an JPEG image into a numpy array img = imread('assets/cat.jpg') print img.dtype, img.shape # Prints \"uint8 (400, 248, 3)\" # We can tint the image by scaling each of the color channels # by a different scalar constant. The image has shape (400, 248, 3); # we multiply it by the array [1, 0.95, 0.9] of shape (3,); # numpy broadcasting means that this leaves the red channel unchanged, # and multiplies the green and blue channels by 0.95 and 0.9 # respectively. img_tinted = img * [1, 0.95, 0.9] # Resize the tinted image to be 300 by 300 pixels. img_tinted = imresize(img_tinted, (300, 300)) # Write the tinted image back to disk imsave('assets/cat_tinted.jpg', img_tinted)","s":"图像操作","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#image-operations","p":1163},{"i":1188,"t":"Scipy 定义了一些有用的函数，用于计算点集合之间的距离。 函数 scipy.spatial.distance.pdist 计算给定单个集合中所有点之间的距离： import numpy as np from scipy.spatial.distance import pdist, squareform # Create the following array where each row is a point in 2D space: # [[0 1] # [1 0] # [2 0]] x = np.array([[0, 1], [1, 0], [2, 0]]) print x # Compute the Euclidean distance between all rows of x. # d[i, j] is the Euclidean distance between x[i, :] and x[j, :], # and d is the following array: # [[ 0. 1.41421356 2.23606798] # [ 1.41421356 0. 1. ] # [ 2.23606798 1. 0. ]] d = squareform(pdist(x, 'euclidean')) print d 你可以在这份文档中阅读有关此功能的所有详细信息。 类似的函数 (scipy.spatial.distance.cdist) 能够计算不同集合内所有点之间的距离；你可以阅读这份文档。","s":"点的距离","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#distance-between-points","p":1163},{"i":1190,"t":"Matplotlib 是一个绘图库。本节简要介绍了 matplotlib.pyplot 模块，该模块提供了与 MATLAB 类似的绘图系统。","s":"Matplotlib","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#matplotlib","p":1163},{"i":1192,"t":"Matplotlib 中最重要的函数是 plot，它可以绘制二维数据。这是一个简单的例子： import numpy as np import matplotlib.pyplot as plt # Compute the x and y coordinates for points on a sine curve x = np.arange(0, 3 * np.pi, 0.1) y = np.sin(x) # Plot the points using matplotlib plt.plot(x, y) plt.show() # You must call plt.show() to make graphics appear. 运行此代码，会生成以下图形： 只需一点额外的工作，我们可以轻松地绘制多行，并添加标题，图例和轴标签： import numpy as np import matplotlib.pyplot as plt # Compute the x and y coordinates for points on sine and cosine curves x = np.arange(0, 3 * np.pi, 0.1) y_sin = np.sin(x) y_cos = np.cos(x) # Plot the points using matplotlib plt.plot(x, y_sin) plt.plot(x, y_cos) plt.xlabel(\"x axis label\") plt.ylabel(\"y axis label\") plt.title(\"Sine and Cosine\") plt.legend([\"Sine\", \"Cosine\"]) plt.show() 关于 plot 函数的更多信息，你可以阅读这份文档。","s":"绘图","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#plotting","p":1163},{"i":1194,"t":"你可以使用 subplot 函数在同一图中绘制不同子图。例如： import numpy as np import matplotlib.pyplot as plt # Compute the x and y coordinates for points on sine and cosine curves x = np.arange(0, 3 * np.pi, 0.1) y_sin = np.sin(x) y_cos = np.cos(x) # Set up a subplot grid that has height 2 and width 1, # and set the first such subplot as active. plt.subplot(2, 1, 1) # Make the first plot plt.plot(x, y_sin) plt.title(\"Sine\") # Set the second subplot as active, and make the second plot. plt.subplot(2, 1, 2) plt.plot(x, y_cos) plt.title(\"Cosine\") # Show the figure. plt.show() 关于 subplot 函数的更多信息，你可以阅读这份文档。","s":"绘制子图","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#subplots","p":1163},{"i":1196,"t":"你可以使用 imshow 功能来显示图像。例如： import numpy as np from scipy.misc import imread, imresize import matplotlib.pyplot as plt img = imread(\"assets/cat.jpg\") img_tinted = img * [1, 0.95, 0.9] # Show the original image plt.subplot(1, 2, 1) plt.imshow(img) # Show the tinted image plt.subplot(1, 2, 2) # A slight gotcha with imshow is that it might give strange results # if presented with data that is not uint8. To work around this, we # explicitly cast the image to uint8 before displaying it. plt.imshow(np.uint8(img_tinted)) plt.show()","s":"图像","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#images","p":1163},{"i":1198,"t":"套袋算法 (Bagging) 是一种集成学习技术，与 MajorityVoteClassifier 相似，不同之处在于 bagging 不是每次使用相同的训练集来拟合单个分类器，而是对初始训练集进行 bootstrap 抽样。这也是 bagging 称为引导聚合 (Bootstrap Aggregating) 的原因。","s":"Bagging","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","h":"","p":1197},{"i":1200,"t":"Bagging 的概念如下图： 为了更具体说明 bagging 分类器如何工作，参见下图中的示例。图中有 n = 7 个训练实例 (以索引 1 - 7 表示)，在每轮 bagging 中进行有放回地抽样 k 次，然后使用这 k 次的聚合样本 (允许包含重复的样本) 来拟合分类器。如果聚合样本中的样本数等于实例，则称为 bootstrap 抽样。 bagging 一般使用在较弱的分类器中使用 (如未修剪的决策树)，以降低其过拟合的问题。在对每个分类器进行拟合后，通过多数投票方法来对结果进行预测。","s":"基本概念","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","h":"#基本概念","p":1197},{"i":1202,"t":"为了对 bagging 方法进行说明，这里使用 Wine 数据集，并提取值为 2 和 3 的分类标签、特征为 Alcohol 和 OD280/OD315 的样本： import pandas as pd df_wine = pd.read_csv( \"https://archive.ics.uci.edu/ml/\" \"machine-learning-databases/wine/wine.data\", header=None, ) df_wine.columns = [ \"Class label\", \"Alcohol\", \"Malic acid\", \"Ash\", \"Alcalinity of ash\", \"Magnesium\", \"Total phenols\", \"Flavanoids\", \"Nonflavanoid phenols\", \"Proanthocyanins\", \"Color intensity\", \"Hue\", \"OD280/OD315 of diluted wines\", \"Proline\", ] df_wine = df_wine[df_wine[\"Class label\"] != 1] y = df_wine[\"Class label\"].values X = df_wine[[\"Alcohol\", \"OD280/OD315 of diluted wines\"]].values 将标签进行编码，并将样本分为 80% 的训练集和 20% 的测试集： from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, random_state=1, stratify=y )","s":"数据导入及预处理","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","h":"#数据导入及预处理","p":1197},{"i":1204,"t":"使用 sklearn.ensemble.BaggingClassifier 进行 bagging。 这里使用未修剪的决策树作为基础分类器，并建立 500 个由不同 bootstrap 样本得到的决策树的集合： from sklearn.ensemble import BaggingClassifier from sklearn.tree import DecisionTreeClassifier tree = DecisionTreeClassifier(criterion=\"entropy\", max_depth=None, random_state=1) bag = BaggingClassifier( base_estimator=tree, n_estimators=500, max_samples=1.0, max_features=1.0, bootstrap=True, bootstrap_features=False, n_jobs=1, random_state=1, ) 接下来，计算训练集和测试集中的预测准确性，以比较 bagging 分类器与单个未裁剪决策树的表现： from sklearn.metrics import accuracy_score tree = tree.fit(X_train, y_train) y_train_pred = tree.predict(X_train) y_test_pred = tree.predict(X_test) tree_train = accuracy_score(y_train, y_train_pred) tree_test = accuracy_score(y_test, y_test_pred) print(\"Decision tree train/test accuracies %.3f/%.3f\" % (tree_train, tree_test)) bag = bag.fit(X_train, y_train) y_train_pred = bag.predict(X_train) y_test_pred = bag.predict(X_test) bag_train = accuracy_score(y_train, y_train_pred) bag_test = accuracy_score(y_test, y_test_pred) print(\"Bagging train/test accuracies %.3f/%.3f\" % (bag_train, bag_test)) 得到结果如下： Decision tree train/test accuracies 1.000/0.833 Bagging train/test accuracies 1.000/0.917 尽管 bagging 和决策树对于训练集的预测准确率均为 100%，但在测试集上 bagging 的准确率要高于测试集，泛化能力更优。 对 bagging 和决策树的决策边界分别绘图。 import numpy as np import matplotlib.pyplot as plt x_min = X_train[:, 0].min() - 1 x_max = X_train[:, 0].max() + 1 y_min = X_train[:, 1].min() - 1 y_max = X_train[:, 1].max() + 1 xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1), np.arange(y_min, y_max, 0.1)) f, axarr = plt.subplots(nrows=1, ncols=2, sharex=\"col\", sharey=\"row\", figsize=(8, 3)) for idx, clf, tt in zip([0, 1], [tree, bag], [\"Decision tree\", \"Bagging\"]): clf.fit(X_train, y_train) Z = clf.predict(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) axarr[idx].contourf(xx, yy, Z, alpha=0.3) axarr[idx].scatter( X_train[y_train == 0, 0], X_train[y_train == 0, 1], c=\"blue\", marker=\"^\" ) axarr[idx].scatter( X_train[y_train == 1, 0], X_train[y_train == 1, 1], c=\"green\", marker=\"o\" ) axarr[idx].set_title(tt) axarr[0].set_ylabel(\"Alcohol\", fontsize=12) plt.text( 10.2, -0.5, s=\"OD280/OD315 of diluted wines\", ha=\"center\", va=\"center\", fontsize=12 ) plt.tight_layout() # plt.savefig('images/07_08.png', dpi=300, bbox_inches='tight') plt.show() 从上图可以看出，bagging 的决策边界相比决策树更为平滑。 在实践中，bagging 往往用于解决由于解决分类器模型的过拟合问题，降低模型的方差。需要注意的是，bagging 无法减少模型偏差 (如某些模型太简单，无法很好地捕捉数据中的趋势)。因此 bagging 更适用于低偏差的模型，如未修剪的决策树。","s":"bagging 的 scikit-learn 实现","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","h":"#bagging-的-scikit-learn-实现","p":1197},{"i":1206,"t":"决策树 (Decision Tree) 是一种特殊的树结构，代表的是样本特征与样本标签之间的一种映射关系。 决策树举例如下，分叉路径则代表某个可能的属性值，而终结节点代表最终决策：","s":"决策树和随机森林","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"","p":1205},{"i":1209,"t":"为了引入决策树分类的算法，先介绍决策树学习中的重要概念：信息增益 (Information Gain)。 这个指标可以衡量分类给数据中带来信息的程度。若分类带来的信息增益越大，就越能减少数据的无序度。 信息增益的表示如下，为父节点和子节点中的不纯度 (Inpurity) 差值： IG(Dp,f)=I(Dp)−∑j=1mNiNpI(Dj)\\begin{align} IG(D_p, f) = I(D_p) - \\sum_{j=1}^m \\cfrac {N_i} {N_p} I(D_j) \\end{align}IG(Dp​,f)=I(Dp​)−j=1∑m​Np​Ni​​I(Dj​)​​ 其中 fff 代表对应的特征，DpD_pDp​ 和 DjD_jDj​ 分别表示父节点的数据和第 jjj 个子节点的数据集，NpN_pNp​ 和 NiN_iNi​ 分别表示父节点的数据和第 jjj 个子节点的样本数量，I()I()I() 代表不纯度的函数。 不纯度的计算有以下几种方法： 熵 (Entropy)：IH(t)=−∑j=1cp(i∣t)⋅log⁡2p(i∣t)I_H(t) = -\\sum_{j=1}^c p(i \\mid t) \\cdot \\log_2 p(i \\mid t)IH​(t)=−∑j=1c​p(i∣t)⋅log2​p(i∣t) Gini 不纯度 (Gini Impurity)：IG(t)=1−∑j=1cp(i∣t)2I_G(t) = 1- \\sum_{j=1}^c p(i \\mid t)^2IG​(t)=1−∑j=1c​p(i∣t)2 分类错误 (Classification Error)：IE(t)=1−max⁡p(i∣t)I_E(t) = 1- \\max p(i \\mid t)IE​(t)=1−maxp(i∣t) 在实际应用中，熵和 Gini 不纯度的结果非常相似，不必纠结于这两个计算标准的选择。而分类错误对节点概率的变化较不敏感，不推荐在决策树增长时使用。","s":"定义","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#定义","p":1205},{"i":1211,"t":"以如下决策树演示不纯度的计算，其中 (a，b)(a，b)(a，b) 代表节点中所属分类的样本数量。 例如父节点，包含 40 个属于类 1 的样本、40 个属于类 2 的样本；其他节点同理。 决策树 A 的熵： IH(Dp)=−(12log⁡12+12log⁡12)=1IH(Dleft)=−(34log⁡34+14log⁡14)=0.81IH(Dright)=−(14log⁡14+34log⁡34)=0.81IGH=1−120.81−120.81=0.19\\begin{align} I_H(D_p) & = -({\\cfrac 1 2} \\log{\\cfrac 1 2} + {\\cfrac 1 2} \\log{\\cfrac 1 2}) = 1 \\\\ I_H(D_{left}) & = -({\\cfrac 3 4} \\log{\\cfrac 3 4} + {\\cfrac 1 4} \\log{\\cfrac 1 4}) = 0.81 \\\\ I_H(D_{right}) & = -({\\cfrac 1 4} \\log{\\cfrac 1 4} + {\\cfrac 3 4} \\log{\\cfrac 3 4}) = 0.81 \\\\ IG_H & = 1 - {\\cfrac 1 2} 0.81 - {\\cfrac 1 2} 0.81 = 0.19 \\end{align}IH​(Dp​)IH​(Dleft​)IH​(Dright​)IGH​​=−(21​log21​+21​log21​)=1=−(43​log43​+41​log41​)=0.81=−(41​log41​+43​log43​)=0.81=1−21​0.81−21​0.81=0.19​​ 决策树 B 的熵： IH(Dp)=−(12log⁡12+12log⁡12)=1IH(Dleft)=−(13log⁡13+23log⁡23)=0.92IH(Dright)=0IGH=1−340.92−0=0.31\\begin{align} I_H(D_p) & = -({\\cfrac 1 2} \\log{\\cfrac 1 2} + {\\cfrac 1 2} \\log{\\cfrac 1 2}) = 1 \\\\ I_H(D_{left}) & = -({\\cfrac 1 3} \\log{\\cfrac 1 3} + {\\cfrac 2 3} \\log{\\cfrac 2 3}) = 0.92 \\\\ I_H(D_{right}) & = 0 \\\\ IG_H & = 1 - {\\cfrac 3 4} 0.92 - 0 = 0.31 \\end{align}IH​(Dp​)IH​(Dleft​)IH​(Dright​)IGH​​=−(21​log21​+21​log21​)=1=−(31​log31​+32​log32​)=0.92=0=1−43​0.92−0=0.31​​ 决策树 A 的 Gini 不纯度： IG(Dp)=1−(12)2−(12)2=12IG(Dleft)=1−(34)2−(14)2=38IG(Dright)=1−(14)2−(34)2=38IGG=1−12⋅38−12⋅38=0.125\\begin{align} I_G(D_p) & = 1 - ({\\cfrac 1 2})^2 - ({\\cfrac 1 2})^2 = \\cfrac 1 2 \\\\ I_G(D_{left}) & = 1 - ({\\cfrac 3 4})^2 - ({\\cfrac 1 4})^2 = \\cfrac 3 8 \\\\ I_G(D_{right}) & = 1 - ({\\cfrac 1 4})^2 - ({\\cfrac 3 4})^2 = \\cfrac 3 8 \\\\ IG_G & = 1 - {\\cfrac 1 2} \\cdot {\\cfrac 3 8} - {\\cfrac 1 2} \\cdot {\\cfrac 3 8} = 0.125 \\end{align}IG​(Dp​)IG​(Dleft​)IG​(Dright​)IGG​​=1−(21​)2−(21​)2=21​=1−(43​)2−(41​)2=83​=1−(41​)2−(43​)2=83​=1−21​⋅83​−21​⋅83​=0.125​​ 决策树 B 的 Gini 不纯度： IG(Dp)=1−(12)2−(12)2=12IG(Dleft)=1−(23)2−(13)2=49IG(Dright)=1−12−02=0IGG=12−34⋅49−0=0.167\\begin{align} I_G(D_p) & = 1 - ({\\cfrac 1 2})^2 - ({\\cfrac 1 2})^2 = \\cfrac 1 2 \\\\ I_G(D_{left}) & = 1 - ({\\cfrac 2 3})^2 - ({\\cfrac 1 3})^2 = \\cfrac 4 9 \\\\ I_G(D_{right}) & = 1 - 1^2 - 0^2 = 0 \\\\ IG_G & = \\cfrac 1 2 - {\\cfrac 3 4} \\cdot {\\cfrac 4 9} - 0 = 0.167 \\end{align}IG​(Dp​)IG​(Dleft​)IG​(Dright​)IGG​​=1−(21​)2−(21​)2=21​=1−(32​)2−(31​)2=94​=1−12−02=0=21​−43​⋅94​−0=0.167​​ 决策树 A 的分类错误： IE(Dp)=1−12=12IE(Dleft)=1−34=14IE(Dright)=1−34=14IGE=12−12⋅14−12⋅14=0.25\\begin{align} I_E(D_p) & = 1 - {\\cfrac 1 2} = \\cfrac 1 2 \\\\ I_E(D_{left}) & = 1 - {\\cfrac 3 4} = \\cfrac 1 4 \\\\ I_E(D_{right}) & = 1 - {\\cfrac 3 4} = \\cfrac 1 4 \\\\ IG_E & = {\\cfrac 1 2} - {\\cfrac 1 2} \\cdot {\\cfrac 1 4} - {\\cfrac 1 2} \\cdot {\\cfrac 1 4} = 0.25 \\end{align}IE​(Dp​)IE​(Dleft​)IE​(Dright​)IGE​​=1−21​=21​=1−43​=41​=1−43​=41​=21​−21​⋅41​−21​⋅41​=0.25​​ 决策树 B 的分类错误： IE(Dp)=1−12=12IE(Dleft)=1−13=13IE(Dright)=1−1=0IGE=12−34⋅13−0=0.25\\begin{align} I_E(D_p) & = 1 - {\\cfrac 1 2} = \\cfrac 1 2 \\\\ I_E(D_{left}) & = 1 - {\\cfrac 1 3} = \\cfrac 1 3 \\\\ I_E(D_{right}) & = 1 - 1 = 0 \\\\ IG_E & = {\\cfrac 1 2} - {\\cfrac 3 4} \\cdot {\\cfrac 1 3} - 0 = 0.25 \\end{align}IE​(Dp​)IE​(Dleft​)IE​(Dright​)IGE​​=1−21​=21​=1−31​=31​=1−1=0=21​−43​⋅31​−0=0.25​​ 为了更直观的比较三种信息增益计算方法的差异，对平均分布 [0,1][0,1][0,1] 的样本应用并绘图： import matplotlib.pyplot as plt import numpy as np def gini(p): return (p) * (1 - (p)) + (1 - p) * (1 - (1 - p)) def entropy(p): return -p * np.log2(p) - (1 - p) * np.log2((1 - p)) def error(p): return 1 - np.max([p, 1 - p]) x = np.arange(0.0, 1.0, 0.01) ent = [entropy(p) if p != 0 else None for p in x] sc_ent = [e * 0.5 if e else None for e in ent] err = [error(i) for i in x] ax = plt.subplot(111) for ( i, lab, ls, c, ) in zip( [ent, sc_ent, gini(x), err], [\"Entropy\", \"Entropy (scaled)\", \"Gini Impurity\", \"Misclassification Error\"], [\"-\", \"-\", \"--\", \"-.\"], [\"black\", \"lightgray\", \"red\", \"green\", \"cyan\"], ): line = ax.plot(x, i, label=lab, linestyle=ls, lw=2, color=c) ax.legend( loc=\"upper center\", bbox_to_anchor=(0.5, 1.15), ncol=5, fancybox=True, shadow=False ) ax.axhline(y=0.5, linewidth=1, color=\"k\", linestyle=\"--\") ax.axhline(y=1.0, linewidth=1, color=\"k\", linestyle=\"--\") plt.ylim([0, 1.1]) plt.xlabel(\"p(i=1)\") plt.ylabel(\"Impurity Index\") plt.show()","s":"计算示例","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#计算示例","p":1205},{"i":1214,"t":"决策树分类的思想是，从树根开始将特征上的数据分割成最大的信息增益，然后在子节点重复这个拆分过程。 在实践中，这可能会导致一个有很多节点的很深的树，很容易导致过度拟合。因此通常要通过设置树的最大深度限制来修剪树。 以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (其中决策边界绘制函数 plot_decision_regions 请参见之前的文章)： import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.tree import DecisionTreeClassifier iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) tree = DecisionTreeClassifier(criterion=\"gini\", max_depth=4, random_state=1) tree.fit(X_train, y_train) X_combined = np.vstack((X_train, X_test)) y_combined = np.hstack((y_train, y_test)) plot_decision_regions(X_combined, y_combined, classifier=tree, test_idx=range(105, 150)) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show()","s":"代码实现","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#代码实现","p":1205},{"i":1216,"t":"Windows 下的 Graphviz 需要： 下载并安装 Graphviz Windows 安装包 graphviz-2.xx.msi 将 C:\\Program Files (x86)\\Graphviz2.xx\\bin\\; 添加到环境变量 Path (计算机——属性——高级系统设置——环境变量) Pip 安装软件包：pip install pydotplus graphviz pyparsing 对上节生成的 tree 进行绘图： from pydotplus import graph_from_dot_data from sklearn.tree import export_graphviz dot_data = export_graphviz( tree, filled=True, rounded=True, class_names=[\"Setosa\", \"Versicolor\", \"Virginica\"], feature_names=[\"petal length\", \"petal width\"], out_file=None, ) graph = graph_from_dot_data(dot_data) graph.write_png(\"tree.png\")","s":"Graphviz 绘图","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#graphviz-绘图","p":1205},{"i":1218,"t":"随机森林是一个包含多个决策树的分类器，并且其输出的分类标签是由每个树的的分类标签的众数而定。 从已知的样本集合 (样本数 MMM，特征数 NNN) 中，有放回地随机取 nnn 个 bootstrap 样本 (n<Nn < Nn<N)。 对取得的 bootstrap 的样本生成决策树：a。无放回地随机选择其中 mmm 个特征 (m<<Mm << Mm<<M)。b。根据目标函数提供的最佳分割特征 (如最大化信息增益) 来分割节点。 重复步骤 1-2 若干次数。 汇总每棵树的预测标签，把其中数量最多的作为随机森林的分类标签。 import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.ensemble import RandomForestClassifier iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) forest = RandomForestClassifier( criterion=\"gini\", n_estimators=25, random_state=1, n_jobs=2 ) forest.fit(X_train, y_train) X_combined = np.vstack((X_train, X_test)) y_combined = np.hstack((y_train, y_test)) plot_decision_regions( X_combined, y_combined, classifier=forest, test_idx=range(105, 150) ) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show() 上面通过 n_estimators 参数从 25 个决策树中训练了一个随机森林，并使用 Gini 不纯度作为分割节点的标准。n_jobs 参数表示可以使用计算机的多个核心 (这里是两个核心) 来并行化训练。","s":"随机森林","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#随机森林","p":1205},{"i":1220,"t":"本文介绍懒惰学习的一个典型示例：K-近邻 (K-Nearest Neighbors，KNN) 算法。之所以称为懒惰，是因为它不从训练样本中学习判别函数，而是在记住已有的样本数据集的基础上对新样本进行分类。","s":"K-近邻","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","h":"","p":1219},{"i":1222,"t":"机器学习算法可以被分为两大类，参数模型和变参模型： 参数模型：学习时更新参数然后将其用于预测，如感知器、逻辑回归、线性 SVM 变参模型：参数不固定，如决策树/随机森林、使用核技巧的 SVM KNN 属于变参模型的一个子类：基于实例的学习 (instance-based learning)，在训练过程中记住整个训练集。懒惰学习是基于实例的学习的特例，在整个学习过程中不涉及损失函数的概念。 KNN 算法非常简单，步骤及图示如下： 确定 kkk 的大小和距离度量。 对于测试集中的一个样本，找到训练集中和它最近的 kkk 个样本。 将这 kkk 个样本的投票结果作为测试样本的类别。","s":"算法思想","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","h":"#算法思想","p":1219},{"i":1224,"t":"以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (设置 k=5k = 5k=5)： from sklearn.neighbors import KNeighborsClassifier knn = KNeighborsClassifier(n_neighbors=5, p=2, metric=\"minkowski\") knn.fit(X_train, y_train) X_combined = np.vstack((X_train, X_test)) y_combined = np.hstack((y_train, y_test)) plot_decision_regions(X_combined, y_combined, classifier=knn, test_idx=range(105, 150)) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show() kkk 的选择对于 KNN 模型来说至关重要，另外一个重要参数为距离度量。 上述代码使用的是 minkowski 距离： d(x(i),x(j))=∑k∣xk(i)−xk(j)∣pp\\begin{align} \\displaystyle d(x^{(i)},x^{(j)}) = \\sqrt[p] {\\sum_k |x^{(i)}_k - x^{(j)}_k|^p} \\end{align}d(x(i),x(j))=p​k∑​∣xk(i)​−xk(j)​∣p​​​ 若 p=2p=2p=2，则代表欧几里得距离；若 p=1p=1p=1，则代表曼哈顿距离。","s":"算法实现","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","h":"#算法实现","p":1219},{"i":1226,"t":"如果特征空间维度非常高，空间中最相似的两个点也可能距离很远，KNN 算法很容易过拟合。 在这种情况下，建议通过特征选择和降维等方法来避免维度问题。","s":"算法的维度问题","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","h":"#算法的维度问题","p":1219},{"i":1228,"t":"支持向量机 (Support Vector Machine，SVM) 是一种监督式学习方法，其学习策略为最大化样本与超平面 (即决策边界) 之间的间隔。本文介绍线性 SVM 的原理及实现。 间隔被定义为分离超平面与最靠近这个超平面的训练样本之间的距离。 这些影响边界的特殊样本称为支持向量，也是算法称为支持向量机的原因。","s":"线性 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-linear","h":"","p":1227},{"i":1230,"t":"为了得到边缘最大化，与决策边界平行的正负超平面可以用数学表示如下： w0+wTxpos=1w0+wTxneg=−1\\begin{align} w_0 + {\\boldsymbol w^T} {\\boldsymbol {x_{pos}}} & = 1 \\\\ w_0 + {\\boldsymbol w^T} {\\boldsymbol {x_{neg}}} & = -1 \\end{align}w0​+wTxpos​w0​+wTxneg​​=1=−1​​ 相减得到： wT(xpos−xneg)=2\\begin{align} {\\boldsymbol w^T} (\\boldsymbol {x_{pos}} - \\boldsymbol {x_{neg}}) = 2 \\end{align}wT(xpos​−xneg​)=2​​ 对上式中的 wT\\boldsymbol w^TwT 进行向量归一化： wT∣∣w∣∣(xpos−xneg)=2∣∣w∣∣,where ∣∣w∣∣=∑j=1m(wj)2\\begin{align} \\frac {\\boldsymbol w^T} {||\\boldsymbol w||} (\\boldsymbol {x_{pos}} - \\boldsymbol {x_{neg}}) = \\frac 2 {||\\boldsymbol w||}, \\quad where \\ ||\\boldsymbol w|| = \\sum_{j=1}^m (w_j)^2 \\end{align}∣∣w∣∣wT​(xpos​−xneg​)=∣∣w∣∣2​,where ∣∣w∣∣=j=1∑m​(wj​)2​​ 这两个超平面之间的距离是 2∣∣w∣∣\\cfrac 2 {||\\boldsymbol w||}∣∣w∣∣2​，要使两平面间的距离最大，我们需要最小化 ∣∣w∣∣||\\boldsymbol w||∣∣w∣∣。 同时为了使得样本数据点都在超平面的间隔区以外，我们需要保证对于所有的 iii 满足以下条件之一： w0+wTx(i)≥1,if y(i)=1w0+wTx(i)≤−1,if y(i)=−1\\begin{align} w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}} & \\ge 1, \\quad if \\ y^{(i)} = 1 \\\\ w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}} & \\le -1, \\quad if \\ y^{(i)} = -1 \\end{align}w0​+wTx(i)w0​+wTx(i)​≥1,if y(i)=1≤−1,if y(i)=−1​​ 上式等同于： y(i)(w0+wTx(i))≥1,∀i\\begin{align} y^{(i)}(w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}}) \\ge 1, \\quad \\forall i \\end{align}y(i)(w0​+wTx(i))≥1,∀i​​ 硬间隔 SVM 的目标是在上式约束条件下，最小化 ∣∣w∣∣||\\boldsymbol w||∣∣w∣∣；在实际中，一般是最小化 12∣∣w∣∣2\\cfrac 1 2 ||\\boldsymbol w||^221​∣∣w∣∣2。","s":"硬间隔 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-linear","h":"#硬间隔-svm","p":1227},{"i":1232,"t":"SVM 在软间隔分类器中引入了松弛变量 ξ\\xiξ，它允许分类器对一些样本犯错，允许一些样本不满足硬间隔约束条件。 这样做可以避免 SVM 分类器过拟合，于是也就避免了模型过于复杂，降低了模型对噪声点的敏感性，提升了模型的泛化性能。 带松弛变量的分类器约束条件如下： w0+wTx(i)≥1−ξ(i),if y(i)=1w0+wTx(i)≤−1+ξ(i),if y(i)=−1\\begin{align} w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}} & \\ge 1 - \\xi ^{(i)}, \\quad if \\ y^{(i)} = 1 \\\\ w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}} & \\le -1 + \\xi ^{(i)}, \\quad if \\ y^{(i)} = -1 \\end{align}w0​+wTx(i)w0​+wTx(i)​≥1−ξ(i),if y(i)=1≤−1+ξ(i),if y(i)=−1​​ 软间隔 SVM 的目标是最小化 12∣∣w∣∣2+C(∑iξ(i))\\cfrac 1 2 ||\\boldsymbol w||^2 + C (\\sum_i \\xi ^{(i)})21​∣∣w∣∣2+C(∑i​ξ(i))。 参数 CCC 可以平衡偏差和方差。CCC 越大，算法分类越严格，方差越高，过大的 CCC 可能会引起过拟合；反之同理。 以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (其中决策边界绘制函数 plot_decision_regions 请参见之前的文章)： import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.svm import SVC from sklearn.preprocessing import StandardScaler iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test) X_combined_std = np.vstack((X_train_std, X_test_std)) y_combined = np.hstack((y_train, y_test)) svm = SVC(kernel=\"linear\", C=1.0, random_state=1) svm.fit(X_train_std, y_train) plot_decision_regions( X_combined_std, y_combined, classifier=svm, test_idx=range(105, 150) ) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show()","s":"软间隔 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-linear","h":"#软间隔-svm","p":1227},{"i":1234,"t":"集合 (Ensemble) 方法的目标是将不同的分类器组合到一起，相比每个单独的分类器具有更好的泛化性能。","s":"使用集合的投票分类方法","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","h":"","p":1233},{"i":1236,"t":"如果 10 位专家的预测分别如下，集合方法可以将其预测结果结合起来，从而得出比每位专家的预测更精确和更稳健的预测： 一致 (Unanimity)：预测情况一致 绝对多数投票 (Majority Voting)：预测情况不同，取高于 50% 的预测结果，适用于二元分类 相对多数投票 (Plurality Voting)：预测情况不同，取其中相对最高的预测结果，适用于多元分类 投票算法用于分类器时，可以取 m 个不同的分类器，然后使用不同的分类算法 (决策树、SVM、逻辑回归等) 构建集合；也可以使用相同的分类算法对不同的测试集进行评估。 以下为使用多数投票的集合方法实例，其中有 m 个分类器 C1，C2，⋯，CmC_1，C_2， \\cdots，C_mC1​，C2​，⋯，Cm​ 以及其评估结果： 记 x\\boldsymbol xx 为输入，y^\\hat yy^​ 为预测的众数： y^=mode{C1(x),C2(x),⋯ ,Cm(x)}\\begin{align} \\hat y = mode \\{C_1(\\boldsymbol x), C_2(\\boldsymbol x), \\cdots, C_m(\\boldsymbol x) \\} \\end{align}y^​=mode{C1​(x),C2​(x),⋯,Cm​(x)}​​ 在统计学中，使用 modemodemode 代表众数，即出现次数最多的元素。","s":"算法描述","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","h":"#算法描述","p":1233},{"i":1238,"t":"接下来阐述为什么集合在绝大多数情况下能够比单个分类器具有更好的表现。 以二元分类为例，假设单个分类器的错误率 \\varepsilon=0.25，使用 11 个分类器 (假设其互不相关、且每个分类器的错误率相同) 的集合错误率显著降低： ERR=∑k=611Ck11εk(1−ε)11−k=0.034\\begin{align} ERR = \\sum_{k=6}^{11} C_k^{11} \\varepsilon^k (1 - \\varepsilon)^{11 - k} = 0.034 \\end{align}ERR=k=6∑11​Ck11​εk(1−ε)11−k=0.034​​ 其中 CknC_k^nCkn​ 为二项式系数 n！k！(n−k)！\\cfrac {n！} {k！(n-k)！}k！(n−k)！n！​。 上述的数学表达式在 python 中实现如下： from scipy.misc import comb import math def ensemble_error(n_classifier, error): k_start = int(math.ceil(n_classifier / 2)) probs = [ comb(n_classifier, k) * error**k * (1 - error) ** (n_classifier - k) for k in range(k_start, n_classifier + 1) ] return sum(probs) print(ensemble_error(11, 0.25)) # Output: 0.034327507019042969 集合错误率和单个分类器错误率之前的关系绘图如下： import numpy as np import matplotlib.pyplot as plt error_range = np.arange(0.0, 1.01, 0.01) ens_errors = [ensemble_error(n_classifier=11, error=err) for err in error_range] plt.plot(error_range, ens_errors, label=\"Ensemble Error\", linewidth=2) plt.plot(error_range, error_range, linestyle=\"--\", label=\"Base Error\", linewidth=2) plt.xlabel(\"Base error\") plt.ylabel(\"Base/Ensemble error\") plt.legend(loc=\"upper left\") plt.show() 可以看的，只要单个分类器错误率小于 0.5 (二元分类可以轻易达到这个水平)，那么使用集合能够模型提高模型的预测能力。","s":"算法思想","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","h":"#算法思想","p":1233},{"i":1240,"t":"加权相对多数分类器的结果如下，其中 jjj 代表第 jjj 个分类器，iii 代表类标签： y^=arg⁡max⁡i∑j=1mwjpij\\begin{align} \\hat y = \\arg \\max_i \\sum_{j=1}^m w_j p_{ij} \\end{align}y^​=argimax​j=1∑m​wj​pij​​​ 为进行说明，假设有二元分类 (类标签 iii 为 0 或 1)，使用三个分类器的集合进行加权评估，每个分类器对于给定输入 x\\boldsymbol xx 的概率和权重如下： 第一个分类器预测为 0 和 1 和概率分别为 C1(x)=[0.9，0.1]C_1 (\\boldsymbol x) = [0.9，0.1]C1​(x)=[0.9，0.1]，权重为 0.2。 第二个分类器预测为 0 和 1 和概率分别为 C1(x)=[0.8，0.2]C_1 (\\boldsymbol x) = [0.8，0.2]C1​(x)=[0.8，0.2]，权重为 0.2。 第三个分类器预测为 0 和 1 和概率分别为 C1(x)=[0.4，0.6]C_1 (\\boldsymbol x) = [0.4，0.6]C1​(x)=[0.4，0.6]，权重为 0.6。 预测为类 0 和类 1 的概率分别为： p(i=0∣x)=0.9×0.2+0.8×0.2+0.4×0.2=0.58p(i=1∣x)=0.1×0.2+0.2×0.2+0.6×0.2=0.42\\begin{align} p(i = 0 \\mid \\boldsymbol x) & = 0.9 \\times 0.2 + 0.8 \\times 0.2 + 0.4 \\times 0.2 = 0.58 \\\\ p(i = 1 \\mid \\boldsymbol x) & = 0.1 \\times 0.2 + 0.2 \\times 0.2 + 0.6 \\times 0.2 = 0.42 \\end{align}p(i=0∣x)p(i=1∣x)​=0.9×0.2+0.8×0.2+0.4×0.2=0.58=0.1×0.2+0.2×0.2+0.6×0.2=0.42​​ 最终的预测分类为 0： y^=arg⁡max⁡i[p(i=0∣x),p(i=1∣x)]=0\\begin{align} \\hat y = \\arg \\max_i [p(i = 0 \\mid \\boldsymbol x), p(i = 1 \\mid \\boldsymbol x)] = 0 \\end{align}y^​=argimax​[p(i=0∣x),p(i=1∣x)]=0​​ ex = np.array([[0.9, 0.1], [0.8, 0.2], [0.4, 0.6]]) p = np.average(ex, axis=0, weights=[0.2, 0.2, 0.6]) print(p) # Output: array([ 0.58, 0.42]) print(np.argmax(p)) # Output: 0 scikit-learn 中实现了投票分类，请参见 sklearn.ensemble.VotingClassifier。","s":"加权相对多数分类器","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","h":"#加权相对多数分类器","p":1233},{"i":1244,"t":"嵌入层：Embedding 输入嵌入层 Input Embedding 输出嵌入层 Output Embedding 位置编码层：Positional Encoding 堆叠层 注意力层： Multi-Head 注意力机制 Mask 注意力机制 前馈神经网络 其他 參差网络 Residual Add 层归一化 Layer Normalization 预测词输出 Linear & SoftMax","s":"分层设计","u":"/docs/machine-learning/transformer/transformer-architecture","h":"#分层设计","p":1241},{"i":1247,"t":"在原始 SVM 只支持线性样本的基础上，引入核技巧 (Kernel Trick) 可以对非线性的样本进行分类。算法思想为将输入向量映射到高维空间，然后用超平面划分。本文中有举例说明。","s":"核技巧和非线性 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","h":"","p":1246},{"i":1249,"t":"下图描述了 SVM 如何将低维非线性可分的问题转换为高维度线性可分。 如图所示，原始的内环 (红色样本) 和外环 (蓝色样本) 不能线性分割。 通过非线性变换 ϕ(x)\\phi (x)ϕ(x)，将原始二维数据集映射到新的三维特征空间，如右上子图。 ϕ(x1,x2)=(z1,z2,z3)=(x1,x2,x12+x22)\\begin{align} \\phi (x_1, x_2) = (z_1, z_2, z_3) = (x_1, x_2, x_1^2 + x_2^2) \\end{align}ϕ(x1​,x2​)=(z1​,z2​,z3​)=(x1​,x2​,x12​+x22​)​​ 将分离样本的线性超平面 z3=cz_3 = cz3​=c 其投影回原始特征空间，则得到原始二维空间的非线性决策边界 x12+x22=cx_1^2 + x_2^2 = cx12​+x22​=c。","s":"核技巧原理","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","h":"#核技巧原理","p":1246},{"i":1251,"t":"核技巧的数学描述如下： k(x(i),x(j))=ϕ(x(i))Tϕ(x(j))\\begin{align} k(\\boldsymbol x^{(i)}, \\boldsymbol x^{(j)}) = \\phi(\\boldsymbol x^{(i)})^T \\phi(\\boldsymbol x^{(j)}) \\end{align}k(x(i),x(j))=ϕ(x(i))Tϕ(x(j))​​ 以常见的 (高斯) 径向基函数 (Radial Basis Function，RBF) 为例，核函数为： k(x(i),x(j))=exp⁡(−∣∣x(i)−x(j)∣∣22σ2)\\begin{align} k(\\boldsymbol x^{(i)}, \\boldsymbol x^{(j)}) = \\exp \\left(- \\cfrac {||\\boldsymbol x^{(i)} - \\boldsymbol x^{(j)}||^2} {2\\sigma^2} \\right) \\end{align}k(x(i),x(j))=exp(−2σ2∣∣x(i)−x(j)∣∣2​)​​ 上式通常简化为： k(x(i),x(j))=exp⁡(−γ∣∣x(i)−x(j)∣∣2)\\begin{align} k(\\boldsymbol x^{(i)}, \\boldsymbol x^{(j)}) = \\exp \\left(- \\gamma {||\\boldsymbol x^{(i)} - \\boldsymbol x^{(j)}||^2} \\right) \\end{align}k(x(i),x(j))=exp(−γ∣∣x(i)−x(j)∣∣2)​​ 其中 γ=12σ2\\gamma = \\cfrac 1 {2\\sigma^2}γ=2σ21​ 为需要优化的超参数。","s":"数学表达","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","h":"#数学表达","p":1246},{"i":1253,"t":"以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (其中决策边界绘制函数 plot_decision_regions 请参见之前的文章)： import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.svm import SVC from sklearn.preprocessing import StandardScaler iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test) X_combined_std = np.vstack((X_train_std, X_test_std)) y_combined = np.hstack((y_train, y_test)) svm = SVC(kernel=\"rbf\", random_state=1, gamma=0.2, C=1.0) svm.fit(X_train_std, y_train) plot_decision_regions( X_combined_std, y_combined, classifier=svm, test_idx=range(105, 150) ) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show() 上图的决策边界是较为合理的曲线。 将 SVC 的超参数 γ\\gammaγ 增大至 100100100，观察决策边界的变化： svm = SVC(kernel=\"rbf\", random_state=1, gamma=100.0, C=1.0) 可以看到，类 1 和类 2 的边界非常紧凑，样本空间远远小于类 3 的样本空间。 当 γ\\gammaγ 较大时，容易出现过拟合情况，在实际应用中需要控制 γ\\gammaγ 的大小在合理范围。","s":"非线性 SVM 实现","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","h":"#非线性-svm-实现","p":1246},{"i":1257,"t":"简单来说，注意力就是我们关注的重点。 以上图的柴犬为例，人类的视觉注意力可以聚焦于图像的某个 (或者某些) 区域，同时忽略其余的区域。","s":"人类的图像注意力","u":"/docs/machine-learning/transformer/transformer-attention","h":"#人类的图像注意力","p":1254},{"i":1259,"t":"类似的，在文本中也有注意力机制，在阅读某一个词的时候，我们会去同时关注其他某些相关的词。","s":"人类的文本注意力","u":"/docs/machine-learning/transformer/transformer-attention","h":"#人类的文本注意力","p":1254},{"i":1261,"t":"Transformer 的注意力机制是 Transformer 架构的核心。","s":"Transformer 的注意力机制","u":"/docs/machine-learning/transformer/transformer-attention","h":"#transformer-的注意力机制","p":1254},{"i":1263,"t":"毫不夸张的说，QQQ、KKK、VVV 是天才设计。也是大模型的基石。如何理解 QQQ、KKK、VVV？ 以爬山为例，假设您想要估算当前的海拔高度，但没有直接获得这个信息。相反，您使用望远镜观察到周围有若干个碑石： 离你最近的上方碑石的信息：海拔 2000 米；离你较远 离你最近的下方碑石的信息：海拔 1800 米；离你较近 我们预测当前的海拔高度为：2000∗0.7+1800∗0.3=19402000 * 0.7 + 1800 * 0.3 = 19402000∗0.7+1800∗0.3=1940 (米)。 现在，让我们将这个过程解释为注意力机制的步骤： QQQ：当前状态，作为查询 KKK：观测到的碑石状态 (键值) VVV：碑石存储的数值信息 QKTQK^TQKT 是点积。SoftMax 让其概率为之和为 1。 为了解决维度过高带来的影响，Transformer 设计的时候，使用了缩放的点积。","s":"理解注意力机制的 QQQ / KKK / VVV","u":"/docs/machine-learning/transformer/transformer-attention","h":"#理解注意力机制的-q--k--v","p":1254},{"i":1265,"t":"我们看一下 QQQ 和 KTK^TKT： Q=(q1q2⋮),K=(k1k2⋮)Q = \\begin{pmatrix} q_1 \\\\ q_2 \\\\ \\vdots \\\\ \\end{pmatrix}, K = \\begin{pmatrix} k_1 \\\\ k_2 \\\\ \\vdots \\\\ \\end{pmatrix}Q=​q1​q2​⋮​​,K=​k1​k2​⋮​​ 其中 qiq_iqi​ 和 kjk_jkj​ 是多维向量，维度为嵌入向量的维度 d_modeld\\_modeld_model。 QKTQK^TQKT 的结果为： (q1k1q1k2⋯q2k1q2k2⋯⋮⋮⋱)\\begin{pmatrix} q_1k_1 & q_1k_2 & \\cdots \\\\ q_2k_1 & q_2k_2 & \\cdots \\\\ \\vdots & \\vdots & \\ddots \\\\ \\end{pmatrix}​q1​k1​q2​k1​⋮​q1​k2​q2​k2​⋮​⋯⋯⋱​​ 上面的 qikjq_ik_jqi​kj​ 是向量的点积结果，用于表征查询 qiq_iqi​ 和键值 kjk_jkj​ 之间的匹配程度。","s":"理解 QKTQK^TQKT","u":"/docs/machine-learning/transformer/transformer-attention","h":"#理解-qkt","p":1254},{"i":1267,"t":"注意力机制为查询和目标之间的注意力，比如在翻译任务中，源语言和翻译的目标语言是不同的。 在查询为目标本身的时候，为注意力的一种特殊形式：自注意力。 自注意力可以分为两种情况： 前向关注 (关注这个 token，和之前的其余 tokens) 双向关注 (关注这个 token，和之前以及之后的 tokens)","s":"自注意力机制","u":"/docs/machine-learning/transformer/transformer-attention","h":"#自注意力机制","p":1254},{"i":1269,"t":"在自注意力相关性中，mask 代表关注的程度。由于矩阵天然具有前后双向关注的特性，如果我们只需要关注于之前的 tokens，则需要添加屏蔽之后 attention 的 mask。 通常来说，前向关注的注意力机制也称为因果注意力 (casual attention)。 在因果注意力中，为了保持自回归性质，注意力机制会限制每个位置只能注意到其之前的位置，而不是整个输入序列。 在代码实现中，可以在计算 QKTQK^TQKT 或者计算 QKTdk\\cfrac{QK^T}{\\sqrt{d_k}}dk​​QKT​ 后，将右上部分 (不包含对角线) 设置成负无穷大或者一个非常大的负值 (如 1e-9)，这样在经过 SoftMax 之后，对应位置的 attention score 接近为 0。","s":"自注意力中的 mask","u":"/docs/machine-learning/transformer/transformer-attention","h":"#自注意力中的-mask","p":1254},{"i":1271,"t":"总体来看，Transformer 模型主要由两个块组成： Encoder (左侧)：编码器接收输入并构建其表示 (其特征)。这意味着对模型进行了优化，以从输入中获得理解。 Decoder (右侧)：解码器使用编码器的表示 (特征) 以及其他输入来生成目标序列。这意味着该模型已针对生成输出进行了优化。 编码组件是若干个 encoder 堆叠而成，解码组件也是若干个 decoder 堆叠而成的。层数是一个超参数，在原始论文中设置为 6。","s":"编码器和解码器","u":"/docs/machine-learning/transformer/transformer-encoders-decoders","h":"","p":1270},{"i":1273,"t":"编码器和解码器实际上是寻找 token 的内在特征。 举例来说： This pear is delicious. The orange is yummy. That watermelon tastes terrible. 假设我们现在对“pear”，“delicious”，“orange”，“yummy”，“watermelon”，“terrible”进行 one-hot 编码： 1 0 0 0 0 0 # pear 0 1 0 0 0 0 # delicious 0 0 1 0 0 0 # orange 0 0 0 1 0 0 # yummy 0 0 0 0 1 0 # watermelon 0 0 0 0 0 1 # terrible 但是这种编码不能代表词语之间的内在联系，因此有了 Word2Vec 编码，比如对于上面的单词，我们编码成二维： 第一维：水果属性 第二维：好吃程度 [64, 0] # pear [0, 80] # delicious [57, 0] # orange [0, 96] # yummy [83, 0] # watermelon [0, -77] # terrible 这种编码格式更符合人们的直觉。但是在实际情况中，语言编码的复杂性非常高： 由于几万个单词，有很多维度，人工编码不可行。 固定的编码不能很好的表征其含义，在不同语境下，相同的单词可能有不同的意义。 Transformer 的解码器和编码器，在翻译任务中，可以理解为 token 的特征提取器。解码器和编码器会自动提取源语言和目标语言中的 token 的特征。","s":"理解编码器和解码器","u":"/docs/machine-learning/transformer/transformer-encoders-decoders","h":"#理解编码器和解码器","p":1270},{"i":1275,"t":"Transformer 是一种采用自注意力机制 (self-attention) 的深度学习模型架构，这一机制可以按输入数据各部分重要性的不同而分配不同的权重。该模型由 Google 机器翻译团队于 2017 年发表于论文 Attention is all you need 中，为 OpenAI 开发的 ChatGPT、Google 的 Gemini、Meta 的 LLaMA 等大语言模型的核心基础架构。 Transformer 模型是迄今发明出最新且最强大的模型之一。","s":"Transformer 概览","u":"/docs/machine-learning/transformer/transformer-overview","h":"","p":1274},{"i":1277,"t":"什么是自然语言处理 (Natural Language Processing，NLP)？NLP 是语言学和机器学习交叉领域，专注于理解与人类语言相关的一切。NLP 任务的目标不仅是单独理解单个单词，而且是能够理解这些单词的上下文。 以下是常见 NLP 任务的列表，每个任务都有一些示例： 对整个句子进行分类：获取评论的情绪，检测电子邮件是否为垃圾邮件，确定句子在语法上是否正确或两个句子在逻辑上是否相关。 对句子中的每个词进行分类：识别句子的语法成分 (名词、动词、形容词) 或命名实体 (人、地点、组织)。 生成文本内容：用自动生成的文本完成提示，用屏蔽词填充文本中的空白 从文本中提取答案：给定问题和上下文，根据上下文中提供的信息提取问题的答案。 从输入文本生成新句子：将文本翻译成另一种语言，总结文本。 NLP 不仅限于书面文本。它还解决了语音识别和计算机视觉中的复杂挑战，例如音频生成、图像识别、图像描述等。 在 Transformer 发明之前，机器学习中 NLP 的任务处理基本是通过 RNN 或者其变体 GRU、LSTM 建模的。相比于这些模型，Transformer 具有以下优势： 并行计算。RNN 和 LSTM 需要顺序处理序列数据，因此很难进行并行计算。而 Transformer 的自注意力机制允许同时处理整个序列，从而可以充分利用 GPU 的并行计算能力，大大提高模型训练和推理的速度。 更好的长期依赖。RNN 在处理长序列时面临梯度消失或梯度爆炸的问题，导致难以建模长期依赖关系。相比之下，Transformer 使用了自注意力机制，能够直接建模序列中不同位置之间的依赖关系，从而更好地捕捉长期依赖关系。 灵活性：Transformer 架构具有很高的灵活性，可以很容易地进行修改和扩展。例如，BERT、GPT 等知名模型都是基于 Transformer 架构的，它们在各种自然语言处理任务中取得了前所未有的成绩。","s":"自然语言处理","u":"/docs/machine-learning/transformer/transformer-overview","h":"#自然语言处理","p":1274},{"i":1278,"t":"我们先将整个模型视为黑盒。 在机器翻译中，接收一种语言的句子作为输入，然后将其翻译成其他语言输出。 Transformer 设计之初就是为了解决 NLP 中的翻译问题。","s":"Transformer 概览","u":"/docs/machine-learning/transformer/transformer-overview","h":"#transformer-概览-1","p":1274},{"i":1281,"t":"#!/usr/bin/env python3 \"\"\" Implementation of Transformer: Attention Is All You Need References: - [Paper arXiv: Attention Is All You Need](https://arxiv.org/abs/1706.03762) - [Blog Post: The Illustrated Transformer](http://jalammar.github.io/illustrated-transformer/) - [YouTube Video: The Illustrated Transformer](https://youtu.be/ISNdQcPhsts?si=VyFfVKoITGOV78OA) \"\"\" import argparse import math import os import sys import torch import torch.nn as nn import torch.optim as optim from torchinfo import summary class PositionalEncoding(nn.Module): def __init__(self, d_model, max_seq_length): super(PositionalEncoding, self).__init__() pe = torch.zeros(max_seq_length, d_model) position = torch.arange(0, max_seq_length, dtype=torch.float).unsqueeze(1) div_term = torch.exp( torch.arange(0, d_model, 2).float() * -(math.log(10000.0) / d_model) ) pe[:, 0::2] = torch.sin(position * div_term) pe[:, 1::2] = torch.cos(position * div_term) self.register_buffer(\"pe\", pe.unsqueeze(0)) def forward(self, x): return x + self.pe[:, : x.size(1)] class MultiHeadAttention(nn.Module): def __init__(self, d_model, num_heads): super(MultiHeadAttention, self).__init__() # Ensure that the model dimension (d_model) is divisible by the number of heads assert d_model % num_heads == 0, \"d_model must be divisible by num_heads\" # Initialize dimensions self.d_model = d_model # Model's dimension self.num_heads = num_heads # Number of attention heads self.d_k = ( d_model // num_heads ) # Dimension of each head's key, query, and value # Linear layers for transforming inputs self.W_q = nn.Linear(d_model, d_model) # Query transformation self.W_k = nn.Linear(d_model, d_model) # Key transformation self.W_v = nn.Linear(d_model, d_model) # Value transformation self.W_o = nn.Linear(d_model, d_model) # Output transformation def scaled_dot_product_attention(self, Q, K, V, mask=None): # Calculate attention scores attn_scores = torch.matmul(Q, K.transpose(-2, -1)) / math.sqrt(self.d_k) # Apply mask if provided (useful for preventing attention to certain parts like padding) if mask is not None: attn_scores = attn_scores.masked_fill(mask == 0, -1e9) # Softmax is applied to obtain attention probabilities attn_probs = torch.softmax(attn_scores, dim=-1) # Multiply by values to obtain the final output output = torch.matmul(attn_probs, V) return output def split_heads(self, x): # Reshape the input to have num_heads for multi-head attention batch_size, seq_length, d_model = x.size() return x.view(batch_size, seq_length, self.num_heads, self.d_k).transpose(1, 2) def combine_heads(self, x): # Combine the multiple heads back to original shape batch_size, _, seq_length, d_k = x.size() return x.transpose(1, 2).contiguous().view(batch_size, seq_length, self.d_model) def forward(self, Q, K, V, mask=None): # Apply linear transformations and split heads Q = self.split_heads(self.W_q(Q)) K = self.split_heads(self.W_k(K)) V = self.split_heads(self.W_v(V)) # Perform scaled dot-product attention attn_output = self.scaled_dot_product_attention(Q, K, V, mask) # Combine heads and apply output transformation output = self.W_o(self.combine_heads(attn_output)) return output class EncoderLayer(nn.Module): def __init__(self, d_model, num_heads, d_ff, dropout): super(EncoderLayer, self).__init__() self.self_attn = MultiHeadAttention(d_model, num_heads) self.feed_forward = PositionWiseFeedForward(d_model, d_ff) self.norm1 = nn.LayerNorm(d_model) self.norm2 = nn.LayerNorm(d_model) self.dropout = nn.Dropout(dropout) def forward(self, x, mask): attn_output = self.self_attn(x, x, x, mask) x = self.norm1(x + self.dropout(attn_output)) ff_output = self.feed_forward(x) x = self.norm2(x + self.dropout(ff_output)) return x class DecoderLayer(nn.Module): def __init__(self, d_model, num_heads, d_ff, dropout): super(DecoderLayer, self).__init__() self.self_attn = MultiHeadAttention(d_model, num_heads) self.cross_attn = MultiHeadAttention(d_model, num_heads) self.feed_forward = PositionWiseFeedForward(d_model, d_ff) self.norm1 = nn.LayerNorm(d_model) self.norm2 = nn.LayerNorm(d_model) self.norm3 = nn.LayerNorm(d_model) self.dropout = nn.Dropout(dropout) def forward(self, x, enc_output, src_mask, tgt_mask): attn_output = self.self_attn(x, x, x, tgt_mask) x = self.norm1(x + self.dropout(attn_output)) attn_output = self.cross_attn(x, enc_output, enc_output, src_mask) x = self.norm2(x + self.dropout(attn_output)) ff_output = self.feed_forward(x) x = self.norm3(x + self.dropout(ff_output)) return x class PositionWiseFeedForward(nn.Module): def __init__(self, d_model, d_ff): super(PositionWiseFeedForward, self).__init__() self.fc1 = nn.Linear(d_model, d_ff) self.fc2 = nn.Linear(d_ff, d_model) self.relu = nn.ReLU() def forward(self, x): return self.fc2(self.relu(self.fc1(x))) class Transformer(nn.Module): def __init__( self, src_vocab_size, tgt_vocab_size, d_model, num_heads, num_layers, d_ff, max_seq_length, dropout, ): super(Transformer, self).__init__() self.encoder_embedding = nn.Embedding(src_vocab_size, d_model) self.decoder_embedding = nn.Embedding(tgt_vocab_size, d_model) self.positional_encoding = PositionalEncoding(d_model, max_seq_length) self.encoder_layers = nn.ModuleList( [EncoderLayer(d_model, num_heads, d_ff, dropout) for _ in range(num_layers)] ) self.decoder_layers = nn.ModuleList( [DecoderLayer(d_model, num_heads, d_ff, dropout) for _ in range(num_layers)] ) self.fc = nn.Linear(d_model, tgt_vocab_size) self.dropout = nn.Dropout(dropout) def generate_mask(self, src, tgt): src_mask = (src != 0).unsqueeze(1).unsqueeze(2) tgt_mask = (tgt != 0).unsqueeze(1).unsqueeze(3) seq_length = tgt.size(1) nopeak_mask = ( 1 - torch.triu(torch.ones(1, seq_length, seq_length), diagonal=1) ).bool() tgt_mask = tgt_mask & nopeak_mask return src_mask, tgt_mask def forward(self, src, tgt): src_mask, tgt_mask = self.generate_mask(src, tgt) src_embedded = self.dropout( self.positional_encoding(self.encoder_embedding(src)) ) tgt_embedded = self.dropout( self.positional_encoding(self.decoder_embedding(tgt)) ) enc_output = src_embedded for enc_layer in self.encoder_layers: enc_output = enc_layer(enc_output, src_mask) dec_output = tgt_embedded for dec_layer in self.decoder_layers: dec_output = dec_layer(dec_output, enc_output, src_mask, tgt_mask) output = self.fc(dec_output) return output def main(args): transformer = Transformer( args.src_vocab_size, args.tgt_vocab_size, args.d_model, args.num_heads, args.num_layers, args.d_ff, args.max_seq_length, args.dropout, ) # Generate random sample data src_data = torch.randint( 1, args.src_vocab_size, (64, args.max_seq_length) ) # (batch_size, seq_length) tgt_data = torch.randint( 1, args.tgt_vocab_size, (64, args.max_seq_length) ) # (batch_size, seq_length) print(summary(transformer, input_data=[src_data, tgt_data], device=\"cpu\")) criterion = nn.CrossEntropyLoss(ignore_index=0) optimizer = optim.Adam( transformer.parameters(), lr=0.0001, betas=(0.9, 0.98), eps=1e-9 ) transformer.train() for epoch in range(10): optimizer.zero_grad() output = transformer(src_data, tgt_data[:, :-1]) loss = criterion( output.contiguous().view(-1, args.tgt_vocab_size), tgt_data[:, 1:].contiguous().view(-1), ) loss.backward() optimizer.step() print(f\"Epoch: {epoch+1}, Loss: {loss.item()}\") transformer.eval() # Generate random sample validation data val_src_data = torch.randint( 1, args.src_vocab_size, (64, args.max_seq_length) ) # (batch_size, seq_length) val_tgt_data = torch.randint( 1, args.tgt_vocab_size, (64, args.max_seq_length) ) # (batch_size, seq_length) with torch.no_grad(): val_output = transformer(val_src_data, val_tgt_data[:, :-1]) val_loss = criterion( val_output.contiguous().view(-1, args.tgt_vocab_size), val_tgt_data[:, 1:].contiguous().view(-1), ) print(f\"Validation Loss: {val_loss.item()}\") if __name__ == \"__main__\": parser = argparse.ArgumentParser( formatter_class=argparse.ArgumentDefaultsHelpFormatter ) parser.add_argument( \"--src_vocab_size\", type=int, default=5000, help=\"source vocabulary size\" ) parser.add_argument( \"--tgt_vocab_size\", type=int, default=5000, help=\"target vocabulary size\" ) parser.add_argument( \"--d_model\", type=int, default=512, help=\"dimensionality of model's input and output\", ) parser.add_argument( \"--num_heads\", type=int, default=8, help=\"number of attention heads in multi-head attention\", ) parser.add_argument( \"--num_layers\", type=int, default=6, help=\"number of layers for both the encoder and the decoder\", ) parser.add_argument( \"--d_ff\", type=int, default=2048, help=\"dimensionality of the inner layer in the feed-forward network\", ) parser.add_argument( \"--max_seq_length\", type=int, default=100, help=\"the maximum length of the sequence\", ) parser.add_argument( \"--dropout\", type=float, default=0.1, help=\"dropout rate for regularization\", ) try: args = parser.parse_args() main(args) except KeyboardInterrupt: print(\"Interrupted\") try: sys.exit(0) except SystemExit: os._exit(0)","s":"PyTorch 代码实现","u":"/docs/machine-learning/transformer/transformer-code-implementation","h":"#pytorch-代码实现","p":1279},{"i":1283,"t":"论文通过添加一种称为“多头”注意力的机制进一步细化了自注意力。它扩展了模型关注不同位置的能力。 比如对于以下语句：“The animal didn’t cross the street because it was too tired” 在语义不同的时候，可以有不同的注意力，比如“it”关注于指代的东西时候，对“animal”有很高的权重；“it”关注于其当前形容词的时候，对“tired”有很高的权重。 如下图所示，原始论文中使用了 8 个注意力头，每个注意力头都有自己的 QQQ / KKK / VVV 矩阵。 这可以理解为有 8 个不同的特征子空间，每个子空间可以提取不同的特征表示，最终嵌入 (投影) 到同一个向量中。 对于这个合成的嵌入向量再做一次矩阵变换，得到最终的注意力矩阵 ZZZ。","s":"分割的多头注意力机制","u":"/docs/machine-learning/transformer/transformer-split-multi-head-attention","h":"","p":1282},{"i":1286,"t":"对于任何一门语言，单词在句子中的位置以及排列顺序是非常重要的，它们不仅是一个句子的语法结构的组成部分，更是表达语义的重要概念。 Transformer 模型抛弃了 RNN、LSTM、GRU 作为序列学习的基本模型。我们知道，RNN 本身就是一种顺序结构，天生就包含了词在序列中的位置信息。当抛弃 RNN 结构，完全采用 Attention 取而代之，这些词序信息就会丢失。","s":"为什么需要位置编码","u":"/docs/machine-learning/transformer/transformer-positional-encoding","h":"#为什么需要位置编码","p":1284},{"i":1288,"t":"最简单的位置编码是：第一个 token 编码为 0，第一个 token 编码为 1，以此类推。这种方法带来的问题是，不仅这些数值会变得非常大，而且模型也会遇到一些比训练中的所有句子都要长的句子。此外，数据集中不一定在所有数值上都会包含相对应长度的句子，也就是模型很有可能没有看到过任何一个这样的长度的样本句子，这会严重影响模型的泛化能力。 因此，一种好的位置编码方案需要满足以下几条要求： 能够为每个时间步输出一个独一无二的编码 给定任意一个位置，编码的值必须是确定性的 (而不是需要在机器学习中的超参数) 固定步长的两个位置的编码，应该存在一定的关系 模型应该能泛化到更长的句子","s":"怎么实现位置编码","u":"/docs/machine-learning/transformer/transformer-positional-encoding","h":"#怎么实现位置编码","p":1284},{"i":1290,"t":"Transformer 的位置编码为： PE(pos,2i)=sin(pos100002i/dmodel),PE(pos,2i+1)=cos(pos100002i/dmodel).\\begin{aligned} \\text{PE}_{(pos,2i)}=sin\\left(\\frac{pos}{10000^{2i/d_{model}}}\\right), \\\\ \\text{PE}_{(pos,2i+1)}=cos\\left(\\frac{pos}{10000^{2i/d_{model}}}\\right). \\end{aligned}PE(pos,2i)​=sin(100002i/dmodel​pos​),PE(pos,2i+1)​=cos(100002i/dmodel​pos​).​ 其中 pospospos 为位置编号，iii 是维度编号。 为什么采用这种编码？我们看一下说明： We chose this function because we hypothesized it would allow the model to easily learn to attend by relative positions, since for any fixed offset kkk, PEpos+kPE_{pos+k}PEpos+k​ can be represented as a linear function of PEposPE_{pos}PEpos​. 这句话的意思是，上面的编码能够让模型轻松关注相对位置。给定距离为 kkk 的两个位置，其编码 PEpos+kPE_{pos+k}PEpos+k​ 和 PEposPE_{pos}PEpos​ 存在固定的线性变换关系。 从结果来看，Transformer 的位置编码能够有效泛化到更长的句子。 需要明确的是，这不代表其为唯一可行的位置编码方案。","s":"Transformer 的位置编码","u":"/docs/machine-learning/transformer/transformer-positional-encoding","h":"#transformer-的位置编码","p":1284},{"i":1292,"t":"下图为对 20 个位置编码为的示例，其中每个位置编码为 512 维的向量。左半部分是维度为 2i2i2i 的正弦编码，右半部分是是维度为 2i2i2i 的余弦编码。 将它们交叉连接，就是 Transformer 使用的位置编码向量。","s":"Transformer 编码的可视化","u":"/docs/machine-learning/transformer/transformer-positional-encoding","h":"#transformer-编码的可视化","p":1284},{"i":1295,"t":"Informer 在论文 Informer：Beyond Efficient Transformer for Long Sequence Time-Series Forecasting 中提出，对经典的 Transformer 提出了一些改进，用于长时间序列预测 (Long sequence time-series forecasting，LSTF) 任务，包括： ProbSparse 自注意力机制，其时间复杂度和内存使用量达到 O(LlogL)O(LlogL)O(LlogL) ，并且在序列的依赖性对齐方面具有相近的性能； 自注意力蒸馏通过将级联层输入减半来突出主导注意力，并有效处理极长的输入序列； 在生成式的解码器中，通过一次前向操作而不是一步一步的方式来预测长时间序列，大大提高了长序列预测的推理速度。 Informer 源码开源在 GitHub - Informer2020。","s":"Informer","u":"/docs/machine-learning/transformer/transformer-variants","h":"#informer","p":1293},{"i":1297,"t":"除了输入 embedding 和位置编码外，informer 还引入了时间维度的 embedding：","s":"Informer 的 Embedding 层","u":"/docs/machine-learning/transformer/transformer-variants","h":"#informer-的-embedding-层","p":1293},{"i":1299,"t":"在注意力机制矩阵中，不是每一列都是有 attention 作用的，因此选择 QQQ 矩阵中贡献率最高的 top-uuu 行，其中 uuu 取值 c∗lnLc * lnLc∗lnL，ccc 是常数。 ProbSparse 通过计算 KL 散度 (Kullback-Leibler divergence) 来得到不同行注意力的贡献率。KL 散度在统计模型中可以反映信息增益，当两个分布差异较大的时候，KL 散度结果数值会越高。 通过计算每一行实际的 attention 和均匀分布 attention 的 KL 散度，可以近似衡量这一行对注意力的贡献。 但是这样计算后，内存使用并没有减少。所以作者又提出了随机选择 lnLlnLlnL 行。 经过以上处理，模型的注意力矩阵内存和时间复杂度都从 O(L2)O(L^2)O(L2) 减少到 O(LlogL)O(LlogL)O(LlogL)。 这里需要注意的是，原始论文中计算 QKTQK^TQKT 后，在经典的 Transformer 的基础上，把 Informer 中没有参与计算的位置，使用平均权重填充。因此第一层注意力层的输出的形状和经典的 Transformer 保持一致。","s":"ProbSparse 自注意力机制","u":"/docs/machine-learning/transformer/transformer-variants","h":"#probsparse-自注意力机制","p":1293},{"i":1301,"t":"原始的注意力层的输出结果数据尺寸不会变化，但是 Informer 中会进行池化减半操作。减小了计算量和训练时间。 这里的减半操作是使用卷积神经网络中步长为 2 的最大池化 (MaxPooling)。","s":"卷积池化减半","u":"/docs/machine-learning/transformer/transformer-variants","h":"#卷积池化减半","p":1293},{"i":1303,"t":"经典的 Transformer 用于 NLP，很多时候每个输出结果和之前的单词具有语义上的紧密联系，因此按照一步一步的输出比较适合。 在 Informer 中，由于预测未来某一些时刻的指标，这些指标之前没有类似于 NLP 中前后强关联的语义关系，因此可以采用单次输出所需要的序列，极大的提高了推理速度。","s":"单次解码器设计","u":"/docs/machine-learning/transformer/transformer-variants","h":"#单次解码器设计","p":1293},{"i":1307,"t":"gdb lldb (gdb) backtrace (gdb) bt (lldb) thread backtrace (lldb) bt","s":"回溯当前线程调用栈","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#回溯当前线程调用栈","p":1304},{"i":1309,"t":"gdb lldb (gdb) thread apply all bt (lldb) thread backtrace all (lldb) bt all","s":"回溯所有线程调用栈","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#回溯所有线程调用栈","p":1304},{"i":1311,"t":"gdb lldb (gdb) bt 5 (lldb) thread backtrace -c 5 (lldb) bt 5","s":"回溯当前线程调用栈的 backtrace 的前几帧","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#回溯当前线程调用栈的-backtrace-的前几帧","p":1304},{"i":1314,"t":"gdb lldb (gdb) disassemble (gdb) disas (lldb) disassemble --frame (lldb) di -f","s":"反汇编当前栈帧函数","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#反汇编当前栈帧函数","p":1304},{"i":1316,"t":"gdb lldb (gdb) disassemble main (lldb) disassemble --name main (lldb) di -n main","s":"反汇编任何名为 main 的函数","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#反汇编任何名为-main-的函数","p":1304},{"i":1318,"t":"gdb lldb (gdb) disassemble 0x1eb8 0x1ec3 (lldb) disassemble --start-address 0x1eb8 --end-address 0x1ec3 (lldb) di -s 0x1eb8 -e 0x1ec3","s":"反汇编某个地址范围","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#反汇编某个地址范围","p":1304},{"i":1320,"t":"gdb lldb (gdb) x/20i 0x1eb8 (lldb) disassemble --start-address 0x1eb8 --count 20 (lldb) di -s 0x1eb8 -c 20","s":"从给定地址反汇编若干条指令","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#从给定地址反汇编若干条指令","p":1304},{"i":1322,"t":"gdb lldb (lldb) disassemble --frame --mixed (lldb) di -f -m","s":"同时显示当前函数的源代码和反汇编代码","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#同时显示当前函数的源代码和反汇编代码","p":1304},{"i":1324,"t":"gdb lldb (lldb) disassemble --frame --bytes (lldb) di -f -b","s":"反汇编当前函数","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#反汇编当前函数","p":1304},{"i":1328,"t":"gdb lldb (gdb) break main (lldb) breakpoint set --name main (lldb) br s -n main (lldb) b main # or breakpoint on C++ method: (lldb) breakpoint set --method main (lldb) br s -M main","s":"根据函数名或者方法名设置断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#根据函数名或者方法名设置断点","p":1325},{"i":1330,"t":"gdb lldb (gdb) break test.c:12 (gdb) b test.c:12 (lldb) breakpoint set --file test.c --line 12 (lldb) br s -f test.c -l 12 (lldb) b test.c:12","s":"根据源文件行号设置断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#根据源文件行号设置断点","p":1325},{"i":1332,"t":"gdb lldb (gdb) break foo if strcmp(y,\"hello\") == 0 (lldb) breakpoint set --name foo --condition '(int)strcmp(y,\"hello\") == 0' (lldb) br s -n foo -c '(int)strcmp(y,\"hello\") == 0'","s":"设置条件断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#设置条件断点","p":1325},{"i":1334,"t":"gdb lldb (gdb) delete 1 # or delete all breakpoints at current line (gdb) clear (lldb) breakpoint delete 1 (lldb) br del 1","s":"删除某个断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#删除某个断点","p":1325},{"i":1336,"t":"禁用断点 gdb lldb (gdb) disable 1 (lldb) breakpoint disable 1 (lldb) br dis 1 启用断点 gdb lldb (gdb) enable 1 (lldb) breakpoint enable 1 (lldb) br en 1","s":"禁用/启用断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#禁用启用断点","p":1325},{"i":1338,"t":"通过正则表达式匹配函数，来设置断点 gdb lldb (gdb) rbreak [REGULAR EXPRESSION] (lldb) breakpoint set --func-regex [REGULAR EXPRESSION] (lldb) br s -r [REGULAR EXPRESSION] 通过正则表达式匹配源文件内容，来设置断点 gdb lldb (gdb) shell grep -e -n [REGULAR EXPRESSION] [SOURCE FILE] (gdb) break source-file:line-number (lldb) breakpoint set --source-pattern [REGULAR EXPRESSION] --file [SOURCE FILE] (lldb) br s -p [REGULAR EXPRESSION] -f [SOURCE FILE]","s":"通过正则表达式设置断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#通过正则表达式设置断点","p":1325},{"i":1340,"t":"gdb lldb (gdb) info break (lldb) breakpoint list (lldb) br l","s":"列出所有断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#列出所有断点","p":1325},{"i":1343,"t":"gdb lldb (gdb) watch global_var (lldb) watchpoint set variable global_var (lldb) wa s v global_var","s":"监控进程中某个变量的值","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控进程中某个变量的值","p":1325},{"i":1345,"t":"如果未指定 -x byte_size，则要监视的区域的大小默认为指针大小。 该命令采用原始输入，计算为表达式，返回指向区域开头的无符号整数，位于 -- 选项终止符之后。 gdb lldb (gdb) watch -location g_char_ptr (lldb) watchpoint set expression -- my_ptr (lldb) wa s e -- my_ptr","s":"监控进程中的某块内存","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控进程中的某块内存","p":1325},{"i":1347,"t":"gdb lldb (lldb) watch set var global (lldb) watchpoint modify -c '(global==5)' (lldb) c ... (lldb) bt * thread #1: tid = 0x1c03, 0x0000000100000ef5 a.out`modify + 21 at main.cpp:16, stop reason = watchpoint 1 frame #0: 0x0000000100000ef5 a.out`modify + 21 at main.cpp:16 frame #1: 0x0000000100000eac a.out`main + 108 at main.cpp:25 frame #2: 0x00007fff8ac9c7e1 libdyld.dylib`start + 1 (lldb) frame var global (int32_t) global = 5","s":"设置监控的条件","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#设置监控的条件","p":1325},{"i":1349,"t":"gdb lldb (gdb) delete 1 (lldb) watchpoint delete 1 (lldb) watch del 1","s":"删除监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#删除监控点","p":1325},{"i":1351,"t":"gdb lldb (gdb) info break (lldb) watchpoint list (lldb) watch l","s":"列出所有的监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#列出所有的监控点","p":1325},{"i":1353,"t":"形式：x/count fmt size address count：整数，默认为 1 fmt: a | Address 地址 i | Instruction 指令 t | Binary 二进制 o | Octal 八进制 h/x | Hex 十六进制 z | Hex，zero padded 十六进制，填充 0 对齐 d | Decimal 十进制 u | Unsigned decimal 无符号十进制 f | Float 浮点 c | Char 字符 s | String 字符串 size: b | 8 bits - byte h | 16 bits - halfword w | 32 bits - word g | 64 bits - giant","s":"检查内存地址的数据","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"","p":1352},{"i":1355,"t":"gdb lldb (gdb) x [ADDRESS] (lldb) memory read [ADDRESS] (lldb) x [ADDRESS]","s":"读取内存","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#读取内存","p":1352},{"i":1357,"t":"gdb lldb (gdb) x/4xw 0xbffff3c0 (lldb) memory read --size 4 --format x --count 4 0xbffff3c0 (lldb) me r -s4 -fx -c4 0xbffff3c0 (lldb) x -s4 -fx -c4 0xbffff3c0 # LLDB now supports the GDB shorthand format syntax but there can’t be space after the command: (lldb) memory read/4xw 0xbffff3c0 (lldb) x/4xw 0xbffff3c0 (lldb) memory read --gdb-format 4xw 0xbffff3c0","s":"读取若干十六进制的内存","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#读取若干十六进制的内存","p":1352},{"i":1359,"t":"gdb lldb (gdb) set logging on (gdb) set logging file /tmp/mem.txt (gdb) x/512bx 0xbffff3c0 (gdb) set logging off (lldb) memory read --outfile /tmp/mem.txt --count 512 0xbffff3c0 (lldb) me r -o/tmp/mem.txt -c512 0xbffff3c0 (lldb) x/512bx -o/tmp/mem.txt 0xbffff3c0","s":"从内存指定地址读取若干字节，并保存到本地文件","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#从内存指定地址读取若干字节并保存到本地文件","p":1352},{"i":1361,"t":"gdb lldb (gdb) dump memory /tmp/mem.bin 0x1000 0x2000 (lldb) memory read --outfile /tmp/mem.bin --binary 0x1000 0x2000 (lldb) me r -o /tmp/mem.bin -b 0x1000 0x2000","s":"从内存指定地址范围读取字节，并保存到本地文件","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#从内存指定地址范围读取字节并保存到本地文件","p":1352},{"i":1364,"t":"gdb lldb (gdb) info shared (lldb) image list","s":"列出可执行文件和所有依赖的共享库","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#列出可执行文件和所有依赖的共享库","p":1362},{"i":1366,"t":"gdb lldb (gdb) info symbol 0x1ec4 (lldb) image lookup --address 0x1ec4 (lldb) im loo -a 0x1ec4","s":"查找可执行文件或任何共享库中原始地址信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#查找可执行文件或任何共享库中原始地址信息","p":1362},{"i":1368,"t":"gdb lldb (gdb) info function <FUNC_REGEX> # This one finds debug symbols: (lldb) image lookup -r -n <FUNC_REGEX> # This one finds non-debug symbols: (lldb) image lookup -r -s <FUNC_REGEX> # Provide a list of binaries as arguments to limit the search.","s":"在二进制文件中查找与正则表达式匹配的函数","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#在二进制文件中查找与正则表达式匹配的函数","p":1362},{"i":1370,"t":"gdb lldb (gdb) info line 0x1ec4 (lldb) image lookup -v --address 0x1ec4 # look for the LineEntry line, which will have the full source path and line range information.","s":"查找完整的源代码行信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#查找完整的源代码行信息","p":1362},{"i":1372,"t":"gdb lldb (lldb) image lookup --address 0x1ec4 a.out (lldb) im loo -a 0x1ec4 a.out","s":"仅在 a.out 中查找地址信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#仅在-aout-中查找地址信息","p":1362},{"i":1374,"t":"gdb lldb (gdb) ptype Point (lldb) image lookup --type Point (lldb) im loo -t Point","s":"按名称查找类型 Point 的信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#按名称查找类型-point-的信息","p":1362},{"i":1378,"t":"gdb lldb (gdb) p bar (gdb) p/x bar (lldb) p bar (lldb) p/x bar","s":"显示变量的内容","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示变量的内容","p":1375},{"i":1380,"t":"gdb lldb (gdb) info args (gdb) info locals (lldb) frame variable (lldb) fr v # add '-no-args' to disable args (lldb) frame variable --no-args (lldb) fr v -a","s":"显示当前栈帧的参数和局部变量","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前栈帧的参数和局部变量","p":1375},{"i":1382,"t":"gdb lldb (gdb) p *ptr@10 (lldb) parray 10 ptr","s":"检查数组","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#检查数组","p":1375},{"i":1385,"t":"gdb lldb (gdb) info registers (lldb) register read","s":"显示当前线程的通用寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程的通用寄存器","p":1375},{"i":1387,"t":"gdb lldb (gdb) info all-registers (lldb) register read --all (lldb) re r -a","s":"显示当前线程的所有寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程的所有寄存器","p":1375},{"i":1389,"t":"gdb lldb (gdb) info all-registers rax rsp rbp (lldb) register read rax rsp rbp","s":"显示当前线程中指定寄存器的值","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程中指定寄存器的值","p":1375},{"i":1391,"t":"gdb lldb (gdb) p/t $rax (lldb) register read --format binary rax (lldb) re r -f b rax # LLDB now supports the GDB shorthand format syntax but there can’t be space after the command (lldb) register read/t rax (lldb) p/t $rax","s":"显示当前线程中指定寄存器的值，格式为二进制","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程中指定寄存器的值格式为二进制","p":1375},{"i":1393,"t":"gdb lldb (gdb) set print object 1 (gdb) p someCPPObjectPtrOrReference (Only works for C++ objects) (lldb) expr -d 1 -- [SomeClass returnAnObject] (lldb) expr -d 1 -- someCPPObjectPtrOrReference # or set dynamic type printing to be the default: (lldb) settings set target.prefer-dynamic run-target","s":"打印表达式结果的动态类型 (C++)","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#打印表达式结果的动态类型-c","p":1375},{"i":1395,"t":"GEF 是对 GDB 的增强，使用 Python API 为 GDB 提供附加功能，在动态分析和漏洞开发过程中提供更容易理解的二进制布局，并且安装简单，无外部依赖。 除了 GEF 外，也有其他的 GDB 增强工具，如： pwndbg peda gdbgui gdb-dashboard 不同的 GDB 增强工具可能有冲突，同一时间只建议安装一种工具。","s":"GEF - GDB 增强工具","u":"/docs/modern-cpp/gdb-lldb/gef","h":"","p":1394},{"i":1397,"t":"$ bash -c \"$(curl -fsSL https://gef.blah.cat/sh)\" 安装后会修改 ~/.gdbinit 文件，其中内容是包含新增的 ~/.gef-.py 文件，从而达到对 GDB 的 hacking。","s":"安装","u":"/docs/modern-cpp/gdb-lldb/gef","h":"#安装","p":1394},{"i":1399,"t":"context / ctx：查看上下文信息 aliases [ls/add/rm]：设置命令别名 tmux-setup：tmux 侧边栏 registers：寄存器 elf：ELF 信息 got：全局偏移表 hexdump：二进制工具 vmmap：内存映射 dereferece：解引用 更多的命令可以在 GEF - Commands 内查看。","s":"GEF 命令","u":"/docs/modern-cpp/gdb-lldb/gef","h":"#gef-命令","p":1394},{"i":1402,"t":"gdb lldb (gdb) maintenance info sections (lldb) image dump sections","s":"dump 可执行文件和所有共享库的 section 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和所有共享库的-section-信息","p":1400},{"i":1404,"t":"gdb lldb (lldb) image dump sections a.out","s":"dump 可执行文件的 section 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件的-section-信息","p":1400},{"i":1406,"t":"gdb lldb (lldb) image dump symtab","s":"dump 可执行文件和所有共享库的 symtab 符号","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和所有共享库的-symtab-符号","p":1400},{"i":1408,"t":"gdb lldb (lldb) image dump symtab a.out liba.so","s":"dump 可执行文件和指定共享库的 symtab 符号","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和指定共享库的-symtab-符号","p":1400},{"i":1411,"t":"如果您的源文件不再位于与程序构建时相同的位置 (例如，如果程序是在另外一台计算机上构建的)，您需要告诉调试器如何在本地文件路径中查找源文件，而不是构建系统的文件路径。 gdb lldb (gdb) set pathname-substitutions /buildbot/path /my/path (lldb) settings set target.source-map /buildbot/path /my/path 在 gdb 中，可以提供文件目录来搜索源文件。 gdb lldb (gdb) directory /my/path","s":"重新映射调试对话的源文件路径","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#重新映射调试对话的源文件路径","p":1409},{"i":1414,"t":"gdb lldb (gdb) target remote eorgadd:8000 (lldb) gdb-remote eorgadd:8000","s":"连接到远程调试服务器","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#连接到远程调试服务器","p":1409},{"i":1416,"t":"gdb lldb (gdb) target remote localhost:8000 (lldb) gdb-remote 8000","s":"连接到本地调试服务器","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#连接到本地调试服务器","p":1409},{"i":1419,"t":"gdb lldb (gdb) set $foo = 5 (gdb) set variable $foo = 5 # or using the print command (gdb) print $foo = 5 # or using the call command (gdb) call $foo = 5 # and if you want to specify the type of the variable: (gdb) set $foo = (unsigned int) 5 # In lldb you evaluate a variable declaration expression as you would write it in C: (lldb) expr unsigned int $foo = 5","s":"创建临时变量并赋值","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#创建临时变量并赋值","p":1409},{"i":1421,"t":"gdb lldb (gdb) print (int) printf (\"Print nine: %d.\", 4 + 5) # or if you don’t want to see void returns: (gdb) call (int) printf (\"Print nine: %d.\", 4 + 5) (lldb) expr (int) printf (\"Print nine: %d.\", 4 + 5) # or using the print alias: (lldb) print (int) printf (\"Print nine: %d.\", 4 + 5)","s":"在当前帧中的计算表达式","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#在当前帧中的计算表达式","p":1409},{"i":1423,"t":"gdb lldb (gdb) echo Here is some text\\n (lldb) script print(\"Here is some text\")","s":"打印信息到屏幕","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#打印信息��到屏幕","p":1409},{"i":1426,"t":"gdb lldb % gdb a.out (gdb) br main (gdb) run % lldb a.out (lldb) br main (lldb) run","s":"设置断点和启动进程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#设置断点和启动进程","p":1424},{"i":1429,"t":"gdb lldb (gdb) step (gdb) s (lldb) thread step-in (lldb) step (lldb) s","s":"step-in 单步调试 (源码级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-in-单步调试-源码级别","p":1424},{"i":1431,"t":"gdb lldb (gdb) next (gdb) n (lldb) thread step-over (lldb) next (lldb) n","s":"step-over 单步调试 (源码级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-单步调试-源码级别","p":1424},{"i":1433,"t":"gdb lldb (gdb) stepi (gdb) si (lldb) thread step-inst (lldb) si","s":"step-in 单步调试 (汇编指令级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-in-单步调试-汇编指令级别","p":1424},{"i":1435,"t":"gdb lldb (gdb) nexti (gdb) ni (lldb) thread step-inst-over (lldb) ni","s":"step-over 单步调试 (汇编指令级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-单步调试-汇编指令级别","p":1424},{"i":1437,"t":"gdb lldb (gdb) finish (lldb) thread step-out (lldb) finish","s":"step-over 跳出栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-跳出栈帧","p":1424},{"i":1440,"t":"gdb lldb (gdb) continue (gdb) c (lldb) continue (lldb) c","s":"跳转到下一个断点","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#跳转到下一个断点","p":1424},{"i":1442,"t":"gdb lldb (gdb) until 12 (lldb) thread until 12","s":"运行到指定行数","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#运行到指定行数","p":1424},{"i":1445,"t":"gdb lldb (gdb) info threads (lldb) thread list","s":"列出程序中的线程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#列出程序中的线程","p":1424},{"i":1447,"t":"gdb lldb (gdb) thread 1 (lldb) thread select 1 (lldb) t 1","s":"设置后续命令的默认线程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#设置后续命令的默认线程","p":1424},{"i":1450,"t":"gdb lldb (gdb) info frame (gdb) i f (lldb) frame info (lldb) fr i","s":"显示当前栈帧简略信息","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#显示当前栈帧简略信息","p":1424},{"i":1452,"t":"gdb lldb # check frame source code (gdb) frame (lldb) frame select (lldb) f (lldb) process status","s":"显示当前栈帧源代码行","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#显示当前栈帧源代码行","p":1424},{"i":1454,"t":"gdb lldb (gdb) frame 12 (lldb) frame select 12 (lldb) fr s 12 (lldb) f 12","s":"通过栈帧号选择栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#通过栈帧号选择栈帧","p":1424},{"i":1456,"t":"gdb lldb (gdb) up (lldb) up (lldb) frame select --relative=1 (lldb) fr s -r 1","s":"选择调用当前栈帧的栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#选择调用当前栈帧的栈帧","p":1424},{"i":1458,"t":"gdb lldb (gdb) down (lldb) down (lldb) frame select --relative=-1 (lldb) fr s -r -1","s":"选择被当前栈帧调用的栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#选择被当前栈帧调用的栈帧","p":1424},{"i":1460,"t":"gdb lldb (gdb) up 2 (gdb) down 3 (lldb) frame select --relative 2 (lldb) fr s -r 2 (lldb) frame select --relative -3 (lldb) fr s -r -3","s":"使用栈帧相对偏移选择栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#使用栈帧相对偏移选择栈帧","p":1424},{"i":1462,"t":"gdb lldb (gdb) return <RETURN EXPRESSION> (lldb) thread return <RETURN EXPRESSION>","s":"从栈帧返回，可以带有返回值","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#从栈帧返回可以带有返回值","p":1424},{"i":1464,"t":"gdb lldb (gdb) set unwindonsignal 0 (gdb) p function_with_a_breakpoint() (lldb) expr -i 0 -- function_with_a_breakpoint()","s":"调用带有断点的函数并在断点处停止","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#调用带有断点的函数并在断点处停止","p":1424},{"i":1466,"t":"gdb lldb (gdb) set unwindonsignal 0 (gdb) p function_which_crashes() (lldb) expr -u 0 -- function_which_crashes()","s":"调用 crash 的函数并在 crash 时停止","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#调用-crash-的函数并在-crash-时停止","p":1424},{"i":1470,"t":"gdb lldb % gdb a.out (gdb) run (gdb) r % lldb a.out (lldb) process launch (lldb) run (lldb) r","s":"启动新的进程","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#启动新的进程","p":1468},{"i":1472,"t":"在调试器启动之前设置参数 gdb lldb % gdb --args a.out <args...> (gdb) run % lldb -- a.out <args...> (lldb) run 在调试器启动之后、运行之前设置参数 gdb lldb (gdb) set args <args...> (gdb) run (lldb) settings set target.run-args <args...> (lldb) run 在运行的时候设置参数 gdb lldb (gdb) run <args...> (gdb) r <args...> (lldb) process launch -- <args...> (lldb) run <args...> (lldb) r <args...>","s":"设置进程的运行参数","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#设置进程的运行参数","p":1468},{"i":1474,"t":"在运行前设置环境变量 gdb lldb (gdb) set env DEBUG 1 (lldb) settings set target.env-vars DEBUG=1 (lldb) set se target.env-vars DEBUG=1 (lldb) env DEBUG=1 单条命令设置环境变量并启动进程 gdb lldb (lldb) process launch -E DEBUG=1 在运行前取消环境变量 gdb lldb (gdb) unset env DEBUG (lldb) settings remove target.env-vars DEBUG (lldb) set rem target.env-vars DEBUG","s":"环境变量设置","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#环境变量设置","p":1468},{"i":1476,"t":"根据进程号 pid 进行 attach gdb lldb (gdb) attach 123 (lldb) process attach --pid 123 (lldb) attach -p 123 根据进程名称进行 attach gdb lldb (gdb) attach a.out (lldb) process attach --name a.out (lldb) pro at -n a.out 等待进程名称并 attach gdb lldb (gdb) attach -waitfor a.out (lldb) process attach --name a.out --waitfor (lldb) pro at -n a.out -w","s":"attach 到已有进程","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#attach-到已有进程","p":1468},{"i":1478,"t":"gdb lldb (gdb) show args Argument list to give program being debugged when it is started is \"1 2 3\". (lldb) settings show target.run-args target.run-args (array of strings) = [0]: \"1\" [1]: \"2\" [2]: \"3\"","s":"显示参数","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#显示参数","p":1468},{"i":1480,"t":"本教程介绍 Linux 命令行 Bash 的基本用法和脚本编程。","s":"Bash 教程","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1504,"t":"((...))语法可以进行整数的算术运算。 $ ((foo = 5 + 5)) $ echo $foo 10 ((...))会自动忽略内部的空格，所以下面的写法都正确，得到同样的结果。 $ ((2+2)) $ (( 2+2 )) $ (( 2 + 2 )) 这个语法不返回值，命令执行的结果根据算术运算的结果而定。只要算术结果不是0，命令就算执行成功。 $ (( 3 + 2 )) $ echo $? 0 上面例子中，3 + 2的结果是 5，命令就算执行成功，环境变量$?为0。 如果算术结果为0，命令就算执行失败。 $ (( 3 - 3 )) $ echo $? 1 上面例子中，3 - 3的结果是0，环境变量$?为1，表示命令执行失败。 如果要读取算术运算的结果，需要在((...))前面加上美元符号$((...))，使其变成算术表达式，返回算术运算的值。 $ echo $((2 + 2)) 4 ((...))语法支持的算术运算符如下。 +：加法 -：减法 *：乘法 /：除法（整除） %：余数 **：指数 ++：自增运算（前缀或后缀） --：自减运算（前缀或后缀） 注意，除法运算符的返回结果总是整数，比如5除以2，得到的结果是2，而不是2.5。 $ echo $((5 / 2)) 2 ++和--这两个运算符有前缀和后缀的区别。作为前缀是先运算后返回值，作为后缀是先返回值后运算。 $ i=0 $ echo $i 0 $ echo $((i++)) 0 $ echo $i 1 $ echo $((++i)) 2 $ echo $i 2 上面例子中，++作为后缀是先返回值，执行echo命令，再进行自增运算；作为前缀则是先进行自增运算，再返回值执行echo命令。 $((...))内部可以用圆括号改变运算顺序。 $ echo $(( (2 + 3) * 4 )) 20 上面例子中，内部的圆括号让加法先于乘法执行。 $((...))结构可以嵌套。 $ echo $(((5**2) * 3)) 75 # 等同于 $ echo $(($((5**2)) * 3)) 75 这个语法只能计算整数，否则会报错。 # 报错 $ echo $((1.5 + 1)) bash: 语法错误 $((...))的圆括号之中，不需要在变量名之前加上$，不过加上也不报错。 $ number=2 $ echo $(($number + 1)) 3 上面例子中，变量number前面有没有美元符号，结果都是一样的。 如果在$((...))里面使用字符串，Bash 会认为那是一个变量名。如果不存在同名变量，Bash 就会将其作为空值，因此不会报错。 $ echo $(( \"hello\" + 2)) 2 $ echo $(( \"hello\" * 2)) 0 上面例子中，\"hello\"会被当作变量名，返回空值，而$((...))会将空值当作0，所以乘法的运算结果就是0。同理，如果$((...))里面使用不存在的变量，也会当作0处理。 如果一个变量的值为字符串，跟上面的处理逻辑是一样的。即该字符串如果不对应已存在的变量，在$((...))里面会被当作空值。 $ foo=hello $ echo $(( foo + 2)) 2 上面例子中，变量foo的值是hello，而hello也会被看作变量名。这使得有可能写出动态替换的代码。 $ foo=hello $ hello=3 $ echo $(( foo + 2 )) 5 上面代码中，foo + 2取决于变量hello的值。 最后，$[...]是以前的语法，也可以做整数运算，不建议使用。 $ echo $[2+2] 4","s":"算术表达式","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#算术表达式","p":1502},{"i":1506,"t":"Bash 的数值默认都是十进制，但是在算术表达式中，也可以使用其他进制。 number：没有任何特殊表示法的数字是十进制数（以 10 为底）。 0number：八进制数。 0xnumber：十六进制数。 base#number：base进制的数。 下面是一些例子。 $ echo $((0xff)) 255 $ echo $((2#11111111)) 255 上面例子中，0xff是十六进制数，2#11111111是二进制数。","s":"数值的进制","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#数值的进制","p":1502},{"i":1508,"t":"$((...))支持以下的二进制位运算符。 <<：位左移运算，把一个数字的所有位向左移动指定的位。 >>：位右移运算，把一个数字的所有位向右移动指定的位。 &：位的“与”运算，对两个数字的所有位执行一个AND操作。 |：位的“或”运算，对两个数字的所有位执行一个OR操作。 ~：位的“否”运算，对一个数字的所有位取反。 ^：位的异或运算（exclusive or），对两个数字的所有位执行一个异或操作。 下面是右移运算符>>的例子。 $ echo $((16>>2)) 4 下面是左移运算符<<的例子。 $ echo $((16<<2)) 64 下面是17（二进制10001）和3（二进制11）的各种二进制运算的结果。 $ echo $((17&3)) 1 $ echo $((17|3)) 19 $ echo $((17^3)) 18","s":"位运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#位运算","p":1502},{"i":1510,"t":"$((...))支持以下的逻辑运算符。 <：小于 >：大于 <=：小于或相等 >=：大于或相等 ==：相等 !=：不相等 &&：逻辑与 ||：逻辑或 !：逻辑否 expr1?expr2:expr3：三元条件运算符。若表达式expr1的计算结果为非零值（算术真），则执行表达式expr2，否则执行表达式expr3。 如果逻辑表达式为真，返回1，否则返回0。 $ echo $((3 > 2)) 1 $ echo $(( (3 > 2) || (4 <= 1) )) 1 三元运算符执行一个单独的逻辑测试。它用起来类似于if/then/else语句。 $ a=0 $ echo $((a<1 ? 1 : 0)) 1 $ echo $((a>1 ? 1 : 0)) 0 上面例子中，第一个表达式为真时，返回第二个表达式的值，否则返回第三个表达式的值。","s":"逻辑运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#逻辑运算","p":1502},{"i":1512,"t":"算术表达式$((...))可以执行赋值运算。 $ echo $((a=1)) 1 $ echo $a 1 上面例子中，a=1对变量a进行赋值。这个式子本身也是一个表达式，返回值就是等号右边的值。 $((...))支持的赋值运算符，有以下这些。 parameter = value：简单赋值。 parameter += value：等价于parameter = parameter + value。 parameter -= value：等价于parameter = parameter – value。 parameter *= value：等价于parameter = parameter * value。 parameter /= value：等价于parameter = parameter / value。 parameter %= value：等价于parameter = parameter % value。 parameter <<= value：等价于parameter = parameter << value。 parameter >>= value：等价于parameter = parameter >> value。 parameter &= value：等价于parameter = parameter & value。 parameter |= value：等价于parameter = parameter | value。 parameter ^= value：等价于parameter = parameter ^ value。 下面是一个例子。 $ foo=5 $ echo $((foo*=2)) 10 如果在表达式内部赋值，可以放在圆括号中，否则会报错。 $ echo $(( a<1 ? (a+=1) : (a-=1) ))","s":"赋值运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#赋值运算","p":1502},{"i":1514,"t":"逗号,在$((...))内部是求值运算符，执行前后两个表达式，并返回后一个表达式的值。 $ echo $((foo = 1 + 2, 3 * 4)) 12 $ echo $foo 3 上面例子中，逗号前后两个表达式都会执行，然后返回后一个表达式的值12。","s":"求值运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#求值运算","p":1502},{"i":1516,"t":"expr命令支持算术运算，可以不使用((...))语法。 $ expr 3 + 2 5 expr命令支持变量替换。 $ foo=3 $ expr $foo + 2 5 expr命令也不支持非整数参数。 $ expr 3.5 + 2 expr: 非整数参数 上面例子中，如果有非整数的运算，expr命令就报错了。","s":"expr 命令","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#expr-命令","p":1502},{"i":1518,"t":"let命令用于将算术运算的结果，赋予一个变量。 $ let x=2+3 $ echo $x 5 上面例子中，变量x等于2+3的运算结果。 注意，x=2+3这个式子里面不能有空格，否则会报错。let命令的详细用法参见《变量》一章。","s":"let 命令","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#let-命令","p":1502},{"i":1520,"t":"数组（array）是一个包含多个值的变量。成员的编号从 0 开始，数量没有上限，也没有要求成员被连续索引。","s":"数组","u":"/docs/modern-linux/bash-tutorial/array","h":"","p":1519},{"i":1522,"t":"数组可以采用逐个赋值的方法创建。 ARRAY[INDEX]=value 上面语法中，ARRAY是数组的名字，可以是任意合法的变量名。INDEX是一个大于或等于零的整数，也可以是算术表达式。注意数组第一个元素的下标是 0，而不是 1。 下面创建一个三个成员的数组。 $ array[0]=val $ array[1]=val $ array[2]=val 数组也可以采用一次性赋值的方式创建。 ARRAY=(value1 value2 ... valueN) # 等同于 ARRAY=( value1 value2 value3 ) 采用上面方式创建数组时，可以按照默认顺序赋值，也可以在每个值前面指定位置。 $ array=(a b c) $ array=([2]=c [0]=a [1]=b) $ days=(Sun Mon Tue Wed Thu Fri Sat) $ days=([0]=Sun [1]=Mon [2]=Tue [3]=Wed [4]=Thu [5]=Fri [6]=Sat) 只为某些值指定位置，也是可以的。 names=(hatter [5]=duchess alice) 上面例子中，hatter是数组的 0 号位置，duchess是 5 号位置，alice是 6 号位置。 没有赋值的数组元素的默认值是空字符串。 定义数组的时候，可以使用通配符。 $ mp3s=( *.mp3 ) 上面例子中，将当前目录的所有 MP3 文件，放进一个数组。 先用declare -a命令声明一个数组，也是可以的。 $ declare -a ARRAYNAME read -a命令则是将用户的命令行输入，存入一个数组。 $ read -a dice 上面命令将用户的命令行输入，存入数组dice。","s":"创建数组","u":"/docs/modern-linux/bash-tutorial/array","h":"#创建数组","p":1519},{"i":1525,"t":"读取数组指定位置的成员，要使用下面的语法。 $ echo ${array[i]} # i 是索引 上面语法里面的大括号是必不可少的，否则 Bash 会把索引部分[i]按照原样输出。 $ array[0]=a $ echo ${array[0]} a $ echo $array[0] a[0] 上面例子中，数组的第一个元素是a。如果不加大括号，Bash 会直接读取$array首成员的值，然后将[0]按照原样输出。","s":"读取单个元素","u":"/docs/modern-linux/bash-tutorial/array","h":"#读取单个元素","p":1519},{"i":1527,"t":"@和*是数组的特殊索引，表示返回数组的所有成员。 $ foo=(a b c d e f) $ echo ${foo[@]} a b c d e f 这两个特殊索引配合for循环，就可以用来遍历数组。 for i in \"${names[@]}\"; do echo $i done @和*放不放在双引号之中，是有差别的。 $ activities=( swimming \"water skiing\" canoeing \"white-water rafting\" surfing ) $ for act in ${activities[@]}; \\ do \\ echo \"Activity: $act\"; \\ done Activity: swimming Activity: water Activity: skiing Activity: canoeing Activity: white-water Activity: rafting Activity: surfing 上面的例子中，数组activities实际包含 5 个成员，但是for...in循环直接遍历${activities[@]}，导致返回 7 个结果。为了避免这种情况，一般把${activities[@]}放在双引号之中。 $ for act in \"${activities[@]}\"; \\ do \\ echo \"Activity: $act\"; \\ done Activity: swimming Activity: water skiing Activity: canoeing Activity: white-water rafting Activity: surfing 上面例子中，${activities[@]}放在双引号之中，遍历就会返回正确的结果。 ${activities[*]}不放在双引号之中，跟${activities[@]}不放在双引号之中是一样的。 $ for act in ${activities[*]}; \\ do \\ echo \"Activity: $act\"; \\ done Activity: swimming Activity: water Activity: skiing Activity: canoeing Activity: white-water Activity: rafting Activity: surfing ${activities[*]}放在双引号之中，所有成员就会变成单个字符串返回。 $ for act in \"${activities[*]}\"; \\ do \\ echo \"Activity: $act\"; \\ done Activity: swimming water skiing canoeing white-water rafting surfing 所以，拷贝一个数组的最方便方法，就是写成下面这样。 $ hobbies=( \"${activities[@]}\" ) 上面例子中，数组activities被拷贝给了另一个数组hobbies。 这种写法也可以用来为新数组添加成员。 $ hobbies=( \"${activities[@]}\" diving ) 上面例子中，新数组hobbies在数组activities的所有成员之后，又添加了一个成员。","s":"读取所有成员","u":"/docs/modern-linux/bash-tutorial/array","h":"#读取所有成员","p":1519},{"i":1529,"t":"如果读取数组成员时，没有读取指定哪一个位置的成员，默认使用0号位置。 $ declare -a foo $ foo=A $ echo ${foo[0]} A 上面例子中，foo是一个数组，赋值的时候不指定位置，实际上是给foo[0]赋值。 引用一个不带下标的数组变量，则引用的是0号位置的数组元素。 $ foo=(a b c d e f) $ echo ${foo} a $ echo $foo a 上面例子中，引用数组元素的时候，没有指定位置，结果返回的是0号位置。","s":"默认位置","u":"/docs/modern-linux/bash-tutorial/array","h":"#默认位置","p":1519},{"i":1531,"t":"要想知道数组的长度（即一共包含多少成员），可以使用下面两种语法。 ${#array[*]} ${#array[@]} 下面是一个例子。 $ a[100]=foo $ echo ${#a[*]} 1 $ echo ${#a[@]} 1 上面例子中，把字符串赋值给100位置的数组元素，这时的数组只有一个元素。 注意，如果用这种语法去读取具体的数组成员，就会返回该成员的字符串长度。这一点必须小心。 $ a[100]=foo $ echo ${#a[100]} 3 上面例子中，${#a[100]}实际上是返回数组第 100 号成员a[100]的值（foo）的字符串长度。","s":"数组的长度","u":"/docs/modern-linux/bash-tutorial/array","h":"#数组的长度","p":1519},{"i":1533,"t":"${!array[@]}或${!array[*]}，可以返回数组的成员序号，即哪些位置是有值的。 $ arr=([5]=a [9]=b [23]=c) $ echo ${!arr[@]} 5 9 23 $ echo ${!arr[*]} 5 9 23 上面例子中，数组的 5、9、23 号位置有值。 利用这个语法，也可以通过for循环遍历数组。 arr=(a b c d) for i in ${!arr[@]};do echo ${arr[i]} done","s":"提取数组序号","u":"/docs/modern-linux/bash-tutorial/array","h":"#提取数组序号","p":1519},{"i":1535,"t":"${array[@]:position:length}的语法可以提取数组成员。 $ food=( apples bananas cucumbers dates eggs fajitas grapes ) $ echo ${food[@]:1:1} bananas $ echo ${food[@]:1:3} bananas cucumbers dates 上面例子中，${food[@]:1:1}返回从数组 1 号位置开始的 1 个成员，${food[@]:1:3}返回从 1 号位置开始的 3 个成员。 如果省略长度参数length，则返回从指定位置开始的所有成员。 $ echo ${food[@]:4} eggs fajitas grapes 上面例子返回从 4 号位置开始到结束的所有成员。","s":"提取数组成员","u":"/docs/modern-linux/bash-tutorial/array","h":"#提取数组成员","p":1519},{"i":1537,"t":"数组末尾追加成员，可以使用+=赋值运算符。它能够自动地把值追加到数组末尾。否则，就需要知道数组的最大序号，比较麻烦。 $ foo=(a b c) $ echo ${foo[@]} a b c $ foo+=(d e f) $ echo ${foo[@]} a b c d e f","s":"追加数组成员","u":"/docs/modern-linux/bash-tutorial/array","h":"#追加数组成员","p":1519},{"i":1539,"t":"删除一个数组成员，使用unset命令。 $ foo=(a b c d e f) $ echo ${foo[@]} a b c d e f $ unset foo[2] $ echo ${foo[@]} a b d e f 上面例子中，删除了数组中的第三个元素，下标为 2。 将某个成员设为空值，可以从返回值中“隐藏”这个成员。 $ foo=(a b c d e f) $ foo[1]='' $ echo ${foo[@]} a c d e f 上面例子中，将数组的第二个成员设为空字符串，数组的返回值中，这个成员就“隐藏”了。 注意，这里是“隐藏”，而不是删除，因为这个成员仍然存在，只是值变成了空值。 $ foo=(a b c d e f) $ foo[1]='' $ echo ${#foo[@]} 6 $ echo ${!foo[@]} 0 1 2 3 4 5 上面代码中，第二个成员设为空值后，数组仍然包含 6 个成员。 由于空值就是空字符串，所以下面这样写也有隐藏效果，但是不建议这种写法。 $ foo[1]= 上面的写法也相当于“隐藏”了数组的第二个成员。 直接将数组变量赋值为空字符串，相当于“隐藏”数组的第一个成员。 $ foo=(a b c d e f) $ foo='' $ echo ${foo[@]} b c d e f 上面的写法相当于“隐藏”了数组的第一个成员。 unset ArrayName可以清空整个数组。 $ unset ARRAY $ echo ${ARRAY[*]} <--no output-->","s":"删除数组","u":"/docs/modern-linux/bash-tutorial/array","h":"#删除数组","p":1519},{"i":1541,"t":"Bash 的新版本支持关联数组。关联数组使用字符串而不是整数作为数组索引。 declare -A可以声明关联数组。 declare -A colors colors[\"red\"]=\"#ff0000\" colors[\"green\"]=\"#00ff00\" colors[\"blue\"]=\"#0000ff\" 关联数组必须用带有-A选项的declare命令声明创建。相比之下，整数索引的数组，可以直接使用变量名创建数组，关联数组就不行。 访问关联数组成员的方式，几乎与整数索引数组相同。 echo ${colors[\"blue\"]}","s":"关联数组","u":"/docs/modern-linux/bash-tutorial/array","h":"#关联数组","p":1519},{"i":1543,"t":"本章介绍 Bash 脚本的条件判断语法。","s":"条件判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"","p":1542},{"i":1545,"t":"if是最常用的条件判断结构，只有符合给定条件时，才会执行指定的命令。它的语法如下。 if commands; then commands [elif commands; then commands...] [else commands] fi 这个命令分成三个部分：if、elif和else。其中，后两个部分是可选的。 if关键字后面是主要的判断条件，elif用来添加在主条件不成立时的其他判断条件，else则是所有条件都不成立时要执行的部分。 if test $USER = \"foo\"; then echo \"Hello foo.\" else echo \"You are not foo.\" fi 上面的例子中，判断条件是环境变量$USER是否等于foo，如果等于就输出Hello foo.，否则输出其他内容。 if和then写在同一行时，需要分号分隔。分号是 Bash 的命令分隔符。它们也可以写成两行，这时不需要分号。 if true; then echo 'hello world' fi if false; then echo 'it is false' # 本行不会执行 fi 上面的例子中，true和false是两个特殊命令，前者代表操作成功，后者代表操作失败。if true意味着命令部分总是会执行，if false意味着命令部分永远不会执行。 除了多行的写法，if结构也可以写成单行。 $ if true; then echo 'hello world'; fi hello world $ if false; then echo \"It's true.\"; fi 注意，if关键字后面也可以是一条命令，该条命令执行成功（返回值0），就意味着判断条件成立。 $ if echo 'hi'; then echo 'hello world'; fi hi hello world 上面命令中，if后面是一条命令echo 'hi'。该命令会执行，如果返回值是0，则执行then的部分。 if后面可以跟任意数量的命令。这时，所有命令都会执行，但是判断真伪只看最后一个命令，即使前面所有命令都失败，只要最后一个命令返回0，就会执行then的部分。 $ if false; true; then echo 'hello world'; fi hello world 上面例子中，if后面有两条命令（false;true;），第二条命令（true）决定了then的部分是否会执行。 elif部分可以有多个。 #!/bin/bash echo -n \"输入一个1到3之间的数字（包含两端）> \" read character if [ \"$character\" = \"1\" ]; then echo 1 elif [ \"$character\" = \"2\" ]; then echo 2 elif [ \"$character\" = \"3\" ]; then echo 3 else echo 输入不符合要求 fi 上面例子中，如果用户输入3，就会连续判断 3 次。","s":"if 结构","u":"/docs/modern-linux/bash-tutorial/condition","h":"#if-结构","p":1542},{"i":1547,"t":"if结构的判断条件，一般使用test命令，有三种形式。 # 写法一 test expression # 写法二 [ expression ] # 写法三 [[ expression ]] 上面三种形式是等价的，但是第三种形式还支持正则判断，前两种不支持。 上面的expression是一个表达式。这个表达式为真，test命令执行成功（返回值为0）；表达式为伪，test命令执行失败（返回值为1）。注意，第二种和第三种写法，[和]与内部的表达式之间必须有空格。 $ test -f /etc/hosts $ echo $? 0 $ [ -f /etc/hosts ] $ echo $? 0 上面的例子中，test命令采用两种写法，判断/etc/hosts文件是否存在，这两种写法是等价的。命令执行后，返回值为0，表示该文件确实存在。 实际上，[这个字符是test命令的一种简写形式，可以看作是一个独立的命令，这解释了为什么它后面必须有空格。 下面把test命令的三种形式，用在if结构中，判断一个文件是否存在。 # 写法一 if test -e /tmp/foo.txt; then echo \"Found foo.txt\" fi # 写法二 if [ -e /tmp/foo.txt ]; then echo \"Found foo.txt\" fi # 写法三 if [[ -e /tmp/foo.txt ]]; then echo \"Found foo.txt\" fi","s":"test 命令","u":"/docs/modern-linux/bash-tutorial/condition","h":"#test-命令","p":1542},{"i":1549,"t":"if关键字后面，跟的是一个命令。这个命令可以是test命令，也可以是其他命令。命令的返回值为0表示判断成立，否则表示不成立。因为这些命令主要是为了得到返回值，所以可以视为表达式。 常用的判断表达式有下面这些。","s":"判断表达式","u":"/docs/modern-linux/bash-tutorial/condition","h":"#判断表达式","p":1542},{"i":1551,"t":"以下表达式用来判断文件状态。 [ -a file ]：如果 file 存在，则为true。 [ -b file ]：如果 file 存在并且是一个块（设备）文件，则为true。 [ -c file ]：如果 file 存在并且是一个字符（设备）文件，则为true。 [ -d file ]：如果 file 存在并且是一个目录，则为true。 [ -e file ]：如果 file 存在，则为true。 [ -f file ]：如果 file 存在并且是一个普通文件，则为true。 [ -g file ]：如果 file 存在并且设置了组 ID，则为true。 [ -G file ]：如果 file 存在并且属于有效的组 ID，则为true。 [ -h file ]：如果 file 存在并且是符号链接，则为true。 [ -k file ]：如果 file 存在并且设置了它的“sticky bit”，则为true。 [ -L file ]：如果 file 存在并且是一个符号链接，则为true。 [ -N file ]：如果 file 存在并且自上次读取后已被修改，则为true。 [ -O file ]：如果 file 存在并且属于有效的用户 ID，则为true。 [ -p file ]：如果 file 存在并且是一个命名管道，则为true。 [ -r file ]：如果 file 存在并且可读（当前用户有可读权限），则为true。 [ -s file ]：如果 file 存在且其长度大于零，则为true。 [ -S file ]：如果 file 存在且是一个网络 socket，则为true。 [ -t fd ]：如果 fd 是一个文件描述符，并且重定向到终端，则为true。这可以用来判断是否重定向了标准输入／输出／错误。 [ -u file ]：如果 file 存在并且设置了 setuid 位，则为true。 [ -w file ]：如果 file 存在并且可写（当前用户拥有可写权限），则为true。 [ -x file ]：如果 file 存在并且可执行（有效用户有执行／搜索权限），则为true。 [ FILE1 -nt FILE2 ]：如果 FILE1 比 FILE2 的更新时间更近，或者 FILE1 存在而 FILE2 不存在，则为true。 [ FILE1 -ot FILE2 ]：如果 FILE1 比 FILE2 的更新时间更旧，或者 FILE2 存在而 FILE1 不存在，则为true。 [ FILE1 -ef FILE2 ]：如果 FILE1 和 FILE2 引用相同的设备和 inode 编号，则为true。 下面是一个示例。 #!/bin/bash FILE=~/.bashrc if [ -e \"$FILE\" ]; then if [ -f \"$FILE\" ]; then echo \"$FILE is a regular file.\" fi if [ -d \"$FILE\" ]; then echo \"$FILE is a directory.\" fi if [ -r \"$FILE\" ]; then echo \"$FILE is readable.\" fi if [ -w \"$FILE\" ]; then echo \"$FILE is writable.\" fi if [ -x \"$FILE\" ]; then echo \"$FILE is executable/searchable.\" fi else echo \"$FILE does not exist\" exit 1 fi 上面代码中，$FILE要放在双引号之中，这样可以防止变量$FILE为空，从而出错。因为$FILE如果为空，这时[ -e $FILE ]就变成[ -e ]，这会被判断为真。而$FILE放在双引号之中，[ -e \"$FILE\" ]就变成[ -e \"\" ]，这会被判断为伪。","s":"文件判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#文件判断","p":1542},{"i":1553,"t":"以下表达式用来判断字符串。 [ string ]：如果string不为空（长度大于 0），则判断为真。 [ -n string ]：如果字符串string的长度大于零，则判断为真。 [ -z string ]：如果字符串string的长度为零，则判断为真。 [ string1 = string2 ]：如果string1和string2相同，则判断为真。 [ string1 == string2 ] 等同于[ string1 = string2 ]。 [ string1 != string2 ]：如果string1和string2不相同，则判断为真。 [ string1 '>' string2 ]：如果按照字典顺序string1排列在string2之后，则判断为真。 [ string1 '<' string2 ]：如果按照字典顺序string1排列在string2之前，则判断为真。 注意，test命令内部的>和<，必须用引号引起来（或者是用反斜杠转义）。否则，它们会被 shell 解释为重定向操作符。 下面是一个示例。 #!/bin/bash ANSWER=maybe if [ -z \"$ANSWER\" ]; then echo \"There is no answer.\" >&2 exit 1 fi if [ \"$ANSWER\" = \"yes\" ]; then echo \"The answer is YES.\" elif [ \"$ANSWER\" = \"no\" ]; then echo \"The answer is NO.\" elif [ \"$ANSWER\" = \"maybe\" ]; then echo \"The answer is MAYBE.\" else echo \"The answer is UNKNOWN.\" fi 上面代码中，首先确定$ANSWER字符串是否为空。如果为空，就终止脚本，并把退出状态设为1。注意，这里的echo命令把错误信息There is no answer.重定向到标准错误，这是处理错误信息的常用方法。如果$ANSWER字符串不为空，就判断它的值是否等于yes、no或者maybe。 注意，字符串判断时，变量要放在双引号之中，比如[ -n \"$COUNT\" ]，否则变量替换成字符串以后，test命令可能会报错，提示参数过多。另外，如果不放在双引号之中，变量为空时，命令会变成[ -n ]，这时会判断为真。如果放在双引号之中，[ -n \"\" ]就判断为伪。","s":"字符串判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#字符串判断","p":1542},{"i":1555,"t":"下面的表达式用于判断整数。 [ integer1 -eq integer2 ]：如果integer1等于integer2，则为true。 [ integer1 -ne integer2 ]：如果integer1不等于integer2，则为true。 [ integer1 -le integer2 ]：如果integer1小于或等于integer2，则为true。 [ integer1 -lt integer2 ]：如果integer1小于integer2，则为true。 [ integer1 -ge integer2 ]：如果integer1大于或等于integer2，则为true。 [ integer1 -gt integer2 ]：如果integer1大于integer2，则为true。 下面是一个用法的例子。 #!/bin/bash INT=-5 if [ -z \"$INT\" ]; then echo \"INT is empty.\" >&2 exit 1 fi if [ $INT -eq 0 ]; then echo \"INT is zero.\" else if [ $INT -lt 0 ]; then echo \"INT is negative.\" else echo \"INT is positive.\" fi if [ $((INT % 2)) -eq 0 ]; then echo \"INT is even.\" else echo \"INT is odd.\" fi fi 上面例子中，先判断变量$INT是否为空，然后判断是否为0，接着判断正负，最后通过求余数判断奇偶。","s":"整数判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#整数判断","p":1542},{"i":1557,"t":"[[ expression ]]这种判断形式，支持正则表达式。 [[ string1 =~ regex ]] 上面的语法中，regex是一个正则表示式，=~是正则比较运算符。 下面是一个例子。 #!/bin/bash INT=-5 if [[ \"$INT\" =~ ^-?[0-9]+$ ]]; then echo \"INT is an integer.\" exit 0 else echo \"INT is not an integer.\" >&2 exit 1 fi 上面代码中，先判断变量INT的字符串形式，是否满足^-?[0-9]+$的正则模式，如果满足就表明它是一个整数。","s":"正则判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#正则判断","p":1542},{"i":1559,"t":"通过逻辑运算，可以把多个test判断表达式结合起来，创造更复杂的判断。三种逻辑运算AND，OR，和NOT，都有自己的专用符号。 AND运算：符号&&，也可使用参数-a。 OR运算：符号||，也可使用参数-o。 NOT运算：符号!。 下面是一个AND的例子，判断整数是否在某个范围之内。 #!/bin/bash MIN_VAL=1 MAX_VAL=100 INT=50 if [[ \"$INT\" =~ ^-?[0-9]+$ ]]; then if [[ $INT -ge $MIN_VAL && $INT -le $MAX_VAL ]]; then echo \"$INT is within $MIN_VAL to $MAX_VAL.\" else echo \"$INT is out of range.\" fi else echo \"INT is not an integer.\" >&2 exit 1 fi 上面例子中，&&用来连接两个判断条件：大于等于$MIN_VAL，并且小于等于$MAX_VAL。 使用否定操作符!时，最好用圆括号确定转义的范围。 if [ ! \\( $INT -ge $MIN_VAL -a $INT -le $MAX_VAL \\) ]; then echo \"$INT is outside $MIN_VAL to $MAX_VAL.\" else echo \"$INT is in range.\" fi 上面例子中，test命令内部使用的圆括号，必须使用引号或者转义，否则会被 Bash 解释。 使用-a连接两个判断条件不太直观，一般推荐使用&&代替，上面的脚本可以改写成下面这样。 if !([ $INT -ge $MIN_VAL ] && [ $INT -le $MAX_VAL ]); then echo \"$INT is outside $MIN_VAL to $MAX_VAL.\" else echo \"$INT is in range.\" fi","s":"test 判断的逻辑运算","u":"/docs/modern-linux/bash-tutorial/condition","h":"#test-判断的逻辑运算","p":1542},{"i":1561,"t":"Bash 还提供了((...))作为算术条件，进行算术运算的判断。 if ((3 > 2)); then echo \"true\" fi 上面代码执行后，会打印出true。 注意，算术判断不需要使用test命令，而是直接使用((...))结构。这个结构的返回值，决定了判断的真伪。 如果算术计算的结果是非零值，则表示判断成立。这一点跟命令的返回值正好相反，需要小心。 $ if ((1)); then echo \"It is true.\"; fi It is true. $ if ((0)); then echo \"It is true.\"; else echo \"it is false.\"; fi It is false. 上面例子中，((1))表示判断成立，((0))表示判断不成立。 算术条件((...))也可以用于变量赋值。 $ if (( foo = 5 ));then echo \"foo is $foo\"; fi foo is 5 上面例子中，(( foo = 5 ))完成了两件事情。首先把5赋值给变量foo，然后根据返回值5，判断条件为真。 注意，赋值语句返回等号右边的值，如果返回的是0，则判断为假。 $ if (( foo = 0 ));then echo \"It is true.\";else echo \"It is false.\"; fi It is false. 下面是用算术条件改写的数值判断脚本。 #!/bin/bash INT=-5 if [[ \"$INT\" =~ ^-?[0-9]+$ ]]; then if ((INT == 0)); then echo \"INT is zero.\" else if ((INT < 0)); then echo \"INT is negative.\" else echo \"INT is positive.\" fi if ((((INT % 2)) == 0)); then echo \"INT is even.\" else echo \"INT is odd.\" fi fi else echo \"INT is not an integer.\" >&2 exit 1 fi 只要是算术表达式，都能用于((...))语法，详见《Bash 的算术运算》一章。","s":"算术判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#算术判断","p":1542},{"i":1563,"t":"如果if结构使用的不是test命令，而是普通命令，比如上一节的((...))算术运算，或者test命令与普通命令混用，那么可以使用 Bash 的命令控制操作符&&（AND）和||（OR），进行多个命令的逻辑运算。 $ command1 && command2 $ command1 || command2 对于&&操作符，先执行command1，只有command1执行成功后，才会执行command2。对于||操作符，先执行command1，只有command1执行失败后，才会执行command2。 $ mkdir temp && cd temp 上面的命令会创建一个名为temp的目录，执行成功后，才会执行第二个命令，进入这个目录。 $ [ -d temp ] || mkdir temp 上面的命令会测试目录temp是否存在，如果不存在，就会执行第二个命令，创建这个目录。这种写法非常有助于在脚本中处理错误。 [ ! -d temp ] && exit 1 上面的命令中，如果temp子目录不存在，脚本会终止，并且返回值为1。 下面就是if与&&结合使用的写法。 if [ condition ] && [ condition ]; then command fi 下面是一个示例。 #! /bin/bash filename=$1 word1=$2 word2=$3 if grep $word1 $filename && grep $word2 $filename; then echo \"$word1 and $word2 are both in $filename.\" fi 上面的例子只有在指定文件里面，同时存在搜索词word1和word2，就会执行if的命令部分。 下面的示例演示如何将一个&&判断表达式，改写成对应的if结构。 [[ -d \"$dir_name\" ]] && cd \"$dir_name\" && rm * # 等同于 if [[ ! -d \"$dir_name\" ]]; then echo \"No such directory: '$dir_name'\" >&2 exit 1 fi if ! cd \"$dir_name\"; then echo \"Cannot cd to '$dir_name'\" >&2 exit 1 fi if ! rm *; then echo \"File deletion failed. Check results\" >&2 exit 1 fi","s":"普通命令的逻辑运算","u":"/docs/modern-linux/bash-tutorial/condition","h":"#普通命令的逻辑运算","p":1542},{"i":1565,"t":"case结构用于多值判断，可以为每个值指定对应的命令，跟包含多个elif的if结构等价，但是语义更好。它的语法如下。 case expression in pattern ) commands ;; pattern ) commands ;; ... esac 上面代码中，expression是一个表达式，pattern是表达式的值或者一个模式，可以有多条，用来匹配多个值，每条以两个分号（;）结尾。 #!/bin/bash echo -n \"输入一个1到3之间的数字（包含两端）> \" read character case $character in 1) echo 1 ;; 2) echo 2 ;; 3) echo 3 ;; *) echo 输入不符合要求 ;; esac 上面例子中，最后一条匹配语句的模式是*，这个通配符可以匹配其他字符和没有输入字符的情况，类似if的else部分。 下面是另一个例子。 #!/bin/bash OS=$(uname -s) case \"$OS\" in FreeBSD) echo \"This is FreeBSD\" ;; Darwin) echo \"This is Mac OSX\" ;; AIX) echo \"This is AIX\" ;; Minix) echo \"This is Minix\" ;; Linux) echo \"This is Linux\" ;; *) echo \"Failed to identify this OS\" ;; esac 上面的例子判断当前是什么操作系统。 case的匹配模式可以使用各种通配符，下面是一些例子。 a)：匹配a。 a|b)：匹配a或b。 [[:alpha:]])：匹配单个字母。 ???)：匹配 3 个字符的单词。 *.txt)：匹配.txt结尾。 *)：匹配任意输入，通常作为case结构的最后一个模式。 #!/bin/bash echo -n \"输入一个字母或数字 > \" read character case $character in [[:lower:]] | [[:upper:]]) echo \"输入了字母 $character\" ;; [0-9]) echo \"输入了数字 $character\" ;; *) echo \"输入不符合要求\" ;; esac 上面例子中，使用通配符[[:lower:]] | [[:upper:]]匹配字母，[0-9]匹配数字。 Bash 4.0 之前，case结构只能匹配一个条件，然后就会退出case结构。Bash 4.0 之后，允许匹配多个条件，这时可以用;;&终止每个条件块。 #!/bin/bash # test.sh read -n 1 -p \"Type a character > \" echo case $REPLY in [[:upper:]]) echo \"'$REPLY' is upper case.\" ;;& [[:lower:]]) echo \"'$REPLY' is lower case.\" ;;& [[:alpha:]]) echo \"'$REPLY' is alphabetic.\" ;;& [[:digit:]]) echo \"'$REPLY' is a digit.\" ;;& [[:graph:]]) echo \"'$REPLY' is a visible character.\" ;;& [[:punct:]]) echo \"'$REPLY' is a punctuation symbol.\" ;;& [[:space:]]) echo \"'$REPLY' is a whitespace character.\" ;;& [[:xdigit:]]) echo \"'$REPLY' is a hexadecimal digit.\" ;;& esac 执行上面的脚本，会得到下面的结果。 $ test.sh Type a character > a 'a' is lower case. 'a' is alphabetic. 'a' is a visible character. 'a' is a hexadecimal digit. 可以看到条件语句结尾添加了;;&以后，在匹配一个条件之后，并没有退出case结构，而是继续判断下一个条件。","s":"case 结构","u":"/docs/modern-linux/bash-tutorial/condition","h":"#case-结构","p":1542},{"i":1567,"t":"The Linux Command Line, William Shotts","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/condition","h":"#参考链接","p":1542},{"i":1569,"t":"本章介绍如何对 Shell 脚本除错。","s":"脚本除错","u":"/docs/modern-linux/bash-tutorial/debug","h":"","p":1568},{"i":1571,"t":"编写 Shell 脚本的时候，一定要考虑到命令失败的情况，否则很容易出错。 #! /bin/bash dir_name=/path/not/exist cd $dir_name rm * 上面脚本中，如果目录$dir_name不存在，cd $dir_name命令就会执行失败。这时，就不会改变当前目录，脚本会继续执行下去，导致rm *命令删光当前目录的文件。 如果改成下面的样子，也会有问题。 cd $dir_name && rm * 上面脚本中，只有cd $dir_name执行成功，才会执行rm *。但是，如果变量$dir_name为空，cd就会进入用户主目录，从而删光用户主目录的文件。 下面的写法才是正确的。 [[ -d $dir_name ]] && cd $dir_name && rm * 上面代码中，先判断目录$dir_name是否存在，然后才执行其他操作。 如果不放心删除什么文件，可以先打印出来看一下。 [[ -d $dir_name ]] && cd $dir_name && echo rm * 上面命令中，echo rm *不会删除文件，只会打印出来要删除的文件。","s":"常见错误","u":"/docs/modern-linux/bash-tutorial/debug","h":"#常见错误","p":1568},{"i":1573,"t":"bash的-x参数可以在执行每一行命令之前，打印该命令。一旦出错，这样就比较容易追查。 下面是一个脚本script.sh。 # script.sh echo hello world 加上-x参数，执行每条命令之前，都会显示该命令。 $ bash -x script.sh + echo hello world hello world 上面例子中，行首为+的行，显示该行是所要执行的命令，下一行才是该命令的执行结果。 下面再看一个-x写在脚本内部的例子。 #! /bin/bash -x # trouble: script to demonstrate common errors number=1 if [ $number = 1 ]; then echo \"Number is equal to 1.\" else echo \"Number is not equal to 1.\" fi 上面的脚本执行之后，会输出每一行命令。 $ trouble + number=1 + '[' 1 = 1 ']' + echo 'Number is equal to 1.' Number is equal to 1. 输出的命令之前的+号，是由系统变量PS4决定，可以修改这个变量。 $ export PS4='$LINENO + ' $ trouble 5 + number=1 7 + '[' 1 = 1 ']' 8 + echo 'Number is equal to 1.' Number is equal to 1. 另外，set命令也可以设置 Shell 的行为参数，有利于脚本除错，详见《set 命令》一章。","s":"bash的-x参数","u":"/docs/modern-linux/bash-tutorial/debug","h":"#bash的-x参数","p":1568},{"i":1575,"t":"有一些环境变量常用于除错。","s":"环境变量","u":"/docs/modern-linux/bash-tutorial/debug","h":"#环境变量","p":1568},{"i":1577,"t":"变量LINENO返回它在脚本里面的行号。 #!/bin/bash echo \"This is line $LINENO\" 执行上面的脚本test.sh，$LINENO会返回3。 $ ./test.sh This is line 3","s":"LINENO","u":"/docs/modern-linux/bash-tutorial/debug","h":"#lineno","p":1568},{"i":1579,"t":"变量FUNCNAME返回一个数组，内容是当前的函数调用堆栈。该数组的 0 号成员是当前调用的函数，1 号成员是调用当前函数的函数，以此类推。 #!/bin/bash function func1() { echo \"func1: FUNCNAME0 is ${FUNCNAME[0]}\" echo \"func1: FUNCNAME1 is ${FUNCNAME[1]}\" echo \"func1: FUNCNAME2 is ${FUNCNAME[2]}\" func2 } function func2() { echo \"func2: FUNCNAME0 is ${FUNCNAME[0]}\" echo \"func2: FUNCNAME1 is ${FUNCNAME[1]}\" echo \"func2: FUNCNAME2 is ${FUNCNAME[2]}\" } func1 执行上面的脚本test.sh，结果如下。 $ ./test.sh func1: FUNCNAME0 is func1 func1: FUNCNAME1 is main func1: FUNCNAME2 is func2: FUNCNAME0 is func2 func2: FUNCNAME1 is func1 func2: FUNCNAME2 is main 上面例子中，执行func1时，变量FUNCNAME的 0 号成员是func1，1 号成员是调用func1的主脚本main。执行func2时，变量FUNCNAME的 0 号成员是func2，1 号成员是调用func2的func1。","s":"FUNCNAME","u":"/docs/modern-linux/bash-tutorial/debug","h":"#funcname","p":1568},{"i":1581,"t":"变量BASH_SOURCE返回一个数组，内容是当前的脚本调用堆栈。该数组的 0 号成员是当前执行的脚本，1 号成员是调用当前脚本的脚本，以此类推，跟变量FUNCNAME是一一对应关系。 下面有两个子脚本lib1.sh和lib2.sh。 # lib1.sh function func1() { echo \"func1: BASH_SOURCE0 is ${BASH_SOURCE[0]}\" echo \"func1: BASH_SOURCE1 is ${BASH_SOURCE[1]}\" echo \"func1: BASH_SOURCE2 is ${BASH_SOURCE[2]}\" func2 } # lib2.sh function func2() { echo \"func2: BASH_SOURCE0 is ${BASH_SOURCE[0]}\" echo \"func2: BASH_SOURCE1 is ${BASH_SOURCE[1]}\" echo \"func2: BASH_SOURCE2 is ${BASH_SOURCE[2]}\" } 然后，主脚本main.sh调用上面两个子脚本。 #!/bin/bash # main.sh source lib1.sh source lib2.sh func1 执行主脚本main.sh，会得到下面的结果。 $ ./main.sh func1: BASH_SOURCE0 is lib1.sh func1: BASH_SOURCE1 is ./main.sh func1: BASH_SOURCE2 is func2: BASH_SOURCE0 is lib2.sh func2: BASH_SOURCE1 is lib1.sh func2: BASH_SOURCE2 is ./main.sh 上面例子中，执行函数func1时，变量BASH_SOURCE的 0 号成员是func1所在的脚本lib1.sh，1 号成员是主脚本main.sh；执行函数func2时，变量BASH_SOURCE的 0 号成员是func2所在的脚本lib2.sh，1 号成员是调用func2的脚本lib1.sh。","s":"BASH_SOURCE","u":"/docs/modern-linux/bash-tutorial/debug","h":"#bash_source","p":1568},{"i":1583,"t":"变量BASH_LINENO返回一个数组，内容是每一轮调用对应的行号。${BASH_LINENO[$i]}跟${FUNCNAME[$i]}是一一对应关系，表示${FUNCNAME[$i]}在调用它的脚本文件${BASH_SOURCE[$i+1]}里面的行号。 下面有两个子脚本lib1.sh和lib2.sh。 # lib1.sh function func1() { echo \"func1: BASH_LINENO is ${BASH_LINENO[0]}\" echo \"func1: FUNCNAME is ${FUNCNAME[0]}\" echo \"func1: BASH_SOURCE is ${BASH_SOURCE[1]}\" func2 } # lib2.sh function func2() { echo \"func2: BASH_LINENO is ${BASH_LINENO[0]}\" echo \"func2: FUNCNAME is ${FUNCNAME[0]}\" echo \"func2: BASH_SOURCE is ${BASH_SOURCE[1]}\" } 然后，主脚本main.sh调用上面两个子脚本。 #!/bin/bash # main.sh source lib1.sh source lib2.sh func1 执行主脚本main.sh，会得到下面的结果。 $ ./main.sh func1: BASH_LINENO is 7 func1: FUNCNAME is func1 func1: BASH_SOURCE is main.sh func2: BASH_LINENO is 8 func2: FUNCNAME is func2 func2: BASH_SOURCE is lib1.sh 上面例子中，函数func1是在main.sh的第 7 行调用，函数func2是在lib1.sh的第 8 行调用的。","s":"BASH_LINENO","u":"/docs/modern-linux/bash-tutorial/debug","h":"#bash_lineno","p":1568},{"i":1585,"t":"本章介绍 Bash 函数的用法。","s":"Bash 函数","u":"/docs/modern-linux/bash-tutorial/function","h":"","p":1584},{"i":1587,"t":"函数（function）是可以重复使用的代码片段，有利于代码的复用。它与别名（alias）的区别是，别名只适合封装简单的单个命令，函数则可以封装复杂的多行命令。 函数总是在当前 Shell 执行，这是跟脚本的一个重大区别，Bash 会新建一个子 Shell 执行脚本。如果函数与脚本同名，函数会优先执行。但是，函数的优先级不如别名，即如果函数与别名同名，那么别名优先执行。 Bash 函数定义的语法有两种。 # 第一种 fn() { # codes } # 第二种 function fn() { # codes } 上面代码中，fn是自定义的函数名，函数代码就写在大括号之中。这两种写法是等价的。 下面是一个简单函数的例子。 hello() { echo \"Hello $1\" } 上面代码中，函数体里面的$1表示函数调用时的第一个参数。 调用时，就直接写函数名，参数跟在函数名后面。 $ hello world Hello world 下面是一个多行函数的例子，显示当前日期时间。 today() { echo -n \"Today's date is: \" date +\"%A, %B %-d, %Y\" } 删除一个函数，可以使用unset命令。 unset -f functionName 查看当前 Shell 已经定义的所有函数，可以使用declare命令。 $ declare -f 上面的declare命令不仅会输出函数名，还会输出所有定义。输出顺序是按照函数名的字母表顺序。由于会输出很多内容，最好通过管道命令配合more或less使用。 declare命令还支持查看单个函数的定义。 $ declare -f functionName declare -F可以输出所有已经定义的函数名，不含函数体。 $ declare -F","s":"简介","u":"/docs/modern-linux/bash-tutorial/function","h":"#简介","p":1584},{"i":1589,"t":"函数体内可以使用参数变量，获取函数参数。函数的参数变量，与脚本参数变量是一致的。 $1~$9：函数的第一个到第 9 个的参数。 $0：函数所在的脚本名。 $#：函数的参数总数。 $@：函数的全部参数，参数之间使用空格分隔。 $*：函数的全部参数，参数之间使用变量$IFS值的第一个字符分隔，默认为空格，但是可以自定义。 如果函数的参数多于 9 个，那么第 10 个参数可以用${10}的形式引用，以此类推。 下面是一个示例脚本test.sh。 #!/bin/bash # test.sh function alice { echo \"alice: $@\" echo \"$0: $1 $2 $3 $4\" echo \"$# arguments\" } alice in wonderland 运行该脚本，结果如下。 $ bash test.sh alice: in wonderland test.sh: in wonderland 2 arguments 上面例子中，由于函数alice只有第一个和第二个参数，所以第三个和第四个参数为空。 下面是一个日志函数的例子。 function log_msg { echo \"[$(date '+ %F %T') ]: $@\" } 使用方法如下。 $ log_msg \"This is sample log message\" [ 2018-08-16 19:56:34 ]: This is sample log message","s":"参数变量","u":"/docs/modern-linux/bash-tutorial/function","h":"#参数变量","p":1584},{"i":1591,"t":"return命令用于从函数返回一个值。函数执行到这条命令，就不再往下执行了，直接返回了。 function func_return_value { return 10 } 函数将返回值返回给调用者。如果命令行直接执行函数，下一个命令可以用$?拿到返回值。 $ func_return_value $ echo \"Value returned by function is: $?\" Value returned by function is: 10 return后面不跟参数，只用于返回也是可以的。 function name { commands return }","s":"return 命令","u":"/docs/modern-linux/bash-tutorial/function","h":"#return-命令","p":1584},{"i":1593,"t":"Bash 函数体内直接声明的变量，属于全局变量，整个脚本都可以读取。这一点需要特别小心。 # 脚本 test.sh fn() { foo=1 echo \"fn: foo = $foo\" } fn echo \"global: foo = $foo\" 上面脚本的运行结果如下。 $ bash test.sh fn: foo = 1 global: foo = 1 上面例子中，变量$foo是在函数fn内部声明的，函数体外也可以读取。 函数体内不仅可以声明全局变量，还可以修改全局变量。 #! /bin/bash foo=1 fn() { foo=2 } fn echo $foo 上面代码执行后，输出的变量$foo值为 2。 函数里面可以用local命令声明局部变量。 #! /bin/bash # 脚本 test.sh fn() { local foo foo=1 echo \"fn: foo = $foo\" } fn echo \"global: foo = $foo\" 上面脚本的运行结果如下。 $ bash test.sh fn: foo = 1 global: foo = 上面例子中，local命令声明的$foo变量，只在函数体内有效，函数体外没有定义。","s":"全局变量和局部变量，local 命令","u":"/docs/modern-linux/bash-tutorial/function","h":"#全局变量和局部变量local-命令","p":1584},{"i":1595,"t":"How to define and use functions in Linux Shell Script, by Pradeep Kumar","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/function","h":"#参考链接","p":1584},{"i":1598,"t":"Shell 接收到用户输入的命令以后，会根据空格将用户的输入，拆分成一个个词元（token）。然后，Shell 会扩展词元里面的特殊字符，扩展完成后才会调用相应的命令。 这种特殊字符的扩展，称为模式扩展（globbing）。其中有些用到通配符，又称为通配符扩展（wildcard expansion）。Bash 一共提供八种扩展。 波浪线扩展 ? 字符扩展 * 字符扩展 方括号扩展 大括号扩展 变量扩展 子命令扩展 算术扩展 本章介绍这八种扩展。 Bash 是先进行扩展，再执行命令。因此，扩展的结果是由 Bash 负责的，与所要执行的命令无关。命令本身并不存在参数扩展，收到什么参数就原样执行。这一点务必需要记住。 模块扩展的英文单词是globbing，这个词来自于早期的 Unix 系统有一个/etc/glob文件，保存扩展的模板。后来 Bash 内置了这个功能，但是这个名字就保留了下来。 模式扩展与正则表达式的关系是，模式扩展早于正则表达式出现，可以看作是原始的正则表达式。它的功能没有正则那么强大灵活，但是优点是简单和方便。 Bash 允许用户关闭扩展。 $ set -o noglob # 或者 $ set -f 下面的命令可以重新打开扩展。 $ set +o noglob # 或者 $ set +f","s":"简介","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#简介","p":1596},{"i":1600,"t":"波浪线~会自动扩展成当前用户的主目录。 $ echo ~ /home/me ~/dir表示扩展成主目录的某个子目录，dir是主目录里面的一个子目录名。 # 进入 /home/me/foo 目录 $ cd ~/foo ~user表示扩展成用户user的主目录。 $ echo ~foo /home/foo $ echo ~root /root 上面例子中，Bash 会根据波浪号后面的用户名，返回该用户的主目录。 如果~user的user是不存在的用户名，则波浪号扩展不起作用。 $ echo ~nonExistedUser ~nonExistedUser ~+会扩展成当前所在的目录，等同于pwd命令。 $ cd ~/foo $ echo ~+ /home/me/foo","s":"波浪线扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#波浪线扩展","p":1596},{"i":1602,"t":"?字符代表文件路径里面的任意单个字符，不包括空字符。比如，Data???匹配所有Data后面跟着三个字符的文件名。 # 存在文件 a.txt 和 b.txt $ ls ?.txt a.txt b.txt 上面命令中，?表示单个字符，所以会同时匹配a.txt和b.txt。 如果匹配多个字符，就需要多个?连用。 # 存在文件 a.txt、b.txt 和 ab.txt $ ls ??.txt ab.txt 上面命令中，??匹配了两个字符。 ? 字符扩展属于文件名扩展，只有文件确实存在的前提下，才会发生扩展。如果文件不存在，扩展就不会发生。 # 当前目录有 a.txt 文件 $ echo ?.txt a.txt # 当前目录为空目录 $ echo ?.txt ?.txt 上面例子中，如果?.txt可以扩展成文件名，echo命令会输出扩展后的结果；如果不能扩展成文件名，echo就会原样输出?.txt。","s":"? 字符扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#-字符扩展","p":1596},{"i":1604,"t":"*字符代表文件路径里面的任意数量的任意字符，包括零个字符。 # 存在文件 a.txt、b.txt 和 ab.txt $ ls *.txt a.txt b.txt ab.txt 上面例子中，*.txt代表后缀名为.txt的所有文件。 如果想输出当前目录的所有文件，直接用*即可。 $ ls * *可以匹配空字符，下面是一个例子。 # 存在文件 a.txt、b.txt 和 ab.txt $ ls a*.txt a.txt ab.txt $ ls *b* b.txt ab.txt 注意，*不会匹配隐藏文件（以.开头的文件），即ls *不会输出隐藏文件。 如果要匹配隐藏文件，需要写成.*。 # 显示所有隐藏文件 $ echo .* 如果要匹配隐藏文件，同时要排除.和..这两个特殊的隐藏文件，可以与方括号扩展结合使用，写成.[!.]*。 $ echo .[!.]* 注意，*字符扩展属于文件名扩展，只有文件确实存在的前提下才会扩展。如果文件不存在，就会原样输出。 # 当前目录不存在 c 开头的文件 $ echo c*.txt c*.txt 上面例子中，当前目录里面没有c开头的文件，导致c*.txt会原样输出。 *只匹配当前目录，不会匹配子目录。 # 子目录有一个 a.txt # 无效的写法 $ ls *.txt # 有效的写法 $ ls */*.txt 上面的例子，文本文件在子目录，*.txt不会产生匹配，必须写成*/*.txt。有几层子目录，就必须写几层星号。 Bash 4.0 引入了一个参数globstar，当该参数打开时，允许**匹配零个或多个子目录。因此，**/*.txt可以匹配顶层的文本文件和任意深度子目录的文本文件。详细介绍请看后面shopt命令的介绍。","s":"* 字符扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#-字符扩展-1","p":1596},{"i":1606,"t":"方括号扩展的形式是[...]，只有文件确实存在的前提下才会扩展。如果文件不存在，就会原样输出。括号之中的任意一个字符。比如，[aeiou]可以匹配五个元音字母中的任意一个。 # 存在文件 a.txt 和 b.txt $ ls [ab].txt a.txt b.txt # 只存在文件 a.txt $ ls [ab].txt a.txt 上面例子中，[ab]可以匹配a或b，前提是确实存在相应的文件。 方括号扩展属于文件名匹配，即扩展后的结果必须符合现有的文件路径。如果不存在匹配，就会保持原样，不进行扩展。 # 不存在文件 a.txt 和 b.txt $ ls [ab].txt ls: 无法访问'[ab].txt': 没有那个文件或目录 上面例子中，由于扩展后的文件不存在，[ab].txt就原样输出了，导致ls命名报错。 方括号扩展还有两种变体：[^...]和[!...]。它们表示匹配不在方括号里面的字符，这两种写法是等价的。比如，[^abc]或[!abc]表示匹配除了a、b、c以外的字符。 # 存在 aaa、bbb、aba 三个文件 $ ls ?[!a]? aba bbb 上面命令中，[!a]表示文件名第二个字符不是a的文件名，所以返回了aba和bbb两个文件。 注意，如果需要匹配[字符，可以放在方括号内，比如[[aeiou]。如果需要匹配连字号-，只能放在方括号内部的开头或结尾，比如[-aeiou]或[aeiou-]。","s":"方括号扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#方括号扩展","p":1596},{"i":1608,"t":"方括号扩展有一个简写形式[start-end]，表示匹配一个连续的范围。比如，[a-c]等同于[abc]，[0-9]匹配[0123456789]。 # 存在文件 a.txt、b.txt 和 c.txt $ ls [a-c].txt a.txt b.txt c.txt # 存在文件 report1.txt、report2.txt 和 report3.txt $ ls report[0-9].txt report1.txt report2.txt report3.txt ... 下面是一些常用简写的例子。 [a-z]：所有小写字母。 [a-zA-Z]：所有小写字母与大写字母。 [a-zA-Z0-9]：所有小写字母、大写字母与数字。 [abc]*：所有以a、b、c字符之一开头的文件名。 program.[co]：文件program.c与文件program.o。 BACKUP.[0-9][0-9][0-9]：所有以BACKUP.开头，后面是三个数字的文件名。 这种简写形式有一个否定形式[!start-end]，表示匹配不属于这个范围的字符。比如，[!a-zA-Z]表示匹配非英文字母的字符。 $ ls report[!1–3].txt report4.txt report5.txt 上面代码中，[!1-3]表示排除 1、2 和 3。","s":"[start-end] 扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#start-end-扩展","p":1596},{"i":1610,"t":"大括号扩展{...}表示分别扩展成大括号里面的所有值，各个值之间使用逗号分隔。比如，{1,2,3}扩展成1 2 3。 $ echo {1,2,3} 1 2 3 $ echo d{a,e,i,u,o}g dag deg dig dug dog $ echo Front-{A,B,C}-Back Front-A-Back Front-B-Back Front-C-Back 注意，大括号扩展不是文件名扩展。它会扩展成所有给定的值，而不管是否有对应的文件存在。 $ ls {a,b,c}.txt ls: 无法访问'a.txt': 没有那个文件或目录 ls: 无法访问'b.txt': 没有那个文件或目录 ls: 无法访问'c.txt': 没有那个文件或目录 上面例子中，即使不存在对应的文件，{a,b,c}依然扩展成三个文件名，导致ls命令报了三个错误。 另一个需要注意的地方是，大括号内部的逗号前后不能有空格。否则，大括号扩展会失效。 $ echo {1 , 2} {1 , 2} 上面例子中，逗号前后有空格，Bash 就会认为这不是大括号扩展，而是三个独立的参数。 逗号前面可以没有值，表示扩展的第一项为空。 $ cp a.log{,.bak} # 等同于 # cp a.log a.log.bak 大括号可以嵌套。 $ echo {j{p,pe}g,png} jpg jpeg png $ echo a{A{1,2},B{3,4}}b aA1b aA2b aB3b aB4b 大括号也可以与其他模式联用，并且总是先于其他模式进行扩展。 $ echo /bin/{cat,b*} /bin/cat /bin/b2sum /bin/base32 /bin/base64 ... ... # 基本等同于 $ echo /bin/cat;echo /bin/b* 上面例子中，会先进行大括号扩展，然后进行*扩展，等同于执行两条echo命令。 大括号可以用于多字符的模式，方括号不行（只能匹配单字符）。 $ echo {cat,dog} cat dog 由于大括号扩展{...}不是文件名扩展，所以它总是会扩展的。这与方括号扩展[...]完全不同，如果匹配的文件不存在，方括号就不会扩展。这一点要注意区分。 # 不存在 a.txt 和 b.txt $ echo [ab].txt [ab].txt $ echo {a,b}.txt a.txt b.txt 上面例子中，如果不存在a.txt和b.txt，那么[ab].txt就会变成一个普通的文件名，而{a,b}.txt可以照样扩展。","s":"大括号扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#大括号扩展","p":1596},{"i":1612,"t":"大括号扩展有一个简写形式{start..end}，表示扩展成一个连续序列。比如，{a..z}可以扩展成 26 个小写英文字母。 $ echo {a..c} a b c $ echo d{a..d}g dag dbg dcg ddg $ echo {1..4} 1 2 3 4 $ echo Number_{1..5} Number_1 Number_2 Number_3 Number_4 Number_5 这种简写形式支持逆序。 $ echo {c..a} c b a $ echo {5..1} 5 4 3 2 1 注意，如果遇到无法理解的简写，大括号模式就会原样输出，不会扩展。 $ echo {a1..3c} {a1..3c} 这种简写形式可以嵌套使用，形成复杂的扩展。 $ echo .{mp{3..4},m4{a,b,p,v}} .mp3 .mp4 .m4a .m4b .m4p .m4v 大括号扩展的常见用途为新建一系列目录。 $ mkdir {2007..2009}-{01..12} 上面命令会新建 36 个子目录，每个子目录的名字都是”年份 - 月份“。 这个写法的另一个常见用途，是直接用于for循环。 for i in {1..4} do echo $i done 上面例子会循环 4 次。 如果整数前面有前导0，扩展输出的每一项都有前导0。 $ echo {01..5} 01 02 03 04 05 $ echo {001..5} 001 002 003 004 005 这种简写形式还可以使用第二个双点号（start..end..step），用来指定扩展的步长。 $ echo {0..8..2} 0 2 4 6 8 上面代码将0扩展到8，每次递增的长度为2，所以一共输出 5 个数字。 多个简写形式连用，会有循环处理的效果。 $ echo {a..c}{1..3} a1 a2 a3 b1 b2 b3 c1 c2 c3","s":"{start..end} 扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#startend-扩展","p":1596},{"i":1614,"t":"Bash 将美元符号$开头的词元视为变量，将其扩展成变量值，详见《Bash 变量》一章。 $ echo $SHELL /bin/bash 变量名除了放在美元符号后面，也可以放在${}里面。 $ echo ${SHELL} /bin/bash ${!string*}或${!string@}返回所有匹配给定字符串string的变量名。 $ echo ${!S*} SECONDS SHELL SHELLOPTS SHLVL SSH_AGENT_PID SSH_AUTH_SOCK 上面例子中，${!S*}扩展成所有以S开头的变量名。","s":"变量扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#变量扩展","p":1596},{"i":1616,"t":"$(...)可以扩展成另一个命令的运行结果，该命令的所有输出都会作为返回值。 $ echo $(date) Tue Jan 28 00:01:13 CST 2020 上面例子中，$(date)返回date命令的运行结果。 还有另一种较老的语法，子命令放在反引号之中，也可以扩展成命令的运行结果。 $ echo `date` Tue Jan 28 00:01:13 CST 2020 $(...)可以嵌套，比如$(ls $(pwd))。","s":"子命令扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#子命令扩展","p":1596},{"i":1618,"t":"$((...))可以扩展成整数运算的结果，详见《Bash 的算术运算》一章。 $ echo $((2 + 2)) 4","s":"算术扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#算术扩展","p":1596},{"i":1620,"t":"[[:class:]]表示一个字符类，扩展成某一类特定字符之中的一个。常用的字符类如下。 [[:alnum:]]：匹配任意英文字母与数字 [[:alpha:]]：匹配任意英文字母 [[:blank:]]：空格和 Tab 键。 [[:cntrl:]]：ASCII 码 0-31 的不可打印字符。 [[:digit:]]：匹配任意数字 0-9。 [[:graph:]]：A-Z、a-z、0-9 和标点符号。 [[:lower:]]：匹配任意小写字母 a-z。 [[:print:]]：ASCII 码 32-127 的可打印字符。 [[:punct:]]：标点符号（除了 A-Z、a-z、0-9 的可打印字符）。 [[:space:]]：空格、Tab、LF（10）、VT（11）、FF（12）、CR（13）。 [[:upper:]]：匹配任意大写字母 A-Z。 [[:xdigit:]]：16 进制字符（A-F、a-f、0-9）。 请看下面的例子。 $ echo [[:upper:]]* 上面命令输出所有大写字母开头的文件名。 字符类的第一个方括号后面，可以加上感叹号!（或^），表示否定。比如，[![:digit:]](或[^[:digit:]]) 匹配所有非数字。 $ echo [![:digit:]]* 上面命令输出所有不以数字开头的文件名。 字符类也属于文件名扩展，如果没有匹配的文件名，字符类就会原样输出。 # 不存在以大写字母开头的文件 $ echo [[:upper:]]* [[:upper:]]* 上面例子中，由于没有可匹配的文件，字符类就原样输出了。","s":"字符类","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#字符类","p":1596},{"i":1622,"t":"通配符有一些使用注意点，不可不知。 （1）通配符是先解释，再执行。 Bash 接收到命令以后，发现里面有通配符，会进行通配符扩展，然后再执行命令。 $ ls a*.txt ab.txt 上面命令的执行过程是，Bash 先将a*.txt扩展成ab.txt，然后再执行ls ab.txt。 （2）文件名扩展在不匹配时，会原样输出。 文件名扩展在没有可匹配的文件时，会原样输出。 # 不存在 r 开头的文件名 $ echo r* r* 上面代码中，由于不存在r开头的文件名，r*会原样输出。 下面是另一个例子。 $ ls *.csv ls: *.csv: No such file or directory 另外，前面已经说过，大括号扩展{...}不是文件名扩展。 （3）只适用于单层路径。 所有文件名扩展只匹配单层路径，不能跨目录匹配，即无法匹配子目录里面的文件。或者说，?或*这样的通配符，不能匹配路径分隔符（/）。 如果要匹配子目录里面的文件，可以写成下面这样。 $ ls */*.txt Bash 4.0 新增了一个globstar参数，允许**匹配零个或多个子目录，详见后面shopt命令的介绍。 （4）文件名可以使用通配符。 Bash 允许文件名使用通配符，即文件名包括特殊字符。这时引用文件名，需要把文件名放在单引号或双引号里面。 $ touch 'fo*' $ ls fo* 上面代码创建了一个fo*文件，这时*就是文件名的一部分。","s":"使用注意点","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#使用注意点","p":1596},{"i":1624,"t":"量词语法用来控制模式匹配的次数。它只有在 Bash 的extglob参数打开的情况下才能使用，不过一般是默认打开的。下面的命令可以查询。 $ shopt extglob extglob on 如果extglob参数是关闭的，可以用下面的命令打开。 $ shopt -s extglob 量词语法有下面几个。 ?(pattern-list)：模式匹配零次或一次。 *(pattern-list)：模式匹配零次或多次。 +(pattern-list)：模式匹配一次或多次。 @(pattern-list)：只匹配一次模式。 !(pattern-list)：匹配给定模式以外的任何内容。 $ ls abc?(.)txt abctxt abc.txt 上面例子中，?(.)匹配零个或一个点。 $ ls abc?(def) abc abcdef 上面例子中，?(def)匹配零个或一个def。 $ ls abc@(.txt|.php) abc.php abc.txt 上面例子中，@(.txt|.php)匹配文件有且只有一个.txt或.php后缀名。 $ ls abc+(.txt) abc.txt abc.txt.txt 上面例子中，+(.txt)匹配文件有一个或多个.txt后缀名。 $ ls a!(b).txt a.txt abb.txt ac.txt 上面例子中，!(b)表示匹配单个字母b以外的任意内容，所以除了ab.txt以外，其他文件名都能匹配。 量词语法也属于文件名扩展，如果不存在可匹配的文件，就会原样输出。 # 没有 abc 开头的文件名 $ ls abc?(def) ls: 无法访问'abc?(def)': 没有那个文件或目录 上面例子中，由于没有可匹配的文件，abc?(def)就原样输出，导致ls命令报错。","s":"量词语法","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#量词语法","p":1596},{"i":1626,"t":"shopt命令可以调整 Bash 的行为。它有好几个参数跟通配符扩展有关。 shopt命令的使用方法如下。 # 打开某个参数 $ shopt -s [optionname] # 关闭某个参数 $ shopt -u [optionname] # 查询某个参数关闭还是打开 $ shopt [optionname] （1）dotglob 参数 dotglob参数可以让扩展结果包括隐藏文件（即点开头的文件）。 正常情况下，扩展结果不包括隐藏文件。 $ ls * abc.txt 打开dotglob，就会包括隐藏文件。 $ shopt -s dotglob $ ls * abc.txt .config （2）nullglob 参数 nullglob参数可以让通配符不匹配任何文件名时，返回空字符。 默认情况下，通配符不匹配任何文件名时，会保持不变。 $ rm b* rm: 无法删除'b*': 没有那个文件或目录 上面例子中，由于当前目录不包括b开头的文件名，导致b*不会发生文件名扩展，保持原样不变，所以rm命令报错没有b*这个文件。 打开nullglob参数，就可以让不匹配的通配符返回空字符串。 $ shopt -s nullglob $ rm b* rm: 缺少操作数 上面例子中，由于没有b*匹配的文件名，所以rm b*扩展成了rm，导致报错变成了”缺少操作数“。 （3）failglob 参数 failglob参数使得通配符不匹配任何文件名时，Bash 会直接报错，而不是让各个命令去处理。 $ shopt -s failglob $ rm b* bash: 无匹配: b* 上面例子中，打开failglob以后，由于b*不匹配任何文件名，Bash 直接报错了，不再让rm命令去处理。 （4）extglob 参数 extglob参数使得 Bash 支持 ksh 的一些扩展语法。它默认应该是打开的。 $ shopt extglob extglob on 它的主要应用是支持量词语法。如果不希望支持量词语法，可以用下面的命令关闭。 $ shopt -u extglob （5）nocaseglob 参数 nocaseglob参数可以让通配符扩展不区分大小写。 $ shopt -s nocaseglob $ ls /windows/program* /windows/ProgramData /windows/Program Files /windows/Program Files (x86) 上面例子中，打开nocaseglob以后，program*就不区分大小写了，可以匹配ProgramData等。 （6）globstar 参数 globstar参数可以使得**匹配零个或多个子目录。该参数默认是关闭的。 假设有下面的文件结构。 a.txt sub1/b.txt sub1/sub2/c.txt 上面的文件结构中，顶层目录、第一级子目录sub1、第二级子目录sub1\\sub2里面各有一个文本文件。请问怎样才能使用通配符，将它们显示出来？ 默认情况下，只能写成下面这样。 $ ls *.txt */*.txt */*/*.txt a.txt sub1/b.txt sub1/sub2/c.txt 这是因为*只匹配当前目录，如果要匹配子目录，只能一层层写出来。 打开globstar参数以后，**匹配零个或多个子目录。因此，**/*.txt就可以得到想要的结果。 $ shopt -s globstar $ ls **/*.txt a.txt sub1/b.txt sub1/sub2/c.txt","s":"shopt 命令","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#shopt-命令","p":1596},{"i":1628,"t":"Think You Understand Wildcards? Think Again Advanced Wildcard Patterns Most People Don’t Know","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#参考链接","p":1596},{"i":1630,"t":"本章介绍 Bash 的最基本语法。","s":"Bash 的基本语法","u":"/docs/modern-linux/bash-tutorial/grammar","h":"","p":1629},{"i":1632,"t":"由于后面的例子会大量用到echo命令，这里先介绍这个命令。 echo命令的作用是在屏幕输出一行文本，可以将该命令的参数原样输出。 $ echo hello world hello world 上面例子中，echo的参数是hello world，可以原样输出。 如果想要输出的是多行文本，即包括换行符。这时就需要把多行文本放在引号里面。 $ echo \"<HTML> <HEAD> <TITLE>Page Title</TITLE> </HEAD> <BODY> Page body. </BODY> </HTML>\" 上面例子中，echo可以原样输出多行文本。","s":"echo 命令","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#echo-命令","p":1629},{"i":1634,"t":"默认情况下，echo输出的文本末尾会有一个回车符。-n参数可以取消末尾的回车符，使得下一个提示符紧跟在输出内容的后面。 $ echo -n hello world hello world$ 上面例子中，world后面直接就是下一行的提示符$。 $ echo a echo b a b $ echo -n a echo b ab 上面例子中，-n参数可以让两个echo命令的输出连在一起，出现在同一行。","s":"-n参数","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#-n参数","p":1629},{"i":1636,"t":"-e参数会解释引号（双引号和单引号）里面的特殊字符（比如换行符\\n）。如果不使用-e参数，即默认情况下，引号会让特殊字符变成普通字符，echo不解释它们，原样输出。 $ echo \"Hello\\nWorld\" Hello\\nWorld # 双引号的情况 $ echo -e \"Hello\\nWorld\" Hello World # 单引号的情况 $ echo -e 'Hello\\nWorld' Hello World 上面代码中，-e参数使得\\n解释为换行符，导致输出内容里面出现换行。","s":"-e参数","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#-e参数","p":1629},{"i":1638,"t":"命令行环境中，主要通过使用 Shell 命令，进行各种操作。Shell 命令基本都是下面的格式。 $ command [ arg1 ... [ argN ]] 上面代码中，command是具体的命令或者一个可执行文件，arg1 ... argN是传递给命令的参数，它们是可选的。 $ ls -l 上面这个命令中，ls是命令，-l是参数。 有些参数是命令的配置项，这些配置项一般都以一个连词线开头，比如上面的-l。同一个配置项往往有长和短两种形式，比如-l是短形式，--list是长形式，它们的作用完全相同。短形式便于手动输入，长形式一般用在脚本之中，可读性更好，利于解释自身的含义。 # 短形式 $ ls -r # 长形式 $ ls --reverse 上面命令中，-r是短形式，--reverse是长形式，作用完全一样。前者便于输入，后者便于理解。 Bash 单个命令一般都是一行，用户按下回车键，就开始执行。有些命令比较长，写成多行会有利于阅读和编辑，这时可以在每一行的结尾加上反斜杠，Bash 就会将下一行跟当前行放在一起解释。 $ echo foo bar # 等同于 $ echo foo \\ bar","s":"命令格式","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#命令格式","p":1629},{"i":1640,"t":"Bash 使用空格（或 Tab 键）区分不同的参数。 $ command foo bar 上面命令中，foo和bar之间有一个空格，所以 Bash 认为它们是两个参数。 如果参数之间有多个空格，Bash 会自动忽略多余的空格。 $ echo this is a test this is a test 上面命令中，a和test之间有多个空格，Bash 会忽略多余的空格。","s":"空格","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#空格","p":1629},{"i":1642,"t":"分号（;）是命令的结束符，使得一行可以放置多个命令，上一个命令执行结束后，再执行第二个命令。 $ clear ls 上面例子中，Bash 先执行clear命令，执行完成后，再执行ls命令。 注意，使用分号时，第二个命令总是接着第一个命令执行，不管第一个命令执行成功或失败。","s":"分号","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#分号","p":1629},{"i":1644,"t":"除了分号，Bash 还提供两个命令组合符&&和||，允许更好地控制多个命令之间的继发关系。 Command1 && Command2 上面命令的意思是，如果Command1命令运行成功，则继续运行Command2命令。 Command1 || Command2 上面命令的意思是，如果Command1命令运行失败，则继续运行Command2命令。 下面是一些例子。 $ cat filelist.txt ls -l filelist.txt 上面例子中，只要cat命令执行结束，不管成功或失败，都会继续执行ls命令。 $ cat filelist.txt && ls -l filelist.txt 上面例子中，只有cat命令执行成功，才会继续执行ls命令。如果cat执行失败（比如不存在文件flielist.txt），那么ls命令就不会执行。 $ mkdir foo || mkdir bar 上面例子中，只有mkdir foo命令执行失败（比如foo目录已经存在），才会继续执行mkdir bar命令。如果mkdir foo命令执行成功，就不会创建bar目录了。","s":"命令的组合符&&和||","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#命令的组合符和","p":1629},{"i":1646,"t":"Bash 本身内置了很多命令，同时也可以执行外部程序。怎么知道一个命令是内置命令，还是外部程序呢？ type命令用来判断命令的来源。 $ type echo echo is a shell builtin $ type ls ls is hashed (/bin/ls) 上面代码中，type命令告诉我们，echo是内部命令，ls是外部程序（/bin/ls）。 type命令本身也是内置命令。 $ type type type is a shell builtin 如果要查看一个命令的所有定义，可以使用type命令的-a参数。 $ type -a echo echo is shell builtin echo is /usr/bin/echo echo is /bin/echo 上面代码表示，echo命令既是内置命令，也有对应的外部程序。 type命令的-t参数，可以返回一个命令的类型：别名（alias），关键词（keyword），函数（function），内置命令（builtin）和文件（file）。 $ type -t bash file $ type -t if keyword 上面例子中，bash是文件，if是关键词。","s":"type 命令","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#type-命令","p":1629},{"i":1648,"t":"Bash 提供很多快捷键，可以大大方便操作。下面是一些最常用的快捷键，完整的介绍参见《行操作》一章。 Ctrl + L：清除屏幕并将当前行移到页面顶部。 Ctrl + C：中止当前正在执行的命令。 Shift + PageUp：向上滚动。 Shift + PageDown：向下滚动。 Ctrl + U：从光标位置删除到行首。 Ctrl + K：从光标位置删除到行尾。 Ctrl + W：删除光标位置前一个单词。 Ctrl + D：关闭 Shell 会话。 ↑，↓：浏览已执行命令的历史记录。 除了上面的快捷键，Bash 还具有自动补全功能。命令输入到一半的时候，可以按下 Tab 键，Bash 会自动完成剩下的部分。比如，输入tou，然后按一下 Tab 键，Bash 会自动补上ch。 除了命令的自动补全，Bash 还支持路径的自动补全。有时，需要输入很长的路径，这时只需要输入前面的部分，然后按下 Tab 键，就会自动补全后面的部分。如果有多个可能的选择，按两次 Tab 键，Bash 会显示所有选项，让你选择。","s":"快捷键","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#快捷键","p":1629},{"i":1650,"t":"Bash 是 Unix 系统和 Linux 系统的一种 Shell（命令行环境），是目前绝大多数 Linux 发行版的默认 Shell。","s":"Bash 简介","u":"/docs/modern-linux/bash-tutorial/intro","h":"","p":1649},{"i":1652,"t":"学习 Bash，首先需要理解 Shell 是什么。Shell 这个单词的原意是“外壳”，跟 kernel（内核）相对应，比喻内核外面的一层，即用户跟内核交互的对话界面。 具体来说，Shell 这个词有多种含义。 首先，Shell 是一个程序，提供一个与用户对话的环境。这个环境只有一个命令提示符，让用户从键盘输入命令，所以又称为命令行环境（command line interface，简写为 CLI）。Shell 接收到用户输入的命令，将命令送入操作系统执行，并将结果返回给用户。本书中，除非特别指明，Shell 指的就是命令行环境。 其次，Shell 是一个命令解释器，解释用户输入的命令。它支持变量、条件判断、循环操作等语法，所以用户可以用 Shell 命令写出各种小程序，又称为脚本（script）。这些脚本都通过 Shell 的解释执行，而不通过编译。 最后，Shell 是一个工具箱，提供了各种小工具，供用户方便地使用操作系统的功能。","s":"Shell 的含义","u":"/docs/modern-linux/bash-tutorial/intro","h":"#shell-的含义","p":1649},{"i":1654,"t":"Shell 有很多种，只要能给用户提供命令行环境的程序，都可以看作是 Shell。 历史上，主要的 Shell 有下面这些。 Bourne Shell (sh) Bourne Again shell (bash) C Shell (csh) TENEX C Shell (tcsh) Korn shell (ksh) Z Shell (zsh) Friendly Interactive Shell (fish) Bash 是目前最常用的 Shell，除非特别指明，下文的 Shell 和 Bash 当作同义词使用，可以互换。 下面的命令可以查看当前设备的默认 Shell。 $ echo $SHELL /bin/bash 当前正在使用的 Shell 不一定是默认 Shell，一般来说，ps命令结果的倒数第二行是当前 Shell。 $ ps PID TTY TIME CMD 4467 pts/0 00:00:00 bash 5379 pts/0 00:00:00 ps 上面示例中，ps命令结果的倒数第二行显示，运行的命令（cmd）是bash，表明当前正在使用的 Shell 是 Bash。 下面的命令可以查看当前的 Linux 系统安装的所有 Shell。 $ cat /etc/shells 上面三个命令中，$是命令行环境的提示符，用户只需要输入提示符后面的内容。 Linux 允许每个用户使用不同的 Shell，用户的默认 Shell 一般都是 Bash，或者与 Bash 兼容。 使用chsh命令，可以改变系统的默认 Shell。举例来说，要将默认 Shell 从 Bash 改成 Fish，首先要找出 Fish 可执行文件的位置。 $ which fish 上面命令找出 Fish 可执行文件的位置，一般是/usr/bin/fish。 然后，使用chsh命令切换默认 Shell。 $ chsh -s /usr/bin/fish 上面命令会将当前的默认 Shell 改成 Fish。","s":"Shell 的种类","u":"/docs/modern-linux/bash-tutorial/intro","h":"#shell-的种类","p":1649},{"i":1657,"t":"如果是不带有图形环境的 Linux 系统（比如专用于服务器的系统），启动后就直接是命令行环境。 不过，现在大部分的 Linux 发行版，尤其是针对普通用户的发行版，都是图形环境。用户登录系统后，自动进入图形环境，需要自己启动终端模拟器，才能进入命令行环境。 所谓“终端模拟器”（terminal emulator）就是一个模拟命令行窗口的程序，让用户在一个窗口中使用命令行环境，并且提供各种附加功能，比如调整颜色、字体大小、行距等等。 不同 Linux 发行版（准确地说是不同的桌面环境）带有的终端程序是不一样的，比如 KDE 桌面环境的终端程序是 konsole，Gnome 桌面环境的终端程序是 gnome-terminal，用户也可以安装第三方的终端程序。所有终端程序，尽管名字不同，基本功能都是一样的，就是让用户可以进入命令行环境，使用 Shell。","s":"终端模拟器","u":"/docs/modern-linux/bash-tutorial/intro","h":"#终端模拟器","p":1649},{"i":1659,"t":"进入命令行环境以后，用户会看到 Shell 的提示符。提示符往往是一串前缀，最后以一个美元符号$结尾，用户可以在这个符号后面输入各种命令。 [user@hostname] $ 上面例子中，完整的提示符是[user@hostname] $，其中前缀是用户名（user）加上@，再加主机名（hostname）。比如，用户名是bill，主机名是home-machine，前缀就是bill@home-machine。 注意，根用户（root）的提示符，不以美元符号（$）结尾，而以井号（#）结尾，用来提醒用户，现在具有根权限，可以执行各种操作，务必小心，不要出现误操作。这个符号是可以自己定义的，详见《命令提示符》一章。 为了简洁，后文的命令行提示符都只使用$表示。","s":"命令行提示符","u":"/docs/modern-linux/bash-tutorial/intro","h":"#命令行提示符","p":1649},{"i":1661,"t":"进入命令行环境以后，一般就已经打开 Bash 了。如果你的 Shell 不是 Bash，可以输入bash命令启动 Bash。 $ bash 退出 Bash 环境，可以使用exit命令，也可以同时按下Ctrl + d。 $ exit Bash 的基本用法就是在命令行输入各种命令，非常直观。作为练习，可以试着输入pwd命令。按下回车键，就会显示当前所在的目录。 $ pwd /home/me 如果不小心输入了pwe，会返回一个提示，表示输入出错，没有对应的可执行程序。 $ pwe bash: pwe：未找到命令","s":"进入和退出方法","u":"/docs/modern-linux/bash-tutorial/intro","h":"#进入和退出方法","p":1649},{"i":1663,"t":"Shell 伴随着 Unix 系统的诞生而诞生。 1969 年，Ken Thompson 和 Dennis Ritchie 开发了第一版的 Unix。 1971 年，Ken Thompson 编写了最初的 Shell，称为 Thompson shell，程序名是sh，方便用户使用 Unix。 1973 年至 1975 年间，John R. Mashey 扩展了最初的 Thompson shell，添加了编程功能，使得 Shell 成为一种编程语言。这个版本的 Shell 称为 Mashey shell。 1976 年，Stephen Bourne 结合 Mashey shell 的功能，重写一个新的 Shell，称为 Bourne shell。 1978 年，加州大学伯克利分校的 Bill Joy 开发了 C shell，为 Shell 提供 C 语言的语法，程序名是csh。它是第一个真正替代sh的 UNIX shell，被合并到 Berkeley UNIX 的 2BSD 版本中。 1979 年，UNIX 第七版发布，内置了 Bourne Shell，导致它成为 Unix 的默认 Shell。注意，Thompson shell、Mashey shell 和 Bourne shell 都是贝尔实验室的产品，程序名都是sh。对于用户来说，它们是同一个东西，只是底层代码不同而已。 1983 年，David Korn 开发了 Korn shell，程序名是ksh。 1985 年，Richard Stallman 成立了自由软件基金会（FSF），由于 Shell 的版权属于贝尔公司，所以他决定写一个自由版权的、使用 GNU 许可证的 Shell 程序，避免 Unix 的版权争议。 1988 年，自由软件基金会的第一个付薪程序员 Brian Fox 写了一个 Shell，功能基本上是 Bourne shell 的克隆，叫做 Bourne-Again SHell，简称 Bash，程序名为bash，任何人都可以免费使用。后来，它逐渐成为 Linux 系统的标准 Shell。 1989 年，Bash 发布 1.0 版。 1996 年，Bash 发布 2.0 版。 2004 年，Bash 发布 3.0 版。 2009 年，Bash 发布 4.0 版。 2019 年，Bash 发布 5.0 版。 用户可以通过bash命令的--version参数或者环境变量$BASH_VERSION，查看本机的 Bash 版本。 $ bash --version GNU bash，版本 5.0.3(1)-release (x86_64-pc-linux-gnu) # 或者 $ echo $BASH_VERSION 5.0.3(1)-release","s":"Shell 和 Bash 的历史","u":"/docs/modern-linux/bash-tutorial/intro","h":"#shell-和-bash-的历史","p":1649},{"i":1666,"t":"Bash 会保留用户的操作历史，即用户输入的每一条命令都会记录，默认是保存最近的 500 条命令。有了操作历史以后，就可以使用方向键的↑和↓，快速浏览上一条和下一条命令。 退出当前 Shell 的时候，Bash 会将用户在当前 Shell 的操作历史写入~/.bash_history文件，该文件默认储存 500 个操作。 环境变量HISTFILE总是指向这个文件。 $ echo $HISTFILE /home/me/.bash_history","s":"简介","u":"/docs/modern-linux/bash-tutorial/history","h":"#简介","p":1664},{"i":1668,"t":"history命令会输出.bash_history文件的全部内容，即输出操作历史。 $ history ... 498 echo Goodbye 499 ls ~ 500 cd 用户可以使用这个命令，查看最近的操作。相比直接读取.bash_history文件，它的优势在于所有命令之前加上了行号。最近的操作在最后面，行号最大。 如果想搜索某个以前执行的命令，可以配合grep命令搜索操作历史。 $ history | grep /usr/bin 上面命令返回.bash_history文件里面，那些包含/usr/bin的命令。 history命令的-c参数可以清除操作历史，即清空.bash_history文件。 $ history -c","s":"history 命令","u":"/docs/modern-linux/bash-tutorial/history","h":"#history-命令","p":1664},{"i":1671,"t":"通过定制环境变量HISTTIMEFORMAT，history的输出结果还可以显示每个操作的时间。 $ export HISTTIMEFORMAT='%F %T ' $ history 1 2013-06-09 10:40:12 cat /etc/issue 2 2013-06-09 10:40:12 clear 上面代码中，%F相当于%Y - %m - %d（年 - 月 - 日），%T相当于 %H : %M : %S（时：分：秒）。 只要设置HISTTIMEFORMAT这个环境变量，就会在.bash_history文件保存命令的执行时间戳。如果不设置，就不会保存时间戳。","s":"HISTTIMEFORMAT","u":"/docs/modern-linux/bash-tutorial/history","h":"#histtimeformat","p":1664},{"i":1673,"t":"环境变量HISTSIZE设置保存历史操作的数量。 $ export HISTSIZE=10000 上面命令设置保存过去 10000 条操作历史。 如果不希望保存本次操作的历史，可以设置HISTSIZE等于 0。 export HISTSIZE=0 如果HISTSIZE=0写入用户主目录的~/.bashrc文件，那么就不会保留该用户的操作历史。如果写入/etc/profile，整个系统都不会保留操作历史。","s":"HISTSIZE","u":"/docs/modern-linux/bash-tutorial/history","h":"#histsize","p":1664},{"i":1675,"t":"环境变量HISTIGNORE可以设置哪些命令不写入操作历史。 export HISTIGNORE='pwd:ls:exit' 上面示例设置，pwd、ls、exit这三个命令不写入操作历史。","s":"HISTIGNORE","u":"/docs/modern-linux/bash-tutorial/history","h":"#histignore","p":1664},{"i":1677,"t":"输入命令时，按下Ctrl + r快捷键，就可以搜索操作历史，选择以前执行过的命令。 Ctrl + r相当于打开一个.bash_history文件的搜索接口，直接键入命令的开头部分，Shell 就会自动在该文件中反向查询（即先查询最近的命令），显示最近一条匹配的结果，这时按下回车键，就会执行那条命令。","s":"Ctrl + r","u":"/docs/modern-linux/bash-tutorial/history","h":"#ctrl--r","p":1664},{"i":1680,"t":"操作历史的每一条记录都有行号。知道了命令的行号以后，可以用感叹号 + 行号执行该命令。如果想要执行.bash_history里面的第 8 条命令，可以像下面这样操作。 $ !8","s":"! + 行号","u":"/docs/modern-linux/bash-tutorial/history","h":"#--行号","p":1664},{"i":1682,"t":"如果想执行本次 Shell 对话中倒数的命令，比如执行倒数第 3 条命令，就可以输入!-3。 $ touch a.txt $ touch b.txt $ touch c.txt $ !-3 touch a.txt 上面示例中，!-3返回倒数第 3 条命令，即touch a.txt。 它跟! + 行号的主要区别是，后者是在.bash_history文件中从头开始计算行数，而!- 数字是从底部开始向上计算行数。","s":"!- 数字","u":"/docs/modern-linux/bash-tutorial/history","h":"#--数字","p":1664},{"i":1684,"t":"!!命令返回上一条命令。如果需要重复执行某一条命令，就可以不断键入!!，这样非常方便。它等同于!-1。 $ echo hello hello $ !! echo hello hello 上面示例中，!!会返回并执行上一条命令echo hello。 有时候，我们使用某条命令，系统报错没有权限，这时就可以使用sudo !!。 # 报错，没有执行权限 $ yum update $ sudo !! sudo yum update 上面示例中，sudo !!返回sudo yum update，从而就可以正确执行了。","s":"!!","u":"/docs/modern-linux/bash-tutorial/history","h":"","p":1664},{"i":1686,"t":"感叹号 + 搜索词可以快速执行匹配的命令。 $ echo Hello World Hello World $ echo Goodbye Goodbye $ !e echo Goodbye Goodbye 上面例子中，!e表示找出操作历史之中，最近的那一条以e开头的命令并执行。Bash 会先输出那一条命令echo Goodbye，然后直接执行。 同理，!echo也会执行最近一条以echo开头的命令。 $ !echo echo Goodbye Goodbye $ !echo H echo Goodbye H Goodbye H $ !echo H G echo Goodbye H G Goodbye H G 注意，感叹号 + 搜索词语法只会匹配命令，不会匹配参数。所以!echo H不会执行echo Hello World，而是会执行echo Goodbye，并把参数H附加在这条命令之后。同理，!echo H G也是等同于echo Goodbye命令之后附加H G。 由于感叹号 + 搜索词会扩展成以前执行过的命令，所以含有!的字符串放在双引号里面，必须非常小心，如果它后面有非空格的字符，就很有可能报错。 $ echo \"I say:\\\"hello!\\\"\" bash: !\\: event not found 上面的命令会报错，原因是感叹号后面是一个反斜杠，Bash 会尝试寻找，以前是否执行过反斜杠开头的命令，一旦找不到就会报错。解决方法就是在感叹号前面，也加上反斜杠。 $ echo \"I say:\\\"hello\\!\\\"\" I say:\"hello\\!\"","s":"! + 搜索词","u":"/docs/modern-linux/bash-tutorial/history","h":"#--搜索词","p":1664},{"i":1688,"t":"!? + 搜索词可以搜索命令的任意部分，包括参数部分。它跟! + 搜索词的主要区别是，后者是从行首开始匹配。 $ cat hello.txt Hello world ..! $ !?hello.txt cat hello.txt Hello world ..! 上面示例中，!?hello.txt会返回最近一条包括hello.txt的命令。","s":"!? + 搜索词","u":"/docs/modern-linux/bash-tutorial/history","h":"#--搜索词-1","p":1664},{"i":1690,"t":"!$代表上一个命令的最后一个参数，它的另一种写法是$_。 !*代表上一个命令的所有参数，即除了命令以外的所有部分。 $ cp a.txt b.txt $ echo !$ b.txt $ cp a.txt b.txt $ echo !* a.txt b.txt 上面示例中，!$代表上一个命令的最后一个参数（b.txt），!*代表上一个命令的所有参数（a.txt b.txt）。 如果想匹配上一个命令的某个指定位置的参数，使用!:n。 $ ls a.txt b.txt c.txt $ echo !:2 b.txt 上面示例中，!:2返回上一条命令的第二个参数（b.txt）。 这种写法的!:$，代表上一个命令的最后一个参数。事实上，!$就是!:$的简写形式。 $ ls a.txt b.txt c.txt $ echo !:$ echo c.txt c.txt 上面示例中，!:$代表上一条命令的最后一个参数（c.txt）。 如果想匹配更久以前的命令的参数，可以使用!<命令>:n（指定位置的参数）和!<命令>:$（最后一个参数）。 $ ls !mkdir:$ 上面示例中，!mkdir:$会返回前面最后一条mkdir命令的最后一个参数。 $ ls !mk:2 上面示例中，!mk:2会返回前面最后一条以mk开头的命令的第二个参数。","s":"!$，!*","u":"/docs/modern-linux/bash-tutorial/history","h":"#-1","p":1664},{"i":1692,"t":"如果只是想输出上一条命令，而不是执行它，可以使用!:p。 $ echo hello $ !:p echo hello 上面示例中，!:p只会输出echo hello，而不会执行这条命令。 如果想输出最近一条匹配的命令，而不执行它，可以使用!<命令>:p。 $ !su:p 上面示例中，!su:p会输出前面最近一条以su开头的命令，而不执行它。","s":"!:p","u":"/docs/modern-linux/bash-tutorial/history","h":"#-2","p":1664},{"i":1694,"t":"^string1^string2用来执行最近一条包含string1的命令，将其替换成string2。 $ rm /var/log/httpd/error.log $ ^error^access rm /var/log/httpd/access.log 上面示例中，^error^access将最近一条含有error的命令里面的error，替换成access。","s":"^string1^string2","u":"/docs/modern-linux/bash-tutorial/history","h":"#string1string2","p":1664},{"i":1696,"t":"上面的那些快捷命令（比如!!命令），都是找到匹配的命令后，直接执行。如果希望增加一个确认步骤，先输出是什么命令，让用户确认后再执行，可以打开 Shell 的histverify选项。 $ shopt -s histverify 打开histverify这个选项后，使用!快捷键所返回的命令，就会先输出，等到用户按下回车键后再执行。","s":"histverify 参数","u":"/docs/modern-linux/bash-tutorial/history","h":"#histverify-参数","p":1664},{"i":1698,"t":"下面是其他一些与操作历史相关的快捷键。 Ctrl + p：显示上一个命令，与向上箭头效果相同（previous）。 Ctrl + n：显示下一个命令，与向下箭头效果相同（next）。 Alt + <：显示第一个命令。 Alt + >：显示最后一个命令，即当前的命令。 Ctrl + o：执行历史文件里面的当前条目，并自动显示下一条命令。这对重复执行某个序列的命令很有帮助。","s":"快捷键","u":"/docs/modern-linux/bash-tutorial/history","h":"#快捷键","p":1664},{"i":1700,"t":"Bash bang commands: A must-know trick for the Linux command line","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/history","h":"#参考链接","p":1664},{"i":1702,"t":"Bash 脚本有时需要创建临时文件或临时目录。常见的做法是，在/tmp目录里面创建文件或目录，这样做有很多弊端，使用mktemp命令是最安全的做法。","s":"mktemp 命令，trap 命令","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"","p":1701},{"i":1704,"t":"直接创建临时文件，尤其在/tmp目录里面，往往会导致安全问题。 首先，/tmp目录是所有人可读写的，任何用户都可以往该目录里面写文件。创建的临时文件也是所有人可读的。 $ touch /tmp/info.txt $ ls -l /tmp/info.txt -rw-r--r-- 1 ruanyf ruanyf 0 12月 28 17:12 /tmp/info.txt 上面命令在/tmp目录直接创建文件，该文件默认是所有人可读的。 其次，如果攻击者知道临时文件的文件名，他可以创建符号链接，链接到临时文件，可能导致系统运行异常。攻击者也可能向脚本提供一些恶意数据。因此，临时文件最好使用不可预测、每次都不一样的文件名，防止被利用。 最后，临时文件使用完毕，应该删除。但是，脚本意外退出时，往往会忽略清理临时文件。 生成临时文件应该遵循下面的规则。 创建前检查文件是否已经存在。 确保临时文件已成功创建。 临时文件必须有权限的限制。 临时文件要使用不可预测的文件名。 脚本退出时，要删除临时文件（使用trap命令）。","s":"临时文件的安全问题","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#临时文件的安全问题","p":1701},{"i":1706,"t":"mktemp命令就是为安全创建临时文件而设计的。虽然在创建临时文件之前，它不会检查临时文件是否存在，但是它支持唯一文件名和清除机制，因此可以减轻安全攻击的风险。 直接运行mktemp命令，就能生成一个临时文件。 $ mktemp /tmp/tmp.4GcsWSG4vj $ ls -l /tmp/tmp.4GcsWSG4vj -rw------- 1 ruanyf ruanyf 0 12月 28 12:49 /tmp/tmp.4GcsWSG4vj 上面命令中，mktemp命令生成的临时文件名是随机的，而且权限是只有用户本人可读写。 Bash 脚本使用mktemp命令的用法如下。 #!/bin/bash TMPFILE=$(mktemp) echo \"Our temp file is $TMPFILE\" 为了确保临时文件创建成功，mktemp命令后面最好使用 OR 运算符（||），保证创建失败时退出脚本。 #!/bin/bash TMPFILE=$(mktemp) || exit 1 echo \"Our temp file is $TMPFILE\" 为了保证脚本退出时临时文件被删除，可以使用trap命令指定退出时的清除操作。 #!/bin/bash trap 'rm -f \"$TMPFILE\"' EXIT TMPFILE=$(mktemp) || exit 1 echo \"Our temp file is $TMPFILE\"","s":"mktemp 命令的用法","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#mktemp-命令的用法","p":1701},{"i":1708,"t":"-d参数可以创建一个临时目录。 $ mktemp -d /tmp/tmp.Wcau5UjmN6 -p参数可以指定临时文件所在的目录。默认是使用$TMPDIR环境变量指定的目录，如果这个变量没设置，那么使用/tmp目录。 $ mktemp -p /home/ruanyf/ /home/ruanyf/tmp.FOKEtvs2H3 -t参数可以指定临时文件的文件名模板，模板的末尾必须至少包含三个连续的X字符，表示随机字符，建议至少使用六个X。默认的文件名模板是tmp.后接十个随机字符。 $ mktemp -t mytemp.XXXXXXX /tmp/mytemp.yZ1HgZV","s":"mktemp 命令的参数","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#mktemp-��命令的参数","p":1701},{"i":1710,"t":"trap命令用来在 Bash 脚本中响应系统信号。 最常见的系统信号就是 SIGINT（中断），即按 Ctrl + C 所产生的信号。trap命令的-l参数，可以列出所有的系统信号。 $ trap -l 1) SIGHUP 2) SIGINT 3) SIGQUIT 4) SIGILL 5) SIGTRAP 6) SIGABRT 7) SIGBUS 8) SIGFPE 9) SIGKILL 10) SIGUSR1 11) SIGSEGV 12) SIGUSR2 13) SIGPIPE 14) SIGALRM 15) SIGTERM 16) SIGSTKFLT 17) SIGCHLD 18) SIGCONT 19) SIGSTOP 20) SIGTSTP 21) SIGTTIN 22) SIGTTOU 23) SIGURG 24) SIGXCPU 25) SIGXFSZ 26) SIGVTALRM 27) SIGPROF 28) SIGWINCH 29) SIGIO 30) SIGPWR 31) SIGSYS 34) SIGRTMIN 35) SIGRTMIN+1 36) SIGRTMIN+2 37) SIGRTMIN+3 38) SIGRTMIN+4 39) SIGRTMIN+5 40) SIGRTMIN+6 41) SIGRTMIN+7 42) SIGRTMIN+8 43) SIGRTMIN+9 44) SIGRTMIN+10 45) SIGRTMIN+11 46) SIGRTMIN+12 47) SIGRTMIN+13 48) SIGRTMIN+14 49) SIGRTMIN+15 50) SIGRTMAX-14 51) SIGRTMAX-13 52) SIGRTMAX-12 53) SIGRTMAX-11 54) SIGRTMAX-10 55) SIGRTMAX-9 56) SIGRTMAX-8 57) SIGRTMAX-7 58) SIGRTMAX-6 59) SIGRTMAX-5 60) SIGRTMAX-4 61) SIGRTMAX-3 62) SIGRTMAX-2 63) SIGRTMAX-1 64) SIGRTMAX trap的命令格式如下。 $ trap [动作] [信号1] [信号2] ... 上面代码中，“动作”是一个 Bash 命令，“信号”常用的有以下几个。 HUP：编号 1，脚本与所在的终端脱离联系。 INT：编号 2，用户按下 Ctrl + C，意图让脚本终止运行。 QUIT：编号 3，用户按下 Ctrl + 斜杠，意图退出脚本。 KILL：编号 9，该信号用于杀死进程。 TERM：编号 15，这是kill命令发出的默认信号。 EXIT：编号 0，这不是系统信号，而是 Bash 脚本特有的信号，不管什么情况，只要退出脚本就会产生。 trap命令响应EXIT信号的写法如下。 $ trap 'rm -f \"$TMPFILE\"' EXIT 上面命令中，脚本遇到EXIT信号时，就会执行rm -f \"$TMPFILE\"。 trap 命令的常见使用场景，就是在 Bash 脚本中指定退出时执行的清理命令。 #!/bin/bash trap 'rm -f \"$TMPFILE\"' EXIT TMPFILE=$(mktemp) || exit 1 ls /etc > $TMPFILE if grep -qi \"kernel\" $TMPFILE; then echo 'find' fi 上面代码中，不管是脚本正常执行结束，还是用户按 Ctrl + C 终止，都会产生EXIT信号，从而触发删除临时文件。 注意，trap命令必须放在脚本的开头。否则，它上方的任何命令导致脚本退出，都不会被它捕获。 如果trap需要触发多条命令，可以封装一个 Bash 函数。 function egress { command1 command2 command3 } trap egress EXIT","s":"trap 命令","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#trap-命令","p":1701},{"i":1712,"t":"Working with Temporary Files and Directories in Shell Scripts, Steven Vona Using Trap to Exit Bash Scripts Cleanly Sending and Trapping Signals","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#参考链接","p":1701},{"i":1714,"t":"Bash 提供三种循环语法for、while和until。","s":"循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"","p":1713},{"i":1716,"t":"while循环有一个判断条件，只要符合条件，就不断循环执行指定的语句。 while condition; do commands done 上面代码中，只要满足条件condition，就会执行命令commands。然后，再次判断是否满足条件condition，只要满足，就会一直执行下去。只有不满足条件，才会退出循环。 循环条件condition可以使用test命令，跟if结构的判断条件写法一致。 #!/bin/bash number=0 while [ \"$number\" -lt 10 ]; do echo \"Number = $number\" number=$((number + 1)) done 上面例子中，只要变量$number小于 10，就会不断加 1，直到$number等于 10，然后退出循环。 关键字do可以跟while不在同一行，这时两者之间不需要使用分号分隔。 while true; do echo 'Hi, while looping ...' done 上面的例子会无限循环，可以按下 Ctrl + c 停止。 while循环写成一行，也是可以的。 $ while true; do echo 'Hi, while looping ...'; done while的条件部分也可以是执行一个命令。 $ while echo 'ECHO'; do echo 'Hi, while looping ...'; done 上面例子中，判断条件是echo 'ECHO'。由于这个命令总是执行成功，所以上面命令会产生无限循环。 while的条件部分可以执行任意数量的命令，但是执行结果的真伪只看最后一个命令的执行结果。 $ while true; false; do echo 'Hi, looping ...'; done 上面代码运行后，不会有任何输出，因为while的最后一个命令是false。","s":"while 循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"#while-循环","p":1713},{"i":1718,"t":"until循环与while循环恰好相反，只要不符合判断条件（判断条件失败），就不断循环执行指定的语句。一旦符合判断条件，就退出循环。 until condition; do commands done 关键字do可以与until不写在同一行，这时两者之间不需要分号分隔。 until condition; do commands done 下面是一个例子。 $ until false; do echo 'Hi, until looping ...'; done Hi, until looping ... Hi, until looping ... Hi, until looping ... ^C 上面代码中，until的部分一直为false，导致命令无限运行，必须按下 Ctrl + c 终止。 #!/bin/bash number=0 until [ \"$number\" -ge 10 ]; do echo \"Number = $number\" number=$((number + 1)) done 上面例子中，只要变量number小于 10，就会不断加 1，直到number大于等于 10，就退出循环。 until的条件部分也可以是一个命令，表示在这个命令执行成功之前，不断重复尝试。 until cp $1 $2; do echo 'Attempt to copy failed. waiting...' sleep 5 done 上面例子表示，只要cp $1 $2这个命令执行不成功，就 5 秒钟后再尝试一次，直到成功为止。 until循环都可以转为while循环，只要把条件设为否定即可。上面这个例子可以改写如下。 while ! cp $1 $2; do echo 'Attempt to copy failed. waiting...' sleep 5 done 一般来说，until用得比较少，完全可以统一都使用while。","s":"until 循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"#until-循环","p":1713},{"i":1720,"t":"for...in循环用于遍历列表的每一项。 for variable in list; do commands done 上面语法中，for循环会依次从list列表中取出一项，作为变量variable，然后在循环体中进行处理。 关键词do可以跟for写在同一行，两者使用分号分隔。 for variable in list; do commands done 下面是一个例子。 #!/bin/bash for i in word1 word2 word3; do echo $i done 上面例子中，word1 word2 word3是一个包含三个单词的列表，变量i依次等于word1、word2、word3，命令echo $i则会相应地执行三次。 列表可以由通配符产生。 for i in *.png; do ls -l $i done 上面例子中，*.png会替换成当前目录中所有 PNG 图片文件，变量i会依次等于每一个文件。 列表也可以通过子命令产生。 #!/bin/bash count=0 for i in $(cat ~/.bash_profile); do count=$((count + 1)) echo \"Word $count ($i) contains $(echo -n $i | wc -c) characters\" done 上面例子中，cat ~/.bash_profile命令会输出~/.bash_profile文件的内容，然后通过遍历每一个词，计算该文件一共包含多少个词，以及每个词有多少个字符。 in list的部分可以省略，这时list默认等于脚本的所有参数$@。但是，为了可读性，最好还是不要省略，参考下面的例子。 for filename; do echo \"$filename\" done # 等同于 for filename in \"$@\"; do echo \"$filename\" done 在函数体中也是一样的，for...in循环省略in list的部分，则list默认等于函数的所有参数。","s":"for...in 循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"#forin-循环","p":1713},{"i":1722,"t":"for循环还支持 C 语言的循环语法。 for ((expression1; expression2; expression3)); do commands done 上面代码中，expression1用来初始化循环条件，expression2用来决定循环结束的条件，expression3在每次循环迭代的末尾执行，用于更新值。 注意，循环条件放在双重圆括号之中。另外，圆括号之中使用变量，不必加上美元符号$。 它等同于下面的while循环。 ((expression1)) while ((expression2)); do commands ((expression3)) done 下面是一个例子。 for ((i = 0; i < 5; i = i + 1)); do echo $i done 上面代码中，初始化变量i的值为 0，循环执行的条件是i小于 5。每次循环迭代结束时，i的值加 1。 for条件部分的三个语句，都可以省略。 for (( ; ; )); do read var if [ \"$var\" = \".\" ]; then break fi done 上面脚本会反复读取命令行输入，直到用户输入了一个点（.）为止，才会跳出循环。","s":"for 循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"#for-循环","p":1713},{"i":1724,"t":"Bash 提供了两个内部命令break和continue，用来在循环内部跳出循环。 break命令立即终止循环，程序继续执行循环块之后的语句，即不再执行剩下的循环。 #!/bin/bash for number in 1 2 3 4 5 6; do echo \"number is $number\" if [ \"$number\" = \"3\" ]; then break fi done 上面例子只会打印 3 行结果。一旦变量$number等于 3，就会跳出循环，不再继续执行。 continue命令立即终止本轮循环，开始执行下一轮循环。 #!/bin/bash while read -p \"What file do you want to test?\" filename; do if [ ! -e \"$filename\" ]; then echo \"The file does not exist.\" continue fi echo \"You entered a valid file..\" done 上面例子中，只要用户输入的文件不存在，continue命令就会生效，直接进入下一轮循环（让用户重新输入文件名），不再执行后面的打印语句。","s":"break，continue","u":"/docs/modern-linux/bash-tutorial/loop","h":"#breakcontinue","p":1713},{"i":1726,"t":"select结构主要用来生成简单的菜单。它的语法与for...in循环基本一致。 select name [in list] do commands done Bash 会对select依次进行下面的处理。 select生成一个菜单，内容是列表list的每一项，并且每一项前面还有一个数字编号。 Bash 提示用户选择一项，输入它的编号。 用户输入以后，Bash 会将该项的内容存在变量name，该项的编号存入环境变量REPLY。如果用户没有输入，就按回车键，Bash 会重新输出菜单，让用户选择。 执行命令体commands。 执行结束后，回到第一步，重复这个过程。 下面是一个例子。 #!/bin/bash # select.sh select brand in Samsung Sony iphone symphony Walton; do echo \"You have chosen $brand\" done 执行上面的脚本，Bash 会输出一个品牌的列表，让用户选择。 $ ./select.sh 1) Samsung 2) Sony 3) iphone 4) symphony 5) Walton #? 如果用户没有输入编号，直接按回车键。Bash 就会重新输出一遍这个菜单，直到用户按下Ctrl + c，退出执行。 select可以与case结合，针对不同项，执行不同的命令。 #!/bin/bash echo \"Which Operating System do you like?\" select os in Ubuntu LinuxMint Windows8 Windows10 WindowsXP; do case $os in \"Ubuntu\" | \"LinuxMint\") echo \"I also use $os.\" ;; \"Windows8\" | \"Windows10\" | \"WindowsXP\") echo \"Why don't you try Linux?\" ;; *) echo \"Invalid entry.\" break ;; esac done 上面例子中，case针对用户选择的不同项，执行不同的命令。","s":"select 结构","u":"/docs/modern-linux/bash-tutorial/loop","h":"#select-结构","p":1713},{"i":1728,"t":"Bash Select Command, Fahmida Yesmin","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/loop","h":"#参考链接","p":1713},{"i":1730,"t":"用户进入 Bash 以后，Bash 会显示一个命令提示符，用来提示用户在该位置后面输入命令。","s":"命令提示符","u":"/docs/modern-linux/bash-tutorial/prompt","h":"","p":1729},{"i":1732,"t":"命令提示符通常是美元符号$，对于根用户则是井号#。这个符号是环境变量PS1决定的，执行下面的命令，可以看到当前命令提示符的定义。 $ echo $PS1 Bash 允许用户自定义命令提示符，只要改写这个变量即可。改写后的PS1，可以放在用户的 Bash 配置文件.bashrc里面，以后新建 Bash 对话时，新的提示符就会生效。要在当前窗口看到修改后的提示符，可以执行下面的命令。 $ source ~/.bashrc 命令提示符的定义，可以包含特殊的转义字符，表示特定内容。 \\a：响铃，计算机发出一记声音。 \\d：以星期、月、日格式表示当前日期，例如“Mon May 26”。 \\h：本机的主机名。 \\H：完整的主机名。 \\j：运行在当前 Shell 会话的工作数。 \\l：当前终端设备名。 \\n：一个换行符。 \\r：一个回车符。 \\s：Shell 的名称。 \\t：24 小时制的hours:minutes:seconds格式表示当前时间。 \\T：12 小时制的当前时间。 \\@：12 小时制的AM/PM格式表示当前时间。 \\A：24 小时制的hours:minutes表示当前时间。 \\u：当前用户名。 \\v：Shell 的版本号。 \\V：Shell 的版本号和发布号。 \\w：当前的工作路径。 \\W：当前目录名。 \\!：当前命令在命令历史中的编号。 \\#：当前 shell 会话中的命令数。 \\$：普通用户显示为$字符，根用户显示为#字符。 \\[：非打印字符序列的开始标志。 \\]：非打印字符序列的结束标志。 举例来说，[\\u@\\h \\W]\\$这个提示符定义，显示出来就是[user@host ~]$（具体的显示内容取决于你的系统）。 [user@host ~]$ echo $PS1 [\\u@\\h \\W]\\$ 改写PS1变量，就可以改变这个命令提示符。 $ PS1=\"\\A \\h \\$ \" 17:33 host $ 注意，$后面最好跟一个空格，这样的话，用户的输入与提示符就不会连在一起。","s":"环境变量 PS1","u":"/docs/modern-linux/bash-tutorial/prompt","h":"#环境变量-ps1","p":1729},{"i":1734,"t":"默认情况下，命令提示符是显示终端预定义的颜色。Bash 允许自定义提示符颜色。 使用下面的代码，可以设定其后文本的颜色。 \\033[0;30m：黑色 \\033[1;30m：深灰色 \\033[0;31m：红色 \\033[1;31m：浅红色 \\033[0;32m：绿色 \\033[1;32m：浅绿色 \\033[0;33m：棕色 \\033[1;33m：黄色 \\033[0;34m：蓝色 \\033[1;34m：浅蓝色 \\033[0;35m：粉红 \\033[1;35m：浅粉色 \\033[0;36m：青色 \\033[1;36m：浅青色 \\033[0;37m：浅灰色 \\033[1;37m：白色 举例来说，如果要将提示符设为红色，可以将PS1设成下面的代码。 PS1='\\[\\033[0;31m\\]<\\u@\\h \\W>\\$' 但是，上面这样设置以后，用户在提示符后面输入的文本也是红色的。为了解决这个问题，可以在结尾添加另一个特殊代码\\[\\033[00m\\]，表示将其后的文本恢复到默认颜色。 PS1='\\[\\033[0;31m\\]<\\u@\\h \\W>\\$\\[\\033[00m\\]' 除了设置前景颜色，Bash 还允许设置背景颜色。 \\033[0;40m：蓝色 \\033[1;44m：黑色 \\033[0;41m：红色 \\033[1;45m：粉红 \\033[0;42m：绿色 \\033[1;46m：青色 \\033[0;43m：棕色 \\033[1;47m：浅灰色 下面是一个带有红色背景的提示符。 PS1='\\[\\033[0;41m\\]<\\u@\\h \\W>\\$\\[\\033[0m\\] '","s":"颜色","u":"/docs/modern-linux/bash-tutorial/prompt","h":"#颜色","p":1729},{"i":1736,"t":"除了PS1，Bash 还提供了提示符相关的另外三个环境变量。 环境变量PS2是命令行折行输入时系统的提示符，默认为> 。 $ echo \"hello > world\" 上面命令中，输入hello以后按下回车键，系统会提示继续输入。这时，第二行显示的提示符就是PS2定义的> 。 环境变量PS3是使用select命令时，系统输入菜单的提示符。 环境变量PS4默认为+ 。它是使用 Bash 的-x参数执行脚本时，每一行命令在执行前都会先打印出来，并且在行首出现的那个提示符。 比如下面是脚本test.sh。 #!/bin/bash echo \"hello world\" 使用-x参数执行这个脚本。 $ bash -x test.sh + echo 'hello world' hello world 上面例子中，输出的第一行前面有一个+ ，这就是变量PS4定义的。","s":"环境变量 PS2，PS3，PS4","u":"/docs/modern-linux/bash-tutorial/prompt","h":"#环境变量-ps2ps3ps4","p":1729},{"i":1738,"t":"Bash 只有一种数据类型，就是字符串。不管用户输入什么数据，Bash 都视为字符串。因此，字符串相关的引号和转义，对 Bash 来说就非常重要。","s":"引号和转义","u":"/docs/modern-linux/bash-tutorial/quotation","h":"","p":1737},{"i":1740,"t":"某些字符在 Bash 里面有特殊含义（比如$、&、*）。 $ echo $date $ 上面例子中，输出$date不会有任何结果，因为$是一个特殊字符。 如果想要原样输出这些特殊字符，就必须在它们前面加上反斜杠，使其变成普通字符。这就叫做“转义”（escape）。 $ echo \\$date $date 上面命令中，只有在特殊字符$前面加反斜杠，才能原样输出。 反斜杠本身也是特殊字符，如果想要原样输出反斜杠，就需要对它自身转义，连续使用两个反斜线（\\\\）。 $ echo \\\\ 上面例子输出了反斜杠本身。 反斜杠除了用于转义，还可以表示一些不可打印的字符。 \\a：响铃 \\b：退格 \\n：换行 \\r：回车 \\t：制表符 如果想要在命令行使用这些不可打印的字符，可以把它们放在引号里面，然后使用echo命令的-e参数。 $ echo a\\tb atb $ echo -e \"a\\tb\" a b 上面例子中，命令行直接输出不可打印字符\\t，Bash 不能正确解释。必须把它们放在引号之中，然后使用echo命令的-e参数。 换行符是一个特殊字符，表示命令的结束，Bash 收到这个字符以后，就会对输入的命令进行解释执行。换行符前面加上反斜杠转义，就使得换行符变成一个普通字符，Bash 会将其当作长度为0的空字符处理，从而可以将一行命令写成多行。 $ mv \\ /path/to/foo \\ /path/to/bar # 等同于 $ mv /path/to/foo /path/to/bar 上面例子中，如果一条命令过长，就可以在行尾使用反斜杠，将其改写成多行。这是常见的多行命令的写法。","s":"转义","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#转义","p":1737},{"i":1742,"t":"Bash 允许字符串放在单引号或双引号之中，加以引用。 单引号用于保留字符的字面含义，各种特殊字符在单引号里面，都会变为普通字符，比如星号（*）、美元符号（$）、反斜杠（\\）等。 $ echo '*' * $ echo '$USER' $USER $ echo '$((2+2))' $((2 + 2)) $ echo '$(echo foo)' $(echo foo) 上面命令中，单引号使得 Bash 扩展、变量引用、算术运算和子命令，都失效了。如果不使用单引号，它们都会被 Bash 自动扩展。 由于反斜杠在单引号里面变成了普通字符，所以如果单引号之中，还要使用单引号，不能使用转义，需要在外层的单引号前面加上一个美元符号（$），然后再对里层的单引号转义。 # 不正确 $ echo it's # 不正确 $ echo 'it\\'s' # 正确 $ echo $'it\\'s' 不过，更合理的方法是改在双引号之中使用单引号。 $ echo \"it's\" it's","s":"单引号","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#单引号","p":1737},{"i":1744,"t":"双引号比单引号宽松，大部分特殊字符在双引号里面，都会失去特殊含义，变成普通字符。 $ echo \"*\" * 上面例子中，通配符*是一个特殊字符，放在双引号之中，就变成了普通字符，会原样输出。这一点需要特别留意，这意味着，双引号里面不会进行文件名扩展。 但是，三个特殊字符除外：美元符号（$）、反引号（`）和反斜杠（\\）。这三个字符在双引号之中，依然有特殊含义，会被 Bash 自动扩展。 $ echo \"$SHELL\" /bin/bash $ echo \"$(date)\" Mon Jan 27 13:33:18 CST 2020 上面例子中，美元符号（$）和反引号（`）在双引号中，都保持特殊含义。美元符号用来引用变量，反引号则是执行子命令。 $ echo \"I'd say: \\\"hello.\\\"\" I'd say: \"hello.\" $ echo \"\\\\\" \\ 上面例子中，反斜杠在双引号之中保持特殊含义，用来转义。所以，可以使用反斜杠，在双引号之中插入双引号，或者插入反斜杠本身。 换行符在双引号之中，会失去特殊含义，Bash 不再将其解释为命令的结束，只是作为普通的换行符。所以可以利用双引号，在命令行输入多行文本。 $ echo \"hello world\" hello world 上面命令中，Bash 正常情况下会将换行符解释为命令结束，但是换行符在双引号之中就失去了这种特殊作用，只用来换行，所以可以输入多行。echo命令会将换行符原样输出，显示的时候正常解释为换行。 双引号的另一个常见的使用场合是，文件名包含空格。这时就必须使用双引号（或单引号），将文件名放在里面。 $ ls \"two words.txt\" 上面命令中，two words.txt是一个包含空格的文件名，如果不放在双引号里面，就会被 Bash 当作两个文件。 双引号会原样保存多余的空格。 $ echo \"this is a test\" this is a test 双引号还有一个作用，就是保存原始命令的输出格式。 # 单行输出 $ echo $(cal) 一月 2020 日 一 二 三 四 五 六 1 2 3 ... 31 # 原始格式输出 $ echo \"$(cal)\" 一月 2020 日 一 二 三 四 五 六 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 上面例子中，如果$(cal)不放在双引号之中，echo就会将所有结果以单行输出，丢弃了所有原始的格式。","s":"双引号","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#双引号","p":1737},{"i":1746,"t":"Here 文档（here document）是一种输入多行字符串的方法，格式如下。 << token text token 它的格式分成开始标记（<< token）和结束标记（token）。开始标记是两个小于号 + Here 文档的名称，名称可以随意取，后面必须是一个换行符；结束标记是单独一行顶格写的 Here 文档名称，如果不是顶格，结束标记不起作用。两者之间就是多行字符串的内容。 下面是一个通过 Here 文档输出 HTML 代码的例子。 $ cat << _EOF_ <html> <head> <title> The title of your page </title> </head> <body> Your page content goes here. </body> </html> _EOF_ Here 文档内部会发生变量替换，同时支持反斜杠转义，但是不支持通配符扩展，双引号和单引号也失去语法作用，变成了普通字符。 $ foo='hello world' $ cat << _example_ $foo \"$foo\" '$foo' _example_ hello world \"hello world\" 'hello world' 上面例子中，变量$foo发生了替换，但是双引号和单引号都原样输出了，表明它们已经失去了引用的功能。 如果不希望发生变量替换，可以把 Here 文档的开始标记放在单引号之中。 $ foo='hello world' $ cat << '_example_' $foo \"$foo\" '$foo' _example_ $foo \"$foo\" '$foo' 上面例子中，Here 文档的开始标记（_example_）放在单引号之中，导致变量替换失效了。 Here 文档的本质是重定向，它将字符串重定向输出给某个命令，相当于包含了echo命令。 $ command << token string token # 等同于 $ echo string | command 上面代码中，Here 文档相当于echo命令的重定向。 所以，Here 字符串只适合那些可以接受标准输入作为参数的命令，对于其他命令无效，比如echo命令就不能用 Here 文档作为参数。 $ echo << _example_ hello _example_ 上面例子不会有任何输出，因为 Here 文档对于echo命令无效。 此外，Here 文档也不能作为变量的值，只能用于命令的参数。","s":"Here 文档","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#here-文档","p":1737},{"i":1748,"t":"Here 文档还有一个变体，叫做 Here 字符串（Here string），使用三个小于号（<<<）表示。 <<< string 它的作用是将字符串通过标准输入，传递给命令。 有些命令直接接受给定的参数，与通过标准输入接受参数，结果是不一样的。所以才有了这个语法，使得将字符串通过标准输入传递给命令更方便，比如cat命令只接受标准输入传入的字符串。 $ cat <<< 'hi there' # 等同于 $ echo 'hi there' | cat 上面的第一种语法使用了 Here 字符串，要比第二种语法看上去语义更好，也更简洁。 $ md5sum <<< 'ddd' # 等同于 $ echo 'ddd' | md5sum 上面例子中，md5sum命令只能接受标准输入作为参数，不能直接将字符串放在命令后面，会被当作文件名，即md5sum ddd里面的ddd会被解释成文件名。这时就可以用 Here 字符串，将字符串传给md5sum命令。","s":"Here 字符串","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#here-字符串","p":1737},{"i":1751,"t":"Bash 内置了 Readline 库，具有这个库提供的很多“行操作”功能，比如命令的自动补全，可以大大加快操作速度。 这个库默认采用 Emacs 快捷键，也可以改成 Vi 快捷键。 $ set -o vi 下面的命令可以改回 Emacs 快捷键。 $ set -o emacs 如果想永久性更改编辑模式（Emacs / Vi），可以将命令写在~/.inputrc文件，这个文件是 Readline 的配置文件。 set editing-mode vi 本章介绍的快捷键都属于 Emacs 模式。Vi 模式的快捷键，读者可以参考 Vi 编辑器的教程。 Bash 默认开启这个库，但是允许关闭。 $ bash --noediting 上面命令中，--noediting参数关闭了 Readline 库，启动的 Bash 就不带有行操作功能。","s":"简介","u":"/docs/modern-linux/bash-tutorial/readline","h":"#简介","p":1749},{"i":1753,"t":"Readline 提供快速移动光标的快捷键。 Ctrl + a：移到行首。 Ctrl + b：向行首移动一个字符，与左箭头作用相同。 Ctrl + e：移到行尾。 Ctrl + f：向行尾移动一个字符，与右箭头作用相同。 Alt + f：移动到当前单词的词尾。 Alt + b：移动到当前单词的词首。 上面快捷键的 Alt 键，也可以用 ESC 键代替。","s":"光标移动","u":"/docs/modern-linux/bash-tutorial/readline","h":"#光标移动","p":1749},{"i":1755,"t":"Ctrl + l快捷键可以清除屏幕，即将当前行移到屏幕的第一行，与clear命令作用相同。","s":"清除屏幕","u":"/docs/modern-linux/bash-tutorial/readline","h":"#清除屏幕","p":1749},{"i":1757,"t":"下面的快捷键可以编辑命令行内容。 Ctrl + d：删除光标位置的字符（delete）。 Ctrl + w：删除光标前面的单词。 Ctrl + t：光标位置的字符与它前面一位的字符交换位置（transpose）。 Alt + t：光标位置的词与它前面一位的词交换位置（transpose）。 Alt + l：将光标位置至词尾转为小写（lowercase）。 Alt + u：将光标位置至词尾转为大写（uppercase）。 使用Ctrl + d的时候，如果当前行没有任何字符，会导致退出当前 Shell，所以要小心。 剪切和粘贴快捷键如下。 Ctrl + k：剪切光标位置到行尾的文本。 Ctrl + u：剪切光标位置到行首的文本。 Alt + d：剪切光标位置到词尾的文本。 Alt + Backspace：剪切光标位置到词首的文本。 Ctrl + y：在光标位置粘贴文本。 同样地，Alt 键可以用 Esc 键代替。","s":"编辑操作","u":"/docs/modern-linux/bash-tutorial/readline","h":"#编辑操作","p":1749},{"i":1759,"t":"命令输入到一半的时候，可以按一下 Tab 键，Readline 会自动补全命令或路径。比如，输入cle，再按下 Tab 键，Bash 会自动将这个命令补全为clear。 如果符合条件的命令或路径有多个，就需要连续按两次 Tab 键，Bash 会提示所有符合条件的命令或路径。 除了命令或路径，Tab 还可以补全其他值。如果一个值以$开头，则按下 Tab 键会补全变量；如果以~开头，则补全用户名；如果以@开头，则补全主机名（hostname），主机名以列在/etc/hosts文件里面的主机为准。 自动补全相关的快捷键如下。 Tab：完成自动补全。 Alt + ?：列出可能的补全，与连按两次 Tab 键作用相同。 Alt + /：尝试文件路径补全。 Ctrl + x /：先按Ctrl + x，再按/，等同于Alt + ?，列出可能的文件路径补全。 Alt + !：命令补全。 Ctrl + x !：先按Ctrl + x，再按!，等同于Alt + !，命令补全。 Alt + ~：用户名补全。 Ctrl + x ~：先按Ctrl + x，再按~，等同于Alt + ~，用户名补全。 Alt + $：变量名补全。 Ctrl + x $：先按Ctrl + x，再按$，等同于Alt + $，变量名补全。 Alt + @：主机名补全。 Ctrl + x @：先按Ctrl + x，再按@，等同于Alt + @，主机名补全。 Alt + *：在命令行一次性插入所有可能的补全。 Alt + Tab：尝试用.bash_history里面以前执行命令，进行补全。 上面的Alt键也可以用 ESC 键代替。","s":"自动补全","u":"/docs/modern-linux/bash-tutorial/readline","h":"#自动补全","p":1749},{"i":1761,"t":"Ctrl + j：等同于回车键（LINEFEED）。 Ctrl + m：等同于回车键（CARRIAGE RETURN）。 Ctrl + o：等同于回车键，并展示操作历史的下一个命令。 Ctrl + v：将下一个输入的特殊字符变成字面量，比如回车变成^M。 Ctrl + [：等同于 ESC。 Alt + .：插入上一个命令的最后一个词。 Alt + _：等同于Alt + .。 上面的Alt + .快捷键，对于很长的文件路径，有时会非常方便。因为 Unix 命令的最后一个参数通常是文件路径。 $ mkdir foo_bar $ cd #按下 Alt + . 上面例子中，在cd命令后按下Alt + .，就会自动插入foo_bar。","s":"其他快捷键","u":"/docs/modern-linux/bash-tutorial/readline","h":"#其他快捷键","p":1749},{"i":1764,"t":"有时，脚本需要在执行过程中，由用户提供一部分数据，这时可以使用read命令。它将用户的输入存入一个变量，方便后面的代码使用。用户按下回车键，就表示输入结束。 read命令的格式如下。 read [-options] [variable...] 上面语法中，options是参数选项，variable是用来保存输入数值的一个或多个变量名。如果没有提供变量名，环境变量REPLY会包含用户输入的一整行数据。 下面是一个例子demo.sh。 #!/bin/bash echo -n \"输入一些文本 > \" read text echo \"你的输入：$text\" 上面例子中，先显示一行提示文本，然后会等待用户输入文本。用户输入的文本，存入变量text，在下一行显示出来。 $ bash demo.sh 输入一些文本 > 你好，世界 你的输入：你好，世界 read可以接受用户输入的多个值。 #!/bin/bash echo Please, enter your firstname and lastname read FN LN echo \"Hi! $LN, $FN !\" 上面例子中，read根据用户的输入，同时为两个变量赋值。 如果用户的输入项少于read命令给出的变量数目，那么额外的变量值为空。如果用户的输入项多于定义的变量，那么多余的输入项会包含到最后一个变量中。 如果read命令之后没有定义变量名，那么环境变量REPLY会包含所有的输入。 #!/bin/bash # read-single: read multiple values into default variable echo -n \"Enter one or more values > \" read echo \"REPLY = '$REPLY'\" 上面脚本的运行结果如下。 $ read-single Enter one or more values > a b c d REPLY = 'a b c d' read命令除了读取键盘输入，可以用来读取文件。 #!/bin/bash filename='/etc/hosts' while read myline do echo \"$myline\" done < $filename 上面的例子通过read命令，读取一个文件的内容。done命令后面的定向符<，将文件内容导向read命令，每次读取一行，存入变量myline，直到文件读取完毕。","s":"用法","u":"/docs/modern-linux/bash-tutorial/read","h":"#用法","p":1762},{"i":1766,"t":"read命令的参数如下。 （1）-t 参数 read命令的-t参数，设置了超时的秒数。如果超过了指定时间，用户仍然没有输入，脚本将放弃等待，继续向下执行。 #!/bin/bash echo -n \"输入一些文本 > \" if read -t 3 response; then echo \"用户已经输入了\" else echo \"用户没有输入\" fi 上面例子中，输入命令会等待 3 秒，如果用户超过这个时间没有输入，这个命令就会执行失败。if根据命令的返回值，转入else代码块，继续往下执行。 环境变量TMOUT也可以起到同样作用，指定read命令等待用户输入的时间（单位为秒）。 $ TMOUT=3 $ read response 上面例子也是等待 3 秒，如果用户还没有输入，就会超时。 （2）-p 参数 -p参数指定用户输入的提示信息。 read -p \"Enter one or more values > \" echo \"REPLY = '$REPLY'\" 上面例子中，先显示Enter one or more values >，再接受用户的输入。 （3）-a 参数 -a参数把用户的输入赋值给一个数组，从零号位置开始。 $ read -a people alice duchess dodo $ echo ${people[2]} dodo 上面例子中，用户输入被赋值给一个数组people，这个数组的 2 号成员就是dodo。 （4）-n 参数 -n参数指定只读取若干个字符作为变量值，而不是整行读取。 $ read -n 3 letter abcdefghij $ echo $letter abc 上面例子中，变量letter只包含 3 个字母。 （5）-e 参数 -e参数允许用户输入的时候，使用readline库提供的快捷键，比如自动补全。具体的快捷键可以参阅《行操作》一章。 #!/bin/bash echo Please input the path to the file: read -e fileName echo $fileName 上面例子中，read命令接受用户输入的文件名。这时，用户可能想使用 Tab 键的文件名“自动补全”功能，但是read命令的输入默认不支持readline库的功能。-e参数就可以允许用户使用自动补全。 （6）其他参数 -d delimiter：定义字符串delimiter的第一个字符作为用户输入的结束，而不是一个换行符。 -r：raw 模式，表示不把用户输入的反斜杠字符解释为转义字符。 -s：使得用户的输入不显示在屏幕上，这常常用于输入密码或保密信息。 -u fd：使用文件描述符fd作为输入。","s":"参数","u":"/docs/modern-linux/bash-tutorial/read","h":"#参数","p":1762},{"i":1768,"t":"read命令读取的值，默认是以空格分隔。可以通过自定义环境变量IFS（内部字段分隔符，Internal Field Separator 的缩写），修改分隔标志。 IFS的默认值是空格、Tab 符号、换行符号，通常取第一个（即空格）。 如果把IFS定义成冒号（:）或分号（;），就可以分隔以这两个符号分隔的值，这对读取文件很有用。 #!/bin/bash # read-ifs: read fields from a file FILE=/etc/passwd read -p \"Enter a username > \" user_name file_info=\"$(grep \"^$user_name:\" $FILE)\" if [ -n \"$file_info\" ]; then IFS=\":\" read user pw uid gid name home shell <<< \"$file_info\" echo \"User = '$user'\" echo \"UID = '$uid'\" echo \"GID = '$gid'\" echo \"Full Name = '$name'\" echo \"Home Dir. = '$home'\" echo \"Shell = '$shell'\" else echo \"No such user '$user_name'\" >&2 exit 1 fi 上面例子中，IFS设为冒号，然后用来分解/etc/passwd文件的一行。IFS的赋值命令和read命令写在一行，这样的话，IFS的改变仅对后面的命令生效，该命令执行后IFS会自动恢复原来的值。如果不写在一行，就要采用下面的写法。 OLD_IFS=\"$IFS\" IFS=\":\" read user pw uid gid name home shell <<< \"$file_info\" IFS=\"$OLD_IFS\" 另外，上面例子中，<<<是 Here 字符串，用于将变量值转为标准输入，因为read命令只能解析标准输入。 如果IFS设为空字符串，就等同于将整行读入一个变量。 #!/bin/bash input=\"/path/to/txt/file\" while IFS= read -r line do echo \"$line\" done < \"$input\" 上面的命令可以逐行读取文件，每一行存入变量line，打印出来以后再读取下一行。","s":"IFS 变量","u":"/docs/modern-linux/bash-tutorial/read","h":"#ifs-变量","p":1762},{"i":1770,"t":"脚本（script）就是包含一系列命令的一个文本文件。Shell 读取这个文件，依次执行里面的所有命令，就好像这些命令直接输入到命令行一样。所有能够在命令行完成的任务，都能够用脚本完成。 脚本的好处是可以重复使用，也可以指定在特定场合自动调用，比如系统启动或关闭时自动执行脚本。","s":"Bash 脚本入门","u":"/docs/modern-linux/bash-tutorial/script","h":"","p":1769},{"i":1772,"t":"脚本的第一行通常是指定解释器，即这个脚本必须通过什么解释器执行。这一行以#!字符开头，这个字符称为 Shebang，所以这一行就叫做 Shebang 行。 #!后面就是脚本解释器的位置，Bash 脚本的解释器一般是/bin/sh或/bin/bash。 #!/bin/sh # 或者 #!/bin/bash #!与脚本解释器之间有没有空格，都是可以的。 如果 Bash 解释器不放在目录/bin，脚本就无法执行了。为了保险，可以写成下面这样。 #!/usr/bin/env bash 上面命令使用env命令（这个命令总是在/usr/bin目录），返回 Bash 可执行文件的位置。env命令的详细介绍，请看后文。 Shebang 行不是必需的，但是建议加上这行。如果缺少该行，就需要手动将脚本传给解释器。举例来说，脚本是script.sh，有 Shebang 行的时候，可以直接调用执行。 $ ./script.sh 上面例子中，script.sh是脚本文件名。脚本通常使用.sh后缀名，不过这不是必需的。 如果没有 Shebang 行，就只能手动将脚本传给解释器来执行。 $ /bin/sh ./script.sh # 或者 $ bash ./script.sh","s":"Shebang 行","u":"/docs/modern-linux/bash-tutorial/script","h":"#shebang-行","p":1769},{"i":1774,"t":"前面说过，只要指定了 Shebang 行的脚本，可以直接执行。这有一个前提条件，就是脚本需要有执行权限。可以使用下面的命令，赋予脚本执行权限。 # 给所有用户执行权限 $ chmod +x script.sh # 给所有用户读权限和执行权限 $ chmod +rx script.sh # 或者 $ chmod 755 script.sh # 只给脚本拥有者读权限和执行权限 $ chmod u+rx script.sh 脚本的权限通常设为755（拥有者有所有权限，其他人有读和执行权限）或者700（只有拥有者可以执行）。 除了执行权限，脚本调用时，一般需要指定脚本的路径（比如path/script.sh）。如果将脚本放在环境变量$PATH指定的目录中，就不需要指定路径了。因为 Bash 会自动到这些目录中，寻找是否存在同名的可执行文件。 建议在主目录新建一个~/bin子目录，专门存放可执行脚本，然后把~/bin加入$PATH。 export PATH=$PATH:~/bin 上面命令改变环境变量$PATH，将~/bin添加到$PATH的末尾。可以将这一行加到~/.bashrc文件里面，然后重新加载一次.bashrc，这个配置就可以生效了。 $ source ~/.bashrc 以后不管在什么目录，直接输入脚本文件名，脚本就会执行。 $ script.sh 上面命令没有指定脚本路径，因为script.sh在$PATH指定的目录中。","s":"执行权限和路径","u":"/docs/modern-linux/bash-tutorial/script","h":"#执行权限和路径","p":1769},{"i":1776,"t":"env命令总是指向/usr/bin/env文件，或者说，这个二进制文件总是在目录/usr/bin。 #!/usr/bin/env NAME这个语法的意思是，让 Shell 查找$PATH环境变量里面第一个匹配的NAME。如果你不知道某个命令的具体路径，或者希望兼容其他用户的机器，这样的写法就很有用。 /usr/bin/env bash的意思就是，返回bash可执行文件的位置，前提是bash的路径是在$PATH里面。其他脚本文件也可以使用这个命令。比如 Node.js 脚本的 Shebang 行，可以写成下面这样。 #!/usr/bin/env node env命令的参数如下。 -i, --ignore-environment：不带环境变量启动。 -u, --unset=NAME：从环境变量中删除一个变量。 --help：显示帮助。 --version：输出版本信息。 下面是一个例子，新建一个不带任何环境变量的 Shell。 $ env -i /bin/sh","s":"env 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#env-命令","p":1769},{"i":1778,"t":"Bash 脚本中，#表示注释，可以放在行首，也可以放在行尾。 # 本行是注释 echo 'Hello World!' echo 'Hello World!' # 井号后面的部分也是注释 建议在脚本开头，使用注释说明当前脚本的作用，这样有利于日后的维护。","s":"注释","u":"/docs/modern-linux/bash-tutorial/script","h":"#注释","p":1769},{"i":1780,"t":"调用脚本的时候，脚本文件名后面可以带有参数。 $ script.sh word1 word2 word3 上面例子中，script.sh是一个脚本文件，word1、word2和word3是三个参数。 脚本文件内部，可以使用特殊变量，引用这些参数。 $0：脚本文件名，即script.sh。 $1~$9：对应脚本的第一个参数到第九个参数。 $#：参数的总数。 $@：全部的参数，参数之间使用空格分隔。 $*：全部的参数，参数之间使用变量$IFS值的第一个字符分隔，默认为空格，但是可以自定义。 如果脚本的参数多于 9 个，那么第 10 个参数可以用${10}的形式引用，以此类推。 注意，如果命令是command -o foo bar，那么-o是$1，foo是$2，bar是$3。 下面是一个脚本内部读取命令行参数的例子。 #!/bin/bash # script.sh echo \"全部参数：\" $@ echo \"命令行参数数量：\" $# echo '$0 = ' $0 echo '$1 = ' $1 echo '$2 = ' $2 echo '$3 = ' $3 执行结果如下。 $ ./script.sh a b c 全部参数：a b c 命令行参数数量：3 $0 = script.sh $1 = a $2 = b $3 = c 用户可以输入任意数量的参数，利用for循环，可以读取每一个参数。 #!/bin/bash for i in \"$@\"; do echo $i done 上面例子中，$@返回一个全部参数的列表，然后使用for循环遍历。 如果多个参数放在双引号里面，视为一个参数。 $ ./script.sh \"a b\" 上面例子中，Bash 会认为\"a b\"是一个参数，$1会返回a b。注意，返回时不包括双引号。","s":"脚本参数","u":"/docs/modern-linux/bash-tutorial/script","h":"#脚本参数","p":1769},{"i":1782,"t":"shift命令可以改变脚本参数，每次执行都会移除脚本当前的第一个参数（$1），使得后面的参数向前一位，即$2变成$1、$3变成$2、$4变成$3，以此类推。 while循环结合shift命令，也可以读取每一个参数。 #!/bin/bash echo \"一共输入了 $# 个参数\" while [ \"$1\" != \"\" ]; do echo \"剩下 $# 个参数\" echo \"参数：$1\" shift done 上面例子中，shift命令每次移除当前第一个参数，从而通过while循环遍历所有参数。 shift命令可以接受一个整数作为参数，指定所要移除的参数个数，默认为1。 shift 3 上面的命令移除前三个参数，原来的$4变成$1。","s":"shift 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#shift-命令","p":1769},{"i":1784,"t":"getopts命令用在脚本内部，可以解析复杂的脚本命令行参数，通常与while循环一起使用，取出脚本所有的带有前置连词线（-）的参数。 getopts optstring name 它带有两个参数。第一个参数optstring是字符串，给出脚本所有的连词线参数。比如，某个脚本可以有三个配置项参数-l、-h、-a，其中只有-a可以带有参数值，而-l和-h是开关参数，那么getopts的第一个参数写成lha:，顺序不重要。注意，a后面有一个冒号，表示该参数带有参数值，getopts规定带有参数值的配置项参数，后面必须带有一个冒号（:）。getopts的第二个参数name是一个变量名，用来保存当前取到的配置项参数，即l、h或a。 下面是一个例子。 while getopts 'lha:' OPTION; do case \"$OPTION\" in l) echo \"linuxconfig\" ;; h) echo \"h stands for h\" ;; a) avalue=\"$OPTARG\" echo \"The value provided is $OPTARG\" ;; ?) echo \"script usage: $(basename $0) [-l] [-h] [-a somevalue]\" >&2 exit 1 ;; esac done shift \"$(($OPTIND - 1))\" 上面例子中，while循环不断执行getopts 'lha:' OPTION命令，每次执行就会读取一个连词线参数（以及对应的参数值），然后进入循环体。变量OPTION保存的是，当前处理的那一个连词线参数（即l、h或a）。如果用户输入了没有指定的参数（比如-x），那么OPTION等于?。循环体内使用case判断，处理这四种不同的情况。 如果某个连词线参数带有参数值，比如-a foo，那么处理a参数的时候，环境变量$OPTARG保存的就是参数值。 注意，只要遇到不带连词线的参数，getopts就会执行失败，从而退出while循环。比如，getopts可以解析command -l foo，但不可以解析command foo -l。另外，多个连词线参数写在一起的形式，比如command -lh，getopts也可以正确处理。 变量$OPTIND在getopts开始执行前是1，然后每次执行就会加1。等到退出while循环，就意味着连词线参数全部处理完毕。这时，$OPTIND - 1就是已经处理的连词线参数个数，使用shift命令将这些参数移除，保证后面的代码可以用$1、$2等处理命令的主参数。","s":"getopts 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#getopts-命令","p":1769},{"i":1786,"t":"-和--开头的参数，会被 Bash 当作配置项解释。但是，有时它们不是配置项，而是实体参数的一部分，比如文件名叫做-f或--file。 $ cat -f $ cat --file 上面命令的原意是输出文件-f和--file的内容，但是会被 Bash 当作配置项解释。 这时就可以使用配置项参数终止符--，它的作用是告诉 Bash，在它后面的参数开头的-和--不是配置项，只能当作实体参数解释。 $ cat -- -f $ cat -- --file 上面命令可以正确展示文件-f和--file的内容，因为它们放在--的后面，开头的-和--就不再当作配置项解释了。 如果要确保某个变量不会被当作配置项解释，就要在它前面放上参数终止符--。 $ ls -- $myPath 上面示例中，--强制变量$myPath只能当作实体参数（即路径名）解释。如果变量不是路径名，就会报错。 $ myPath=\"-l\" $ ls -- $myPath ls: 无法访问'-l': 没有那个文件或目录 上面例子中，变量myPath的值为-l，不是路径。但是，--强制$myPath只能作为路径解释，导致报错“不存在该路径”。 下面是另一个实际的例子，如果想在文件里面搜索--hello，这时也要使用参数终止符--。 $ grep -- \"--hello\" example.txt 上面命令在example.txt文件里面，搜索字符串--hello。这个字符串是--开头，如果不用参数终止符，grep命令就会把--hello当作配置项参数，从而报错。","s":"配置项参数终止符 --","u":"/docs/modern-linux/bash-tutorial/script","h":"#配置项参数终止符---","p":1769},{"i":1788,"t":"exit命令用于终止当前脚本的执行，并向 Shell 返回一个退出值。 $ exit 上面命令中止当前脚本，将最后一条命令的退出状态，作为整个脚本的退出状态。 exit命令后面可以跟参数，该参数就是退出状态。 # 退出值为0（成功） $ exit 0 # 退出值为1（失败） $ exit 1 退出时，脚本会返回一个退出值。脚本的退出值，0表示正常，1表示发生错误，2表示用法不对，126表示不是可执行脚本，127表示命令没有发现。如果脚本被信号N终止，则退出值为128 + N。简单来说，只要退出值非 0，就认为执行出错。 下面是一个例子。 if [ $(id -u) != \"0\" ]; then echo \"根用户才能执行当前脚本\" exit 1 fi 上面的例子中，id -u命令返回用户的 ID，一旦用户的 ID 不等于0（根用户的 ID），脚本就会退出，并且退出码为1，表示运行失败。 exit与return命令的差别是，return命令是函数的退出，并返回一个值给调用者，脚本依然执行。exit是整个脚本的退出，如果在函数之中调用exit，则退出函数，并终止脚本执行。","s":"exit 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#exit-命令","p":1769},{"i":1790,"t":"命令执行结束后，会有一个返回值。0表示执行成功，非0（通常是1）表示执行失败。环境变量$?可以读取前一个命令的返回值。 利用这一点，可以在脚本中对命令执行结果进行判断。 cd /path/to/somewhere if [ \"$?\" = \"0\" ]; then rm * else echo \"无法切换目录！\" 1>&2 exit 1 fi 上面例子中，cd /path/to/somewhere这个命令如果执行成功（返回值等于0），就删除该目录里面的文件，否则退出脚本，整个脚本的返回值变为1，表示执行失败。 由于if可以直接判断命令的执行结果，执行相应的操作，上面的脚本可以改写成下面的样子。 if cd /path/to/somewhere; then rm * else echo \"Could not change directory! Aborting.\" 1>&2 exit 1 fi 更简洁的写法是利用两个逻辑运算符&&（且）和||（或）。 # 第一步执行成功，才会执行第二步 cd /path/to/somewhere && rm * # 第一步执行失败，才会执行第二步 cd /path/to/somewhere || exit 1","s":"命令执行结果","u":"/docs/modern-linux/bash-tutorial/script","h":"#命令执行结果","p":1769},{"i":1792,"t":"source命令用于执行一个脚本，通常用于重新加载一个配置文件。 $ source .bashrc source命令最大的特点是在当前 Shell 执行脚本，不像直接执行脚本时，会新建一个子 Shell。所以，source命令执行脚本时，不需要export变量。 #!/bin/bash # test.sh echo $foo 上面脚本输出$foo变量的值。 # 当前 Shell 新建一个变量 foo $ foo=1 # 打印输出 1 $ source test.sh 1 # 打印输出空字符串 $ bash test.sh 上面例子中，当前 Shell 的变量foo并没有export，所以直接执行无法读取，但是source执行可以读取。 source命令的另一个用途，是在脚本内部加载外部库。 #!/bin/bash source ./lib.sh function_from_lib 上面脚本在内部使用source命令加载了一个外部库，然后就可以在脚本里面，使用这个外部库定义的函数。 source有一个简写形式，可以使用一个点（.）来表示。 $ . .bashrc","s":"source 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#source-命令","p":1769},{"i":1794,"t":"alias命令用来为一个命令指定别名，这样更便于记忆。下面是alias的格式。 alias NAME=DEFINITION 上面命令中，NAME是别名的名称，DEFINITION是别名对应的原始命令。注意，等号两侧不能有空格，否则会报错。 一个常见的例子是为grep命令起一个search的别名。 alias search=grep alias也可以用来为长命令指定一个更短的别名。下面是通过别名定义一个today的命令。 $ alias today='date +\"%A, %B %-d, %Y\"' $ today 星期一, 一月 6, 2020 有时为了防止误删除文件，可以指定rm命令的别名。 $ alias rm='rm -i' 上面命令指定rm命令是rm -i，每次删除文件之前，都会让用户确认。 alias定义的别名也可以接受参数，参数会直接传入原始命令。 $ alias echo='echo It says: ' $ echo hello world It says: hello world 上面例子中，别名定义了echo命令的前两个参数，等同于修改了echo命令的默认行为。 指定别名以后，就可以像使用其他命令一样使用别名。一般来说，都会把常用的别名写在~/.bashrc的末尾。另外，只能为命令定义别名，为其他部分（比如很长的路径）定义别名是无效的。 直接调用alias命令，可以显示所有别名。 $ alias unalias命令可以解除别名。 $ unalias lt","s":"别名，alias 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#别名alias-命令","p":1769},{"i":1796,"t":"How to use getopts to parse a script options, Egidio Docile","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/script","h":"#参考链接","p":1769},{"i":1798,"t":"set命令是 Bash 脚本的重要环节，却常常被忽视，导致脚本的安全性和可维护性出问题。本章介绍set的基本用法，帮助你写出更安全的 Bash 脚本。","s":"set 命令，shopt 命令","u":"/docs/modern-linux/bash-tutorial/set","h":"","p":1797},{"i":1800,"t":"我们知道，Bash 执行脚本时，会创建一个子 Shell。 $ bash script.sh 上面代码中，script.sh是在一个子 Shell 里面执行。这个子 Shell 就是脚本的执行环境，Bash 默认给定了这个环境的各种参数。 set命令用来修改子 Shell 环境的运行参数，即定制环境。一共有十几个参数可以定制，官方手册有完整清单，本章介绍其中最常用的几个。 顺便提一下，如果命令行下不带任何参数，直接运行set，会显示所有的环境变量和 Shell 函数。 $ set","s":"简介","u":"/docs/modern-linux/bash-tutorial/set","h":"#简介","p":1797},{"i":1802,"t":"执行脚本时，如果遇到不存在的变量，Bash 默认忽略它。 #!/usr/bin/env bash echo $a echo bar 上面代码中，$a是一个不存在的变量。执行结果如下。 $ bash script.sh bar 可以看到，echo $a输出了一个空行，Bash 忽略了不存在的$a，然后继续执行echo bar。大多数情况下，这不是开发者想要的行为，遇到变量不存在，脚本应该报错，而不是一声不响地往下执行。 set -u就用来改变这种行为。脚本在头部加上它，遇到不存在的变量就会报错，并停止执行。 #!/usr/bin/env bash set -u echo $a echo bar 运行结果如下。 $ bash script.sh bash: script.sh:行4: a: 未绑定的变量 可以看到，脚本报错了，并且不再执行后面的语句。 -u还有另一种写法-o nounset，两者是等价的。 set -o nounset","s":"set -u","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--u","p":1797},{"i":1804,"t":"默认情况下，脚本执行后，只输出运行结果，没有其他内容。如果多个命令连续执行，它们的运行结果就会连续输出。有时会分不清，某一段内容是什么命令产生的。 set -x用来在运行结果之前，先输出执行的那一行命令。 #!/usr/bin/env bash set -x echo bar 执行上面的脚本，结果如下。 $ bash script.sh + echo bar bar 可以看到，执行echo bar之前，该命令会先打印出来，行首以+表示。这对于调试复杂的脚本是很有用的。 -x还有另一种写法-o xtrace。 set -o xtrace 脚本当中如果要关闭命令输出，可以使用set +x。 #!/bin/bash number=1 set -x if [ $number = \"1\" ]; then echo \"Number equals 1\" else echo \"Number does not equal 1\" fi set +x 上面的例子中，只对特定的代码段打开命令输出。","s":"set -x","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--x","p":1797},{"i":1806,"t":"如果脚本里面有运行失败的命令（返回值非0），Bash 默认会继续执行后面的命令。 #!/usr/bin/env bash foo echo bar 上面脚本中，foo是一个不存在的命令，执行时会报错。但是，Bash 会忽略这个错误，继续往下执行。 $ bash script.sh script.sh:行3: foo: 未找到命令 bar 可以看到，Bash 只是显示有错误，并没有终止执行。 这种行为很不利于脚本安全和除错。实际开发中，如果某个命令失败，往往需要脚本停止执行，防止错误累积。这时，一般采用下面的写法。 command || exit 1 上面的写法表示只要command有非零返回值，脚本就会停止执行。 如果停止执行之前需要完成多个操作，就要采用下面三种写法。 # 写法一 command || { echo \"command failed\"; exit 1; } # 写法二 if ! command; then echo \"command failed\"; exit 1; fi # 写法三 command if [ \"$?\" -ne 0 ]; then echo \"command failed\"; exit 1; fi 另外，除了停止执行，还有一种情况。如果两个命令有继承关系，只有第一个命令成功了，才能继续执行第二个命令，那么就要采用下面的写法。 command1 && command2","s":"Bash 的错误处理","u":"/docs/modern-linux/bash-tutorial/set","h":"#bash-的错误处理","p":1797},{"i":1808,"t":"上面这些写法多少有些麻烦，容易疏忽。set -e从根本上解决了这个问题，它使得脚本只要发生错误，就终止执行。 #!/usr/bin/env bash set -e foo echo bar 执行结果如下。 $ bash script.sh script.sh:行4: foo: 未找到命令 可以看到，第 4 行执行失败以后，脚本就终止执行了。 set -e根据返回值来判断，一个命令是否运行失败。但是，某些命令的非零返回值可能不表示失败，或者开发者希望在命令失败的情况下，脚本继续执行下去。这时可以暂时关闭set -e，该命令执行结束后，再重新打开set -e。 set +e command1 command2 set -e 上面代码中，set +e表示关闭-e选项，set -e表示重新打开-e选项。 还有一种方法是使用command || true，使得该命令即使执行失败，脚本也不会终止执行。 #!/bin/bash set -e foo || true echo bar 上面代码中，true使得这一行语句总是会执行成功，后面的echo bar会执行。 -e还有另一种写法-o errexit。 set -o errexit","s":"set -e","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--e","p":1797},{"i":1810,"t":"set -e有一个例外情况，就是不适用于管道命令。 所谓管道命令，就是多个子命令通过管道运算符（|）组合成为一个大的命令。Bash 会把最后一个子命令的返回值，作为整个命令的返回值。也就是说，只要最后一个子命令不失败，管道命令总是会执行成功，因此它后面命令依然会执行，set -e就失效了。 请看下面这个例子。 #!/usr/bin/env bash set -e foo | echo a echo bar 执行结果如下。 $ bash script.sh a script.sh:行4: foo: 未找到命令 bar 上面代码中，foo是一个不存在的命令，但是foo | echo a这个管道命令会执行成功，导致后面的echo bar会继续执行。 set -o pipefail用来解决这种情况，只要一个子命令失败，整个管道命令就失败，脚本就会终止执行。 #!/usr/bin/env bash set -eo pipefail foo | echo a echo bar 运行后，结果如下。 $ bash script.sh a script.sh:行4: foo: 未找到命令 可以看到，echo bar没有执行。","s":"set -o pipefail","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--o-pipefail","p":1797},{"i":1812,"t":"一旦设置了-e参数，会导致函数内的错误不会被trap命令捕获（参考《trap 命令》一章）。-E参数可以纠正这个行为，使得函数也能继承trap命令。 #!/bin/bash set -e trap \"echo ERR trap fired!\" ERR myfunc() { # 'foo' 是一个不存在的命令 foo } myfunc 上面示例中，myfunc函数内部调用了一个不存在的命令foo，导致执行这个函数会报错。 $ bash test.sh test.sh:行9: foo：未找到命令 但是，由于设置了set -e，函数内部的报错并没有被trap命令捕获，需要加上-E参数才可以。 #!/bin/bash set -Eeuo pipefail trap \"echo ERR trap fired!\" ERR myfunc() { # 'foo' 是一个不存在的命令 foo } myfunc 执行上面这个脚本，就可以看到trap命令生效了。 $ bash test.sh test.sh:行9: foo：未找到命令 ERR trap fired!","s":"set -E","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--e-1","p":1797},{"i":1814,"t":"set命令还有一些其他参数。 set -n：等同于set -o noexec，不运行命令，只检查语法是否正确。 set -f：等同于set -o noglob，表示不对通配符进行文件名扩展。 set -v：等同于set -o verbose，表示打印 Shell 接收到的每一行输入。 set -o noclobber：防止使用重定向运算符>覆盖已经存在的文件。 上面的-f和-v参数，可以分别使用set +f、set +v关闭。","s":"其他参数","u":"/docs/modern-linux/bash-tutorial/set","h":"#其他参数","p":1797},{"i":1816,"t":"上面重点介绍的set命令的几个参数，一般都放在一起使用。 # 写法一 set -Eeuxo pipefail # 写法二 set -Eeux set -o pipefail 这两种写法建议放在所有 Bash 脚本的头部。 另一种办法是在执行 Bash 脚本的时候，从命令行传入这些参数。 $ bash -euxo pipefail script.sh","s":"set 命令总结","u":"/docs/modern-linux/bash-tutorial/set","h":"#set-命令总结","p":1797},{"i":1818,"t":"shopt命令用来调整 Shell 的参数，跟set命令的作用很类似。之所以会有这两个类似命令的主要原因是，set是从 Ksh 继承的，属于 POSIX 规范的一部分，而shopt是 Bash 特有的。 直接输入shopt可以查看所有参数，以及它们各自打开和关闭的状态。 $ shopt shopt命令后面跟着参数名，可以查询该参数是否打开。 $ shopt globstar globstar off 上面例子表示globstar参数默认是关闭的。 （1）-s -s用来打开某个参数。 $ shopt -s optionNameHere （2）-u -u用来关闭某个参数。 $ shopt -u optionNameHere 举例来说，histappend这个参数表示退出当前 Shell 时，将操作历史追加到历史文件中。这个参数默认是打开的，如果使用下面的命令将其关闭，那么当前 Shell 的操作历史将替换掉整个历史文件。 $ shopt -u histappend （3）-q -q的作用也是查询某个参数是否打开，但不是直接输出查询结果，而是通过命令的执行状态（$?）表示查询结果。如果状态为0，表示该参数打开；如果为1，表示该参数关闭。 $ shopt -q globstar $ echo $? 1 上面命令查询globstar参数是否打开。返回状态为1，表示该参数是关闭的。 这个用法主要用于脚本，供if条件结构使用。下面例子是如果打开了这个参数，就执行if结构内部的语句。 if (shopt -q globstar); then ... fi","s":"shopt 命令","u":"/docs/modern-linux/bash-tutorial/set","h":"#shopt-命令","p":1797},{"i":1820,"t":"The Set Builtin Safer bash scripts with 'set -euxo pipefail' Writing Robust Bash Shell Scripts","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/set","h":"#参考链接","p":1797},{"i":1822,"t":"为了方便用户在不同目录之间切换，Bash 提供了目录堆栈功能。","s":"目录堆栈","u":"/docs/modern-linux/bash-tutorial/stack","h":"","p":1821},{"i":1824,"t":"Bash 可以记忆用户进入过的目录。默认情况下，只记忆前一次所在的目录，cd -命令可以返回前一次的目录。 # 当前目录是 /path/to/foo $ cd bar # 重新回到 /path/to/foo $ cd - 上面例子中，用户原来所在的目录是/path/to/foo，进入子目录bar以后，使用cd -可以回到原来的目录。","s":"cd -","u":"/docs/modern-linux/bash-tutorial/stack","h":"#cd--","p":1821},{"i":1826,"t":"如果希望记忆多重目录，可以使用pushd命令和popd命令。它们用来操作目录堆栈。 pushd命令的用法类似cd命令，可以进入指定的目录。 $ pushd dirname 上面命令会进入目录dirname，并将该目录放入堆栈。 第一次使用pushd命令时，会将当前目录先放入堆栈，然后将所要进入的目录也放入堆栈，位置在前一个记录的上方。以后每次使用pushd命令，都会将所要进入的目录，放在堆栈的顶部。 popd命令不带有参数时，会移除堆栈的顶部记录，并进入新的栈顶目录（即原来的第二条目录）。 下面是一个例子。 # 当前处在主目录，堆栈为空 $ pwd /home/me # 进入 /home/me/foo # 当前堆栈为 /home/me/foo /home/me $ pushd ~/foo # 进入 /etc # 当前堆栈为 /etc /home/me/foo /home/me $ pushd /etc # 进入 /home/me/foo # 当前堆栈为 /home/me/foo /home/me $ popd # 进入 /home/me # 当前堆栈为 /home/me $ popd # 目录不变，当前堆栈为空 $ popd 这两个命令的参数如下。 （1）-n 参数 -n的参数表示仅操作堆栈，不改变目录。 $ popd -n 上面的命令仅删除堆栈顶部的记录，不改变目录，执行完成后还停留在当前目录。 （2）整数参数 这两个命令还可以接受一个整数作为参数，该整数表示堆栈中指定位置的记录（从 0 开始）。pushd命令会把这条记录移动到栈顶，同时切换到该目录；popd则从堆栈中删除这条记录，不会切换目录。 # 将从栈顶算起的3号目录（从0开始）移动到栈顶，同时切换到该目录 $ pushd +3 # 将从栈底算起的3号目录（从0开始）移动到栈顶，同时切换到该目录 $ pushd -3 # 删除从栈顶算起的3号目录（从0开始），不改变当前目录 $ popd +3 # 删除从栈底算起的3号目录（从0开始），不改变当前目录 $ popd -3 上面例子的整数编号都是从 0 开始计算，popd +0是删除第一个目录，popd +1是删除第二个，popd -0是删除最后一个目录，popd -1是删除倒数第二个。 （3）目录参数 pushd可以接受一个目录作为参数，表示将该目录放到堆栈顶部，并进入该目录。 $ pushd dir popd没有这个参数。","s":"pushd，popd","u":"/docs/modern-linux/bash-tutorial/stack","h":"#pushdpopd","p":1821},{"i":1828,"t":"dirs命令可以显示目录堆栈的内容，一般用来查看pushd和popd操作后的结果。 $ dirs ~/foo/bar ~/foo ~ 该命令会输出一行文本，列出目录堆栈，目录之间使用空格分隔。栈顶（最晚入栈的目录）在最左边，栈底（最早入栈的目录）在最右边。 它有以下参数。 -c：清空目录栈。 -l：用户主目录不显示波浪号前缀，而打印完整的目录。 -p：每行一个条目打印目录栈，默认是打印在一行。 -v：每行一个条目，每个条目之前显示位置编号（从 0 开始）。 +N：N为整数，表示显示堆顶算起的第 N 个目录，从零开始。 -N：N为整数，表示显示堆底算起的第 N 个目录，从零开始。","s":"dirs 命令","u":"/docs/modern-linux/bash-tutorial/stack","h":"#dirs-命令","p":1821},{"i":1831,"t":"用户每次使用 Shell，都会开启一个与 Shell 的 Session（对话）。 Session 有两种类型：登录 Session 和非登录 Session，也可以叫做 login shell 和 non-login shell。","s":"Session","u":"/docs/modern-linux/bash-tutorial/startup","h":"#session","p":1829},{"i":1833,"t":"登录 Session 是用户登录系统以后，系统为用户开启的原始 Session，通常需要用户输入用户名和密码进行登录。 登录 Session 一般进行整个系统环境的初始化，启动的初始化脚本依次如下。 /etc/profile：所有用户的全局配置脚本。 /etc/profile.d目录里面所有.sh文件 ~/.bash_profile：用户的个人配置脚本。如果该脚本存在，则执行完就不再往下执行。 ~/.bash_login：如果~/.bash_profile没找到，则尝试执行这个脚本（C shell 的初始化脚本）。如果该脚本存在，则执行完就不再往下执行。 ~/.profile：如果~/.bash_profile和~/.bash_login都没找到，则尝试读取这个脚本（Bourne shell 和 Korn shell 的初始化脚本）。 Linux 发行版更新的时候，会更新/etc里面的文件，比如/etc/profile，因此不要直接修改这个文件。如果想修改所有用户的登陆环境，就在/etc/profile.d目录里面新建.sh脚本。 如果想修改你个人的登录环境，一般是写在~/.bash_profile里面。下面是一个典型的.bash_profile文件。 # .bash_profile PATH=/sbin:/usr/sbin:/bin:/usr/bin:/usr/local/bin PATH=$PATH:$HOME/bin SHELL=/bin/bash MANPATH=/usr/man:/usr/X11/man EDITOR=/usr/bin/vi PS1='\\h:\\w\\$ ' PS2='> ' if [ -f ~/.bashrc ]; then . ~/.bashrc fi export PATH export EDITOR 可以看到，这个脚本定义了一些最基本的环境变量，然后执行了~/.bashrc。 bash命令的--login参数，会强制执行登录 Session 会执行的脚本。 $ bash --login bash命令的--noprofile参数，会跳过上面这些 Profile 脚本。 $ bash --noprofile","s":"登录 Session","u":"/docs/modern-linux/bash-tutorial/startup","h":"#登录-session","p":1829},{"i":1835,"t":"非登录 Session 是用户进入系统以后，手动新建的 Session，这时不会进行环境初始化。比如，在命令行执行bash命令，就会新建一个非登录 Session。 非登录 Session 的初始化脚本依次如下。 /etc/bash.bashrc：对全体用户有效。 ~/.bashrc：仅对当前用户有效。 对用户来说，~/.bashrc通常是最重要的脚本。非登录 Session 默认会执行它，而登录 Session 一般也会通过调用执行它。每次新建一个 Bash 窗口，就相当于新建一个非登录 Session，所以~/.bashrc每次都会执行。注意，执行脚本相当于新建一个非互动的 Bash 环境，但是这种情况不会调用~/.bashrc。 bash命令的--norc参数，可以禁止在非登录 Session 执行~/.bashrc脚本。 $ bash --norc bash命令的--rcfile参数，指定另一个脚本代替.bashrc。 $ bash --rcfile testrc","s":"非登录 Session","u":"/docs/modern-linux/bash-tutorial/startup","h":"#非登录-session","p":1829},{"i":1837,"t":"~/.bash_logout脚本在每次退出 Session 时执行，通常用来做一些清理工作和记录工作，比如删除临时文件，记录用户在本次 Session 花费的时间。 如果没有退出时要执行的命令，这个文件也可以不存在。","s":".bash_logout","u":"/docs/modern-linux/bash-tutorial/startup","h":"#bash_logout","p":1829},{"i":1839,"t":"为了方便 Debug，有时在启动 Bash 的时候，可以加上启动参数。 -n：不运行脚本，只检查是否有语法错误。 -v：输出每一行语句运行结果前，会先输出该行语句。 -x：每一个命令处理之前，先输出该命令，再执行该命令。 $ bash -n scriptname $ bash -v scriptname $ bash -x scriptname","s":"启动选项","u":"/docs/modern-linux/bash-tutorial/startup","h":"#启动选项","p":1829},{"i":1841,"t":"Bash 允许用户定义自己的快捷键。全局的键盘绑定文件默认为/etc/inputrc，你可以在主目录创建自己的键盘绑定文件.inputrc文件。如果定义了这个文件，需要在其中加入下面这行，保证全局绑定不会被遗漏。 $include /etc/inputrc .inputrc文件里面的快捷键，可以像这样定义，\"\\C-t\":\"pwd\\n\"表示将Ctrl + t绑定为运行pwd命令。","s":"键盘绑定","u":"/docs/modern-linux/bash-tutorial/startup","h":"#键盘绑定","p":1829},{"i":1843,"t":"本章介绍 Bash 字符串操作的语法。","s":"字符串操作","u":"/docs/modern-linux/bash-tutorial/string","h":"","p":1842},{"i":1845,"t":"获取字符串长度的语法如下。 ${#varname} 下面是一个例子。 $ myPath=/home/cam/book/long.file.name $ echo ${#myPath} 29 大括号{}是必需的，否则 Bash 会将$#理解成脚本的参数个数，将变量名理解成文本。 $ echo $#myvar 0myvar 上面例子中，Bash 将$#和myvar分开解释了。","s":"字符串的长度","u":"/docs/modern-linux/bash-tutorial/string","h":"#字符串的长度","p":1842},{"i":1847,"t":"字符串提取子串的语法如下。 ${varname:offset:length} 上面语法的含义是返回变量$varname的子字符串，从位置offset开始（从0开始计算），长度为length。 $ count=frogfootman $ echo ${count:4:4} foot 上面例子返回字符串frogfootman从 4 号位置开始的长度为 4 的子字符串foot。 这种语法不能直接操作字符串，只能通过变量来读取字符串，并且不会改变原始字符串。 # 报错 $ echo ${\"hello\":2:3} 上面例子中，\"hello\"不是变量名，导致 Bash 报错。 如果省略length，则从位置offset开始，一直返回到字符串的结尾。 $ count=frogfootman $ echo ${count:4} footman 上面例子是返回变量count从 4 号位置一直到结尾的子字符串。 如果offset为负值，表示从字符串的末尾开始算起。注意，负数前面必须有一个空格，以防止与${variable:-word}的变量的设置默认值语法混淆。这时还可以指定length，length可以是正值，也可以是负值（负值不能超过offset的长度）。 $ foo=\"This string is long.\" $ echo ${foo: -5} long. $ echo ${foo: -5:2} lo $ echo ${foo: -5:-2} lon 上面例子中，offset为-5，表示从倒数第 5 个字符开始截取，所以返回long.。如果指定长度length为2，则返回lo；如果length为-2，表示要排除从字符串末尾开始的 2 个字符，所以返回lon。","s":"子字符串","u":"/docs/modern-linux/bash-tutorial/string","h":"#子字符串","p":1842},{"i":1849,"t":"Bash 提供字符串搜索和替换的多种方法。 （1）字符串头部的模式匹配。 以下两种语法可以检查字符串开头，是否匹配给定的模式。如果匹配成功，就删除匹配的部分，返回剩下的部分。原始变量不会发生变化。 # 如果 pattern 匹配变量 variable 的开头， # 删除最短匹配（非贪婪匹配）的部分，返回剩余部分 ${variable#pattern} # 如果 pattern 匹配变量 variable 的开头， # 删除最长匹配（贪婪匹配）的部分，返回剩余部分 ${variable##pattern} 上面两种语法会删除变量字符串开头的匹配部分（将其替换为空），返回剩下的部分。区别是一个是最短匹配（又称非贪婪匹配），另一个是最长匹配（又称贪婪匹配）。 匹配模式pattern可以使用*、?、[]等通配符。 $ myPath=/home/cam/book/long.file.name $ echo ${myPath#/*/} cam/book/long.file.name $ echo ${myPath##/*/} long.file.name 上面例子中，匹配的模式是/*/，其中*可以匹配任意数量的字符，所以最短匹配是/home/，最长匹配是/home/cam/book/。 下面写法可以删除文件路径的目录部分，只留下文件名。 $ path=/home/cam/book/long.file.name $ echo ${path##*/} long.file.name 上面例子中，模式*/匹配目录部分，所以只返回文件名。 下面再看一个例子。 $ phone=\"555-456-1414\" $ echo ${phone#*-} 456-1414 $ echo ${phone##*-} 1414 如果匹配不成功，则返回原始字符串。 $ phone=\"555-456-1414\" $ echo ${phone#444} 555-456-1414 上面例子中，原始字符串里面无法匹配模式444，所以原样返回。 如果要将头部匹配的部分，替换成其他内容，采用下面的写法。 # 模式必须出现在字符串的开头 ${variable/#pattern/string} # 示例 $ foo=JPG.JPG $ echo ${foo/#JPG/jpg} jpg.JPG 上面例子中，被替换的JPG必须出现在字符串头部，所以返回jpg.JPG。 （2）字符串尾部的模式匹配。 以下两种语法可以检查字符串结尾，是否匹配给定的模式。如果匹配成功，就删除匹配的部分，返回剩下的部分。原始变量不会发生变化。 # 如果 pattern 匹配变量 variable 的结尾， # 删除最短匹配（非贪婪匹配）的部分，返回剩余部分 ${variable%pattern} # 如果 pattern 匹配变量 variable 的结尾， # 删除最长匹配（贪婪匹配）的部分，返回剩余部分 ${variable%%pattern} 上面两种语法会删除变量字符串结尾的匹配部分（将其替换为空），返回剩下的部分。区别是一个是最短匹配（又称非贪婪匹配），另一个是最长匹配（又称贪婪匹配）。 $ path=/home/cam/book/long.file.name $ echo ${path%.*} /home/cam/book/long.file $ echo ${path%%.*} /home/cam/book/long 上面例子中，匹配模式是.*，其中*可以匹配任意数量的字符，所以最短匹配是.name，最长匹配是.file.name。 下面写法可以删除路径的文件名部分，只留下目录部分。 $ path=/home/cam/book/long.file.name $ echo ${path%/*} /home/cam/book 上面例子中，模式/*匹配文件名部分，所以只返回目录部分。 下面的写法可以替换文件的后缀名。 $ file=foo.png $ echo ${file%.png}.jpg foo.jpg 上面的例子将文件的后缀名，从.png改成了.jpg。 下面再看一个例子。 $ phone=\"555-456-1414\" $ echo ${phone%-*} 555-456 $ echo ${phone%%-*} 555 如果匹配不成功，则返回原始字符串。 如果要将尾部匹配的部分，替换成其他内容，采用下面的写法。 # 模式必须出现在字符串的结尾 ${variable/%pattern/string} # 示例 $ foo=JPG.JPG $ echo ${foo/%JPG/jpg} JPG.jpg 上面例子中，被替换的JPG必须出现在字符串尾部，所以返回JPG.jpg。 （3）任意位置的模式匹配。 以下两种语法可以检查字符串内部，是否匹配给定的模式。如果匹配成功，就删除匹配的部分，换成其他的字符串返回。原始变量不会发生变化。 # 如果 pattern 匹配变量 variable 的一部分， # 最长匹配（贪婪匹配）的那部分被 string 替换，但仅替换第一个匹配 ${variable/pattern/string} # 如果 pattern 匹配变量 variable 的一部分， # 最长匹配（贪婪匹配）的那部分被 string 替换，所有匹配都替换 ${variable//pattern/string} 上面两种语法都是最长匹配（贪婪匹配）下的替换，区别是前一个语法仅仅替换第一个匹配，后一个语法替换所有匹配。 $ path=/home/cam/foo/foo.name $ echo ${path/foo/bar} /home/cam/bar/foo.name $ echo ${path//foo/bar} /home/cam/bar/bar.name 上面例子中，前一个命令只替换了第一个foo，后一个命令将两个foo都替换了。 下面的例子将分隔符从:换成换行符。 $ echo -e ${PATH//:/'\\n'} /usr/local/bin /usr/bin /bin ... 上面例子中，echo命令的-e参数，表示将替换后的字符串的\\n字符，解释为换行符。 模式部分可以使用通配符。 $ phone=\"555-456-1414\" $ echo ${phone/5?4/-} 55-56-1414 上面的例子将5-4替换成-。 如果省略了string部分，那么就相当于匹配的部分替换成空字符串，即删除匹配的部分。 $ path=/home/cam/foo/foo.name $ echo ${path/.*/} /home/cam/foo/foo 上面例子中，第二个斜杠后面的string部分省略了，所以模式.*匹配的部分.name被删除后返回。 前面提到过，这个语法还有两种扩展形式。 # 模式必须出现在字符串的开头 ${variable/#pattern/string} # 模式必须出现在字符串的结尾 ${variable/%pattern/string}","s":"搜索和替换","u":"/docs/modern-linux/bash-tutorial/string","h":"#搜索和替换","p":1842},{"i":1851,"t":"下面的语法可以改变变量的大小写。 # 转为大写 ${varname^^} # 转为小写 ${varname,,} 下面是一个例子。 $ foo=heLLo $ echo ${foo^^} HELLO $ echo ${foo,,} hello","s":"改变大小写","u":"/docs/modern-linux/bash-tutorial/string","h":"#改变大小写","p":1842},{"i":1854,"t":"Bash 变量分成环境变量和自定义变量两类。","s":"简介","u":"/docs/modern-linux/bash-tutorial/variable","h":"#简介","p":1852},{"i":1856,"t":"环境变量是 Bash 环境自带的变量，进入 Shell 时已经定义好了，可以直接使用。它们通常是系统定义好的，也可以由用户从父 Shell 传入子 Shell。 env命令或printenv命令，可以显示所有环境变量。 $ env # 或者 $ printenv 下面是一些常见的环境变量。 BASHPID：Bash 进程的进程 ID。 BASHOPTS：当前 Shell 的参数，可以用shopt命令修改。 DISPLAY：图形环境的显示器名字，通常是:0，表示 X Server 的第一个显示器。 EDITOR：默认的文本编辑器。 HOME：用户的主目录。 HOST：当前主机的名称。 IFS：词与词之间的分隔符，默认为空格。 LANG：字符集以及语言编码，比如zh_CN.UTF-8。 PATH：由冒号分开的目录列表，当输入可执行程序名后，会搜索这个目录列表。 PS1：Shell 提示符。 PS2：输入多行命令时，次要的 Shell 提示符。 PWD：当前工作目录。 RANDOM：返回一个 0 到 32767 之间的随机数。 SHELL：Shell 的名字。 SHELLOPTS：启动当前 Shell 的set命令的参数，参见《set 命令》一章。 TERM：终端类型名，即终端仿真器所用的协议。 UID：当前用户的 ID 编号。 USER：当前用户的用户名。 很多环境变量很少发生变化，而且是只读的，可以视为常量。由于它们的变量名全部都是大写，所以传统上，如果用户要自己定义一个常量，也会使用全部大写的变量名。 注意，Bash 变量名区分大小写，HOME和home是两个不同的变量。 查看单个环境变量的值，可以使用printenv命令或echo命令。 $ printenv PATH # 或者 $ echo $PATH 注意，printenv命令后面的变量名，不用加前缀$。","s":"环境变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#环境变量","p":1852},{"i":1858,"t":"自定义变量是用户在当前 Shell 里面自己定义的变量，仅在当前 Shell 可用。一旦退出当前 Shell，该变量就不存在了。 set命令可以显示所有变量（包括环境变量和自定义变量），以及所有的 Bash 函数。 $ set","s":"自定义变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#自定义变量","p":1852},{"i":1860,"t":"用户创建变量的时候，变量名必须遵守下面的规则。 字母、数字和下划线字符组成。 第一个字符必须是一个字母或一个下划线，不能是数字。 不允许出现空格和标点符号。 变量声明的语法如下。 variable=value 上面命令中，等号左边是变量名，右边是变量。注意，等号两边不能有空格。 如果变量的值包含空格，则必须将值放在引号中。 myvar=\"hello world\" Bash 没有数据类型的概念，所有的变量值都是字符串。 下面是一些自定义变量的例子。 a=z # 变量 a 赋值为字符串 z b=\"a string\" # 变量值包含空格，就必须放在引号里面 c=\"a string and $b\" # 变量值可以引用其他变量的值 d=\"\\t\\ta string\\n\" # 变量值可以使用转义字符 e=$(ls -l foo.txt) # 变量值可以是命令的执行结果 f=$((5 * 7)) # 变量值可以是数学运算的结果 变量可以重复赋值，后面的赋值会覆盖前面的赋值。 $ foo=1 $ foo=2 $ echo $foo 2 上面例子中，变量foo的第二次赋值会覆盖第一次赋值。 如果同一行定义多个变量，必须使用分号（;）分隔。 $ foo=1;bar=2 上面例子中，同一行定义了foo和bar两个变量。","s":"创建变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#创建变量","p":1852},{"i":1862,"t":"读取变量的时候，直接在变量名前加上$就可以了。 $ foo=bar $ echo $foo bar 每当 Shell 看到以$开头的单词时，就会尝试读取这个变量名对应的值。 如果变量不存在，Bash 不会报错，而会输出空字符。 由于$在 Bash 中有特殊含义，把它当作美元符号使用时，一定要非常小心， $ echo The total is $100.00 The total is 00.00 上面命令的原意是输入$100，但是 Bash 将$1解释成了变量，该变量为空，因此输入就变成了00.00。所以，如果要使用$的原义，需要在$前面放上反斜杠，进行转义。 $ echo The total is \\$100.00 The total is $100.00 读取变量的时候，变量名也可以使用花括号{}包围，比如$a也可以写成${a}。这种写法可以用于变量名与其他字符连用的情况。 $ a=foo $ echo $a_file $ echo ${a}_file foo_file 上面代码中，变量名a_file不会有任何输出，因为 Bash 将其整个解释为变量，而这个变量是不存在的。只有用花括号区分$a，Bash 才能正确解读。 事实上，读取变量的语法$foo，可以看作是${foo}的简写形式。 如果变量的值本身也是变量，可以使用${!varname}的语法，读取最终的值。 $ myvar=USER $ echo ${!myvar} ruanyf 上面的例子中，变量myvar的值是USER，${!myvar}的写法将其展开成最终的值。 如果变量值包含连续空格（或制表符和换行符），最好放在双引号里面读取。 $ a=\"1 2 3\" $ echo $a 1 2 3 $ echo \"$a\" 1 2 3 上面示例中，变量a的值包含两个连续空格。如果直接读取，Shell 会将连续空格合并成一个。只有放在双引号里面读取，才能保持原来的格式。","s":"读取变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#读取变量","p":1852},{"i":1864,"t":"unset命令用来删除一个变量。 unset NAME 这个命令不是很有用。因为不存在的 Bash 变量一律等于空字符串，所以即使unset命令删除了变量，还是可以读取这个变量，值为空字符串。 所以，删除一个变量，也可以将这个变量设成空字符串。 $ foo='' $ foo= 上面两种写法，都是删除了变量foo。由于不存在的值默认为空字符串，所以后一种写法可以在等号右边不写任何值。","s":"删除变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#删除变量","p":1852},{"i":1866,"t":"用户创建的变量仅可用于当前 Shell，子 Shell 默认读取不到父 Shell 定义的变量。为了把变量传递给子 Shell，需要使用export命令。这样输出的变量，对于子 Shell 来说就是环境变量。 export命令用来向子 Shell 输出变量。 NAME=foo export NAME 上面命令输出了变量NAME。变量的赋值和输出也可以在一个步骤中完成。 export NAME=value 上面命令执行后，当前 Shell 及随后新建的子 Shell，都可以读取变量$NAME。 子 Shell 如果修改继承的变量，不会影响父 Shell。 # 输出变量 $foo $ export foo=bar # 新建子 Shell $ bash # 读取 $foo $ echo $foo bar # 修改继承的变量 $ foo=baz # 退出子 Shell $ exit # 读取 $foo $ echo $foo bar 上面例子中，子 Shell 修改了继承的变量$foo，对父 Shell 没有影响。","s":"输出变量，export 命令","u":"/docs/modern-linux/bash-tutorial/variable","h":"#输出变量export-命令","p":1852},{"i":1868,"t":"Bash 提供一些特殊变量。这些变量的值由 Shell 提供，用户不能进行赋值。 （1）$? $?为上一个命令的退出码，用来判断上一个命令是否执行成功。返回值是0，表示上一个命令执行成功；如果不是零，表示上一个命令执行失败。 $ ls doesnotexist ls: doesnotexist: No such file or directory $ echo $? 1 上面例子中，ls命令查看一个不存在的文件，导致报错。$?为 1，表示上一个命令执行失败。 （2）$$ $$为当前 Shell 的进程 ID。 $ echo $$ 10662 这个特殊变量可以用来命名临时文件。 LOGFILE=/tmp/output_log.$$ （3）$_ $_为上一个命令的最后一个参数。 $ grep dictionary /usr/share/dict/words dictionary $ echo $_ /usr/share/dict/words （4）$! $!为最近一个后台执行的异步命令的进程 ID。 $ firefox & [1] 11064 $ echo $! 11064 上面例子中，firefox是后台运行的命令，$!返回该命令的进程 ID。 （5）$0 $0为当前 Shell 的名称（在命令行直接执行时）或者脚本名（在脚本中执行时）。 $ echo $0 bash 上面例子中，$0返回当前运行的是 Bash。 （6）$- $-为当前 Shell 的启动参数。 $ echo $- himBHs （7）$@和$# $#表示脚本的参数数量，$@表示脚本的参数值，参见脚本一章。","s":"特殊变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#特殊变量","p":1852},{"i":1870,"t":"Bash 提供四个特殊语法，跟变量的默认值有关，目的是保证变量不为空。 ${varname:-word} 上面语法的含义是，如果变量varname存在且不为空，则返回它的值，否则返回word。它的目的是返回一个默认值，比如${count:-0}表示变量count不存在时返回0。 ${varname:=word} 上面语法的含义是，如果变量varname存在且不为空，则返回它的值，否则将它设为word，并且返回word。它的目的是设置变量的默认值，比如${count:=0}表示变量count不存在时返回0，且将count设为0。 ${varname:+word} 上面语法的含义是，如果变量名存在且不为空，则返回word，否则返回空值。它的目的是测试变量是否存在，比如${count:+1}表示变量count存在时返回1（表示true），否则返回空值。 ${varname:?message} 上面语法的含义是，如果变量varname存在且不为空，则返回它的值，否则打印出varname: message，并中断脚本的执行。如果省略了message，则输出默认的信息“parameter null or not set.”。它的目的是防止变量未定义，比如${count:?\"undefined!\"}表示变量count未定义时就中断执行，抛出错误，返回给定的报错信息undefined!。 上面四种语法如果用在脚本中，变量名的部分可以用数字1到9，表示脚本的参数。 filename=${1:?\"filename missing.\"} 上面代码出现在脚本中，1表示脚本的第一个参数。如果该参数不存在，就退出脚本并报错。","s":"变量的默认值","u":"/docs/modern-linux/bash-tutorial/variable","h":"#变量的默认值","p":1852},{"i":1872,"t":"declare命令可以声明一些特殊类型的变量，为变量设置一些限制，比如声明只读类型的变量和整数类型的变量。 它的语法形式如下。 declare OPTION VARIABLE=value declare命令的主要参数（OPTION）如下。 -a：声明数组变量。 -f：输出所有函数定义。 -F：输出所有函数名。 -i：声明整数变量。 -l：声明变量为小写字母。 -p：查看变量信息。 -r：声明只读变量。 -u：声明变量为大写字母。 -x：该变量输出为环境变量。 declare命令如果用在函数中，声明的变量只在函数内部有效，等同于local命令。 不带任何参数时，declare命令输出当前环境的所有变量，包括函数在内，等同于不带有任何参数的set命令。 $ declare （1）-i参数 -i参数声明整数变量以后，可以直接进行数学运算。 $ declare -i val1=12 val2=5 $ declare -i result $ result=val1*val2 $ echo $result 60 上面例子中，如果变量result不声明为整数，val1*val2会被当作字面量，不会进行整数运算。另外，val1和val2其实不需要声明为整数，因为只要result声明为整数，它的赋值就会自动解释为整数运算。 注意，一个变量声明为整数以后，依然可以被改写为字符串。 $ declare -i var=12 $ var=foo $ echo $var 0 上面例子中，变量var声明为整数，覆盖以后，Bash 不会报错，但会赋以不确定的值，上面的例子中可能输出 0，也可能输出的是 3。 （2）-x参数 -x参数等同于export命令，可以输出一个变量为子 Shell 的环境变量。 $ declare -x foo # 等同于 $ export foo （3）-r参数 -r参数可以声明只读变量，无法改变变量值，也不能unset变量。 $ declare -r bar=1 $ bar=2 bash: bar：只读变量 $ echo $? 1 $ unset bar bash: bar：只读变量 $ echo $? 1 上面例子中，后两个赋值语句都会报错，命令执行失败。 （4）-u参数 -u参数声明变量为大写字母，可以自动把变量值转成大写字母。 $ declare -u foo $ foo=upper $ echo $foo UPPER （5）-l参数 -l参数声明变量为小写字母，可以自动把变量值转成小写字母。 $ declare -l bar $ bar=LOWER $ echo $bar lower （6）-p参数 -p参数输出变量信息。 $ foo=hello $ declare -p foo declare -- foo=\"hello\" $ declare -p bar bar：未找到 上面例子中，declare -p可以输出已定义变量的值，对于未定义的变量，会提示找不到。 如果不提供变量名，declare -p输出所有变量的信息。 $ declare -p （7）-f参数 -f参数输出当前环境的所有函数，包括它的定义。 $ declare -f （8）-F参数 -F参数输出当前环境的所有函数名，不包含函数定义。 $ declare -F","s":"declare 命令","u":"/docs/modern-linux/bash-tutorial/variable","h":"#declare-命令","p":1852},{"i":1874,"t":"readonly命令等同于declare -r，用来声明只读变量，不能改变变量值，也不能unset变量。 $ readonly foo=1 $ foo=2 bash: foo：只读变量 $ echo $? 1 上面例子中，更改只读变量foo会报错，命令执行失败。 readonly命令有三个参数。 -f：声明的变量为函数名。 -p：打印出所有的只读变量。 -a：声明的变量为数组。","s":"readonly 命令","u":"/docs/modern-linux/bash-tutorial/variable","h":"#readonly-命令","p":1852},{"i":1876,"t":"let命令声明变量时，可以直接执行算术表达式。 $ let foo=1+2 $ echo $foo 3 上面例子中，let命令可以直接计算1 + 2。 let命令的参数表达式如果包含空格，就需要使用引号。 $ let \"foo = 1 + 2\" let可以同时对多个变量赋值，赋值表达式之间使用空格分隔。 $ let \"v1 = 1\" \"v2 = v1++\" $ echo $v1,$v2 2,1 上面例子中，let声明了两个变量v1和v2，其中v2等于v1++，表示先返回v1的值，然后v1自增。 这种语法支持的运算符，参考《Bash 的算术运算》一章。","s":"let 命令","u":"/docs/modern-linux/bash-tutorial/variable","h":"#let-命令","p":1852},{"i":1878,"t":"It is based on Ubuntu Latest LTS (currently 22.04) or ArchLinux. You can use these in WSL2.","s":"Modern Linux","u":"/docs/modern-linux/intro","h":"","p":1877},{"i":1880,"t":"For modern CLI Tools on x86_64 Linux distros, see: CLI Prebuilts. I'll recommend some best plugins I use frequently.","s":"Modern CLI Tools","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"","p":1879},{"i":1882,"t":"mise is a runtime manager to auto install and manager different software versions, like asdf, but much faster as it's built upon Rust. Suppose you need to use node version 21, but your distro do not support now. With mise, you can skip the procedure from downloading the package, build, and add to environment variable PATH; instead, you only need to: mise global node@21 Later in some day, you find some legacy projects and it's build upon node 18, you can simply do: mise local node@18 mise is compatible with asdf. you can see all supported plugins on asdf-plugins.","s":"mise","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#mise","p":1879},{"i":1884,"t":"Fast grep-like, git-aware code-search with colourized output, written in Rust. It’s a tool intended for performing blazing fast searches of your code, but unlike grep, it respects the patterns defined in your .gitignore file, and it doesn’t search your .git directory either. To search with rg, use: -t > rg md README README.md 1:# README black/README.md 974: Use the badge in your project README.md: 980: Using the badge in README.rst:","s":"rg","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#rg","p":1879},{"i":1886,"t":"Fast git-aware file searching with colourized output. fd is for find what Ripgrep is for grep: It searches filenames and respects your .gitignore patterns. But unlike the find command, the options are easy to remember. To search with filename: passwd > fd /etc /etc/default/passwd /etc/pam.d/passwd /etc/passwd To search all markdown files, use -e: -e > fd md CONTRIBUTING.md README.md","s":"fd","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#fd","p":1879},{"i":1888,"t":"fzf is a general-purpose command-line fuzzy finder. 备注 Suggest to install rg and fd before using fzf. It offers key bindings CTRL-T to search for filenames with fuzzy in an interactive way.","s":"fzf","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#fzf","p":1879},{"i":1890,"t":"eza and lsd are git-aware ls replacements with clever utilization of colour. eza is a fork of original project exa which is not under maintained anymore.","s":"eza or lsd.","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#eza-or-lsd","p":1879},{"i":1892,"t":"信息 I've created a dotfiles for multi softwares including multi configurations, see GitHub - ShangjinTang/dotfiles. You can clone it or take it as a dotfiles sample. Dotfiles are important files that will play an integral role in your career as a software developer. First, they can help make you more productive. But not only that - you'll be able to have that productive setup you created for youself on any machine. This article is an introduction on how to get started with dotfiles.","s":"Manage Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"","p":1891},{"i":1894,"t":"Many computer software programs store their configuration settings in plain, text-based files or directories. Dotfiles are configuration files for various programs, and they help those programs manage their functionality. What sets them apart from regular files and directories is their prefix. Dotfiles are named that way because each file and directory starts with a dot (.) On Unix based systems, dotfiles are hidden by the Operating System by default. Examples of common dotfiles Most programs store their configurations in your home directory by default. Some common dotfiles that you may have heard of or used before are: If you use the Bash shell, you might have a .bash_profile and .bashrc file, both of which contain scripts that load each time you start a new terminal session and configure the shell. If you use the Zsh shell, you would have (or would've created) a .zshrc file which configures and customises the shell. If you use the command line code editor Vim, you would store its configurations in a .vimrc file. After setting up and configuring Git on your local machine, you would have a .gitconfig file, which would contain all your information and settings. Many programs, instead of storing their configurations in your home directory, instead store them in the hidden .config directory (folder) on your system.","s":"What are dotfiles?","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#what-are-dotfiles","p":1891},{"i":1896,"t":"Your dotfiles are personal to you. You spend a sufficient amount of time fine-tuning your setup. You curate configurations and settings that best suit your workflow, aesthetic, and preferences. And you end up with a development environment that helps you, personally, be more productive. What if after all that time you spent, you now have to switch to a new, different machine? Does that mean you have to start all over again from the beginning? How would you remember the exact settings and commands you used? Or what if you have a second machine and you want your set up to be exactly the same on both systems? One of the main goals of developers is to automate repetitive tasks. Creating a dotfile repository that is source-controlled and hosted on GitHub will save you time when you want to set up a new computer and install the exact same settings you created for your previous one. That way all your settings and preferences can be reusable and consistent on other machines.","s":"Why Use Dotfiles?","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#why-use-dotfiles","p":1891},{"i":1898,"t":"It's good practice to have all your dotfiles in their own folder. For simplicity's sake, I'll show an example of how to create a folder at the root of your home directory. But you can add the folder wherever is more convenient for you. Also, I'll be showing examples of how to create a .zshrc and .vimrc file, but similar ideas apply to any other dotfiles you create. cd ~ mkdir .dotfiles cp ~/.zshrc ~/.dotfiles/.zshrc ~/.dotfiles/.vimrc","s":"How to Create Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#how-to-create-dotfiles","p":1891},{"i":1900,"t":"You may have noticed that none of the settings you added to the files in the dotfiles folder have any effect on your system. A program's configuration files, as mentioned previously, are hidden and stored in the home directory by default. This is where the program will look for and read its settings from. It's a good idea to symlink (or create a symbolic link -a pointer) the file in the dotfiles directory where you have stored your preferred settings alongside with other files you created, with the file in its default home directory. It's like the file will be in two places at the same time! The file will be in both the dotfiles directory and there will also be a 'copy' of it in the home directory. To create a link, you use the ln (stands for link) command with the -s argument (which stands for symbolic). Here's how to symlink the .zshrc and .vimrc files: ln -s ~/dotfiles/.vimrc ~/.vimrc ln -s ~/dotfiles/.zshrc ~/.zshrc","s":"How to Symlink your Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#how-to-symlink-your-dotfiles","p":1891},{"i":1902,"t":"Having your files under version control will help you track all the changes you make to them over time, and will also allow you to share them on GitHub. Make sure to change directory into the dotfiles directory (cd ~/.dotfiles). Follow these steps to organise your files in a git repository: Initialise the repository: git init Add all the files you've created so far: git add . Commit the changes and add a commit message: git commit -m \"Added dotfiles\" Once git repository is created, you can upload it to GitHub or GitLab so it won't be lost. 危险 Do you create public repository if you want to store some privacy data, such as GitHub token, ssh keys, etc. 信息 These link procedure are done by hand and hard to maintain across different environments; for automatically installation with config files, I recommend to use GitHub - dotbot.","s":"How to Version Control your Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#how-to-version-control-your-dotfiles","p":1891},{"i":1904,"t":"Linux is an operating system, similar to Windows, but with many different versions due to the nature of being open source and fully customizable. To install Linux, you must choose an install method and choose a Linux distribution. To install Linux: Choose an install method: Windows Subsystem for Linux (WSL), bare metal Linux, or create a Virtual Machine (VM) to run Linux locally. Choose a Linux distribution: Ubuntu, Debian, Kali Linux, openSUSE, ArchLinux, etc. Follow the steps for your preferred install method: Use the install Linux command with Windows Subsystem for Linux (WSL) Create a Linux Virtual Machine (VM) on your local machine Create a bootable USB to install bare-metal Linux After installing Linux: Get familiar with your distribution's package manager, update and upgrade the packages available, and get familiar with the other Linux resources at Microsoft, such as training courses, Linux-versions of popular tools, news, and Open Source events.","s":"Linux Installation","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"","p":1903},{"i":1906,"t":"The choice of which method to use for installing Linux depends on your needs and preferences. Only want to run Linux as your primary operating system? If you are good with a slightly more complicated install process and don't need access to Windows tools (like Outlook, Teams, Word, PowerPoint, etc), you can run Linux on bare metal to access the full potential of your hardware without any overhead from virtualization or emulation. New to using Linux? We recommend starting with Windows Subsystem for Linux (WSL) as it's the easiest way to get up and running. Learn more about these options below.","s":"Step 1 - Choose a method to install Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-1---choose-a-method-to-install-linux","p":1903},{"i":1908,"t":"Available to those with a Windows machine, this is the most simple way to install Linux. Just run the Linux install command: wsl --install to install the Ubuntu distribution. This method uses virtualization to integrate the Windows operating system (OS) with the Linux OS (running on an actual Linux kernel). You can add as many different Linux distributions as you please and run your favorite Linux tools, including GUI apps, alongside your favorite Windows tools. You can also mix and match Bash and PowerShell commands in the same command line. A Linux file system hosts your project files, while a separate Windows file systems hosts any developer tools, such as VS Code, that you'd like to work on the files with. This method of running Linux is highly efficient and performant. Once you choose a Linux distribution or opt to use the default Ubuntu distro, follow the instructions to Use the install Linux command with Windows Subsystem for Linux or learn more in the WSL documentation.","s":"Windows Subsystem for Linux (WSL)","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-2---choose-a-linux-distribution-choose-wsl","p":1903},{"i":1910,"t":"Available to everyone regardless if you're using a Windows or MacOS-based machine, but will require a virtualization software, if creating a VM directly on your machine (locally). A VM is a digital version of a physical computer and is a popular option for running Linux in environments that may require you to scale the level of hardware support (Memory and processing power required) and the level of Security (antimalware, encryption, backups, policy management, etc). Like with WSL, you can create VM instances of as many different Linux distributions as you'd like, running them in an isolated environment, free from any conflicts and great for software development testing. While running a Linux distribution on WSL has slightly faster performance, a Linux VM is easier to clone or migrate. Creating a VM on your local machine requires virtualization using a hypervisor. Windows includes a \"type 1\" hypervisor called Hyper-V to run virtualization directly on your device hardware. There are also \"type 2\" hypervisors that run on top of the operating system, like VirtualBox or VMware Workstation Pro. If you are using a Mac, the most commonly recommended hypervisor is Parallels Desktop, though this is a paid service. VirtualBox also supports both Windows and MacOS. You are responsible for managing the virtual machine when using a hypervisor, including allocating resources like memory and disk space, and ensuring that it is secure and up-to-date. This requires more technical expertise than some of the other options and may not be as scalable or fault-tolerant. Once you've chosen a distribution and decided whether you want to run the VM locally, using a hypervisor, follow the instructions to Create a Linux Virtual Machine locally using a Hypervisor.","s":"Create a Virtual Machine (VM)","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-2---choose-a-linux-distribution-create-vm","p":1903},{"i":1912,"t":"Bare metal Linux just means that Linux is running directly on the device hardware. This install method requires you to create a bootable USB drive by downloading an iso install file from the site hosting your chosen Linux distribution. You will need to use a Windows computer (or any desktop device with an existing OS) to create this drive. Many users choose the traditional method of installing bare metal Linux on a device that is also running Windows and using the \"dual boot\" method. To boot Linux and Windows, you need to partition your hard drive to create separate spaces for both the Linux and Windows OS. The performance speed between WSL, virtual machines, and bare metal Linux has become so close that few developers choose this method due to the overhead of needing to restart (reboot) your device any time you want to switch between the operating systems. If you choose the bare metal Linux install route, you may also need to deal with potential driver issues or hardware compatibility problems that may arise with Linux on some devices. You can find a list of Popular Linux Distributions available for download on Linux.org. Once you've chosen a distro, follow the instructions to Create a bootable USB to install bare-metal Linux.","s":"Bare metal Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-2---choose-a-linux-distribution-bare-metal-linux","p":1903},{"i":1914,"t":"The different versions of Linux are called \"distributions\" (sometimes shortened to “distros”). So there isn’t actually a way to just “install Linux”, you first need to choose which distribution that uses the Linux kernel you want to download and install. There are over 600 active Linux distributions, such as Ubuntu, Debian, Kali Linux, openSUSE, and more. There are a number of factors to consider in choosing a distribution, such as:","s":"Step 2 - Choose a Linux distribution","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-2---choose-a-linux-distribution","p":1903},{"i":1916,"t":"If you’re new to Linux, you may want to start with Ubuntu. This is one of the most common starting places for Linux users due to the level of support and ease of use. Ubuntu offers a desktop-version and a server-version depending on how you plan to use it. The specific tasks that the operating system will be responsible for may help you determine which distribution to use. Arch Linux is a popular choice for those who want a highly customizable, do-it-yourself approach that is still stable and well-supported by a large user base. It is a much more complicated place to start, but can help you to get a better understanding of how Linux works due to the amount of custom configuration.","s":"Required Linux experience","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#required-linux-experience","p":1903},{"i":1918,"t":"A minimal, or \"lightweight\", distribution means a small footprint, with lower memory and processing speed requirements. Alpine Linux is a popular option where users will find most features disabled or not installed by default, but still has everything you need for a containerized app. Security needs: Some Linux users may have specific security concerns to consider. Kali Linux is an example of a distro designed for security tasks, such as Penetration Testing, Security Research, Computer Forensics and Reverse Engineering.","s":"System requirements","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#system-requirements","p":1903},{"i":1920,"t":"A large user community that consistently contributes to the distribution, fixing bugs, adding features, helping with questions, etc. is another good consideration. Ubuntu is one of the most popular distos. Many other distros rapidly grow popular as the needs and preferences of the user community change. The Linux.org site has resources to help you assess what's available, well-supported, or growing in popularity.","s":"Community support","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#community-support","p":1903},{"i":1923,"t":"To install Linux on a Windows PC, use the install Linux command. Open PowerShell or Windows Command Prompt in administrator mode by right-clicking and selecting \"Run as administrator\". Enter the Linux install command: wsl --install. Restart your machine.","s":"Install Linux with Windows Subsystem for Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#install-linux-with-windows-subsystem-for-linux","p":1903},{"i":1925,"t":"By default, the install command will use the Ubuntu distribution of Linux. You can see the other distributions that are available in the Microsoft Store by entering the command: wsl -l -o. If you'd like to install a distribution other than Ubuntu, just add -d to the command with the name of the distribution you'd like to install: wsl --install -d <Distro Name> Some distributions are not official supported, but you can find them in open source projects. For example, ArchLinux is a great distribution and can be installed using GitHub - yuk7/ArchWSL.","s":"Install Linux command options","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#install-linux-command-options","p":1903},{"i":1927,"t":"To create a Linux VM that is hosted on your local machine using a hypervisor, you can choose a virtual machine software: VMware Workstation Pro VirtualBox The most obvious distinction between the two is that VirtualBox is a free and open-source software programme.","s":"Create a Linux Virtual Machine locally using a hypervisor","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#create-a-linux-virtual-machine-locally-using-a-hypervisor","p":1903},{"i":1929,"t":"If you want bare-metal Linux, whether to run a distribution alone on a device or to dual-boot between the distribution and Windows, here are the steps: Download an image file for your chosen Linux distribution. This is usually an ISO file. As an example, you can find an image file for the most recent version of Ubuntu at Download Ubuntu Desktop. Some Linux distributions may require you to verify the image signature before downloading. Some Linux distributions also cannot be installed unless Windows Secure Boot is disabled (which is not recommended). Create a bootable USB drive. You will typically need a USB drive with at least 16gb of space. You will also need software to create the bootable drive. There are many options (such as balenaEtcher, Rufus, UNetbootin, etc.). Often the download site for your chosen Linux distribution will recommend which startup disk creater software to use. Boot your device from the USB drive. When restarting the device, you will need to enter the boot menu. This is typically done by holding down the F12 key during startup. You can then select the USB drive containing your Linux distribution ISO to install from. Select install options. Typically the installer for your Linux distribution will include a set of installation steps that will involve choosing options about whether you want to include certain features, third-party software packages, etc. You may also need to specify whether to erase the disk in the case that this Linux distro will be the only operating system, or to use a partition, if you plan to run multiple operating systems. You may also be asked about whether you'd like to enable encryption. Finally, as with any Linux installation, you will be asked to create a user name and password.","s":"Create a bootable USB drive to install bare-metal Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#create-a-bootable-usb-drive-to-install-bare-metal-linux","p":1903},{"i":1931,"t":"Once you have successfully installed a Linux distribution, there are a few more important steps: Get familiar with the preferred package manager used by your chosen Linux distribution. Linux uses package manager's to download and update any software that you plan to use. For example, Ubuntu uses the Advanced Packaging Tool (apt), ArchLinux uses the Package Manager (pacman). Use your distribution's package manager to update and upgrade your distribution. Software packages in a stable release of a Linux distribution are often outdated. It is recommended to regularly run an update. You may also want to run an upgrade, which installs newer versions of any packages that you've already installed. For example, if you're using Ubuntu, run: sudo apt update && sudo apt upgrade; if you're using ArchLinux, run: sudo pacman -Syu. Learn more about the Linux tools, such as Visual Studio Code, vim, git to speed up your development and usage.","s":"Step 4 - After installing Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-4---after-installing-linux","p":1903},{"i":1934,"t":"The Vim editor is a successor to the vi editor found on the original UNIX. As a fork of Vim, Neovim is an editor that aims to improve the quality of life for all developers, better than Vim.","s":"What is NVIM?","u":"/docs/modern-linux/nvim/use-nvim","h":"#what-is-nvim","p":1932},{"i":1936,"t":"Project maintenance and feature improvements: Vim codebase is less maintainable compared to Neovim; and compared to Vim Language, NeoVim uses Lua which is easier to read and write. Code auto-completion (LSP): Neovim ships with out-of-box support for LSP and uses Lua for further configuration. Support for better plugins: With an actual programming language, this configuration is comparatively easier than Vim.","s":"Why use NVIM?","u":"/docs/modern-linux/nvim/use-nvim","h":"#why-use-nvim","p":1932},{"i":1938,"t":"If you are using ArchLinux, just run sudo pacman -Syu neovim. If you are using Ubuntu, follow the steps: Download NVIM appimage with latest version. Install fuse by sudo apt install -y fuse. Run chmod u+x nvim.appimage && mkdir ~/bin && mv nvim.appimage ./bin/nvim","s":"How to install NVIM","u":"/docs/modern-linux/nvim/use-nvim","h":"#how-to-install-nvim","p":1932},{"i":1940,"t":"Pick up one of the top NVIM framework. LazyVim NvChad LunarVim AstroNvim I use LunarVim and the configurations are as below, managed by dotfiles for syncing. See: NVIM Plugins and Configurations LunarVim Customization Diff Files","s":"NVIM-based configurations","u":"/docs/modern-linux/nvim/use-nvim","h":"#nvim-based-configurations","p":1932},{"i":1942,"t":"Bash, or the Bourne Again Shell, is a hallmark of Linux systems. However, there are other shells out there that may offer extra functionality. Here's how to install one popular alternative, ZSH.","s":"Use ZSH","u":"/docs/modern-linux/zsh/use-zsh","h":"","p":1941},{"i":1944,"t":"ZSH, also called the Z shell, is an extended version of the Bourne Shell (sh), with new features and support for plugins and themes. Since it's based on the same shell as Bash, ZSH has many of the same features, and switching over is a breeze. ZSH vs. Bash: The Important Differences ZSH has too many features to list here, some just minor improvements to Bash, but here are some of the major ones: Automatic cd: Just type the name of the directory Recursive path expansion: For example /u/lo/b expands to /usr/local/bin Automatic Syntax Highlighting: Words, file extensions, and other things visible in the Terminal are color-coded Spelling correction and approximate completion: If you make a minor mistake typing a directory name, ZSH will fix it for you Plugin and theme support: ZSH includes many different plugin frameworks Plugin and theme support is probably the coolest feature of ZSH and is what we'll focus on here. If you're on Linux, the command to install ZSH varies by the distro, but it should be a default package in your package manager.","s":"What is ZSH?","u":"/docs/modern-linux/zsh/use-zsh","h":"#what-is-zsh","p":1941},{"i":1946,"t":"To install ZSH on Ubuntu, or any other Debian-based distro, open up the Terminal, then run: sudo apt install zsh To install ZSH on ArchLinux, run: sudo pacman -Syu zsh Confirm that zsh has been installed correctly by running zsh --version in the console. Now that ZSH has been downloaded and installed correctly, we need to change the default shell from Bash to ZSH. Run: chsh -s $(which zsh) If you are using a command line SSH (including WSL), logout and re-login. If you are using a graphics distribution, you should restart your PC to make it work. When you reopen the Terminal, you'll be given some configuration options for ZSH. Once you've installed ZSH you can start adding themes and using plugins. We've covered how to do that in the last two sections of the article.","s":"How to install ZSH?","u":"/docs/modern-linux/zsh/use-zsh","h":"#how-to-install-zsh","p":1941},{"i":1948,"t":"Generally speaking, you'll want to use your distros default package manager to install ZSH, as it is included by default in most repositories (repos). If it is not present for some reason, you can always download the source code and install that. Additionally, the ZSH GitHub has instructions for installing it on the most popular Linux distros. Oh-My-Zsh is the most popular plugin manager for ZSH, and it comes with many built-in plugins and themes as well. There are also a couple of other plugin frameworks, including Antigen, which is a full package manager for ZSH, but Oh-My-Zsh has loads of plugins built right in and does its job well. Oh-My-Zsh has a simple install script you can run: sh -c \"$(curl -fsSL https://raw.githubusercontent.com/robbyrussell/oh-my-zsh/master/tools/install.sh)\"","s":"Install ZSH on Other Linux Systems","u":"/docs/modern-linux/zsh/use-zsh","h":"#install-zsh-on-other-linux-systems","p":1941},{"i":1950,"t":"There are plenty of themes to go around, but powerlevel10k is by far the coolest. It adds a right-aligned info box, integration with git and command history, incredible customization, and wraps it all up in a slick interface based on the powerline plugin for vim. You'll want to use iTerm on macOS, or any terminal with 24-bit color, to get the most out of powerlevel10k (or any ZSH theme, really). See Powerlevel10k for details. You can also use Starship. Install Nerd Font You need to install the Nerd Fonts to use modern icons and themes in zsh. You can either download and manual install in Nerd Fonts Releases, or use a script getnf.","s":"How to Use ZSH Themes","u":"/docs/modern-linux/zsh/use-zsh","h":"#how-to-use-zsh-themes","p":1941},{"i":1952,"t":"zsh-autosuggestions zsh-syntax-highlighting The plugins required are not included in Oh My Zsh plugins. We will add them manually: git clone https://github.com/zsh-users/zsh-autosuggestions.git $ZSH/plugins/zsh-autosuggestions git clone https://github.com/zsh-users/zsh-syntax-highlighting.git $ZSH/plugins/zsh-syntax-highlighting Open the .zshrc file, replace the line plugins=(git z) by plugins=(git z zsh-autosuggestions zsh-syntax-highlighting). Reload ZSH to make it work: exec zsh","s":"Recommend Plugins","u":"/docs/modern-linux/zsh/use-zsh","h":"#recommend-plugins","p":1941},{"i":1954,"t":"备注 npm package create-react-app is not under maintained, but it's very helpful for starters.","s":"Create React App with TypeScript","u":"/docs/typescript-react/create-react-app-with-typescript","h":"","p":1953},{"i":1956,"t":"yarn npx yarn create react-app react-typescript-app --template typescript && cd react-typescript-app npx create-react-app react-typescript-app --template typescript && cd react-typescript-app do not use globally If you've previously installed create-react-app globally via npm install -g create-react-app, we recommend you uninstall the package using npm uninstall -g create-react-app or yarn global remove create-react-app to ensure that npx always uses the latest version. Global installs of create-react-app are no longer supported.","s":"Installation","u":"/docs/typescript-react/create-react-app-with-typescript","h":"#installation","p":1953},{"i":1958,"t":". ├── node_modules │ ├── ... │ ├── ... │ └── ... ├── public │ ├── favicon.ico │ ├── index.html │ ├── logo192.png │ ├── logo512.png │ ├── manifest.json │ └── robots.txt ├── src │ ├── App.css │ ├── App.test.tsx │ ├── App.tsx │ ├── index.css │ ├── index.tsx │ ├── logo.svg │ ├── react-app-env.d.ts │ ├── reportWebVitals.ts │ └── setupTests.ts ├── package-lock.json ├── package.json ├── README.md └── tsconfig.json","s":"File Structure","u":"/docs/typescript-react/create-react-app-with-typescript","h":"#file-structure","p":1953},{"i":1960,"t":"React 是著名的开源 JavaScript 库，它已成为寻求构建响应式且功能强大的用户界面的开发人员青睐的工具。 同时，TypeScript 是一个静态类型的 JavaScript 超集，拥有许多优点，例如类定义、接口和类型注释、为代码库提供结构和可靠性以及简化错误检测。","s":"TypeScript 和 React","u":"/docs/typescript-react/intro","h":"","p":1959},{"i":1963,"t":"TypeScript 将静态类型引入 JavaScript，使开发人员能够在开发过程中捕获与类型相关的错误。这可以提高代码质量、提高可维护性并减少运行时错误。","s":"静态类型和类型安全","u":"/docs/typescript-react/intro","h":"#static-safety","p":1959},{"i":1965,"t":"TypeScript 提供出色的工具和 IDE 支持，包括自动完成、类型检查和重构工具等功能。这提高了开发人员的工作效率，并有助于快速识别和修复错误。","s":"增强的工具和 IDE 支持","u":"/docs/typescript-react/intro","h":"#ide-support","p":1959},{"i":1967,"t":"TypeScript 的静态类型和清晰的界面使代码更加自文档化并且更易于理解。这提高了代码的可维护性并促进开发团队内部更好的协作。","s":"改进代码可维护性和协作","u":"/docs/typescript-react/intro","h":"#maintainability-collaboration","p":1959},{"i":1969,"t":"TypeScript 是 JavaScript 的超集，允许开发者在现有 JavaScript 项目中逐步采用 TypeScript。这种兼容性使得迁移代码库和利用现有 JavaScript 库变得更加容易。","s":"与 JavaScript 和现有代码库的兼容性","u":"/docs/typescript-react/intro","h":"#compatible-with-js","p":1959},{"i":1971,"t":"TypeScript 允许开发人员定义和强制执行 API 类型，使它们更加明确和不言自明。这可以带来更好的文档、改进的代码可发现性以及更轻松地与外部库集成。","s":"强类型 API 和更好的文档","u":"/docs/typescript-react/intro","h":"#strongly-typed-apis","p":1959},{"i":1974,"t":"React 遵循基于组件的架构，允许开发人员构建可重用和模块化的 UI 组件。这提高了代码的可重用性、可维护性和可扩展性。","s":"基于组件的架构","u":"/docs/typescript-react/intro","h":"#component-architecture","p":1959},{"i":1976,"t":"React 使用虚拟 DOM 来优化渲染过程。它仅更新必要的组件，最大限度地减少 DOM 操作并提高性能。","s":"虚拟 DOM 和高效渲染","u":"/docs/typescript-react/intro","h":"#virtual-dom","p":1959},{"i":1978,"t":"React 提倡单向数据流的概念，即数据从父组件向子组件单向流动。这有助于维护可预测的数据流并简化状态管理。它还使得调试和优化 React 应用程序变得更加容易。","s":"单向数据流和状态管理","u":"/docs/typescript-react/intro","h":"#unidirection-data-and-state-management","p":1959},{"i":1980,"t":"React 可以与 React Native 结合使用来开发适用于 iOS 和 Android 平台的移动应用程序。通过共享单一代码库，开发人员可以节省构建跨平台应用程序的时间和精力。","s":"用于跨平台开发的 React Native","u":"/docs/typescript-react/intro","h":"#cross-platform","p":1959},{"i":1982,"t":"React 拥有庞大的生态系统，其中包含社区开发的众多库、工具和资源。这使开发人员能够利用现有解决方案并加速开发。","s":"丰富的生态系统和社区支持","u":"/docs/typescript-react/intro","h":"#rich-ecosystem","p":1959},{"i":1984,"t":"通过将 React 基于组件的方法与 TypeScript 的静态类型相结合，开发人员可以从 Web 开发项目中改进的代码质量、可维护性、生产力和协作中受益。","s":"结合","u":"/docs/typescript-react/intro","h":"#combination","p":1959},{"i":1986,"t":"信息 Pandas 是用于数据分析 Python 的软件库，提供了大量快速便捷地处理数据的函数和方法。 本文翻译自官方文档 10 Minutes to pandas，对应的 pandas 版本为 2.1.3。 导入所需的软件包： In [1]: import numpy as np In [2]: import pandas as pd","s":"Pandas 快速入门","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"","p":1985},{"i":1988,"t":"Pandas 提供了两类处理数据的类别： Series：任何类型的一维标签阵列数据 例如整数、字符串、Python 对象等。 DataFrame：二维数据结构，它储存着像一个二维数组或带行列的表的数据。","s":"Pandas 基础数据结构","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#basic-data-structures","p":1985},{"i":1990,"t":"通过传递列表创建 Series，其中 pandas 会创建默认的整数索引： In [3]: s = pd.Series([1, 3, 5, np.nan, 6, 8]) In [4]: s Out[4]: 0 1.0 1 3.0 2 5.0 3 NaN 4 6.0 5 8.0 dtype: float64 通过传递具有日期时间索引和标签列的 NumPy 数组来创建 DataFrame： In [5]: dates = pd.date_range(\"20130101\", periods=6) In [6]: dates Out[6]: DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04', '2013-01-05', '2013-01-06'], dtype='datetime64[ns]', freq='D') In [7]: df = pd.DataFrame(np.random.randn(6, 4), index=dates, columns=list(\"ABCD\")) In [8]: df Out[8]: A B C D 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 2013-01-06 -0.673690 0.113648 -1.478427 0.524988 通过传递对象字典来创建 DataFrame： In [9]: df2 = pd.DataFrame( ...: { ...: \"A\": 1.0, ...: \"B\": pd.Timestamp(\"20130102\"), ...: \"C\": pd.Series(1, index=list(range(4)), dtype=\"float32\"), ...: \"D\": np.array([3] * 4, dtype=\"int32\"), ...: \"E\": pd.Categorical([\"test\", \"train\", \"test\", \"train\"]), ...: \"F\": \"foo\", ...: } ...: ) ...: In [10]: df2 Out[10]: A B C D E F 0 1.0 2013-01-02 1.0 3 test foo 1 1.0 2013-01-02 1.0 3 train foo 2 1.0 2013-01-02 1.0 3 test foo 3 1.0 2013-01-02 1.0 3 train foo 生成的 DataFrame 列有不同的数据类型 dtypes： In [11]: df2.dtypes Out[11]: A float64 B datetime64[s] C float32 D int32 E category F object dtype: object 使用 IPython 时，按 TAB 可以自动补全： In [12]: df2.<TAB> # noqa: E225, E999 df2.A df2.bool df2.abs df2.boxplot df2.add df2.C df2.add_prefix df2.clip df2.add_suffix df2.columns df2.align df2.copy df2.all df2.count df2.any df2.combine df2.append df2.D df2.apply df2.describe df2.applymap df2.diff df2.B df2.duplicated 正如你可以看到的那样，A、B、C 和 D 等列在自动补全中。后续列已简略。","s":"对象创建","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#object-creation","p":1985},{"i":1992,"t":"使用 DataFrame.head 和 DataFrame.tail 分别查看 df 的顶部和底部的行： In [13]: df.head() Out[13]: A B C D 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 In [14]: df.tail(3) Out[14]: A B C D 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 2013-01-06 -0.673690 0.113648 -1.478427 0.524988 显示索引 DataFrame.index，列 DataFrame.columns 和 numpy 数据： In [15]: df.index Out[15]: DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04', '2013-01-05', '2013-01-06'], dtype='datetime64[ns]', freq='D') In [16]: df.columns Out[16]: Index(['A', 'B', 'C', 'D'], dtype='object') 以 DataFrame.to_numpy 返回底层数据的数字表示，而不带索引或列标签： In [17]: df.to_numpy() Out[17]: array([[ 0.4691, -0.2829, -1.5091, -1.1356], [ 1.2121, -0.1732, 0.1192, -1.0442], [-0.8618, -2.1046, -0.4949, 1.0718], [ 0.7216, -0.7068, -1.0396, 0.2719], [-0.425 , 0.567 , 0.2762, -1.0874], [-0.6737, 0.1136, -1.4784, 0.525 ]]) 信息 NumPy 整个数组是同一种类型，而 pandas DataFrames 每列有一种类型。当你调用 DataFrame.to_numpy 时，pandas 将找到可以容纳 DataFrame 中所有数据类型的 NumPy 数据类型。如果通用数据类型是 object，DataFrame.to_numpy 将复制数据。 In [18]: df2.dtypes Out[18]: A float64 B datetime64[s] C float32 D int32 E category F object dtype: object In [19]: df2.to_numpy() Out[19]: array([[1.0, Timestamp('2013-01-02 00:00:00'), 1.0, 3, 'test', 'foo'], [1.0, Timestamp('2013-01-02 00:00:00'), 1.0, 3, 'train', 'foo'], [1.0, Timestamp('2013-01-02 00:00:00'), 1.0, 3, 'test', 'foo'], [1.0, Timestamp('2013-01-02 00:00:00'), 1.0, 3, 'train', 'foo']], dtype=object) DataFrame.description 显示数据的快速统计摘要： In [20]: df.describe() Out[20]: A B C D count 6.000000 6.000000 6.000000 6.000000 mean 0.073711 -0.431125 -0.687758 -0.233103 std 0.843157 0.922818 0.779887 0.973118 min -0.861849 -2.104569 -1.509059 -1.135632 25% -0.611510 -0.600794 -1.368714 -1.076610 50% 0.022070 -0.228039 -0.767252 -0.386188 75% 0.658444 0.041933 -0.034326 0.461706 max 1.212112 0.567020 0.276232 1.071804 对数据 df 进行转置： In [21]: df.T Out[21]: 2013-01-01 2013-01-02 2013-01-03 2013-01-04 2013-01-05 2013-01-06 A 0.469112 1.212112 -0.861849 0.721555 -0.424972 -0.673690 B -0.282863 -0.173215 -2.104569 -0.706771 0.567020 0.113648 C -1.509059 0.119209 -0.494929 -1.039575 0.276232 -1.478427 D -1.135632 -1.044236 1.071804 0.271860 -1.087401 0.524988 DataFrame.sort_index 按轴排序： In [22]: df.sort_index(axis=1, ascending=False) Out[22]: D C B A 2013-01-01 -1.135632 -1.509059 -0.282863 0.469112 2013-01-02 -1.044236 0.119209 -0.173215 1.212112 2013-01-03 1.071804 -0.494929 -2.104569 -0.861849 2013-01-04 0.271860 -1.039575 -0.706771 0.721555 2013-01-05 -1.087401 0.276232 0.567020 -0.424972 2013-01-06 0.524988 -1.478427 0.113648 -0.673690 DataFrame.sort_values 按值排序： In [23]: df.sort_values(by=\"B\") Out[23]: A B C D 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-06 -0.673690 0.113648 -1.478427 0.524988 2013-01-05 -0.424972 0.567020 0.276232 -1.087401","s":"查看数据","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#viewing_data","p":1985},{"i":1994,"t":"信息 虽然标准 Python / Numpy 表达式非常直观并且可以方便地用于交互式工作，但对于生产代码，我们建议使用优化的 pandas 数据访问方法 DataFrame.at、DataFrame.iat、DataFrame.loc 和 DataFrame.iloc。","s":"选择数据","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#selection","p":1985},{"i":1996,"t":"传递单个标签会选择一个列，将会返回一个 Series，相当于 df.A： In [24]: df[\"A\"] Out[24]: 2013-01-01 0.469112 2013-01-02 1.212112 2013-01-03 -0.861849 2013-01-04 0.721555 2013-01-05 -0.424972 2013-01-06 -0.673690 Freq: D, Name: A, dtype: float64 对于 DataFrame，传递一个分片 : 对行进行切片： In [25]: df[0:3] Out[25]: A B C D 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 In [26]: df[\"20130102\":\"20130104\"] Out[26]: A B C D 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 2013-01-04 0.721555 -0.706771 -1.039575 0.271860","s":"获取数据项 ([])","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#getitem","p":1985},{"i":1998,"t":"选择匹配标签的行： In [27]: df.loc[dates[0]] Out[27]: A 0.469112 B -0.282863 C -1.509059 D -1.135632 Name: 2013-01-01 00:00:00, dtype: float64 选择所有行 (:)，并选择列标签： In [28]: df.loc[:, [\"A\", \"B\"]] Out[28]: A B 2013-01-01 0.469112 -0.282863 2013-01-02 1.212112 -0.173215 2013-01-03 -0.861849 -2.104569 2013-01-04 0.721555 -0.706771 2013-01-05 -0.424972 0.567020 2013-01-06 -0.673690 0.113648 对于标签切片，起止两个端点都包括在内： In [29]: df.loc[\"20130102\":\"20130104\", [\"A\", \"B\"]] Out[29]: A B 2013-01-02 1.212112 -0.173215 2013-01-03 -0.861849 -2.104569 2013-01-04 0.721555 -0.706771 选择单个行和列标签，将返回一个标量： In [30]: df.loc[dates[0], \"A\"] Out[30]: 0.4691122999071863 快速访问标量 (相当于上面的方法)： In [31]: df.at[dates[0], \"A\"] Out[31]: 0.4691122999071863","s":"按标签选择","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#selection-by-label","p":1985},{"i":2000,"t":"通过传递整数位置进行选择： In [32]: df.iloc[3] Out[32]: A 0.721555 B -0.706771 C -1.039575 D 0.271860 Name: 2013-01-04 00:00:00, dtype: float64 使用整数进行切片，类似于 NumPy/Python： In [33]: df.iloc[3:5, 0:2] Out[33]: A B 2013-01-04 0.721555 -0.706771 2013-01-05 -0.424972 0.567020 指定整数位置列表取行列： In [34]: df.iloc[[1, 2, 4], [0, 2]] Out[34]: A C 2013-01-02 1.212112 0.119209 2013-01-03 -0.861849 -0.494929 2013-01-05 -0.424972 0.276232 对行进行切片： In [35]: df.iloc[1:3, :] Out[35]: A B C D 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 对列进行切片： In [36]: df.iloc[:, 1:3] Out[36]: B C 2013-01-01 -0.282863 -1.509059 2013-01-02 -0.173215 0.119209 2013-01-03 -2.104569 -0.494929 2013-01-04 -0.706771 -1.039575 2013-01-05 0.567020 0.276232 2013-01-06 0.113648 -1.478427 按位置取值： In [37]: df.iloc[1, 1] Out[37]: -0.17321464905330858 快速按位置取值 (相当于上面的方法)： In [38]: df.iat[1, 1] Out[38]: -0.17321464905330858","s":"按位置选择","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#selection-by-position","p":1985},{"i":2002,"t":"选择 df.A 大于 0 的行。 In [39]: df[df[\"A\"] > 0] Out[39]: A B C D 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 从符合布尔条件的 DataFrame 中选择值： In [40]: df[df > 0] Out[40]: A B C D 2013-01-01 0.469112 NaN NaN NaN 2013-01-02 1.212112 NaN 0.119209 NaN 2013-01-03 NaN NaN NaN 1.071804 2013-01-04 0.721555 NaN NaN 0.271860 2013-01-05 NaN 0.567020 0.276232 NaN 2013-01-06 NaN 0.113648 NaN 0.524988 使用 Series.isin 方法进行过滤： In [41]: df2 = df.copy() In [42]: df2[\"E\"] = [\"one\", \"one\", \"two\", \"three\", \"four\", \"three\"] In [43]: df2 Out[43]: A B C D E 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 one 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 one 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 two 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 three 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 four 2013-01-06 -0.673690 0.113648 -1.478427 0.524988 three In [44]: df2[df2[\"E\"].isin([\"two\", \"four\"])] Out[44]: A B C D E 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 two 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 four","s":"布尔索引","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#boolean-indexing","p":1985},{"i":2004,"t":"设置新列会自动按索引对齐数据： In [45]: s1 = pd.Series([1, 2, 3, 4, 5, 6], index=pd.date_range(\"20130102\", periods=6)) In [46]: s1 Out[46]: 2013-01-02 1 2013-01-03 2 2013-01-04 3 2013-01-05 4 2013-01-06 5 2013-01-07 6 Freq: D, dtype: int64 In [47]: df[\"F\"] = s1 按标签设置新的值： In [48]: df.at[dates[0], \"A\"] = 0 按位置设置新的值： In [49]: df.iat[0, 1] = 0 通过 NumPy 数组来设置新的值： In [50]: df.loc[:, \"D\"] = np.array([5] * len(df)) 上述操作结果如下： In [51]: df Out[51]: A B C D F 2013-01-01 0.000000 0.000000 -1.509059 5.0 NaN 2013-01-02 1.212112 -0.173215 0.119209 5.0 1.0 2013-01-03 -0.861849 -2.104569 -0.494929 5.0 2.0 2013-01-04 0.721555 -0.706771 -1.039575 5.0 3.0 2013-01-05 -0.424972 0.567020 0.276232 5.0 4.0 2013-01-06 -0.673690 0.113648 -1.478427 5.0 5.0 通过 where 设置值： In [52]: df2 = df.copy() In [53]: df2[df2 > 0] = -df2 In [54]: df2 Out[54]: A B C D F 2013-01-01 0.000000 0.000000 -1.509059 -5.0 NaN 2013-01-02 -1.212112 -0.173215 -0.119209 -5.0 -1.0 2013-01-03 -0.861849 -2.104569 -0.494929 -5.0 -2.0 2013-01-04 -0.721555 -0.706771 -1.039575 -5.0 -3.0 2013-01-05 -0.424972 -0.567020 -0.276232 -5.0 -4.0 2013-01-06 -0.673690 -0.113648 -1.478427 -5.0 -5.0","s":"设置值","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#setting","p":1985},{"i":2006,"t":"pandas 使用 np.nan 来表示缺失值，缺失值默认不参与任何计算。 reindex() 允许更改/添加/删除指定轴上的索引，并返回数据的副本： In [55]: df1 = df.reindex(index=dates[0:4], columns=list(df.columns) + [\"E\"]) In [56]: df1.loc[dates[0] : dates[1], \"E\"] = 1 In [57]: df1 Out[57]: A B C D F E 2013-01-01 0.000000 0.000000 -1.509059 5.0 NaN 1.0 2013-01-02 1.212112 -0.173215 0.119209 5.0 1.0 1.0 2013-01-03 -0.861849 -2.104569 -0.494929 5.0 2.0 NaN 2013-01-04 0.721555 -0.706771 -1.039575 5.0 3.0 NaN DataFramework.dropna 将删除任何包含缺失值的行： In [58]: df1.dropna(how=\"any\") Out[58]: A B C D F E 2013-01-02 1.212112 -0.173215 0.119209 5.0 1.0 1.0 DataFramework.fillna 对缺失值进行填充： In [59]: df1.fillna(value=5) Out[59]: A B C D F E 2013-01-01 0.000000 0.000000 -1.509059 5.0 5.0 1.0 2013-01-02 1.212112 -0.173215 0.119209 5.0 1.0 1.0 2013-01-03 -0.861849 -2.104569 -0.494929 5.0 2.0 5.0 2013-01-04 0.721555 -0.706771 -1.039575 5.0 3.0 5.0 isna 获取 nan 值的布尔值掩码： In [60]: pd.isna(df1) Out[60]: A B C D F E 2013-01-01 False False False False True False 2013-01-02 False False False False False False 2013-01-03 False False False False False True 2013-01-04 False False False False False True","s":"缺失值","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#missing-data","p":1985},{"i":2009,"t":"一般情况下，操作会排除缺失值。 计算每列的平均值： In [61]: df.mean() Out[61]: A -0.004474 B -0.383981 C -0.687758 D 5.000000 F 3.000000 dtype: float64 计算每行的平均值： In [62]: df.mean(axis=1) Out[62]: 2013-01-01 0.872735 2013-01-02 1.431621 2013-01-03 0.707731 2013-01-04 1.395042 2013-01-05 1.883656 2013-01-06 1.592306 Freq: D, dtype: float64 使用具有不同索引或列的另一个 Series 或 DataFrame 进行操作会将结果与索引或列标签的并集对齐。此外，pandas 会自动沿指定维度进行广播，并会用 np.nan 填充未对齐的标签。 In [63]: s = pd.Series([1, 3, 5, np.nan, 6, 8], index=dates).shift(2) In [64]: s Out[64]: 2013-01-01 NaN 2013-01-02 NaN 2013-01-03 1.0 2013-01-04 3.0 2013-01-05 5.0 2013-01-06 NaN Freq: D, dtype: float64 In [65]: df.sub(s, axis=\"index\") Out[65]: A B C D F 2013-01-01 NaN NaN NaN NaN NaN 2013-01-02 NaN NaN NaN NaN NaN 2013-01-03 -1.861849 -3.104569 -1.494929 4.0 1.0 2013-01-04 -2.278445 -3.706771 -4.039575 2.0 0.0 2013-01-05 -5.424972 -4.432980 -4.723768 0.0 -1.0 2013-01-06 NaN NaN NaN NaN NaN","s":"状态","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#stats","p":1985},{"i":2011,"t":"DataFrame.agg 和 DataFrame.transform 分别应用一个用户自定义的函数来减少或广播其结果。 In [66]: df.agg(lambda x: np.mean(x) * 5.6) Out[66]: A -0.025054 B -2.150294 C -3.851445 D 28.000000 F 16.800000 dtype: float64 In [67]: df.transform(lambda x: x * 101.2) Out[67]: A B C D F 2013-01-01 0.000000 0.000000 -152.716721 506.0 NaN 2013-01-02 122.665737 -17.529322 12.063922 506.0 101.2 2013-01-03 -87.219115 -212.982405 -50.086843 506.0 202.4 2013-01-04 73.021382 -71.525239 -105.204988 506.0 303.6 2013-01-05 -43.007200 57.382459 27.954680 506.0 404.8 2013-01-06 -68.177398 11.501219 -149.616767 506.0 506.0","s":"用户自定义函数","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#user-defined-functions","p":1985},{"i":2013,"t":"In [68]: s = pd.Series(np.random.randint(0, 7, size=10)) In [69]: s Out[69]: 0 4 1 2 2 1 3 2 4 6 5 4 6 4 7 6 8 4 9 4 dtype: int64 In [70]: s.value_counts() Out[70]: 4 5 2 2 6 2 1 1 Name: count, dtype: int64","s":"值计数","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#value-counts","p":1985},{"i":2015,"t":"Series 在 str 属性中配备了一组字符串处理方法，可以方便地对数组的每个元素进行操作，如下面的代码片段所示。 In [71]: s = pd.Series([\"A\", \"B\", \"C\", \"Aaba\", \"Baca\", np.nan, \"CABA\", \"dog\", \"cat\"]) In [72]: s.str.lower() Out[72]: 0 a 1 b 2 c 3 aaba 4 baca 5 NaN 6 caba 7 dog 8 cat dtype: object","s":"字符串方法","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#string-methods","p":1985},{"i":2018,"t":"pandas 提供了各种工具，可以在连接/合并类型操作的情况下轻松地将 Series 和 DataFrame 与索引和关系代数功能的各种集合逻辑组合在一起。 使用 concat 将 pandas 对象按行连接在一起： In [73]: df = pd.DataFrame(np.random.randn(10, 4)) In [74]: df Out[74]: 0 1 2 3 0 -0.548702 1.467327 -1.015962 -0.483075 1 1.637550 -1.217659 -0.291519 -1.745505 2 -0.263952 0.991460 -0.919069 0.266046 3 -0.709661 1.669052 1.037882 -1.705775 4 -0.919854 -0.042379 1.247642 -0.009920 5 0.290213 0.495767 0.362949 1.548106 6 -1.131345 -0.089329 0.337863 -0.945867 7 -0.932132 1.956030 0.017587 -0.016692 8 -0.575247 0.254161 -1.143704 0.215897 9 1.193555 -0.077118 -0.408530 -0.862495 # break it into pieces In [75]: pieces = [df[:3], df[3:7], df[7:]] In [76]: pd.concat(pieces) Out[76]: 0 1 2 3 0 -0.548702 1.467327 -1.015962 -0.483075 1 1.637550 -1.217659 -0.291519 -1.745505 2 -0.263952 0.991460 -0.919069 0.266046 3 -0.709661 1.669052 1.037882 -1.705775 4 -0.919854 -0.042379 1.247642 -0.009920 5 0.290213 0.495767 0.362949 1.548106 6 -1.131345 -0.089329 0.337863 -0.945867 7 -0.932132 1.956030 0.017587 -0.016692 8 -0.575247 0.254161 -1.143704 0.215897 9 1.193555 -0.077118 -0.408530 -0.862495 信息 向 DataFrame 添加列相对较快。但是，添加行需要副本，并且可能很昂贵。我们建议将预先构建的记录列表传递给 DataFrame 构造函数，而不是通过迭代地向其追加记录来构建 DataFrame。","s":"Concat","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#concat","p":1985},{"i":2020,"t":"merge 启用沿特定列的 SQL 样式联接类型。 In [77]: left = pd.DataFrame({\"key\": [\"foo\", \"foo\"], \"lval\": [1, 2]}) In [78]: right = pd.DataFrame({\"key\": [\"foo\", \"foo\"], \"rval\": [4, 5]}) In [79]: left Out[79]: key lval 0 foo 1 1 foo 2 In [80]: right Out[80]: key rval 0 foo 4 1 foo 5 In [81]: pd.merge(left, right, on=\"key\") Out[81]: key lval rval 0 foo 1 4 1 foo 1 5 2 foo 2 4 3 foo 2 5 按值 merge： In [82]: left = pd.DataFrame({\"key\": [\"foo\", \"bar\"], \"lval\": [1, 2]}) In [83]: right = pd.DataFrame({\"key\": [\"foo\", \"bar\"], \"rval\": [4, 5]}) In [84]: left Out[84]: key lval 0 foo 1 1 bar 2 In [85]: right Out[85]: key rval 0 foo 4 1 bar 5 In [86]: pd.merge(left, right, on=\"key\") Out[86]: key lval rval 0 foo 1 4 1 bar 2 5","s":"Join","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#join","p":1985},{"i":2022,"t":"group by 指的是涉及一个或多个以下步骤的过程： 根据一些规则将数据分组 对于每组数据分别应用函数 将结果组合成一个数据结构 In [87]: df = pd.DataFrame( ....: { ....: \"A\": [\"foo\", \"bar\", \"foo\", \"bar\", \"foo\", \"bar\", \"foo\", \"foo\"], ....: \"B\": [\"one\", \"one\", \"two\", \"three\", \"two\", \"two\", \"one\", \"three\"], ....: \"C\": np.random.randn(8), ....: \"D\": np.random.randn(8), ....: } ....: ) ....: In [88]: df Out[88]: A B C D 0 foo one 1.346061 -1.577585 1 bar one 1.511763 0.396823 2 foo two 1.627081 -0.105381 3 bar three -0.990582 -0.532532 4 foo two -0.441652 1.453749 5 bar two 1.211526 1.208843 6 foo one 0.268520 -0.080952 7 foo three 0.024580 -0.264610 按多列分组会生成分层索引，然后应用函数 sum： In [89]: df.groupby(\"A\")[[\"C\", \"D\"]].sum() Out[89]: C D A bar 1.732707 1.073134 foo 2.824590 -0.574779 按多列标签分组形成 MultiIndex。 In [90]: df.groupby([\"A\", \"B\"]).sum() Out[90]: C D A B bar one 1.511763 0.396823 three -0.990582 -0.532532 two 1.211526 1.208843 foo one 1.614581 -1.658537 three 0.024580 -0.264610 two 1.185429 1.348368","s":"分组","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#grouping","p":1985},{"i":2025,"t":"In [91]: arrays = [ ....: [\"bar\", \"bar\", \"baz\", \"baz\", \"foo\", \"foo\", \"qux\", \"qux\"], ....: [\"one\", \"two\", \"one\", \"two\", \"one\", \"two\", \"one\", \"two\"], ....: ] ....: In [92]: index = pd.MultiIndex.from_arrays(arrays, names=[\"first\", \"second\"]) In [93]: df = pd.DataFrame(np.random.randn(8, 2), index=index, columns=[\"A\", \"B\"]) In [94]: df2 = df[:4] In [95]: df2 Out[95]: A B first second bar one -0.727965 -0.589346 two 0.339969 -0.693205 baz one -0.339355 0.593616 two 0.884345 1.591431 The DataFrame.stack 方法对 DataFrame 的列进行“压缩”。 In [96]: stacked = df2.stack(future_stack=True) In [97]: stacked Out[97]: first second bar one A -0.727965 B -0.589346 two A 0.339969 B -0.693205 baz one A -0.339355 B 0.593616 two A 0.884345 B 1.591431 dtype: float64 对于“堆叠的”DataFrame 或 Series (多索引)，stack() 的逆操作是 unstack()，默认拆下最后一层： In [98]: stacked.unstack() Out[98]: A B first second bar one -0.727965 -0.589346 two 0.339969 -0.693205 baz one -0.339355 0.593616 two 0.884345 1.591431 In [99]: stacked.unstack(1) Out[99]: second one two first bar A -0.727965 0.339969 B -0.589346 -0.693205 baz A -0.339355 0.884345 B 0.593616 1.591431 In [100]: stacked.unstack(0) Out[100]: first bar baz second one A -0.727965 -0.339355 B -0.589346 0.593616 two A 0.339969 0.884345 B -0.693205 1.591431","s":"堆叠","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#stack","p":1985},{"i":2027,"t":"In [101]: df = pd.DataFrame( .....: { .....: \"A\": [\"one\", \"one\", \"two\", \"three\"] * 3, .....: \"B\": [\"A\", \"B\", \"C\"] * 4, .....: \"C\": [\"foo\", \"foo\", \"foo\", \"bar\", \"bar\", \"bar\"] * 2, .....: \"D\": np.random.randn(12), .....: \"E\": np.random.randn(12), .....: } .....: ) .....: In [102]: df Out[102]: A B C D E 0 one A foo -1.202872 0.047609 1 one B foo -1.814470 -0.136473 2 two C foo 1.018601 -0.561757 3 three A bar -0.595447 -1.623033 4 one B bar 1.395433 0.029399 5 one C bar -0.392670 -0.542108 6 two A foo 0.007207 0.282696 7 three B foo 1.928123 -0.087302 8 one C foo -0.055224 -1.575170 9 one A bar 2.395985 1.771208 10 two B bar 1.552825 0.816482 11 three C bar 0.166599 1.100230 从上述数据指定 values，index and columns 生成透视表： In [103]: pd.pivot_table(df, values=\"D\", index=[\"A\", \"B\"], columns=[\"C\"]) Out[103]: C bar foo A B one A 2.395985 -1.202872 B 1.395433 -1.814470 C -0.392670 -0.055224 three A -0.595447 NaN B NaN 1.928123 C 0.166599 NaN two A NaN 0.007207 B 1.552825 NaN C NaN 1.018601","s":"透视表","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#pivot-tables","p":1985},{"i":2029,"t":"pandas 在对频率转换进行重新采样时拥有简单、强大且高效的功能 (如将按秒采样的数据转换为按 5 分钟为单位进行采样的数据)。这种操作常见于 (但并不限于) 金融领域。 In [104]: rng = pd.date_range(\"1/1/2012\", periods=100, freq=\"S\") In [105]: ts = pd.Series(np.random.randint(0, 500, len(rng)), index=rng) In [106]: ts.resample(\"5Min\").sum() Out[106]: 2012-01-01 24182 Freq: 5T, dtype: int64 Series.tz_localize 将时间序列本地化到时区： In [107]: rng = pd.date_range(\"3/6/2012 00:00\", periods=5, freq=\"D\") In [108]: ts = pd.Series(np.random.randn(len(rng)), rng) In [109]: ts Out[109]: 2012-03-06 1.857704 2012-03-07 -1.193545 2012-03-08 0.677510 2012-03-09 -0.153931 2012-03-10 0.520091 Freq: D, dtype: float64 In [110]: ts_utc = ts.tz_localize(\"UTC\") In [111]: ts_utc Out[111]: 2012-03-06 00:00:00+00:00 1.857704 2012-03-07 00:00:00+00:00 -1.193545 2012-03-08 00:00:00+00:00 0.677510 2012-03-09 00:00:00+00:00 -0.153931 2012-03-10 00:00:00+00:00 0.520091 Freq: D, dtype: float64 Series.tz_convert 将时区感知时间序列转换为另一个时区： In [112]: ts_utc.tz_convert(\"US/Eastern\") Out[112]: 2012-03-05 19:00:00-05:00 1.857704 2012-03-06 19:00:00-05:00 -1.193545 2012-03-07 19:00:00-05:00 0.677510 2012-03-08 19:00:00-05:00 -0.153931 2012-03-09 19:00:00-05:00 0.520091 Freq: D, dtype: float64 向时间序列添加非固定持续时间 pandas.tseries.offsets.BusinessDay： In [113]: rng Out[113]: DatetimeIndex(['2012-03-06', '2012-03-07', '2012-03-08', '2012-03-09', '2012-03-10'], dtype='datetime64[ns]', freq='D') In [114]: rng + pd.offsets.BusinessDay(5) Out[114]: DatetimeIndex(['2012-03-13', '2012-03-14', '2012-03-15', '2012-03-16', '2012-03-16'], dtype='datetime64[ns]', freq=None)","s":"时间序列","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#time-series","p":1985},{"i":2031,"t":"pandas 可以在“DataFrame”中包含分类数据。 In [115]: df = pd.DataFrame( .....: {\"id\": [1, 2, 3, 4, 5, 6], \"raw_grade\": [\"a\", \"b\", \"b\", \"a\", \"a\", \"e\"]} .....: ) .....: Converting the raw grades to a categorical data type: In [116]: df[\"grade\"] = df[\"raw_grade\"].astype(\"category\") In [117]: df[\"grade\"] Out[117]: 0 a 1 b 2 b 3 a 4 a 5 e Name: grade, dtype: category Categories (3, object): ['a', 'b', 'e'] 将类别重命名为更有意义的名称： In [118]: new_categories = [\"very good\", \"good\", \"very bad\"] In [119]: df[\"grade\"] = df[\"grade\"].cat.rename_categories(new_categories) 对类别重新排序并同时添加缺少的类别 (Series.cat 方法默认返回一个新的 Series)： In [120]: df[\"grade\"] = df[\"grade\"].cat.set_categories( .....: [\"very bad\", \"bad\", \"medium\", \"good\", \"very good\"] .....: ) .....: In [121]: df[\"grade\"] Out[121]: 0 very good 1 good 2 good 3 very good 4 very good 5 very bad Name: grade, dtype: category Categories (5, object): ['very bad', 'bad', 'medium', 'good', 'very good'] 排序是按照类别中的顺序，而不是词汇顺序： In [122]: df.sort_values(by=\"grade\") Out[122]: id raw_grade grade 5 6 e very bad 1 2 b good 2 3 b good 0 1 a very good 3 4 a very good 4 5 a very good 按带有 observed=False 的分类列分组也会显示空类别： In [123]: df.groupby(\"grade\", observed=False).size() Out[123]: grade very bad 1 bad 0 medium 0 good 2 very good 3 dtype: int64","s":"分类数据","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#categoricals","p":1985},{"i":2033,"t":"我们使用标准约定来引用 matplotlib API： In [124]: import matplotlib.pyplot as plt In [125]: plt.close(\"all\") The plt.close method is used to close a figure window: In [126]: ts = pd.Series(np.random.randn(1000), index=pd.date_range(\"1/1/2000\", periods=1000)) In [127]: ts = ts.cumsum() In [128]: ts.plot(); 信息 使用 Jupyter 时，绘图将使用 Series.plot 显示。或使用 matplotlib.pyplot.show 显示绘图，或使用 matplotlib.pyplot.savefig 将其写入文件。 DataFrame.plot 绘制所有列： In [129]: df = pd.DataFrame( .....: np.random.randn(1000, 4), index=ts.index, columns=[\"A\", \"B\", \"C\", \"D\"] .....: ) .....: In [130]: df = df.cumsum() In [131]: plt.figure(); In [132]: df.plot(); In [133]: plt.legend(loc='best');","s":"绘图","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#plotting","p":1985},{"i":2036,"t":"使用 DataFrame.to_csv 写入 csv 文件： In [134]: df = pd.DataFrame(np.random.randint(0, 5, (10, 5))) In [135]: df.to_csv(\"foo.csv\") 使用 pandas.to_csv 读取 csv 文件： In [136]: pd.read_csv(\"foo.csv\") Out[136]: Unnamed: 0 0 1 2 3 4 0 0 4 3 1 1 2 1 1 1 0 2 3 2 2 2 1 4 2 1 2 3 3 0 4 0 2 2 4 4 4 2 2 3 4 5 5 4 0 4 3 1 6 6 2 1 2 0 3 7 7 4 0 4 4 4 8 8 4 4 1 0 1 9 9 0 4 3 0 3","s":"CSV","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#csv","p":1985},{"i":2038,"t":"使用 DataFrame.read_parquet 写入 Parquet 文件： In [137]: df.to_parquet(\"foo.parquet\") 使用 pandas.read_parquet 读取 Parquet 文件： In [138]: pd.read_parquet(\"foo.parquet\") Out[138]: 0 1 2 3 4 0 4 3 1 1 2 1 1 0 2 3 2 2 1 4 2 1 2 3 0 4 0 2 2 4 4 2 2 3 4 5 4 0 4 3 1 6 2 1 2 0 3 7 4 0 4 4 4 8 4 4 1 0 1 9 0 4 3 0 3","s":"Parquet","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#parquet","p":1985},{"i":2040,"t":"使用 DataFrame.to_excel 写入 Excel 文件： In [139]: df.to_excel(\"foo.xlsx\", sheet_name=\"Sheet1\") 使用 pandas.read_parquet 读取 Excel 文件： In [140]: pd.read_excel(\"foo.xlsx\", \"Sheet1\", index_col=None, na_values=[\"NA\"]) Out[140]: Unnamed: 0 0 1 2 3 4 1 1 1 0 2 3 2 0 0 4 3 1 1 2 2 2 1 4 2 1 2 3 3 0 4 0 2 2 4 4 4 2 2 3 4 5 5 4 0 4 3 1 6 6 2 1 2 0 3 7 7 4 0 4 4 4 8 8 4 4 1 0 1 9 9 0 4 3 0 3","s":"Excel","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#excel","p":1985},{"i":2042,"t":"如果您尝试对 Series 或 DataFrame 执行布尔运算，您可能会看到如下异常： In [141]: if pd.Series([False, True, False]): .....: print(\"I was true\") .....: --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-141-b27eb9c1dfc0> in ?() ----> 1 if pd.Series([False, True, False]): 2 print(\"I was true\") ~/work/pandas/pandas/pandas/core/generic.py in ?(self) 1517 @final 1518 def __nonzero__(self) -> NoReturn: -> 1519 raise ValueError( 1520 f\"The truth value of a {type(self).__name__} is ambiguous. \" 1521 \"Use a.empty, a.bool(), a.item(), a.any() or a.all().\" 1522 ) ValueError: The truth value of a Series is ambiguous. Use a.empty, a.bool(), a.item(), a.any() or 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(watchpoint)","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控点-watchpoint","p":1325},{"i":1342,"t":"监控进程中某个变量的值","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控进程中某个变量的值","p":1325},{"i":1344,"t":"监控进程中的某块内存","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控进程中的某块内存","p":1325},{"i":1346,"t":"设置监控的条件","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#设置监控的条件","p":1325},{"i":1348,"t":"删除监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#删除监控点","p":1325},{"i":1350,"t":"列出所有的监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#列出所有的监控点","p":1325},{"i":1354,"t":"读取内存","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#读取内存","p":1352},{"i":1356,"t":"读取若干十六进制的内存","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#读取若干十六进制的内存","p":1352},{"i":1358,"t":"从内存指定地址读取若干字节，并保存到本地文件","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#从内存指定地址读取若干字节并保存到本地文件","p":1352},{"i":1360,"t":"从内存指定地址范围读取字节，并保存到本地文件","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#从内存指定地址范围读取字节并保存到本地文件","p":1352},{"i":1363,"t":"列出可执行文件和所有依赖的共享库","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#列出可执行文件和所有依赖的共享库","p":1362},{"i":1365,"t":"查找可执行文件或任何共享库中原始地址信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#查找可执行文件或任何共享库中原始地址信息","p":1362},{"i":1367,"t":"在二进制文件中查找与正则表达式匹配的函数","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#在二进制文件中查找与正则表达式匹配的函数","p":1362},{"i":1369,"t":"查找完整的源代码行信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#查找完整的源代码行信息","p":1362},{"i":1371,"t":"仅在 a.out 中查找地址信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#仅在-aout-中查找地址信息","p":1362},{"i":1373,"t":"按名称查找类型 Point 的信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#按名称查找类型-point-的信息","p":1362},{"i":1376,"t":"检查变量","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#检查变量","p":1375},{"i":1377,"t":"显示变量的内容","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示变量的内容","p":1375},{"i":1379,"t":"显示当前栈帧的参数和局部变量","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前栈帧的参数和局部变量","p":1375},{"i":1381,"t":"检查数组","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#检查数组","p":1375},{"i":1383,"t":"检查寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#检查寄存器","p":1375},{"i":1384,"t":"显示当前线程的通用寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程的通用寄存器","p":1375},{"i":1386,"t":"显示当前线程的所有寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程的所有寄存器","p":1375},{"i":1388,"t":"显示当前线程中指定寄存器的值","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程中指定寄存器的值","p":1375},{"i":1390,"t":"显示当前线程中指定寄存器的值，格式为二进制","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程中指定寄存器的值格式为二进制","p":1375},{"i":1392,"t":"打印表达式结果的动态类型 (C++)","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#打印表达式结果的动态类型-c","p":1375},{"i":1396,"t":"安装","u":"/docs/modern-cpp/gdb-lldb/gef","h":"#安装","p":1394},{"i":1398,"t":"GEF 命令","u":"/docs/modern-cpp/gdb-lldb/gef","h":"#gef-命令","p":1394},{"i":1401,"t":"dump 可执行文件和所有共享库的 section 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和所有共享库的-section-信息","p":1400},{"i":1403,"t":"dump 可执行文件的 section 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件的-section-信息","p":1400},{"i":1405,"t":"dump 可执行文件和所有共享库的 symtab 符号","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和所有共享库的-symtab-符号","p":1400},{"i":1407,"t":"dump 可执行文件和指定共享库的 symtab 符号","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和指定共享库的-symtab-符号","p":1400},{"i":1410,"t":"设置断点和启动进程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#设置断点和启动进程","p":1409},{"i":1412,"t":"单步调试","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#单步调试","p":1409},{"i":1413,"t":"step-in 单步调试 (源码级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-in-单步调试-源码级别","p":1409},{"i":1415,"t":"step-over 单步调试 (源码级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-单步调试-源码级别","p":1409},{"i":1417,"t":"step-in 单步调试 (汇编指令级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-in-单步调试-汇编指令级别","p":1409},{"i":1419,"t":"step-over 单步调试 (汇编指令级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-单步调试-汇编指令级别","p":1409},{"i":1421,"t":"step-over 跳出栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-跳出栈帧","p":1409},{"i":1423,"t":"断点调试","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#断点调试","p":1409},{"i":1424,"t":"跳转到下一个断点","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#跳转到下一个断点","p":1409},{"i":1426,"t":"运行到指定行数","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#运行到指定行数","p":1409},{"i":1428,"t":"线程切换","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#线程切换","p":1409},{"i":1429,"t":"列出程序中的线程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#列出程序中的线程","p":1409},{"i":1431,"t":"设置后续命令的默认线程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#设置后续命令的默认线程","p":1409},{"i":1433,"t":"栈帧切换","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#栈帧切换","p":1409},{"i":1434,"t":"显示当前栈帧简略信息","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#显示当前栈帧简略信息","p":1409},{"i":1436,"t":"显示当前栈帧源代码行","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#显示当前栈帧源代码行","p":1409},{"i":1438,"t":"通过栈帧号选择栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#通过栈帧号选择栈帧","p":1409},{"i":1440,"t":"选择调用当前栈帧的栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#选择调用当前栈帧的栈帧","p":1409},{"i":1442,"t":"选择被当前栈帧调用的栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#选择被当前栈帧调用的栈帧","p":1409},{"i":1444,"t":"使用栈帧相对偏移选择栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#使用栈帧相对偏移选择栈帧","p":1409},{"i":1446,"t":"从栈帧返回，可以带有返回值","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#从栈帧返回可以带有返回值","p":1409},{"i":1448,"t":"调用带有断点的函数并在断点处停止","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#调用带有断点的函数并在断点处停止","p":1409},{"i":1450,"t":"调用 crash 的函数并在 crash 时停止","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#调用-crash-的函数并在-crash-时停止","p":1409},{"i":1453,"t":"重新映射调试对话的源文件路径","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#重新映射调试对话的源文件路径","p":1452},{"i":1455,"t":"调试服务器设置","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#调试服务器设置","p":1452},{"i":1456,"t":"连接到远程调试服务器","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#连接到远程调试服务器","p":1452},{"i":1458,"t":"连接到本地调试服务器","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#连接到本地调试服务器","p":1452},{"i":1460,"t":"临时变量和打印","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#临时变量和打印","p":1452},{"i":1461,"t":"创建临时变量并赋值","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#创建临时变量并赋值","p":1452},{"i":1463,"t":"在当前帧中的计算表达式","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#在当前帧中的计算表达式","p":1452},{"i":1465,"t":"打印信息到屏幕","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#打印信息��到屏幕","p":1452},{"i":1468,"t":"启动新的进程","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#启动新的进程","p":1467},{"i":1470,"t":"设置进程的运行参数","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#设置进程的运行参数","p":1467},{"i":1472,"t":"环境变量设置","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#环境变量设置","p":1467},{"i":1474,"t":"attach 到已有进程","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#attach-到已有进程","p":1467},{"i":1476,"t":"显示参数","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#显示参数","p":1467},{"i":1481,"t":"📄️ Bash 简介","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1482,"t":"📄️ Bash 的基本语法","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1483,"t":"📄️ Bash 的模式扩展","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1484,"t":"📄️ 引号和转义","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1485,"t":"📄️ Bash 变量","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1486,"t":"📄️ 字符串操作","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1487,"t":"📄️ Bash 的算术运算","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1488,"t":"📄️ 操作历史","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1489,"t":"📄️ Bash 行操作","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1490,"t":"📄️ 目录堆栈","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1491,"t":"📄️ Bash 脚本入门","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1492,"t":"📄️ read 命令","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1493,"t":"📄️ 条件判断","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1494,"t":"📄️ 循环","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1495,"t":"📄️ Bash 函数","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1496,"t":"📄️ 数组","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1497,"t":"📄️ set 命令，shopt 命令","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1498,"t":"📄️ 脚本除错","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1499,"t":"📄️ mktemp 命令，trap 命令","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1500,"t":"📄️ Bash 启动环境","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1501,"t":"📄️ 命令提示符","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1503,"t":"算术表达式","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#算术表达式","p":1502},{"i":1505,"t":"数值的进制","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#数值的进制","p":1502},{"i":1507,"t":"位运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#位运算","p":1502},{"i":1509,"t":"逻辑运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#逻辑运算","p":1502},{"i":1511,"t":"赋值运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#赋值运算","p":1502},{"i":1513,"t":"求值运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#求值运算","p":1502},{"i":1515,"t":"expr 命令","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#expr-命令","p":1502},{"i":1517,"t":"let 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等大语言模型的核心基础架构。","s":"Transformer 概览","u":"/docs/machine-learning/transformer/transformer-overview","p":1277},{"i":1282,"t":"为什么需要位置编码","s":"位置编码","u":"/docs/machine-learning/transformer/transformer-positional-encoding","p":1282},{"i":1291,"t":"论文通过添加一种称为“多头”注意力的机制进一步细化了自注意力。它扩展了模型关注不同位置的能力。","s":"分割的多头注意力机制","u":"/docs/machine-learning/transformer/transformer-split-multi-head-attention","p":1291},{"i":1293,"t":"Informer","s":"Transformer 的变种","u":"/docs/machine-learning/transformer/transformer-variants","p":1293},{"i":1304,"t":"回溯 (backtrace)","s":"回溯和反汇编","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","p":1304},{"i":1325,"t":"断点 (breakpoint)","s":"断点和监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","p":1325},{"i":1352,"t":"形式：x/count fmt size 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模板元编程可以解决这个问题，在编译时计算斐波那契数列，从而提高执行效率。 斐波那契数列有两种： 从 000 开始： 0,1,1,2,3,5,8,...0,1,1,2,3,5,8,...0,1,1,2,3,5,8,... 从 111 开始： 1,1,2,3,5,8,...1,1,2,3,5,8,...1,1,2,3,5,8,... 我们假设从 000 开始，即 f(0)=0，f(1)=1，f(2)=1，... f(0) = 0，f(1) = 1，f(2) = 1，...f(0)=0，f(1)=1，f(2)=1，...。","s":"模板元编程：斐波那契数列","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"","p":3},{"i":6,"t":"/** * @file fibonacci_recursive.cpp * @brief calculate fibonacci value recursively */ #include <iostream> unsigned int calc_fibonacci(unsigned int i) { if (i == 0 || i == 1) { return i; } return calc_fibonacci(i - 1) + calc_fibonacci(i - 2); }; int main() { std::cout << calc_fibonacci(42) << '\\n'; return 0; } > g++ -O0 -g a.out fibonacci_recursive.cpp -o prog_fibonacci_recursive > ./prog_fibonacci_recursive 267914296 > hyperfine \"./prog_fibonacci_recursive\" Benchmark 1: ./prog_fibonacci_recursive Time (mean ± σ): 1.657 s ± 0.015 s [User: 1.652 s, System: 0.002 s] Range (min … max): 1.647 s … 1.696 s 10 runs","s":"传统递归","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#传统递归","p":3},{"i":9,"t":"首先，我们定义一个模板类 fibonacci，它具有一个静态成员变量 value，用于存储斐波那契数列的值。该模板类使用递归定义，根据给定的大小计算斐波那契数列值。 template <int size> struct fibonacci { static constexpr unsigned int value = fibonacci<size - 1>::value + fibonacci<size - 2>::value; }; template <> struct fibonacci<0> { static constexpr unsigned int value = 0; }; template <> struct fibonacci<1> { static constexpr unsigned int value = 1; }; 使用 fibonacci<42>::value 则可以得到对应的结果。这个语法类似于传统的递归，但是会在编译期进行求值。 使用模板元编程的斐波那契数列计算方法相比于传统的递归方法具有更高的效率。它在编译时完成计算，避免了运行时的重复计算，从而提高了程序的性能。 这里使用了编译期求值的关键字 constexpr，因此需要 C++11 版本及以上。 > g++ -O0 -g -std=c++11 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp > ./prog_fibonacci_tmp 267914296 > hyperfine \"./prog_fibonacci_tmp\" Benchmark 1: ./prog_fibonacci_tmp Time (mean ± σ): 0.8 ms ± 0.1 ms [User: 0.9 ms, System: 0.2 ms] Range (min … max): 0.6 ms … 1.5 ms 1605 runs 在计算第 42 个斐波那契数的时候，运行时间仅需 ~0.8ms，相当于传统递归方法 ~1.6s 的 1/2000。","s":"C++11","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#c11","p":3},{"i":11,"t":"在 C++17 中，通常使用 _v 结尾当作 value 类型 (参见这篇 proposal)，比如： template <struct T> constexpr bool is_integral_v = is_integral<T>::value; 类似的，我们可以定义一个模板变量 fibonacci_v，用于方便地获取斐波那契数列的值。 template <int size> constexpr auto fibonacci_v = fibonacci<size>::value; 注意，这种 _v 的实现并不需要 C++17 的编译器；C++14 的编译器即可以满足需求。 编译： > g++ -O0 -g -std=c++14 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp","s":"C++14","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#c14","p":3},{"i":13,"t":"C++20 中，我们可以使用 concept / requires，合并两个偏特化模板。 template <int size> concept FibonacciBaseCase = (size == 0) || (size == 1); template <int size> requires FibonacciBaseCase<size> struct fibonacci<size> { public: static constexpr unsigned int value = size; }; 编译： > g++ -O0 -g -std=c++20 a.out fibonacci_tmp.cpp -o prog_fibonacci_tmp","s":"C++20","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#c20","p":3},{"i":15,"t":"c++11 c++14 c++20 #include <iostream> template <int size> struct fibonacci { public: static constexpr unsigned int value = fibonacci<size - 1>::value + fibonacci<size - 2>::value; }; template <> struct fibonacci<0> { public: static constexpr unsigned int value = 0; }; template <> struct fibonacci<1> { public: static constexpr unsigned int value = 1; }; int main() { std::cout << fibonacci<42>::value << '\\n'; return 0; } #include <iostream> template <int size> struct fibonacci { public: static constexpr unsigned int value = fibonacci<size - 1>::value + fibonacci<size - 2>::value; }; template <> struct fibonacci<0> { public: static constexpr unsigned int value = 0; }; template <> struct fibonacci<1> { public: static constexpr unsigned int value = 1; }; template <int size> constexpr auto fibonacci_v = fibonacci<size>::value; int main() { // std::cout << fibonacci<42>::value << '\\n'; std::cout << fibonacci_v<42> << '\\n'; return 0; } #include <iostream> template <int size> struct fibonacci { public: static constexpr unsigned int value = fibonacci<size - 1>::value + fibonacci<size - 2>::value; }; // template <> // struct fibonacci<0> { // public: // static constexpr unsigned int value = 0; // }; // template <> // struct fibonacci<1> { // public: // static constexpr unsigned int value = 1; // }; template <int size> concept FibonacciBaseCase = (size == 0) || (size == 1); template <int size> requires FibonacciBaseCase<size> struct fibonacci<size> { public: static constexpr unsigned int value = size; }; template <int size> constexpr auto fibonacci_v = fibonacci<size>::value; int main() { std::cout << fibonacci_v<42> << '\\n'; return 0; } 通过使用模板元编程技术，我们可以在编译时计算斐波那契数列，避免了递归函数的重复计算，在一些需要高效计算斐波那契数列的场景下，这种方法可以提供更好的性能。 希望这篇博客能帮助你理解如何使用模板元编程实现斐波那契数列的编译期计算，并对此有所启发。","s":"完整代码","u":"/blog/cpp/calculate-fibonnaci-with-template-meta-programming","h":"#完整代码","p":3},{"i":17,"t":"Ubuntu 22.04 默认使用 g++-11 和 clang++-14 作为默认的 g++ 和 clang++。 本文说明如何升级 C++ 编译器并设置默认版本，从而使用最新的 C++ 语言特性。","s":"Ubuntu 22.04 更新 C++ 编译器","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"","p":16},{"i":20,"t":"sudo apt update sudo add-apt-repository ppa:ubuntu-toolchain-r/test sudo apt install gcc-12 g++-12 -y sudo apt install gcc-13 g++-13 -y","s":"安装最新的 g++","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#install-latest-g++","p":16},{"i":22,"t":"参见 LLVM Debian/Ubuntu Packages 中的安装指南： wget https://apt.llvm.org/llvm.sh chmod +x llvm.sh # sudo ./llvm.sh <version number> all # or # sudo ./llvm.sh all sudo ./llvm.sh 18 all","s":"安装最新的 clang++","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#install-latest-clang++","p":16},{"i":24,"t":"上述命令执行之后，我们会发现，g++ 仍然是 g++11，clang++ 仍然是 clang++-14。 这里介绍一下 update-alternatives，由于管理 Ubuntu 上软件版本的切换，使其多版本共存。语法： 注册可选的软件版本： sudo update-alternatives --install link name path priority \\ [--slave link name path] 切换默认的软件版本： sudo update-alternatives --config name 注意 切换编译器软件包可能有风险，建议只在个人计算机上使用。","s":"切换编译器的默认版本","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#change-default-version","p":16},{"i":26,"t":"注册 gcc / g++ 版本： sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-11 11 --slave /usr/bin/g++ g++ /usr/bin/g++-11 sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-12 12 --slave /usr/bin/g++ g++ /usr/bin/g++-12 sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-13 13 --slave /usr/bin/g++ g++ /usr/bin/g++-13 选择默认 gcc / g++ 版本： sudo update-alternatives --config gcc 会弹出以下选项： There are 3 choices for the alternative gcc (providing /usr/bin/gcc). Selection Path Priority Status ------------------------------------------------------------ * 0 /usr/bin/gcc-13 13 auto mode 1 /usr/bin/gcc-11 11 manual mode 2 /usr/bin/gcc-12 12 manual mode 3 /usr/bin/gcc-13 13 manual mode Press <enter> to keep the current choice[*], or type selection number: 输入序号即可。","s":"切换 g++ 的默认版本","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#change-g++-default-version","p":16},{"i":28,"t":"clang / clang++ 是 LLVM 工具链的一部分，更新的时候，建议把 llvm 所有工具一起更新。 这里使用以下脚本 update-alternatives-clang.sh 进行批量注册： #!/usr/bin/env bash # Colors RESET=$(tput sgr0) RED=$(tput setaf 1) GREEN=$(tput setaf 2) BOLD=$(tput bold) # Get available versions from /lib/llvm-* # You can also use specific versions, e.g. VERSIONS=(\"14\" \"17\" \"18\"), but not recommend VERSIONS=() for dir in /lib/llvm-*; do if [[ -d \"$dir\" ]]; then version=$(basename \"$dir\" | cut -d'-' -f2) VERSIONS+=(\"$version\") fi done # Loop through versions for VERSION in \"${VERSIONS[@]}\"; do # Check if /lib/llvm-${VERSION} directory exists if [[ -d \"/lib/llvm-${VERSION}\" ]]; then # Scan paths and generate string alternative_string=\"\" alternative_cmds=() for cmd in \"/lib/llvm-${VERSION}/bin/\"*; do if [[ -x \"$cmd\" ]] && [[ \"$(basename \"$cmd\")\" != \"clang\" ]]; then base_cmd=$(basename \"$cmd\") symlink=\"/usr/bin/${base_cmd}-${VERSION}\" if [[ -x \"${symlink}\" ]]; then alternative_cmds+=($(basename ${symlink})) alternative_string+=\"--slave /usr/bin/${base_cmd} ${base_cmd} ${symlink} \" fi fi done # Remove specific alternative configuration sudo update-alternatives --remove clang \"/usr/bin/clang-${VERSION}\" > /dev/null # Install alternatives install_command=\"sudo update-alternatives \\ --quiet \\ --install /usr/bin/clang clang /usr/bin/clang-${VERSION} ${VERSION} \\ ${alternative_string}\" # Print the concatenated string echo \"${BOLD}${GREEN}[Adding alternative /usr/bin/clang-${VERSION} ...]${RESET}\" echo \"Master command: clang-${VERSION}\" echo \"Slave commands: ${alternative_cmds[*]}\" eval \"$install_command\" # Check eval command's return value if [[ $? -eq 0 ]]; then echo \"${BOLD}${GREEN}[Adding alternative /usr/bin/clang-${VERSION}: succeeded]${RESET}\" else echo \"${BOLD}${RED}[Adding alternative /usr/bin/clang-${VERSION}: failed]${RESET}\" fi echo \"\" else # Remove specific alternative configuration if /lib/llvm-${VERSION} directory does not exist sudo update-alternatives --remove clang \"/usr/bin/clang-${VERSION}\" &> /dev/null fi done clang_path=$(sudo update-alternatives --get-selections | grep ^clang | awk '{print $NF}') echo \"======================================================================\" echo \"${GREEN}clang alternative is set to: ${clang_path}${RESET}\" echo \"======================================================================\" # print helps echo \"\" echo \"Info:\" num_versions=${#VERSIONS[@]} if [[ num_versions -gt 1 ]]; then echo \" use '${GREEN}sudo update-alternatives --config clang${RESET}' to change default clang alternative\" fi echo \" use '${GREEN}sudo update-alternatives --remove clang /usr/bin/clang-*${RESET}' to delete a clang alternative\" echo \" use '${GREEN}sudo update-alternatives --remove-all clang${RESET}' to delete all clang alternatives\" sudo bash update-alternatives-clang.sh 结果如下： [Adding alternative /usr/bin/clang-14 ...] Master command: clang-14 Slave commands: analyze-build-14 bugpoint-14 ... [Adding alternative /usr/bin/clang-14: succeeded] [Adding alternative /usr/bin/clang-18 ...] Master command: clang-18 Slave commands: amdgpu-arch-18 analyze-build-18 ... [Adding alternative /usr/bin/clang-18: succeeded] ====================================================================== clang alternative is set to: /usr/bin/clang-18 ====================================================================== ... 同上面的 gcc/g++ 版本切换，切换 clang / llvm 工具链版本命令如下： sudo update-alternatives --config clang 会弹出以下选项： There are 2 choices for the alternative clang (providing /usr/bin/clang). Selection Path Priority Status ------------------------------------------------------------ * 0 /usr/bin/clang-18 18 auto mode 1 /usr/bin/clang-14 14 manual mode 2 /usr/bin/clang-18 18 manual mode Press <enter> to keep the current choice[*], or type selection number: 输入序号即可。","s":"切换 clang++ 的默认版本","u":"/blog/cpp/update-compiler-on-ubuntu2204","h":"#change-clang++-default-version","p":16},{"i":30,"t":"Leaflet 是地理信息系统（GIS）中流行的开源 JavaScript 库。 本文在 MDX 中使用 Leaflet 绘制交互式地图。","s":"使用 Leaflet 绘制地图","u":"/blog/mdx/interactive-map-with-leaflet","h":"","p":29},{"i":32,"t":"博客文章支持 Docusaurus Markdown 功能，例如 MDX。","s":"React 支持","u":"/blog/mdx/react-support","h":"","p":31},{"i":34,"t":"提示 使用 React 的强大功能来创建交互式博客文章。 <button onClick={() => alert('按钮被点击了!')}>点击这里！</button> 点击这里！","s":"交互式","u":"/blog/mdx/react-support","h":"#interactive","p":31},{"i":36,"t":"提示 使用 React 的强大功能来创建图表。 import {Chart} from './_asset/snowfall.js'; export const year = 2013; # 去年降雪 {year} 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。 <Chart year={year} color=\"#fcb32c\" />; 去年降雪 2013 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。","s":"图表式","u":"/blog/mdx/react-support","h":"#diagram","p":31},{"i":38,"t":"2013 年的降雪量高于平均水平。随之而来的暖春，导致附近许多河流发生洪水。","s":"去年降雪","u":"/blog/mdx/react-support","h":"","p":31},{"i":40,"t":"现在可以在 mdx 中使用 Font Awesome 图标。 <FontAwesomeIcon icon=\"fa-brands fa-react\" /> 这是 React 图标。 <FontAwesomeIcon icon=\"fa-brands fa-github\" size=\"xl\" /> 这是加大的 GitHub 图标。 这是 React 图标。 这是加大的 GitHub 图标。 默认情况下，图标继承其父容器的字体大小。现代浏览器使用默认字体大小 16px。 要更改字体大小，请在 FontAwesomeIcon 中添加以下 size 属性： 2xs: 0.625em (10px) xs: 0.75em (12px) sm: 0.875em (14px) lg: 1.25em (20px) xl: 1.5em (24px) 2xl: 2em (32px) 1x ~ 10x: 1em ~ 10em","s":"支持 Font Awesome","u":"/blog/mdx/support-fontawesome","h":"","p":39},{"i":42,"t":"Docusaurus 提供了 <Tabs> 和 <TabItem> 组件，可以通过 MDX 在 Markdown 中使用该组件。 我们在全局内对其进行了配置，因此该功能可在本站任何页面使用。 <Tabs> <TabItem value=\"apple\" label=\"Apple\" default> This is an apple 🍎 </TabItem> <TabItem value=\"orange\" label=\"Orange\"> This is an orange 🍊 </TabItem> <TabItem value=\"banana\" label=\"Banana\"> This is a banana 🍌 </TabItem> </Tabs> This is an apple 🍎 This is an orange 🍊 This is a banana 🍌","s":"支持全局 Tabs 和 TabItem","u":"/blog/mdx/support-global-tabs-tabitem","h":"","p":41},{"i":44,"t":"数学公式可以使用 KaTeX 渲染，目前本站已经支持。","s":"支持 LaTeX 数学公式","u":"/blog/mdx/support-math-latex","h":"","p":43},{"i":46,"t":"请阅读 KaTeX 文档了解更多详细信息。","s":"用法","u":"/blog/mdx/support-math-latex","h":"#usage","p":43},{"i":48,"t":"对于行内数学公式，将 LaTeX 包裹在 $ 之间： 假设 $f\\colon[a,b]\\to\\R$ 是黎曼可积的，定义 $F\\colon[a,b]\\to\\R$ 为 $F(x)=\\int_{a}^{x} f(t)\\,dt$。那么， $F$ 是连续的；并且 $x$ 在 $f$ 在 $x$ 处连续；$F$ 在 $x$ 处可微，且 $F'(x)=f(x)$。 假设 f ⁣:[a,b]→Rf\\colon[a,b]\\to\\Rf:[a,b]→R 是黎曼可积的，定义 F ⁣:[a,b]→RF\\colon[a,b]\\to\\RF:[a,b]→R 为 F(x)=∫axf(t) dtF(x)=\\int_{a}^{x} f(t)\\,dtF(x)=∫ax​f(t)dt。那么， FFF 是连续的；并且 xxx 在 fff 在 xxx 处连续；FFF 在 xxx 处可微，且 F′(x)=f(x)F'(x)=f(x)F′(x)=f(x)。","s":"行内公式","u":"/blog/mdx/support-math-latex","h":"#inline","p":43},{"i":50,"t":"对于公式块，使用换行符和 $$ 隔开： $$ I = \\int_0^{2\\pi} \\sin(x)\\,dx $$ I=∫02πsin⁡(x) dxI = \\int_0^{2\\pi} \\sin(x)\\,dxI=∫02π​sin(x)dx","s":"公式块","u":"/blog/mdx/support-math-latex","h":"#blocks","p":43},{"i":52,"t":"Mermaid 是一个绘制图表的工具。 请参阅 Mermaid 教程 并使用 Mermaid 实时编辑 来进行绘图。","s":"支持 Mermaid 图表","u":"/blog/mdx/support-mermaid-diagrams","h":"","p":51},{"i":54,"t":"Example Mermaid sequence diagram ```mermaid graph TD; A-->B; A-->C; B-->D; C-->D; ```","s":"序列图","u":"/blog/mdx/support-mermaid-diagrams","h":"#序列图","p":51},{"i":56,"t":"Example Mermaid flowchart ```mermaid flowchart TD A[Christmas] -->|Get money| B(Go shopping) B --> C{Let me think} C -->|One| D[Laptop] C -->|Two| E[iPhone] C -->|Three| F[fa:fa-car Car] ```","s":"流程图","u":"/blog/mdx/support-mermaid-diagrams","h":"#流程图","p":51},{"i":58,"t":"基于 Docusaurus 提供的 MDX 组件，本站支持嵌入 YouTube 和 Bilibili 视频。","s":"支持嵌入 YouTube 和 Bilibili 视频","u":"/blog/mdx/support-video-link","h":"","p":57},{"i":60,"t":"React 组件： YouTube / Bilibili 组件参数： id: 必选 YouTube: https://www.youtube.com/watch?v=<id>?... 或者 https://youtu.be/<id>?... Bilibili: https://www.bilibili.com/video/<id>/?...，由 BV 开头。 title: 可选。位置在视频上方；左对齐。","s":"参数说明","u":"/blog/mdx/support-video-link","h":"#参数说明","p":57},{"i":63,"t":"<YouTube id=\"sEQf5lcnj_o\" title=\"Animenz - Unravel [Piano Ver.]\" /> Animenz - Unravel [Piano Ver.]","s":"YouTube 嵌入","u":"/blog/mdx/support-video-link","h":"#youtube-嵌入","p":57},{"i":65,"t":"<Bilibili id=\"BV1bi4y1675m\" title=\"Animenz - Unravel [钢琴版]\" /> Animenz - Unravel [钢琴版]","s":"Bilibili 嵌入","u":"/blog/mdx/support-video-link","h":"#bilibili-嵌入","p":57},{"i":68,"t":"2023年11月24日 Sol 千里之行，始于足下。","s":"支持 LaTeX 数学公式","u":"/blog/page/2","h":"","p":66},{"i":70,"t":"2023年11月23日 Sol 千里之行，始于足下。","s":"React 支持","u":"/blog/page/2","h":"","p":66},{"i":72,"t":"2019年5月28日 Sol 千里之行，始于足下。","s":"欢迎","u":"/blog/page/2","h":"","p":66},{"i":74,"t":"本站默认字体现已更改为 LxgwWenKai Screen.","s":"更改默认字体","u":"/blog/site/change-default-fonts","h":"","p":73},{"i":76,"t":"删除所有的文章的国际化支持。之前所有文章均有双语版本，后续所有文章只会有单个语言版本。 由于难以长期维护和保证内容的一致性，删除所有的双语文章和 docusaurus i18n 国际化配置： 双语文章需要额外的翻译时间。 本站使用 docusaurus 部署，但是 docusaurus 在全局化存在各种问题，包括但不限于： 需要保证文章链接的一致性，否则无法相互跳转。 需要保证锚点 (anchor tag) 的一致性。 假设配置是英文为主语言，这种情况下，不可以单独发表中文文章。如果要写中文文章，必须先存在的英文文章。 中英文链接在不同目录，且层级不同，来回切换不方便。 翻译不是一劳永逸的事情，每次更新某个语言的文章的时候，需要更新同时两种语言。","s":"停止国际化支持","u":"/blog/site/remove-i18n-support","h":"","p":75},{"i":78,"t":"本站使用 autocorrect 对中文内容进行统一排版和修正。","s":"统一中文排版","u":"/blog/tools/cli/autocorrect","h":"","p":77},{"i":80,"t":"Docusaurus 博客功能由 blog 插件提供支持。 使用 <!-- truncate --> 注释来限制博客预览。 只需要将 Markdown 文件 (或文件夹) 添加到 blog 目录即可。 常用的博客作者可以添加到 authors.yml 中。 可以从文件名中提取博客文章日期，例如： 2019-05-30-welcome.md 2019-05-30-welcome/index.md 写博客时，可以方便地在同级文件夹内引用图像： 博客也支持标签！ 如果不需要博客：删除此目录，并在 Docusaurus 配置中使用 blog: false 即可。","s":"欢迎","u":"/blog/welcome","h":"","p":79},{"i":83,"t":"MainActivity.kt 内的 onCreate() 最后添加： val looperThread = LooperThread() looperThread.start() thread { Thread.sleep(3000) val message = Message() message.what = LooperThread.EVENT_INIT message.target = looperThread.getHandler() Log.d( \"MainActivity\", \"send message ${message.what} at thread id ${Thread.currentThread().id}\" ) message.sendToTarget() } 新建 LooperThread.kt： package com.example.myapplication import android.os.Handler import android.os.Looper import android.os.Message import android.util.Log class LooperThread : Thread() { private var handler: Handler? = null private var isInitialized = false fun getHandler(): Handler? { return handler } override fun run() { Looper.prepare() handler = object : Handler(Looper.myLooper()!!) { override fun handleMessage(msg: Message) { Log.d( TAG, \"Received message ${msg.what} at thread id ${ currentThread().id }\" ) when (msg.what) { EVENT_INIT -> { performInit() } else -> println(\"Unknown Event: \" + msg.what) } } } isInitialized = true Looper.loop() } fun isInitialized(): Boolean { return isInitialized } private fun performInit() { Log.d(TAG, \"performInit() called\") sleep(1000); } companion object { const val EVENT_INIT: Int = 1 private const val TAG = \"LooperThread\" } }","s":"方法一：创建一个 Thread 线程","u":"/docs/android-framework/handler/create-a-thread-with-looper","h":"#方法一创建一个-thread-线程","p":81},{"i":85,"t":"MainActivity.kt 内的 onCreate() 最后添加： val myHandlerThread = MyHandlerThread(\"MyHandlerThreadA\") myHandlerThread.start() thread { Thread.sleep(3000) val message = Message() message.what = MyHandlerThread.EVENT_INIT message.target = myHandlerThread.handler Log.d( \"MainActivity\", \"send message ${message.what} at thread id ${Thread.currentThread().id}\" ) message.sendToTarget() } 新建 MyHandlerThread.kt： package com.example.myapplication import android.os.Handler import android.os.HandlerThread import android.os.Looper import android.os.Message import android.util.Log public class MyHandlerThread(name: String?) : HandlerThread(name) { lateinit var handler: Handler; override fun onLooperPrepared() { super.onLooperPrepared() handler = object : Handler(Looper.myLooper()!!) { override fun handleMessage(msg: Message) { Log.d( TAG, \"Received message ${msg.what} at thread id ${ currentThread().id }\" ) when (msg.what) { EVENT_INIT -> performInit() else -> println(\"Unknown Event: \" + msg.what) } } } } private fun performInit() { Log.d(TAG, \"performInit() called\") sleep(1000); } companion object { const val EVENT_INIT: Int = 1 private const val TAG = \"MyHandlerThread\" } }","s":"方法二：创建一个 HandlerThread 线程","u":"/docs/android-framework/handler/create-a-thread-with-looper","h":"#方法二创建一个-handlerthread-线程","p":81},{"i":88,"t":"一套 Android 消息传递机制 / 异步通信机制","s":"定义","u":"/docs/android-framework/handler/handler-introduction","h":"#定义","p":86},{"i":90,"t":"在 Android 开发中，UI 线程 (主线程) 负责处理用户界面的交互和更新。 如果 UI 线程被长时间阻塞或执行耗时操作，将会导致用户界面的响应性降低，用户体验很差。 如果在主线程进行大量耗时操作，没有响应用户输入事件 (如点击、滑动等) 时，Android 系统会认为应用程序无响应，并弹出 ANR (Application Not Responding) 对话框提醒用户。这个时间阈值通常为 5 秒。","s":"背景","u":"/docs/android-framework/handler/handler-introduction","h":"#背景","p":86},{"i":92,"t":"UI 线程 (主线程) 不能进行大量耗时的工作，需要使用子线程 (工作线程) 处理。 如果工作线程直接尝试更新 UI 组件，就会违反 Android 的线程安全规定，可能会导致应用程序崩溃或界面异常。","s":"问题","u":"/docs/android-framework/handler/handler-introduction","h":"#问题","p":86},{"i":94,"t":"使用 Handler 机制进行线程间通信： 启动一个子线程 (工作线程) 进行耗时的任务处理，可以向 UI 线程的 Handler 发送消息。 UI 线程的 Handler 收到消息后，在主线程中更新 UI 组件。 这样可以保证 UI 操作在主线程中执行，从而避免线程安全问题。","s":"解决方案","u":"/docs/android-framework/handler/handler-introduction","h":"#解决方案","p":86},{"i":96,"t":"下图说明了子线程进行耗时操作，并且更新主线程的流程。 流程 Handler 类流程 真实世界类比 1 创建 Looper 对象并启动 创建一个工厂车间的传送带系统 2 创建 MessageQueue 对象 准备用于存放货物的货物槽链 3 创建 Handler 对象并和 Looper 对象关联 为传送带指派一名专门的处理人员 4 在工作线程中执行耗时操作 在另一个车间进行耗时的生产加工 5 将需要通知主线程的更新信息封装在 Message 对象中 将需要通知处理人员的货物信息打包到货物槽 6 将 Message 对象添加到 MessageQueue 中 将打包好的货物放入货物槽 7 Looper 不断循环读取 MessageQueue 中的 Message 传送带不断运转，读取其中的货物槽的信息 8 Looper 取出 Message 对象，并分发给关联的 Handler 处理 处理人员取出货物槽，交给对应的处理人员进行处理 9 Handler 的 handleMessage() 方法中更新 UI 组件 处理人员根据货物槽内的信息，执行相应的处理操作","s":"和真实世界类比","u":"/docs/android-framework/handler/handler-introduction","h":"#和真实世界类比","p":86},{"i":98,"t":"一个线程最多只有一个 Looper 对象，一个 Looper 对象只和一个线程关联 主线程创建 Looper：Android 主线程都是 Activity，在 ActivityThread 内会自动创建 子线程创建 Looper： 继承于 Thread，在 run() 里面调用 Looper.prepare() 和 Looper.loop() 继承于 HandlerThread，自动创建 一个 Looper 对象中必须有且仅有一个 MessageQueue 对象 一个 Looper 对象可以关联 0 到多个 Handler 对象","s":"Handler / Looper / Thread 的关系","u":"/docs/android-framework/handler/handler-introduction","h":"#handler--looper--thread-的关系","p":86},{"i":101,"t":"创建 Looper 时会同步创建 MessageQueue 对象 主线程 Looper 的创建​ ActivityThread.main() 调用 Looper.prepareMainLooper() 和 Looper.loop() /** * 源码分析：Looper.prepareMainLooper() * 作用：为主线程（UI 线程）创建 1 个循环器对象（Looper），同时也生成了 1 个消息队列对象（MessageQueue） * 注：该方法在主线程（UI 线程）创建时自动调用，即 主线程的 Looper 对象自动生成，不需手动生成 */ // 在Android应用进程启动时，会默认创建1个主线程（ActivityThread，也叫 UI 线程） // 创建时，会自动调用 ActivityThread 的1个静态的 main() 方法 = 应用程序的入口 // main() 内则会调用 Looper.prepareMainLooper() 为主线程生成 1 个 Looper 对象 public static void main(String[] args) { ... // 1. 为主线程创建 1 个 Looper 对象，同时生成 1 个消息队列对象（MessageQueue） // 方法逻辑类似 Looper.prepare() // 注：prepare()：为子线程中创建 1 个 Looper 对象 Looper.prepareMainLooper(); ... // 2. 创建主线程 ActivityThread thread = new ActivityThread(); ... // 3. 自动开启消息循环 Looper.loop(); } Looper.prepareMainLooper()：在主线程中创建 1 个 Looper 对象 (自动生成) /** * Initialize the current thread as a looper, marking it as an * application's main looper. See also: {@link #prepare()} * * @deprecated The main looper for your application is created by the Android environment, * so you should never need to call this function yourself. */ @Deprecated public static void prepareMainLooper() { prepare(false); synchronized (Looper.class) { if (sMainLooper != null) { throw new IllegalStateException(\"The main Looper has already been prepared.\"); } sMainLooper = myLooper(); } } Looper.myLooper() /** * Return the Looper object associated with the current thread. Returns * null if the calling thread is not associated with a Looper. */ public static @Nullable Looper myLooper() { return sThreadLocal.get(); } sThreadLocal // sThreadLocal.get() will return null unless you've called prepare(). @UnsupportedAppUsage static final ThreadLocal<Looper> sThreadLocal= new ThreadLocal<Looper>(); 子线程 Looper 的创建​ Looper.prepare()：在子线程中创建 1 个 Looper 对象 (手动创建) /** Initialize the current thread as a looper. * This gives you a chance to create handlers that then reference * this looper, before actually starting the loop. Be sure to call * {@link #loop()} after calling this method, and end it by calling * {@link #quit()}. */ public static void prepare() { prepare(true); } private static void prepare(boolean quitAllowed) { // 1. 判断 sThreadLocal 是否为 null，否则抛出异常 // 即 Looper.prepare() 方法不能被调用两次， 1 个线程中只能对应 1 个 Looper 实例 // 注：sThreadLocal 为 ThreadLocal 对象，用于存储线程的变量 if (sThreadLocal.get() != null) { throw new RuntimeException(\"Only one Looper may be created per thread\"); } sThreadLocal.set(new Looper(quitAllowed)); } Looper.Looper() private Looper(boolean quitAllowed) { // 创建 1 个 Looper 实例时，会自动创建 1 个与之配对的 MessageQueue mQueue = new MessageQueue(quitAllowed); mThread = Thread.currentThread(); }","s":"Looper 对象创建 & MessageQueue 对象创建","u":"/docs/android-framework/handler/handler-introduction","h":"#looper-对象创建--messagequeue-对象创建","p":86},{"i":103,"t":"Handler 对象创建 private Handler mHandler = new Handler(Looper.myLooper()){ }; Handler() 创建时，关联 Looper 对象和 Queue 对象。 public Handler(@NonNull Looper looper) { this(looper, null, false); } Handler() final Looper mLooper; final MessageQueue mQueue; @UnsupportedAppUsage public Handler(@NonNull Looper looper, @Nullable Callback callback, boolean async) { mLooper = looper; mQueue = looper.mQueue; mCallback = callback; mAsynchronous = async; }","s":"Handler 对象创建","u":"/docs/android-framework/handler/handler-introduction","h":"#handler-对象创建","p":86},{"i":105,"t":"Handler.sendMessageAtTime(Message msg，long uptimeMillis)：调用 enqueueMessage() /** * 分析：sendMessageAtTime(Message msg, long uptimeMillis) * 作用：在指定时间发出消息，消息会加入到消息队列 MessageQueue */ /** * Enqueue a message into the message queue after all pending messages * before the absolute time (in milliseconds) <var>uptimeMillis</var>. * <b>The time-base is {@link android.os.SystemClock#uptimeMillis}.</b> * Time spent in deep sleep will add an additional delay to execution. * You will receive it in {@link #handleMessage}, in the thread attached * to this handler. * * @param uptimeMillis The absolute time at which the message should be * delivered, using the * {@link android.os.SystemClock#uptimeMillis} time-base. * * @return Returns true if the message was successfully placed in to the * message queue. Returns false on failure, usually because the * looper processing the message queue is exiting. Note that a * result of true does not mean the message will be processed -- if * the looper is quit before the delivery time of the message * occurs then the message will be dropped. */ public boolean sendMessageAtTime(@NonNull Message msg, long uptimeMillis) { MessageQueue queue = mQueue; if (queue == null) { RuntimeException e = new RuntimeException( this + \" sendMessageAtTime() called with no mQueue\"); Log.w(\"Looper\", e.getMessage(), e); return false; } return enqueueMessage(queue, msg, uptimeMillis); } Handler.enqueueMessage(MessageQueue queue, Message msg, long uptimeMillis) private boolean enqueueMessage(@NonNull MessageQueue queue, @NonNull Message msg, long uptimeMillis) { msg.target = this; msg.workSourceUid = ThreadLocalWorkSource.getUid(); if (mAsynchronous) { msg.setAsynchronous(true); } return queue.enqueueMessage(msg, uptimeMillis); } MessageQueue.enqueueMessage(Message msg，long when)：将 Message 对象加入消息队列 /** * 分析：MessageQueue.enqueueMessage() * 作用：入队消息，即将新的消息加入消息队列 */ // mMessages 为链表结构，头部为优先执行 // 即优先执行 mMessages，执行完之后 mMessages = mMessages.next，直到 mMessages 为空为止 Message mMessages; ... boolean enqueueMessage(Message msg, long when) { // msg.target 即目标 Handler，如果为 null 则抛出异常 if (msg.target == null) { throw new IllegalArgumentException(\"Message must have a target.\"); } // 可能出现存在多个线程同时插入消息多情况，用 synchronized 同步 synchronized (this) { if (msg.isInUse()) { throw new IllegalStateException(msg + \" This message is already in use.\"); } ... // msg：当前（需要加入消息队列的）消息 msg.markInUse(); msg.when = when; // p (mMessages)：指针，指向当前队列的头部 Message p = mMessages; boolean needWake; // 如果以下出现情况之一：当前队列为空；当前 msg 需要马上执行；当前 msg 需要执行的时间 < 头部消息需要执行的时间，则将当前消息插入队列头部；反止插入队列头部之后（中间或尾部）。 if (p == null || when == 0 || when < p.when) { // 将当前消息插入队列头部 // New head, wake up the event queue if blocked. msg.next = p; mMessages = msg; needWake = mBlocked; } else { // Inserted within the middle of the queue. Usually we don't have to wake // up the event queue unless there is a barrier at the head of the queue // and the message is the earliest asynchronous message in the queue. // 是否需要队列保持唤醒状态 needWake = mBlocked && p.target == null && msg.isAsynchronous(); // 将当前消息插入队列中间 Message prev; for (;;) { prev = p; p = p.next; if (p == null || when < p.when) { break; } if (needWake && p.isAsynchronous()) { needWake = false; } } msg.next = p; // invariant: p == prev.next prev.next = msg; } // We can assume mPtr != 0 because mQuitting is false. if (needWake) { nativeWake(mPtr); } } return true; }","s":"Message 发送","u":"/docs/android-framework/handler/handler-introduction","h":"#message-发送","p":86},{"i":107,"t":"Looper.loop()：取出 Looper 中的消息队列，使用 MessageQueue.next() 无限循环取出 msg 并发送到对应的 handler /** * 作用：消息循环，即从消息队列中获取消息、分发消息到 Handler * 特别注意： * a. 主线程的消息循环不允许退出，即无限循环 * b. 子线程的消息循环允许退出：调用消息队列 MessageQueue 的 quit() */ /** * Run the message queue in this thread. Be sure to call * {@link #quit()} to end the loop. */ public static void loop() { // 1. 获取当前Looper的消息队列 // myLooper()作用：返回 sThreadLocal 存储的 Looper 实例；若为 null 则抛出异常 final Looper me = myLooper(); // 若为 null 则抛出异常，即 loop（）执行前必须执行 prepare() 创建 Looper 实例 if (me == null) { throw new RuntimeException(\"No Looper; Looper.prepare() wasn't called on this thread.\"); } ... me.mInLoop = true; // 获取Looper实例中的消息队列对象 (MessageQueue) final MessageQueue queue = me.mQueue; // 2. 消息循环（for 无限循环） for (;;) { // 2.1 从消息队列取出消息 msg，若取出消息为空则线程阻塞 Message msg = queue.next(); // might block if (msg == null) { // No message indicates that the message queue is quitting. return; } try { // 2.2 把消息 msg 派发给消息对象 msg.target（实际是 handler 对象） msg.target.dispatchMessage(msg); ... } ... ... // 3. 释放资源 msg.recycleUnchecked(); } } MessageQueue.next()：从消息队列中取出下一个 Message 对象 /** * 分析：MessageQueue.next() * 作用：出队消息，即从消息队列中移出头部消息 */ // mMessages 为链表结构，头部为优先执行 // 即优先执行 mMessages，执行完之后 mMessages = mMessages.next，直到 mMessages 为空为止 Message mMessages; ... Message next() { // 该参数用于确定消息队列中是否还有消息 // 从而决定消息队列应处于出队消息状态 or 等待状态 int nextPollTimeoutMillis = 0; for (;;) { if (nextPollTimeoutMillis != 0) { Binder.flushPendingCommands(); } // nativePollOnce 方法在 native 层，若是 nextPollTimeoutMillis 为 -1，此时消息队列处于等待状态 nativePollOnce(ptr, nextPollTimeoutMillis); synchronized (this) { final long now = SystemClock.uptimeMillis(); Message prevMsg = null; // 从消息队列中取出头部消息对象作为当前的 msg Message msg = mMessages; if (msg != null) { // 如果当前 msg 时间大于当前时间，重新计算 nextPollTimeoutMillis 并设置超时唤醒 if (now < msg.when) { nextPollTimeoutMillis = (int) Math.min(msg.when - now, Integer.MAX_VALUE); } else { // 如果当前 msg 时间等于或者小于当前时间，取出当前 msg mBlocked = false; if (prevMsg != null) { prevMsg.next = msg.next; } else { mMessages = msg.next; } msg.next = null; if (DEBUG) Log.v(TAG, \"Returning message: \" + msg); msg.markInUse(); return msg; } } else { // 若消息队列中已无消息，则将 nextPollTimeoutMillis 参数设为 -1 // 下次循环时，消息队列则处于等待状态 nextPollTimeoutMillis = -1; } ... } ... } } Handler.dispatchMessage()：将消息分发给接收者/回调方，由接收者/回调方进行相应处理 /** * 分析：dispatchMessage(Message msg) * 作用：派发消息到对应的 Handler 实例，根据传入的 msg 作出对应的操作 */ /** * Handle system messages here. */ public void dispatchMessage(@NonNull Message msg) { // 若 msg.callback 属性不为空，则代表使用了 post(Runnable r) 发送消息 if (msg.callback != null) { handleCallback(msg); } else { // 若 mCallback 不为空，则代表使用了 Handler(Looper looper, Callback callback) 传入了 callback 参数；之后调用 callback 自己实现的 handleMessage() 方法（必须进行 override 重写，返回 true 或 false） if (mCallback != null) { if (mCallback.handleMessage(msg)) { return; } } // 若msg.callback属性为空，则代表使用了 sendMessage（Message msg）发送消息；之后调用 handleMessage(msg)（一般都会进行 override 重写） handleMessage(msg); } }","s":"Message 分发和 Handler 处理","u":"/docs/android-framework/handler/handler-introduction","h":"#message-分发和-handler-处理","p":86},{"i":110,"t":"亦称：Abstract Factory","s":"抽象工厂模式","u":"/docs/design-patterns/abstract-factory","h":"","p":109},{"i":112,"t":"抽象工厂模式是一种创建型设计模式，它能创建一系列相关的对象，而无需指定其具体类。","s":"意图","u":"/docs/design-patterns/abstract-factory","h":"#意图","p":109},{"i":114,"t":"假设你正在开发一款家具商店模拟器。你的代码中包括一些类，用于表示： 一系列相关产品，例如 椅子 Chair、沙发 Sofa 和 咖啡桌 Coffee­Table。 系列产品的不同变体。例如，你可以使用 现代 Modern、维多利亚 Victorian、装饰风艺术 Art­Deco 等风格生成 椅子、沙发 和 咖啡桌。 系列产品及其不同变体。 你需要设法单独生成每件家具对象，这样才能确保其风格一致。如果顾客收到的家具风格不一样，他们可不会开心。 现代风格的沙发和维多利亚风格的椅子不搭。 此外，你也不希望在添加新产品或新风格时修改已有代码。家具供应商对于产品目录的更新非常频繁，你不会想在每次更新时都去修改核心代码的。","s":"问题","u":"/docs/design-patterns/abstract-factory","h":"#问题","p":109},{"i":116,"t":"首先，抽象工厂模式建议为系列中的每件产品明确声明接口 (例如椅子、沙发或咖啡桌)。然后，确保所有产品变体都继承这些接口。例如，所有风格的椅子都实现 椅子 接口；所有风格的咖啡桌都实现 咖啡桌 接口，以此类推。 同一对象的所有变体都必须放置在同一个类层次结构之中。 接下来，我们需要声明抽象工厂——包含系列中所有产品构造方法的接口。例如 create­Chair 创建椅子、create­Sofa 创建沙发和 create­Coffee­Table 创建咖啡桌。这些方法必须返回抽象产品类型，即我们之前抽取的那些接口：椅子，沙发 和 咖啡桌 等等。 每个具体工厂类都对应一个特定的产品变体。 那么该如何处理产品变体呢？对于系列产品的每个变体，我们都将基于 抽象工厂 接口创建不同的工厂类。每个工厂类都只能返回特定类别的产品，例如，现代家具工厂 Modern­Furniture­Factory 只能创建 现代椅子 Modern­Chair、现代沙发 Modern­Sofa 和 现代咖啡桌 Modern­Coffee­Table 对象。 客户端代码可以通过相应的抽象接口调用工厂和产品类。你无需修改实际客户端代码，就能更改传递给客户端的工厂类，也能更改客户端代码接收的产品变体。 客户端无需了解其所调用工厂的具体类信息。 假设客户端想要工厂创建一把椅子。客户端无需了解工厂类，也不用管工厂类创建出的椅子类型。无论是现代风格，还是维多利亚风格的椅子，对于客户端来说没有分别，它只需调用抽象 椅子 接口就可以了。这样一来，客户端只需知道椅子以某种方式实现了 sit­On 坐下方法就足够了。此外，无论工厂返回的是何种椅子变体，它都会和由同一工厂对象创建的沙发或咖啡桌风格一致。 最后一点说明：如果客户端仅接触抽象接口，那么谁来创建实际的工厂对象呢？一般情况下，应用程序会在初始化阶段创建具体工厂对象。而在此之前，应用程序必须根据配置文件或环境设定选择工厂类别。","s":"解决方案","u":"/docs/design-patterns/abstract-factory","h":"#解决方案","p":109},{"i":118,"t":"抽象产品 (Abstract Product) 为构成系列产品的一组不同但相关的产品声明接口。 具体产品 (Concrete Product) 是抽象产品的多种不同类型实现。所有变体 (维多利亚/现代) 都必须实现相应的抽象产品 (椅子/沙发)。 抽象工厂 (Abstract Factory) 接口声明了一组创建各种抽象产品的方法。 具体工厂 (Concrete Factory) 实现抽象工厂的构建方法。每个具体工厂都对应特定产品变体，且仅创建此种产品变体。 尽管具体工厂会对具体产品进行初始化，其构建方法签名必须返回相应的抽象产品。这样，使用工厂类的客户端代码就不会与工厂创建的特定产品变体耦合。客户端 (Client) 只需通过抽象接口调用工厂和产品对象，就能与任何具体工厂/产品变体交互。","s":"抽象工厂模式结构","u":"/docs/design-patterns/abstract-factory","h":"#抽象工厂模式结构","p":109},{"i":120,"t":"下面例子通过应用抽象工厂模式，使得客户端代码无需与具体 UI 类耦合，就能创建跨平台的 UI 元素，同时确保所创建的元素与指定的操作系统匹配。 跨平台 UI 类示例。 跨平台应用中的相同 UI 元素功能类似，但是在不同操作系统下的外观有一定差异。此外，你需要确保 UI 元素与当前操作系统风格一致。你一定不希望在 Windows 系统下运行的应用程序中显示 macOS 的控件。 抽象工厂接口声明一系列构建方法，客户端代码可调用它们生成不同风格的 UI 元素。每个具体工厂对应特定操作系统，并负责生成符合该操作系统风格的 UI 元素。 其运作方式如下：应用程序启动后检测当前操作系统。根据该信息，应用程序通过与该操作系统对应的类创建工厂对象。其余代码使用该工厂对象创建 UI 元素。这样可以避免生成错误类型的元素。 使用这种方法，客户端代码只需调用抽象接口，而无需了解具体工厂类和 UI 元素。此外，客户端代码还支持未来添加新的工厂或 UI 元素。 这样一来，每次在应用程序中添加新的 UI 元素变体时，你都无需修改客户端代码。你只需创建一个能够生成这些 UI 元素的工厂类，然后稍微修改应用程序的初始代码，使其能够选择合适的工厂类即可。 // 抽象工厂接口声明了一组能返回不同抽象产品的方法。这些产品属于同一个系列 // 且在高层主题或概念上具有相关性。同系列的产品通常能相互搭配使用。系列产 // 品可有多个变体，但不同变体的产品不能搭配使用。 interface GUIFactory is method createButton():Button method createCheckbox():Checkbox // 具体工厂可生成属于同一变体的系列产品。工厂会确保其创建的产品能相互搭配 // 使用。具体工厂方法签名会返回一个抽象产品，但在方法内部则会对具体产品进 // 行实例化。 class WinFactory implements GUIFactory is method createButton():Button is return new WinButton() method createCheckbox():Checkbox is return new WinCheckbox() // 每个具体工厂中都会包含一个相应的产品变体。 class MacFactory implements GUIFactory is method createButton():Button is return new MacButton() method createCheckbox():Checkbox is return new MacCheckbox() // 系列产品中的特定产品必须有一个基础接口。所有产品变体都必须实现这个接口。 interface Button is method paint() // 具体产品由相应的具体工厂创建。 class WinButton implements Button is method paint() is // 根据 Windows 样式渲染按钮。 class MacButton implements Button is method paint() is // 根据 macOS 样式渲染按钮 // 这是另一个产品的基础接口。所有产品都可以互动，但是只有相同具体变体的产 // 品之间才能够正确地进行交互。 interface Checkbox is method paint() class WinCheckbox implements Checkbox is method paint() is // 根据 Windows 样式渲染复选框。 class MacCheckbox implements Checkbox is method paint() is // 根据 macOS 样式渲染复选框。 // 客户端代码仅通过抽象类型（GUIFactory、Button 和 Checkbox）使用工厂 // 和产品。这让你无需修改任何工厂或产品子类就能将其传递给客户端代码。 class Application is private field factory: GUIFactory private field button: Button constructor Application(factory: GUIFactory) is this.factory = factory method createUI() is this.button = factory.createButton() method paint() is button.paint() // 程序会根据当前配置或环境设定选择工厂类型，并在运行时创建工厂（通常在初 // 始化阶段）。 class ApplicationConfigurator is method main() is config = readApplicationConfigFile() if (config.OS == \"Windows\") then factory = new WinFactory() else if (config.OS == \"Mac\") then factory = new MacFactory() else throw new Exception(\"错误！未知的操作系统。\") Application app = new Application(factory)","s":"伪代码","u":"/docs/design-patterns/abstract-factory","h":"#伪代码","p":109},{"i":122,"t":"如果代码需要与多个不同系列的相关产品交互，但是由于无法提前获取相关信息，或者出于对未来扩展性的考虑，你不希望代码基于产品的具体类进行构建，在这种情况下，你可以使用抽象工厂。 抽象工厂为你提供了一个接口，可用于创建每个系列产品的对象。只要代码通过该接口创建对象，那么你就不会生成与应用程序已生成的产品类型不一致的产品。 如果你有一个基于一组抽象方法的类，且其主要功能因此变得不明确，那么在这种情况下可以考虑使用抽象工厂模式。 在设计良好的程序中，每个类仅负责一件事。如果一个类与多种类型产品交互，就可以考虑将工厂方法抽取到独立的工厂类或具备完整功能的抽象工厂类中。 实现方式 以不同的产品类型与产品变体为维度绘制矩阵。 为所有产品声明抽象产品接口。然后让所有具体产品类实现这些接口。 声明抽象工厂接口，并且在接口中为所有抽象产品提供一组构建方法。 为每种产品变体实现一个具体工厂类。 在应用程序中开发初始化代码。该代码根据应用程序配置或当前环境，对特定具体工厂类进行初始化。然后将该工厂对象传递给所有需要创建产品的类。 找出代码中所有对产品构造函数的直接调用，将其替换为对工厂对象中相应构建方法的调用。","s":"抽象工厂模式适合应用场景","u":"/docs/design-patterns/abstract-factory","h":"#抽象工厂模式适合应用场景","p":109},{"i":124,"t":"✔️ 你可以确保同一工厂生成的产品相互匹配。 ✔️ 你可以避免客户端和具体产品代码的耦合。 ✔️ 单一职责原则。你可以将产品生成代码抽取到同一位置，使得代码易于维护。 ✔️ 开闭原则。向应用程序中引入新产品变体时，你无需修改客户端代码。 ❌ 由于采用该模式需要向应用中引入众多接口和类，代码可能会比之前更加复杂。","s":"抽象工厂模式优缺点","u":"/docs/design-patterns/abstract-factory","h":"#抽象工厂模式优缺点","p":109},{"i":126,"t":"在许多设计工作的初期都会使用工厂方法模式 (较为简单，而且可以更方便地通过子类进行定制)，随后演化为使用抽象工厂模式、原型模式或生成器模式 (更灵活但更加复杂)。 生成器重点关注如何分步生成复杂对象。抽象工厂专门用于生产一系列相关对象。抽象工厂会马上返回产品，生成器则允许你在获取产品前执行一些额外构造步骤。 抽象工厂模式通常基于一组工厂方法，但你也可以使用原型模式来生成这些类的方法。 当只需对客户端代码隐藏子系统创建对象的方式时，你可以使用抽象工厂来代替外观模式。 你可以将抽象工厂和桥接模式搭配使用。如果由桥接定义的抽象只能与特定实现合作，这一模式搭配就非常有用。在这种情况下，抽象工厂可以对这些关系进行封装，并且对客户端代码隐藏其复杂性。 抽象工厂、生成器和原型都可以用单例模式来实现。","s":"与其他模式的关系","u":"/docs/design-patterns/abstract-factory","h":"#与其他模式的关系","p":109},{"i":128,"t":"亦称：封装器模式、Wrapper、Adapter","s":"适配器模式","u":"/docs/design-patterns/adapter","h":"","p":127},{"i":130,"t":"适配器模式是一种结构型设计模式，它能使接口不兼容的对象能够相互合作。","s":"意图","u":"/docs/design-patterns/adapter","h":"#意图","p":127},{"i":132,"t":"假如你正在开发一款股票市场监测程序，它会从不同来源下载 XML 格式的股票数据，然后向用户呈现出美观的图表。 在开发过程中，你决定在程序中整合一个第三方智能分析函数库。但是遇到了一个问题，那就是分析函数库只兼容 JSON 格式的数据。 你无法“直接”使用分析函数库，因为它所需的输入数据格式与你的程序不兼容。 你可以修改程序库来支持 XML。但是，这可能需要修改部分依赖该程序库的现有代码。甚至还有更糟糕的情况，你可能根本没有程序库的源代码，从而无法对其进行修改。","s":"问题","u":"/docs/design-patterns/adapter","h":"#问题","p":127},{"i":134,"t":"你可以创建一个适配器。这是一个特殊的对象，能够转换对象接口，使其能与其他对象进行交互。 适配器模式通过封装对象将复杂的转换过程隐藏于幕后。被封装的对象甚至察觉不到适配器的存在。例如，你可以使用一个将所有数据转换为英制单位 (如英尺和英里) 的适配器封装运行于米和千米单位制中的对象。 适配器不仅可以转换不同格式的数据，其还有助于采用不同接口的对象之间的合作。它的运作方式如下： 适配器实现与其中一个现有对象兼容的接口。 现有对象可以使用该接口安全地调用适配器方法。 适配器方法被调用后将以另一个对象兼容的格式和顺序将请求传递给该对象。 有时你甚至可以创建一个双向适配器来实现双向转换调用。 让我们回到股票市场程序。为了解决数据格式不兼容的问题，你可以为分析函数库中的每个类创建将 XML 转换为 JSON 格式的适配器，然后让客户端仅通过这些适配器来与函数库进行交流。当某个适配器被调用时，它会将传入的 XML 数据转换为 JSON 结构，并将其传递给被封装分析对象的相应方法。","s":"解决方案","u":"/docs/design-patterns/adapter","h":"#解决方案","p":127},{"i":136,"t":"出国旅行前后的旅行箱。 如果你是第一次从美国到欧洲旅行，那么在给笔记本充电时可能会大吃一惊。不同国家的电源插头和插座标准不同。美国插头和德国插座不匹配。同时提供美国标准插座和欧洲标准插头的电源适配器可以解决你的难题。","s":"真实世界类比","u":"/docs/design-patterns/adapter","h":"#真实世界类比","p":127},{"i":139,"t":"实现时使用了构成原则：适配器实现了其中一个对象的接口，并对另一个对象进行封装。所有流行的编程语言都可以实现适配器。 客户端 (Client) 是包含当前程序业务逻辑的类。 客户端接口 (Client Interface) 描述了其他类与客户端代码合作时必须遵循的协议。 服务 (Service) 中有一些功能类 (通常来自第三方或遗留系统)。客户端与其接口不兼容，因此无法直接调用其功能。 适配器 (Adapter) 是一个可以同时与客户端和服务交互的类：它在实现客户端接口的同时封装了服务对象。适配器接受客户端通过适配器接口发起的调用，并将其转换为适用于被封装服务对象的调用。 客户端代码只需通过接口与适配器交互即可，无需与具体的适配器类耦合。因此，你可以向程序中添加新类型的适配器而无需修改已有代码。这在服务类的接口被更改或替换时很有用：你无需修改客户端代码就可以创建新的适配器类。","s":"对象适配器","u":"/docs/design-patterns/adapter","h":"#对象适配器","p":127},{"i":141,"t":"这一实现使用了继承机制：适配器同时继承两个对象的接口。请注意，这种方式仅能在支持多重继承的编程语言中实现，例如 C++。 类适配器不需要封装任何对象，因为它同时继承了客户端和服务的行为。适配功能在重写的方法中完成。最后生成的适配器可替代已有的客户端类进行使用。","s":"类适配器","u":"/docs/design-patterns/adapter","h":"#类适配器","p":127},{"i":143,"t":"下列适配器模式演示基于经典的“方钉和圆孔”问题。 让方钉适配圆孔。 适配器假扮成一个圆钉 (Round­Peg)，其半径等于方钉 (Square­Peg) 横截面对角线的一半 (即能够容纳方钉的最小外接圆的半径)。 // 假设你有两个接口相互兼容的类：圆孔（Round­Hole）和圆钉（Round­Peg）。 class RoundHole is constructor RoundHole(radius) { …… } method getRadius() is // 返回孔的半径。 method fits(peg: RoundPeg) is return this.getRadius() >= peg.getRadius() class RoundPeg is constructor RoundPeg(radius) { …… } method getRadius() is // 返回钉子的半径。 // 但还有一个不兼容的类：方钉（Square­Peg）。 class SquarePeg is constructor SquarePeg(width) { …… } method getWidth() is // 返回方钉的宽度。 // 适配器类让你能够将方钉放入圆孔中。它会对 RoundPeg 类进行扩展，以接收适 // 配器对象作为圆钉。 class SquarePegAdapter extends RoundPeg is // 在实际情况中，适配器中会包含一个 SquarePeg 类的实例。 private field peg: SquarePeg constructor SquarePegAdapter(peg: SquarePeg) is this.peg = peg method getRadius() is // 适配器会假扮为一个圆钉，其半径刚好能与适配器实际封装的方钉搭配 // 起来。 return peg.getWidth() * Math.sqrt(2) / 2 // 客户端代码中的某个位置。 hole = new RoundHole(5) rpeg = new RoundPeg(5) hole.fits(rpeg) // true small_sqpeg = new SquarePeg(5) large_sqpeg = new SquarePeg(10) hole.fits(small_sqpeg) // 此处无法编译（类型不一致）。 small_sqpeg_adapter = new SquarePegAdapter(small_sqpeg) large_sqpeg_adapter = new SquarePegAdapter(large_sqpeg) hole.fits(small_sqpeg_adapter) // true hole.fits(large_sqpeg_adapter) // false","s":"伪代码","u":"/docs/design-patterns/adapter","h":"#伪代码","p":127},{"i":145,"t":"当你希望使用某个类，但是其接口与其他代码不兼容时，可以使用适配器类。 适配器模式允许你创建一个中间层类，其可作为代码与遗留类、第三方类或提供怪异接口的类之间的转换器。 如果您需要复用这样一些类，他们处于同一个继承体系，并且他们又有了额外的一些共同的方法，但是这些共同的方法不是所有在这一继承体系中的子类所具有的共性。 你可以扩展每个子类，将缺少的功能添加到新的子类中。但是，你必须在所有新子类中重复添加这些代码，这样会使得代码有坏味道。 将缺失功能添加到一个适配器类中是一种优雅得多的解决方案。然后你可以将缺少功能的对象封装在适配器中，从而动态地获取所需功能。如要这一点正常运作，目标类必须要有通用接口，适配器的成员变量应当遵循该通用接口。这种方式同装饰模式非常相似。 实现方式 确保至少有两个类的接口不兼容： 一个无法修改 (通常是第三方、遗留系统或者存在众多已有依赖的类) 的功能性服务类。 一个或多个将受益于使用服务类的客户端类。 声明客户端接口，描述客户端如何与服务交互。 创建遵循客户端接口的适配器类。所有方法暂时都为空。 在适配器类中添加一个成员变量用于保存对于服务对象的引用。通常情况下会通过构造函数对该成员变量进行初始化，但有时在调用其方法时将该变量传递给适配器会更方便。 依次实现适配器类客户端接口的所有方法。适配器会将实际工作委派给服务对象，自身只负责接口或数据格式的转换。 客户端必须通过客户端接口使用适配器。这样一来，你就可以在不影响客户端代码的情况下修改或扩展适配器。","s":"适配器模式适合应用场景","u":"/docs/design-patterns/adapter","h":"#适配器模式适合应用场景","p":127},{"i":147,"t":"✔️ 单一职责原则你可以将接口或数据转换代码从程序主要业务逻辑中分离。 ✔️ 开闭原则。只要客户端代码通过客户端接口与适配器进行交互，你就能在不修改现有客户端代码的情况下在程序中添加新类型的适配器。 ❌ 代码整体复杂度增加，因为你需要新增一系列接口和类。有时直接更改服务类使其与其他代码兼容会更简单。","s":"适配器模式优缺点","u":"/docs/design-patterns/adapter","h":"#适配器模式优缺点","p":127},{"i":149,"t":"桥接模式通常会于开发前期进行设计，使你能够将程序的各个部分独立开来以便开发。另一方面，适配器模式通常在已有程序中使用，让相互不兼容的类能很好地合作。 适配器可以对已有对象的接口进行修改，装饰模式则能在不改变对象接口的前提下强化对象功能。此外，装饰还支持递归组合，适配器则无法实现。 适配器能为被封装对象提供不同的接口，代理模式能为对象提供相同的接口，装饰则能为对象提供加强的接口。 外观模式为现有对象定义了一个新接口，适配器则会试图运用已有的接口。适配器通常只封装一个对象，外观通常会作用于整个对象子系统上。 桥接、状态模式和策略模式 (在某种程度上包括适配器) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。","s":"与其他模式的关系","u":"/docs/design-patterns/adapter","h":"#与其他模式的关系","p":127},{"i":151,"t":"行为模式负责对象间的高效沟通和职责委派。","s":"行为模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":153,"t":"允许你将请求沿着处理者链进行发送。收到请求后，每个处理者均可对请求进行处理，或将其传递给链上的下个处理者。","s":"📄️ 责任链模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":155,"t":"它可将请求转换为一个包含与请求相关的所有信息的独立对象。该转换让你能根据不同的请求将方法参数化、延迟请求执行或将其放入队列中，且能实现可撤销操作。","s":"📄️ 命令模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":157,"t":"让你能在不暴露集合底层表现形式（列表、栈和树等）的情况下遍历集合中所有的元素。","s":"📄️ 迭代器模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":159,"t":"能让你减少对象之间混乱无序的依赖关系。该模式会限制对象之间的直接交互，迫使它们通过一个中介者对象进行合作。","s":"📄️ 中介者模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":161,"t":"允许在不暴露对象实现细节的情况下保存和恢复对象之前的状态。","s":"📄️ 备忘录模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":163,"t":"允许你定义一种订阅机制，可在对象事件发生时通知多个“观察”该对象的其他对象。","s":"📄️ 观察者模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":165,"t":"让你能在一个对象的内部状态变化时改变其行为，使其看上去就像改变了自身所属的类一样。","s":"📄️ 状态模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":167,"t":"能让你定义一系列算法，并将每种算法分别放入独立的类中，以使算法的对象能够相互替换。","s":"📄️ 策略模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":169,"t":"在超类中定义一个算法的框架，允许子类在不修改结构的情况下重写算法的特定步骤。","s":"📄️ 模板方法模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":171,"t":"将算法与其所作用的对象隔离开来。","s":"📄️ 访问者模式","u":"/docs/design-patterns/behavioral-patterns/","h":"","p":150},{"i":173,"t":"亦称：Bridge","s":"桥接模式","u":"/docs/design-patterns/bridge","h":"","p":172},{"i":175,"t":"桥接模式是一种结构型设计模式，可将一个大类或一系列紧密相关的类拆分为抽象和实现两个独立的层次结构，从而能在开发时分别使用。","s":"意图","u":"/docs/design-patterns/bridge","h":"#意图","p":172},{"i":177,"t":"*抽象？实现？*听上去挺吓人？让我们慢慢来，先考虑一个简单的例子。 假如你有一个几何 形状 Shape 类，从它能扩展出两个子类：圆形 Circle 和 方形 Square。你希望对这样的类层次结构进行扩展以使其包含颜色，所以你打算创建名为 红色 Red 和 蓝色 Blue 的形状子类。但是，由于你已有两个子类，所以总共需要创建四个类才能覆盖所有组合，例如 蓝色圆形 Blue­Circle 和 红色方形 Red­Square。 所有组合类的数量将以几何级数增长。 在层次结构中新增形状和颜色将导致代码复杂程度指数增长。例如添加三角形状，你需要新增两个子类，也就是每种颜色一个；此后新增一种新颜色需要新增三个子类，即每种形状一个。如此以往，情况会越来越糟糕。","s":"问题","u":"/docs/design-patterns/bridge","h":"#问题","p":172},{"i":179,"t":"问题的根本原因是我们试图在两个独立的维度——形状与颜色——上扩展形状类。这在处理类继承时是很常见的问题。 桥接模式通过将继承改为组合的方式来解决这个问题。具体来说，就是抽取其中一个维度并使之成为独立的类层次，这样就可以在初始类中引用这个新层次的对象，从而使得一个类不必拥有所有的状态和行为。 将一个类层次转化为多个相关的类层次，避免单个类层次的失控。 根据该方法，我们可以将颜色相关的代码抽取到拥有 红色 和 蓝色 两个子类的颜色类中，然后在 形状 类中添加一个指向某一颜色对象的引用成员变量。现在，形状类可以将所有与颜色相关的工作委派给连入的颜色对象。这样的引用就成为了 形状 和 颜色 之间的桥梁。此后，新增颜色将不再需要修改形状的类层次，反之亦然。","s":"解决方案","u":"/docs/design-patterns/bridge","h":"#解决方案","p":172},{"i":181,"t":"设计模式四人组的著作在桥接定义中提出了抽象部分和实现部分两个术语。我觉得这些术语过于学术了，反而让模式看上去比实际情况更加复杂。在介绍过形状和颜色的简单例子后，我们来看看四人组著作中让人望而生畏的词语的含义。 抽象部分 (也被称为接口) 是一些实体的高阶控制层。该层自身不完成任何具体的工作，它需要将工作委派给实现部分层 (也被称为平台)。 注意，这里提到的内容与编程语言中的接口或抽象类无关。它们并不是一回事。 在实际的程序中，抽象部分是图形用户界面 (GUI)，而实现部分则是底层操作系统代码 (API)，GUI 层调用 API 层来对用户的各种操作做出响应。 一般来说，你可以在两个独立方向上扩展这种应用： 开发多个不同的 GUI (例如面向普通用户和管理员进行分别配置) 支持多个不同的 API (例如，能够在 Windows、Linux 和 macOS 上运行该程序)。 在最糟糕的情况下，程序可能会是一团乱麻，其中包含数百种条件语句，连接着代码各处不同种类的 GUI 和各种 API。 在庞杂的代码中，即使是很小的改动都非常难以完成，因为你必须要在整体上对代码有充分的理解。而在较小且定义明确的模块中，进行修改则要容易得多。 你可以将特定接口 - 平台的组合代码抽取到独立的类中，以在混乱中建立一些秩序。但是，你很快会发现这种类的数量很多。类层次将以指数形式增长，因为每次添加一个新的 GUI 或支持一种新的 API 都需要创建更多的类。 让我们试着用桥接模式来解决这个问题。该模式建议将类拆分为两个类层次结构： 抽象部分：程序的 GUI 层。 实现部分：操作系统的 API。 创建跨平台应用程序的一种方法 抽象对象控制程序的外观，并将真实工作委派给连入的实现对象。不同的实现只要遵循相同的接口就可以互换，使同一 GUI 可在 Windows 和 Linux 下运行。 最后的结果是：你无需改动与 API 相关的类就可以修改 GUI 类。此外如果想支持一个新的操作系统，只需在实现部分层次中创建一个子类即可。","s":"抽象部分和实现部分","u":"/docs/design-patterns/bridge","h":"#抽象部分和实现部分","p":172},{"i":183,"t":"抽象部分 (Abstraction) 提供高层控制逻辑，依赖于完成底层实际工作的实现对象。 实现部分 (Implementation) 为所有具体实现声明通用接口。抽象部分仅能通过在这里声明的方法与实现对象交互。 抽象部分可以列出和实现部分一样的方法，但是抽象部分通常声明一些复杂行为，这些行为依赖于多种由实现部分声明的原语操作。 具体实现 (Concrete Implementations) 中包括特定于平台的代码。 精确抽象 (Refined Abstraction) 提供控制逻辑的变体。与其父类一样，它们通过通用实现接口与不同的实现进行交互。 通常情况下，客户端 (Client) 仅关心如何与抽象部分合作。但是，客户端需要将抽象对象与一个实现对象连接起来。","s":"桥接模式结构","u":"/docs/design-patterns/bridge","h":"#桥接模式结构","p":172},{"i":185,"t":"示例演示了桥接模式如何拆分程序中同时管理设备及其遥控器的庞杂代码。设备 Device 类作为实现部分，而 遥控器 Remote 类则作为抽象部分。 最初类层次结构被拆分为两个部分：设备和遥控器。 遥控器基类声明了一个指向设备对象的引用成员变量。所有遥控器通过通用设备接口与设备进行交互，使得同一个遥控器可以支持不同类型的设备。 你可以开发独立于设备类的遥控器类，只需新建一个遥控器子类即可。例如，基础遥控器可能只有两个按钮，但你可在其基础上扩展新功能，比如额外的一节电池或一块触摸屏。 客户端代码通过遥控器构造函数将特定种类的遥控器与设备对象连接起来。 // “抽象部分”定义了两个类层次结构中“控制”部分的接口。它管理着一个指向“实 // 现部分”层次结构中对象的引用，并会将所有真实工作委派给该对象。 class RemoteControl is protected field device: Device constructor RemoteControl(device: Device) is this.device = device method togglePower() is if (device.isEnabled()) then device.disable() else device.enable() method volumeDown() is device.setVolume(device.getVolume() - 10) method volumeUp() is device.setVolume(device.getVolume() + 10) method channelDown() is device.setChannel(device.getChannel() - 1) method channelUp() is device.setChannel(device.getChannel() + 1) // 你可以独立于设备类的方式从抽象层中扩展类。 class AdvancedRemoteControl extends RemoteControl is method mute() is device.setVolume(0) // “实现部分”接口声明了在所有具体实现类中通用的方法。它不需要与抽象接口相 // 匹配。实际上，这两个接口可以完全不一样。通常实现接口只提供原语操作，而 // 抽象接口则会基于这些操作定义较高层次的操作。 interface Device is method isEnabled() method enable() method disable() method getVolume() method setVolume(percent) method getChannel() method setChannel(channel) // 所有设备都遵循相同的接口。 class Tv implements Device is // …… class Radio implements Device is // …… // 客户端代码中的某个位置。 tv = new Tv() remote = new RemoteControl(tv) remote.togglePower() radio = new Radio() remote = new AdvancedRemoteControl(radio)","s":"伪代码","u":"/docs/design-patterns/bridge","h":"#伪代码","p":172},{"i":187,"t":"如果你想要拆分或重组一个具有多重功能的庞杂类 (例如能与多个数据库服务器进行交互的类)，可以使用桥接模式。 类的代码行数越多，弄清其运作方式就越困难，对其进行修改所花费的时间就越长。一个功能上的变化可能需要在整个类范围内进行修改，而且常常会产生错误，甚至还会有一些严重的副作用。 桥接模式可以将庞杂类拆分为几个类层次结构。此后，你可以修改任意一个类层次结构而不会影响到其他类层次结构。这种方法可以简化代码的维护工作，并将修改已有代码的风险降到最低。 如果你希望在几个独立维度上扩展一个类，可使用该模式。 桥接建议将每个维度抽取为独立的类层次。初始类将相关工作委派给属于对应类层次的对象，无需自己完成所有工作。 如果你需要在运行时切换不同实现方法，可使用桥接模式。 当然并不是说一定要实现这一点，桥接模式可替换抽象部分中的实现对象，具体操作就和给成员变量赋新值一样简单。 顺便提一句，最后一点是很多人混淆桥接模式和策略模式的主要原因。记住，设计模式并不仅是一种对类进行组织的方式，它还能用于沟通意图和解决问题。 实现方式 明确类中独立的维度。独立的概念可能是：抽象/平台，域/基础设施，前端/后端或接口/实现。 了解客户端的业务需求，并在抽象基类中定义它们。 确定在所有平台上都可执行的业务。并在通用实现接口中声明抽象部分所需的业务。 为你域内的所有平台创建实现类，但需确保它们遵循实现部分的接口。 在抽象类中添加指向实现类型的引用成员变量。抽象部分会将大部分工作委派给该成员变量所指向的实现对象。 如果你的高层逻辑有多个变体，则可通过扩展抽象基类为每个变体创建一个精确抽象。 客户端代码必须将实现对象传递给抽象部分的构造函数才能使其能够相互关联。此后，客户端只需与抽象对象进行交互，无需和实现对象打交道。","s":"桥接模式适合应用场景","u":"/docs/design-patterns/bridge","h":"#桥接模式适合应用场景","p":172},{"i":189,"t":"✔️ 你可以创建与平台无关的类和程序。 ✔️ 客户端代码仅与高层抽象部分进行互动，不会接触到平台的详细信息。 ✔️ 开闭原则。你可以新增抽象部分和实现部分，且它们之间不会相互影响。 ✔️ 单一职责原则。抽象部分专注于处理高层逻辑，实现部分处理平台细节。 ❌ 对高内聚的类使用该模式可能会让代码更加复杂。","s":"桥接模式优缺点","u":"/docs/design-patterns/bridge","h":"#桥接模式优缺点","p":172},{"i":191,"t":"桥接模式通常会于开发前期进行设计，使你能够将程序的各个部分独立开来以便开发。另一方面，适配器模式通常在已有程序中使用，让相互不兼容的类能很好地合作。 桥接、状态模式和策略模式 (在某种程度上包括适配器) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。 你可以将抽象工厂模式和桥接搭配使用。如果由桥接定义的抽象只能与特定实现合作，这一模式搭配就非常有用。在这种情况下，抽象工厂可以对这些关系进行封装，并且对客户端代码隐藏其复杂性。 你可以结合使用生成器模式和桥接模式：主管类负责抽象工作，各种不同的生成器负责实现工作。","s":"与其他模式的关系","u":"/docs/design-patterns/bridge","h":"#与其他模式的关系","p":172},{"i":193,"t":"亦称：建造者模式、Builder","s":"生成器模式","u":"/docs/design-patterns/builder","h":"","p":192},{"i":195,"t":"生成器模式是一种创建型设计模式，使你能够分步骤创建复杂对象。该模式允许你使用相同的创建代码生成不同类型和形式的对象。","s":"意图","u":"/docs/design-patterns/builder","h":"#意图","p":192},{"i":197,"t":"假设有这样一个复杂对象，在对其进行构造时需要对诸多成员变量和嵌套对象进行繁复的初始化工作。这些初始化代码通常深藏于一个包含众多参数且让人基本看不懂的构造函数中；甚至还有更糟糕的情况，那就是这些代码散落在客户端代码的多个位置。 如果为每种可能的对象都创建一个子类，这可能会导致程序变得过于复杂。 例如，我们来思考如何创建一个 房屋 House 对象。建造一栋简单的房屋，首先你需要建造四面墙和地板，安装房门和一套窗户，然后再建造一个屋顶。但是如果你想要一栋更宽敞更明亮的房屋，还要有院子和其他设施 (例如暖气、排水和供电设备)，那又该怎么办呢？ 最简单的方法是扩展 房屋 基类，然后创建一系列涵盖所有参数组合的子类。但最终你将面对相当数量的子类。任何新增的参数 (例如门廊类型) 都会让这个层次结构更加复杂。 另一种方法则无需生成子类。你可以在 房屋 基类中创建一个包括所有可能参数的超级构造函数，并用它来控制房屋对象。这种方法确实可以避免生成子类，但它却会造成另外一个问题。 拥有大量输入参数的构造函数也有缺陷：这些参数也不是每次都要全部用上的。 通常情况下，绝大部分的参数都没有使用，这使得对于构造函数的调用十分不简洁。例如，只有很少的房子有游泳池，因此与游泳池相关的参数十之八九是毫无用处的。","s":"问题","u":"/docs/design-patterns/builder","h":"#问题","p":192},{"i":199,"t":"生成器模式建议将对象构造代码从产品类中抽取出来，并将其放在一个名为生成器的独立对象中。 生成器模式让你能够分步骤创建复杂对象。生成器不允许其他对象访问正在创建中的产品。 该模式会将对象构造过程划分为一组步骤，比如 build­Walls 创建墙壁和 build­Door 创建房门创建房门等。每次创建对象时，你都需要通过生成器对象执行一系列步骤。重点在于你无需调用所有步骤，而只需调用创建特定对象配置所需的那些步骤即可。 当你需要创建不同形式的产品时，其中的一些构造步骤可能需要不同的实现。例如，木屋的房门可能需要使用木头制造，而城堡的房门则必须使用石头制造。 在这种情况下，你可以创建多个不同的生成器，用不同方式实现一组相同的创建步骤。然后你就可以在创建过程中使用这些生成器 (例如按顺序调用多个构造步骤) 来生成不同类型的对象。 不同生成器以不同方式执行相同的任务。 例如，假设第一个建造者使用木头和玻璃制造房屋，第二个建造者使用石头和钢铁，而第三个建造者使用黄金和钻石。在调用同一组步骤后，第一个建造者会给你一栋普通房屋，第二个会给你一座小城堡，而第三个则会给你一座宫殿。但是，只有在调用构造步骤的客户端代码可以通过通用接口与建造者进行交互时，这样的调用才能返回需要的房屋。","s":"解决方案","u":"/docs/design-patterns/builder","h":"#解决方案","p":192},{"i":201,"t":"你可以进一步将用于创建产品的一系列生成器步骤调用抽取成为单独的主管类。主管类可定义创建步骤的执行顺序，而生成器则提供这些步骤的实现。 主管知道需要哪些创建步骤才能获得可正常使用的产品。 严格来说，你的程序中并不一定需要主管类。客户端代码可直接以特定顺序调用创建步骤。不过，主管类中非常适合放入各种例行构造流程，以便在程序中反复使用。 此外，对于客户端代码来说，主管类完全隐藏了产品构造细节。客户端只需要将一个生成器与主管类关联，然后使用主管类来构造产品，就能从生成器处获得构造结果了。","s":"主管","u":"/docs/design-patterns/builder","h":"#主管","p":192},{"i":203,"t":"生成器 (Builder) 接口声明在所有类型生成器中通用的产品构造步骤。 具体生成器 (Concrete Builders) 提供构造过程的不同实现。具体生成器也可以构造不遵循通用接口的产品。 产品 (Products) 是最终生成的对象。由不同生成器构造的产品无需属于同一类层次结构或接口。 主管 (Director) 类定义调用构造步骤的顺序，这样你就可以创建和复用特定的产品配置。 客户端 (Client) 必须将某个生成器对象与主管类关联。一般情况下，你只需通过主管类构造函数的参数进行一次性关联即可。此后主管类就能使用生成器对象完成后续所有的构造任务。但在客户端将生成器对象传递给主管类制造方法时还有另一种方式。在这种情况下，你在使用主管类生产产品时每次都可以使用不同的生成器。","s":"生成器模式结构","u":"/docs/design-patterns/builder","h":"#生成器模式结构","p":192},{"i":205,"t":"下面关于生成器模式的例子演示了你可以如何复用相同的对象构造代码来生成不同类型的产品——例如汽车 (Car)——及其相应的使用手册 (Manual)。 分步骤制造汽车并制作对应型号用户使用手册的示例 汽车是一个复杂对象，有数百种不同的制造方法。我们没有在 汽车 类中塞入一个巨型构造函数，而是将汽车组装代码抽取到单独的汽车生成器类中。该类中有一组方法可用来配置汽车的各种部件。 如果客户端代码需要组装一辆与众不同、精心调教的汽车，它可以直接调用生成器。或者，客户端可以将组装工作委托给主管类，因为主管类知道如何使用生成器制造最受欢迎的几种型号汽车。 你或许会感到吃惊，但确实每辆汽车都需要一本使用手册 (说真的，谁会去读它们呢？)。使用手册会介绍汽车的每一项功能，因此不同型号的汽车，其使用手册内容也不一样。因此，你可以复用现有流程来制造实际的汽车及其对应的手册。当然，编写手册和制造汽车不是一回事，所以我们需要另外一个生成器对象来专门编写使用手册。该类与其制造汽车的兄弟类都实现了相同的制造方法，但是其功能不是制造汽车部件，而是描述每个部件。将这些生成器传递给相同的主管对象，我们就能够生成一辆汽车或是一本使用手册了。 最后一个部分是获取结果对象。尽管金属汽车和纸质手册存在关联，但它们却是完全不同的东西。我们无法在主管类和具体产品类不发生耦合的情况下，在主管类中提供获取结果对象的方法。因此，我们只能通过负责制造过程的生成器来获取结果对象。 // 只有当产品较为复杂且需要详细配置时，使用生成器模式才有意义。下面的两个 // 产品尽管没有同样的接口，但却相互关联。 class Car is // 一辆汽车可能配备有 GPS 设备、行车电脑和几个座位。不同型号的汽车（ // 运动型轿车、SUV 和敞篷车）可能会安装或启用不同的功能。 class Manual is // 用户使用手册应该根据汽车配置进行编制，并介绍汽车的所有功能。 // 生成器接口声明了创建产品对象不同部件的方法。 interface Builder is method reset() method setSeats(……) method setEngine(……) method setTripComputer(……) method setGPS(……) // 具体生成器类将遵循生成器接口并提供生成步骤的具体实现。你的程序中可能会 // 有多个以不同方式实现的生成器变体。 class CarBuilder implements Builder is private field car:Car // 一个新的生成器实例必须包含一个在后续组装过程中使用的空产品对象。 constructor CarBuilder() is this.reset() // reset（重置）方法可清除正在生成的对象。 method reset() is this.car = new Car() // 所有生成步骤都会与同一个产品实例进行交互。 method setSeats(……) is // 设置汽车座位的数量。 method setEngine(……) is // 安装指定的引擎。 method setTripComputer(……) is // 安装行车电脑。 method setGPS(……) is // 安装全球定位系统。 // 具体生成器需要自行提供获取结果的方法。这是因为不同类型的生成器可能 // 会创建不遵循相同接口的、完全不同的产品。所以也就无法在生成器接口中 // 声明这些方法（至少在静态类型的编程语言中是这样的）。 // // 通常在生成器实例将结果返回给客户端后，它们应该做好生成另一个产品的 // 准备。因此生成器实例通常会在 `getProduct（获取产品）` 方法主体末尾 // 调用重置方法。但是该行为并不是必需的，你也可让生成器等待客户端明确 // 调用重置方法后再去处理之前的结果。 method getProduct():Car is product = this.car this.reset() return product // 生成器与其他创建型模式的不同之处在于：它让你能创建不遵循相同接口的产品。 class CarManualBuilder implements Builder is private field manual:Manual constructor CarManualBuilder() is this.reset() method reset() is this.manual = new Manual() method setSeats(……) is // 添加关于汽车座椅功能的文档。 method setEngine(……) is // 添加关于引擎的介绍。 method setTripComputer(……) is // 添加关于行车电脑的介绍。 method setGPS(……) is // 添加关于 GPS 的介绍。 method getProduct():Manual is // 返回使用手册并重置生成器。 // 主管只负责按照特定顺序执行生成步骤。其在根据特定步骤或配置来生成产品时 // 会很有帮助。由于客户端可以直接控制生成器，所以严格意义上来说，主管类并 // 不是必需的。 class Director is // 主管可同由客户端代码传递给自身的任何生成器实例进行交互。客户端可通 // 过这种方式改变最新组装完毕的产品的最终类型。主管可使用同样的生成步 // 骤创建多个产品变体。 method constructSportsCar(builder: Builder) is builder.reset() builder.setSeats(2) builder.setEngine(new SportEngine()) builder.setTripComputer(true) builder.setGPS(true) method constructSUV(builder: Builder) is // …… // 客户端代码会创建生成器对象并将其传递给主管，然后执行构造过程。最终结果 // 将需要从生成器对象中获取。 class Application is method makeCar() is director = new Director() CarBuilder builder = new CarBuilder() director.constructSportsCar(builder) Car car = builder.getProduct() CarManualBuilder builder = new CarManualBuilder() director.constructSportsCar(builder) // 最终产品通常需要从生成器对象中获取，因为主管不知晓具体生成器和 // 产品的存在，也不会对其产生依赖。 Manual manual = builder.getProduct()","s":"伪代码","u":"/docs/design-patterns/builder","h":"#伪代码","p":192},{"i":207,"t":"使用生成器模式可避免“重叠构造函数 (telescoping function)”的出现。 假设你的构造函数中有十个可选参数，那么调用该函数会非常不方便；因此，你需要重载这个构造函数，新建几个只有较少参数的简化版。但这些构造函数仍需调用主构造函数，传递一些默认数值来替代省略掉的参数。 class Pizza { Pizza(int size) { …… } Pizza(int size, boolean cheese) { …… } Pizza(int size, boolean cheese, boolean pepperoni) { …… } // …… 只有在 C# 或 Java 等支持方法重载的编程语言中才能写出如此复杂的构造函数。 生成器模式让你可以分步骤生成对象，而且允许你仅使用必须的步骤。应用该模式后，你再也不需要将几十个参数塞进构造函数里了。 当你希望使用代码创建不同形式的产品 (例如石头或木头房屋) 时，可使用生成器模式。 如果你需要创建的各种形式的产品，它们的制造过程相似且仅有细节上的差异，此时可使用生成器模式。 基本生成器接口中定义了所有可能的制造步骤，具体生成器将实现这些步骤来制造特定形式的产品。同时，主管类将负责管理制造步骤的顺序。 使用生成器构造组合树或其他复杂对象。 生成器模式让你能分步骤构造产品。你可以延迟执行某些步骤而不会影响最终产品。你甚至可以递归调用这些步骤，这在创建对象树时非常方便。 生成器在执行制造步骤时，不能对外发布未完成的产品。这可以避免客户端代码获取到不完整结果对象的情况。","s":"生成器模式适合应用场景","u":"/docs/design-patterns/builder","h":"#生成器模式适合应用场景","p":192},{"i":209,"t":"清晰地定义通用步骤，确保它们可以制造所有形式的产品。否则你将无法进一步实施该模式。 在基本生成器接口中声明这些步骤。 为每个形式的产品创建具体生成器类，并实现其构造步骤。 不要忘记实现获取构造结果对象的方法。你不能在生成器接口中声明该方法，因为不同生成器构造的产品可能没有公共接口，因此你就不知道该方法返回的对象类型。但是，如果所有产品都位于单一类层次中，你就可以安全地在基本接口中添加获取生成对象的方法。 考虑创建主管类。它可以使用同一生成器对象来封装多种构造产品的方式。 客户端代码会同时创建生成器和主管对象。构造开始前，客户端必须将生成器对象传递给主管对象。通常情况下，客户端只需调用主管类构造函数一次即可。主管类使用生成器对象完成后续所有制造任务。还有另一种方式，那就是客户端可以将生成器对象直接传递给主管类的制造方法。 只有在所有产品都遵循相同接口的情况下，构造结果可以直接通过主管类获取。否则，客户端应当通过生成器获取构造结果。","s":"实现方法","u":"/docs/design-patterns/builder","h":"#实现方法","p":192},{"i":211,"t":"✔️ 你可以分步创建对象，暂缓创建步骤或递归运行创建步骤。 ✔️ 生成不同形式的产品时，你可以复用相同的制造代码。 ✔️ 单一职责原则。你可以将复杂构造代码从产品的业务逻辑中分离出来。 ❌ 由于该模式需要新增多个类，因此代码整体复杂程度会有所增加。","s":"生成器模式优缺点","u":"/docs/design-patterns/builder","h":"#生成器模式优缺点","p":192},{"i":213,"t":"在许多设计工作的初期都会使用工厂方法模式 (较为简单，而且可以更方便地通过子类进行定制)，随后演化为使用抽象工厂模式、原型模式或生成器模式 (更灵活但更加复杂)。 生成器重点关注如何分步生成复杂对象。抽象工厂专门用于生产一系列相关对象。抽象工厂会马上返回产品，生成器则允许你在获取产品前执行一些额外构造步骤。 你可以在创建复杂组合模式树时使用生成器，因为这可使其构造步骤以递归的方式运行。 你可以结合使用生成器和桥接模式：主管类负责抽象工作，各种不同的生成器负责实现工作。 抽象工厂、生成器和原型都可以用单例模式来实现。","s":"与其他模式的关系","u":"/docs/design-patterns/builder","h":"#与其他模式的关系","p":192},{"i":215,"t":"亦称：职责链模式、命令链、CoR、Chain of Command、Chain of Responsibility","s":"责任链模式","u":"/docs/design-patterns/chain-of-responsibility","h":"","p":214},{"i":217,"t":"责任链模式是一种行为设计模式，允许你将请求沿着处理者链进行发送。收到请求后，每个处理者均可对请求进行处理，或将其传递给链上的下个处理者。","s":"意图","u":"/docs/design-patterns/chain-of-responsibility","h":"#意图","p":214},{"i":219,"t":"假如你正在开发一个在线订购系统。你希望对系统访问进行限制，只允许认证用户创建订单。此外，拥有管理权限的用户也拥有所有订单的完全访问权限。 简单规划后，你会意识到这些检查必须依次进行。只要接收到包含用户凭据的请求，应用程序就可尝试对进入系统的用户进行认证。但如果由于用户凭据不正确而导致认证失败，那就没有必要进行后续检查了。 请求必须经过一系列检查后才能由订购系统来处理。 在接下来的几个月里，你实现了后续的几个检查步骤。 一位同事认为直接将原始数据传递给订购系统存在安全隐患。因此你新增了额外的验证步骤来清理请求中的数据。 过了一段时间，有人注意到系统无法抵御暴力密码破解方式的攻击。为了防范这种情况，你立刻添加了一个检查步骤来过滤来自同一 IP 地址的重复错误请求。 又有人提议你可以对包含同样数据的重复请求返回缓存中的结果，从而提高系统响应速度。因此，你新增了一个检查步骤，确保只有没有满足条件的缓存结果时请求才能通过并被发送给系统。 代码变得越来越多，也越来越混乱。 检查代码本来就已经混乱不堪，而每次新增功能都会使其更加臃肿。修改某个检查步骤有时会影响其他的检查步骤。最糟糕的是，当你希望复用这些检查步骤来保护其他系统组件时，你只能复制部分代码，因为这些组件只需部分而非全部的检查步骤。 系统会变得让人非常费解，而且其维护成本也会激增。你在艰难地和这些代码共处一段时间后，有一天终于决定对整个系统进行重构。","s":"问题","u":"/docs/design-patterns/chain-of-responsibility","h":"#问题","p":214},{"i":221,"t":"与许多其他行为设计模式一样，责任链会将特定行为转换为被称作处理者的独立对象。在上述示例中，每个检查步骤都可被抽取为仅有单个方法的类，并执行检查操作。请求及其数据则会被作为参数传递给该方法。 模式建议你将这些处理者连成一条链。链上的每个处理者都有一个成员变量来保存对于下一处理者的引用。除了处理请求外，处理者还负责沿着链传递请求。请求会在链上移动，直至所有处理者都有机会对其进行处理。 最重要的是：处理者可以决定不再沿着链传递请求，这可高效地取消所有后续处理步骤。 在我们的订购系统示例中，处理者会在进行请求处理工作后决定是否继续沿着链传递请求。如果请求中包含正确的数据，所有处理者都将执行自己的主要行为，无论该行为是身份验证还是数据缓存。 处理者依次排列，组成一条链。 不过还有一种稍微不同的方式 (也是更经典一种)，那就是处理者接收到请求后自行决定是否能够对其进行处理。如果自己能够处理，处理者就不再继续传递请求。因此在这种情况下，每个请求要么最多有一个处理者对其进行处理，要么没有任何处理者对其进行处理。在处理图形用户界面元素栈中的事件时，这种方式非常常见。 例如，当用户点击按钮时，按钮产生的事件将沿着 GUI 元素链进行传递，最开始是按钮的容器 (如窗体或面板)，直至应用程序主窗口。链上第一个能处理该事件的元素会对其进行处理。此外，该例还有另一个值得我们关注的地方：它表明我们总能从对象树中抽取出链来。 对象树的枝干可以组成一条链。 所有处理者类均实现同一接口是关键所在。每个具体处理者仅关心下一个包含 execute 执行方法的处理者。这样一来，你就可以在运行时使用不同的处理者来创建链，而无需将相关代码与处理者的具体类进行耦合。","s":"解决方案","u":"/docs/design-patterns/chain-of-responsibility","h":"#解决方案","p":214},{"i":223,"t":"给技术支持打电话时你可能得应对多名接听人员。 最近，你刚为自己的电脑购买并安装了一个新的硬件设备。身为一名极客，你显然在电脑上安装了多个操作系统，所以你会试着启动所有操作系统来确认其是否支持新的硬件设备。Windows 检测到了该硬件设备并对其进行了自动启用。但是你喜爱的 Linux 系统并不支持新硬件设备。抱着最后一点希望，你决定拨打包装盒上的技术支持电话。 首先你会听到自动回复器的机器合成语音，它提供了针对各种问题的九个常用解决方案，但其中没有一个与你遇到的问题相关。过了一会儿，机器人将你转接到人工接听人员处。 这位接听人员同样无法提供任何具体的解决方案。他不断地引用手册中冗长的内容，并不会仔细聆听你的回应。在第 10 次听到“你是否关闭计算机后重新启动呢？”这句话后，你要求与一位真正的工程师通话。 最后，接听人员将你的电话转接给了工程师，他或许正缩在某幢办公大楼的阴暗地下室中，坐在他所深爱的服务器机房里，焦躁不安地期待着同一名真人交流。工程师告诉了你新硬件设备驱动程序的下载网址，以及如何在 Linux 系统上进行安装。问题终于解决了！你挂断了电话，满心欢喜。","s":"真实世界类比","u":"/docs/design-patterns/chain-of-responsibility","h":"#真实世界类比","p":214},{"i":225,"t":"处理者 (Handler) 声明了所有具体处理者的通用接口。该接口通常仅包含单个方法用于请求处理，但有时其还会包含一个设置链上下个处理者的方法。 基础处理者 (Base Handler) 是一个可选的类，你可以将所有处理者共用的样本代码放置在其中。 通常情况下，该类中定义了一个保存对于下个处理者引用的成员变量。客户端可通过将处理者传递给上个处理者的构造函数或设定方法来创建链。该类还可以实现默认的处理行为：确定下个处理者存在后再将请求传递给它。 具体处理者 (Concrete Handlers) 包含处理请求的实际代码。每个处理者接收到请求后，都必须决定是否进行处理，以及是否沿着链传递请求。 处理者通常是独立且不可变的，需要通过构造函数一次性地获得所有必要地数据。 客户端 (Client) 可根据程序逻辑一次性或者动态地生成链。值得注意的是，请求可发送给链上的任意一个处理者，而非必须是第一个处理者。","s":"责任链模式结构","u":"/docs/design-patterns/chain-of-responsibility","h":"#责任链模式结构","p":214},{"i":227,"t":"在本例中，责任链模式负责为活动的 GUI 元素显示上下文帮助信息。 GUI 类使用组合模式生成。每个元素都链接到自己的容器元素。你可随时构建从当前元素开始的、遍历其所有容器的元素链。 应用程序的 GUI 通常为对象树结构。例如，负责渲染程序主窗口的 对话框 类就是对象树的根节点。对话框包含 面板，而面板可能包含其他面板，或是 按钮 和 文本框 等下层元素。 只要给一个简单的组件指定帮助文本，它就可显示简短的上下文提示。但更复杂的组件可自定义上下文帮助文本的显示方式，例如显示手册摘录内容或在浏览器中打开一个网页。 帮助请求如何在 GUI 对象中移动。 当用户将鼠标指针移动到某个元素并按下 F1 键时，程序检测到指针下的组件并对其发送帮助请求。该请求不断向上传递到该元素所有的容器，直至某个元素能够显示帮助信息。 `// 处理者接口声明了一个创建处理者链的方法。还声明了一个执行请求的方法。 interface ComponentWithContextualHelp ismethod showHelp() // 简单组件的基础类。 abstract class Component implements ComponentWithContextualHelp isfield tooltipText：string // 组件容器在处理者链中作为“下一个”链接。 protected field container: Container // 如果组件设定了帮助文字，那它将会显示提示信息。如果组件没有帮助文字 // 且其容器存在，那它会将调用传递给容器。 method showHelp() isif (tooltipText != null) // 显示提示信息。 elsecontainer.showHelp() // 容器可以将简单组件和其他容器作为其子项目。链关系将在这里建立。该类将从 // 其父类处继承 showHelp (显示帮助) 的行为。 abstract class Container extends Component isprotected field children：array of Component method add(child) ischildren.add(child) child.container = this// 原始组件应该能够使用帮助操作的默认实现…… class Button extends Component is// …… // 但复杂组件可能会对默认实现进行重写。如果无法以新的方式来提供帮助文字，// 那组件总是还能调用基础实现的 (参见 Component 类)。 class Panel extends Container isfield modalHelpText：string method showHelp() isif (modalHelpText != null) // 显示包含帮助文字的模态窗口。 elsesuper.showHelp() // ……同上…… class Dialog extends Container isfield wikiPageURL：string method showHelp() isif (wikiPageURL != null) // 打开百科帮助页面。 elsesuper.showHelp() // 客户端代码。 class Application is// 每个程序都能以不同方式对链进行配置。 method createUI() isdialog = new Dialog (“预算报告”) dialog.wikiPageURL = “http://……”panel = new Panel(0，0，400，800) panel.modalHelpText = “本面板用于……”ok = new Button(250，760，50，20，“确认”) ok.tooltipText = “这是一个确认按钮……”cancel = new Button(320，760，50，20，“取消”) // …… panel.add(ok) panel.add(cancel) dialog.add(panel) // 想象这里会发生什么。 method onF1KeyPress() iscomponent = this.getComponentAtMouseCoords() component.showHelp()`","s":"伪代码","u":"/docs/design-patterns/chain-of-responsibility","h":"#伪代码","p":214},{"i":229,"t":"当程序需要使用不同方式处理不同种类请求，而且请求类型和顺序预先未知时，可以使用责任链模式。 该模式能将多个处理者连接成一条链。接收到请求后，它会“询问”每个处理者是否能够对其进行处理。这样所有处理者都有机会来处理请求。 当必须按顺序执行多个处理者时，可以使用该模式。 无论你以何种顺序将处理者连接成一条链，所有请求都会严格按照顺序通过链上的处理者。 如果所需处理者及其顺序必须在运行时进行改变，可以使用责任链模式。 如果在处理者类中有对引用成员变量的设定方法，你将能动态地插入和移除处理者，或者改变其顺序。 实现方式 声明处理者接口并描述请求处理方法的签名。确定客户端如何将请求数据传递给方法。最灵活的方式是将请求转换为对象，然后将其以参数的形式传递给处理函数。 为了在具体处理者中消除重复的样本代码，你可以根据处理者接口创建抽象处理者基类。该类需要有一个成员变量来存储指向链上下个处理者的引用。你可以将其设置为不可变类。但如果你打算在运行时对链进行改变，则需要定义一个设定方法来修改引用成员变量的值。为了使用方便，你还可以实现处理方法的默认行为。如果还有剩余对象，该方法会将请求传递给下个对象。具体处理者还能够通过调用父对象的方法来使用这一行为。 依次创建具体处理者子类并实现其处理方法。每个处理者在接收到请求后都必须做出两个决定： 是否自行处理这个请求。 是否将该请求沿着链进行传递。 客户端可以自行组装链，或者从其他对象处获得预先组装好的链。在后一种情况下，你必须实现工厂类以根据配置或环境设置来创建链。 客户端可以触发链中的任意处理者，而不仅仅是第一个。请求将通过链进行传递，直至某个处理者拒绝继续传递，或者请求到达链尾。 由于链的动态性，客户端需要准备好处理以下情况： 链中可能只有单个链接。 部分请求可能无法到达链尾。 其他请求可能直到链尾都未被处理。","s":"责任链模式适合应用场景","u":"/docs/design-patterns/chain-of-responsibility","h":"#责任链模式适合应用场景","p":214},{"i":231,"t":"✔️ 你可以控制请求处理的顺序。 ✔️ 单一职责原则。你可对发起操作和执行操作的类进行解耦。 ✔️ 开闭原则。你可以在不更改现有代码的情况下在程序中新增处理者。 ❌ 部分请求可能未被处理。","s":"责任链模式优缺点","u":"/docs/design-patterns/chain-of-responsibility","h":"#责任链模式优缺点","p":214},{"i":233,"t":"责任链模式、命令模式、中介者模式和观察者模式用于处理请求发送者和接收者之间的不同连接方式： 责任链按照顺序将请求动态传递给一系列的潜在接收者，直至其中一名接收者对请求进行处理。 命令在发送者和请求者之间建立单向连接。 中介者清除了发送者和请求者之间的直接连接，强制它们通过一个中介对象进行间接沟通。 观察者允许接收者动态地订阅或取消接收请求。 责任链通常和组合模式结合使用。在这种情况下，叶组件接收到请求后，可以将请求沿包含全体父组件的链一直传递至对象树的底部。 责任链的管理者可使用命令模式实现。在这种情况下，你可以对由请求代表的同一个上下文对象执行许多不同的操作。还有另外一种实现方式，那就是请求自身就是一个命令对象。在这种情况下，你可以对由一系列不同上下文连接而成的链执行相同的操作。 责任链和装饰模式的类结构非常相似。两者都依赖递归组合将需要执行的操作传递给一系列对象。但是，两者有几点重要的不同之处。 责任链的管理者可以相互独立地执行一切操作，还可以随时停止传递请求。另一方面，各种装饰可以在遵循基本接口的情况下扩展对象的行为。此外，装饰无法中断请求的传递。","s":"与其他模式的关系","u":"/docs/design-patterns/chain-of-responsibility","h":"#与其他模式的关系","p":214},{"i":235,"t":"亦称：动作、事务、Action、Transaction、Command","s":"命令模式","u":"/docs/design-patterns/command","h":"","p":234},{"i":237,"t":"命令模式是一种行为设计模式，它可将请求转换为一个包含与请求相关的所有信息的独立对象。该转换让你能根据不同的请求将方法参数化、延迟请求执行或将其放入队列中，且能实现可撤销操作。","s":"意图","u":"/docs/design-patterns/command","h":"#意图","p":234},{"i":239,"t":"假如你正在开发一款新的文字编辑器，当前的任务是创建一个包含多个按钮的工具栏，并让每个按钮对应编辑器的不同操作。你创建了一个非常简洁的 按钮 类，它不仅可用于生成工具栏上的按钮，还可用于生成各种对话框的通用按钮。 应用中的所有按钮都可以继承相同的类 尽管所有按钮看上去都很相似，但它们可以完成不同的操作 (打开、保存、打印和应用等)。你会在哪里放置这些按钮的点击处理代码呢？最简单的解决方案是在使用按钮的每个地方都创建大量的子类。这些子类中包含按钮点击后必须执行的代码。 大量的按钮子类。没关系的。 你很快就意识到这种方式有严重缺陷。首先，你创建了大量的子类，当每次修改基类 按钮 时，你都有可能需要修改所有子类的代码。简单来说，GUI 代码以一种拙劣的方式依赖于业务逻辑中的不稳定代码。 多个类实现同一功能。 还有一个部分最难办。复制/粘贴文字等操作可能会在多个地方被调用。例如用户可以点击工具栏上小小的“复制”按钮，或者通过上下文菜单复制一些内容，又或者直接使用键盘上的 Ctrl+C。 我们的程序最初只有工具栏，因此可以使用按钮子类来实现各种不同操作。换句话来说，复制按钮 Copy­Button 子类包含复制文字的代码是可行的。在实现了上下文菜单、快捷方式和其他功能后，你要么需要将操作代码复制进许多个类中，要么需要让菜单依赖于按钮，而后者是更糟糕的选择。","s":"问题","u":"/docs/design-patterns/command","h":"#问题","p":234},{"i":241,"t":"优秀的软件设计通常会将关注点进行分离，而这往往会导致软件的分层。最常见的例子：一层负责用户图像界面；另一层负责业务逻辑。GUI 层负责在屏幕上渲染美观的图形，捕获所有输入并显示用户和程序工作的结果。当需要完成一些重要内容时 (比如计算月球轨道或撰写年度报告)，GUI 层则会将工作委派给业务逻辑底层。 这在代码中看上去就像这样：一个 GUI 对象传递一些参数来调用一个业务逻辑对象。这个过程通常被描述为一个对象发送请求给另一个对象。 GUI 层可以直接访问业务逻辑层。 命令模式建议 GUI 对象不直接提交这些请求。你应该将请求的所有细节 (例如调用的对象、方法名称和参数列表) 抽取出来组成命令类，该类中仅包含一个用于触发请求的方法。 命令对象负责连接不同的 GUI 和业务逻辑对象。此后，GUI 对象无需了解业务逻辑对象是否获得了请求，也无需了解其对请求进行处理的方式。GUI 对象触发命令即可，命令对象会自行处理所有细节工作。 通过命令访问业务逻辑层。 下一步是让所有命令实现相同的接口。该接口通常只有一个没有任何参数的执行方法，让你能在不和具体命令类耦合的情况下使用同一请求发送者执行不同命令。此外还有额外的好处，现在你能在运行时切换连接至发送者的命令对象，以此改变发送者的行为。 你可能会注意到遗漏的一块拼图——请求的参数。GUI 对象可以给业务层对象提供一些参数。但执行命令方法没有任何参数，所以我们如何将请求的详情发送给接收者呢？答案是：使用数据对命令进行预先配置，或者让其能够自行获取数据。 GUI 对象将命令委派给命令对象。 让我们回到文本编辑器。应用命令模式后，我们不再需要任何按钮子类来实现点击行为。我们只需在 按钮 Button 基类中添加一个成员变量来存储对于命令对象的引用，并在点击后执行该命令即可。 你需要为每个可能的操作实现一系列命令类，并且根据按钮所需行为将命令和按钮连接起来。 其他菜单、快捷方式或整个对话框等 GUI 元素都可以通过相同方式来实现。当用户与 GUI 元素交互时，与其连接的命令将会被执行。现在你很可能已经猜到了，与相同操作相关的元素将会被连接到相同的命令，从而避免了重复代码。 最后，命令成为了减少 GUI 和业务逻辑层之间耦合的中间层。而这仅仅是命令模式所提供的一小部分好处！","s":"解决方案","u":"/docs/design-patterns/command","h":"#解决方案","p":234},{"i":243,"t":"在餐厅里点餐。 在市中心逛了很久的街后，你找到了一家不错的餐厅，坐在了临窗的座位上。一名友善的服务员走近你，迅速记下你点的食物，写在一张纸上。服务员来到厨房，把订单贴在墙上。过了一段时间，厨师拿到了订单，他根据订单来准备食物。厨师将做好的食物和订单一起放在托盘上。服务员看到托盘后对订单进行检查，确保所有食物都是你要的，然后将食物放到了你的桌上。 那张纸就是一个命令，它在厨师开始烹饪前一直位于队列中。命令中包含与烹饪这些食物相关的所有信息。厨师能够根据它马上开始烹饪，而无需跑来直接和你确认订单详情。","s":"真实世界类比","u":"/docs/design-patterns/command","h":"#真实世界类比","p":234},{"i":245,"t":"发送者 (Sender)——亦称“触发者 (Invoker)”——类负责对请求进行初始化，其中必须包含一个成员变量来存储对于命令对象的引用。发送者触发命令，而不向接收者直接发送请求。注意，发送者并不负责创建命令对象：它通常会通过构造函数从客户端处获得预先生成的命令。 命令 (Command) 接口通常仅声明一个执行命令的方法。 具体命令 (Concrete Commands) 会实现各种类型的请求。具体命令自身并不完成工作，而是会将调用委派给一个业务逻辑对象。但为了简化代码，这些类可以进行合并。 接收对象执行方法所需的参数可以声明为具体命令的成员变量。你可以将命令对象设为不可变，仅允许通过构造函数对这些成员变量进行初始化。 接收者 (Receiver) 类包含部分业务逻辑。几乎任何对象都可以作为接收者。绝大部分命令只处理如何将请求传递到接收者的细节，接收者自己会完成实际的工作。 客户端 (Client) 会创建并配置具体命令对象。客户端必须将包括接收者实体在内的所有请求参数传递给命令的构造函数。此后，生成的命令就可以与一个或多个发送者相关联了。","s":"命令模式结构","u":"/docs/design-patterns/command","h":"#命令模式结构","p":234},{"i":247,"t":"在本例中，命令模式会记录已执行操作的历史记录，以在需要时撤销操作。 文本编辑器中的可撤销操作。 有些命令会改变编辑器的状态 (例如剪切和粘贴)，它们可在执行相关操作前对编辑器的状态进行备份。命令执行后会和当前点备份的编辑器状态一起被放入命令历史 (命令对象栈)。此后，如果用户需要进行回滚操作，程序可从历史记录中取出最近的命令，读取相应的编辑器状态备份，然后进行恢复。 客户端代码 (GUI 元素和命令历史等) 没有和具体命令类相耦合，因为它通过命令接口来使用命令。这使得你能在无需修改已有代码的情况下在程序中增加新的命令。 // 命令基类会为所有具体命令定义通用接口。 abstract class Command is protected field app: Application protected field editor: Editor protected field backup: text constructor Command(app: Application, editor: Editor) is this.app = app this.editor = editor // 备份编辑器状态。 method saveBackup() is backup = editor.text // 恢复编辑器状态。 method undo() is editor.text = backup // 执行方法被声明为抽象以强制所有具体命令提供自己的实现。该方法必须根 // 据命令是否更改编辑器的状态返回 true 或 false。 abstract method execute() // 这里是具体命令。 class CopyCommand extends Command is // 复制命令不会被保存到历史记录中，因为它没有改变编辑器的状态。 method execute() is app.clipboard = editor.getSelection() return false class CutCommand extends Command is // 剪切命令改变了编辑器的状态，因此它必须被保存到历史记录中。只要方法 // 返回 true，它就会被保存。 method execute() is saveBackup() app.clipboard = editor.getSelection() editor.deleteSelection() return true class PasteCommand extends Command is method execute() is saveBackup() editor.replaceSelection(app.clipboard) return true // 撤销操作也是一个命令。 class UndoCommand extends Command is method execute() is app.undo() return false // 全局命令历史记录就是一个堆桟。 class CommandHistory is private field history: array of Command // 后进…… method push(c: Command) is // 将命令压入历史记录数组的末尾。 // ……先出 method pop():Command is // 从历史记录中取出最近的命令。 // 编辑器类包含实际的文本编辑操作。它会担任接收者的角色：最后所有命令都会 // 将执行工作委派给编辑器的方法。 class Editor is field text: string method getSelection() is // 返回选中的文字。 method deleteSelection() is // 删除选中的文字。 method replaceSelection(text) is // 在当前位置插入剪贴板中的内容。 // 应用程序类会设置对象之间的关系。它会担任发送者的角色：当需要完成某些工 // 作时，它会创建并执行一个命令对象。 class Application is field clipboard: string field editors: array of Editors field activeEditor: Editor field history: CommandHistory // 将命令分派给 UI 对象的代码可能会是这样的。 method createUI() is // …… copy = function() { executeCommand( new CopyCommand(this, activeEditor)) } copyButton.setCommand(copy) shortcuts.onKeyPress(\"Ctrl+C\", copy) cut = function() { executeCommand( new CutCommand(this, activeEditor)) } cutButton.setCommand(cut) shortcuts.onKeyPress(\"Ctrl+X\", cut) paste = function() { executeCommand( new PasteCommand(this, activeEditor)) } pasteButton.setCommand(paste) shortcuts.onKeyPress(\"Ctrl+V\", paste) undo = function() { executeCommand( new UndoCommand(this, activeEditor)) } undoButton.setCommand(undo) shortcuts.onKeyPress(\"Ctrl+Z\", undo) // 执行一个命令并检查它是否需要被添加到历史记录中。 method executeCommand(command) is if (command.execute()) history.push(command) // 从历史记录中取出最近的命令并运行其 undo（撤销）方法。请注意，你并 // 不知晓该命令所属的类。但是我们不需要知晓，因为命令自己知道如何撤销 // 其动作。 method undo() is command = history.pop() if (command != null) command.undo()","s":"伪代码","u":"/docs/design-patterns/command","h":"#伪代码","p":234},{"i":249,"t":"如果你需要通过操作来参数化对象，可使用命令模式。 命令模式可将特定的方法调用转化为独立对象。这一改变也带来了许多有趣的应用：你可以将命令作为方法的参数进行传递、将命令保存在其他对象中，或者在运行时切换已连接的命令等。 举个例子：你正在开发一个 GUI 组件 (例如上下文菜单)，你希望用户能够配置菜单项，并在点击菜单项时触发操作。 如果你想要将操作放入队列中、操作的执行或者远程执行操作，可使用命令模式。 同其他对象一样，命令也可以实现序列化 (序列化的意思是转化为字符串)，从而能方便地写入文件或数据库中。一段时间后，该字符串可被恢复成为最初的命令对象。因此，你可以延迟或计划命令的执行。但其功能远不止如此！使用同样的方式，你还可以将命令放入队列、记录命令或者通过网络发送命令。 如果你想要实现操作回滚功能，可使用命令模式。 尽管有很多方法可以实现撤销和恢复功能，但命令模式可能是其中最常用的一种。 为了能够回滚操作，你需要实现已执行操作的历史记录功能。命令历史记录是一种包含所有已执行命令对象及其相关程序状态备份的栈结构。 这种方法有两个缺点。首先，程序状态的保存功能并不容易实现，因为部分状态可能是私有的。你可以使用备忘录模式来在一定程度上解决这个问题。 其次，备份状态可能会占用大量内存。因此，有时你需要借助另一种实现方式：命令无需恢复原始状态，而是执行反向操作。反向操作也有代价：它可能会很难甚至是无法实现。 实现方式 声明仅有一个执行方法的命令接口。 抽取请求并使之成为实现命令接口的具体命令类。每个类都必须有一组成员变量来保存请求参数和对于实际接收者对象的引用。所有这些变量的数值都必须通过命令构造函数进行初始化。 找到担任发送者职责的类。在这些类中添加保存命令的成员变量。发送者只能通过命令接口与其命令进行交互。发送者自身通常并不创建命令对象，而是通过客户端代码获取。 修改发送者使其执行命令，而非直接将请求发送给接收者。 客户端必须按照以下顺序来初始化对象： 创建接收者。 创建命令，如有需要可将其关联至接收者。 创建发送者并将其与特定命令关联。","s":"命令模式适合应用场景","u":"/docs/design-patterns/command","h":"#命令模式适合应用场景","p":234},{"i":251,"t":"✔️ 单一职责原则。你可以解耦触发和执行操作的类。 ✔️ 开闭原则。你可以在不修改已有客户端代码的情况下在程序中创建新的命令。 ✔️ 你可以实现撤销和恢复功能。 ✔️ 你可以实现操作的延迟执行。 ✔️ 你可以将一组简单命令组合成一个复杂命令。 ❌ 代码可能会变得更加复杂，因为你在发送者和接收者之间增加了一个全新的层次。","s":"命令模式优缺点","u":"/docs/design-patterns/command","h":"#命令模式优缺点","p":234},{"i":253,"t":"责任链模式、命令模式、中介者模式和观察者模式用于处理请求发送者和接收者之间的不同连接方式： 责任链按照顺序将请求动态传递给一系列的潜在接收者，直至其中一名接收者对请求进行处理。 命令在发送者和请求者之间建立单向连接。 中介者清除了发送者和请求者之间的直接连接，强制它们通过一个中介对象进行间接沟通。 观察者允许接收者动态地订阅或取消接收请求。 责任链的管理者可使用命令模式实现。在这种情况下，你可以对由请求代表的同一个上下文对象执行许多不同的操作。还有另外一种实现方式，那就是请求自身就是一个命令对象。在这种情况下，你可以对由一系列不同上下文连接而成的链执行相同的操作。 你可以同时使用命令和备忘录模式来实现“撤销”。在这种情况下，命令用于对目标对象执行各种不同的操作，备忘录用来保存一条命令执行前该对象的状态。 命令和策略模式看上去很像，因为两者都能通过某些行为来参数化对象。但是，它们的意图有非常大的不同。 你可以使用命令来将任何操作转换为对象。操作的参数将成为对象的成员变量。你可以通过转换来延迟操作的执行、将操作放入队列、保存历史命令或者向远程服务发送命令等。 另一方面，策略通常可用于描述完成某件事的不同方式，让你能够在同一个上下文类中切换算法。 原型模式可用于保存命令的历史记录。 你可以将访问者模式视为命令模式的加强版本，其对象可对不同类的多种对象执行操作。","s":"与其他模式的关系","u":"/docs/design-patterns/command","h":"#与其他模式的关系","p":234},{"i":255,"t":"亦称：对象树、Object Tree、Composite","s":"组合模式","u":"/docs/design-patterns/composite","h":"","p":254},{"i":257,"t":"组合模式是一种结构型设计模式，你可以使用它将对象组合成树状结构，并且能像使用独立对象一样使用它们。","s":"意图","u":"/docs/design-patterns/composite","h":"#意图","p":254},{"i":259,"t":"如果应用的核心模型能用树状结构表示，在应用中使用组合模式才有价值。 例如，你有两类对象：产品 和 盒子。一个盒子中可以包含多个 产品 或者几个较小的 盒子。这些小 盒子 中同样可以包含一些 产品 或更小的 盒子，以此类推。 假设你希望在这些类的基础上开发一个定购系统。订单中可以包含无包装的简单产品，也可以包含装满产品的盒子…… 以及其他盒子。此时你会如何计算每张订单的总价格呢？ 订单中可能包括各种产品，这些产品放置在盒子中，然后又被放入一层又一层更大的盒子中。整个结构看上去像是一棵倒过来的树。 你可以尝试直接计算：打开所有盒子，找到每件产品，然后计算总价。这在真实世界中或许可行，但在程序中，你并不能简单地使用循环语句来完成该工作。你必须事先知道所有 产品 和 盒子 的类别，所有盒子的嵌套层数以及其他繁杂的细节信息。因此，直接计算极不方便，甚至完全不可行。","s":"问题","u":"/docs/design-patterns/composite","h":"#问题","p":254},{"i":261,"t":"组合模式建议使用一个通用接口来与 产品 和 盒子 进行交互，并且在该接口中声明一个计算总价的方法。 那么方法该如何设计呢？对于一个产品，该方法直接返回其价格；对于一个盒子，该方法遍历盒子中的所有项目，询问每个项目的价格，然后返回该盒子的总价格。如果其中某个项目是小一号的盒子，那么当前盒子也会遍历其中的所有项目，以此类推，直到计算出所有内部组成部分的价格。你甚至可以在盒子的最终价格中增加额外费用，作为该盒子的包装费用。 组合模式以递归方式处理对象树中的所有项目 该方式的最大优点在于你无需了解构成树状结构的对象的具体类。你也无需了解对象是简单的产品还是复杂的盒子。你只需调用通用接口以相同的方式对其进行处理即可。当你调用该方法后，对象会将请求沿着树结构传递下去。","s":"解决方案","u":"/docs/design-patterns/composite","h":"#解决方案","p":254},{"i":263,"t":"部队结构的例子。 大部分国家的军队都采用层次结构管理。每支部队包括几个师，师由旅构成，旅由团构成，团可以继续划分为排。最后，每个排由一小队实实在在的士兵组成。军事命令由最高层下达，通过每个层级传递，直到每位士兵都知道自己应该服从的命令。","s":"真实世界类比","u":"/docs/design-patterns/composite","h":"#真实世界类比","p":254},{"i":265,"t":"组件 (Component) 接口描述了树中简单项目和复杂项目所共有的操作。 叶节点 (Leaf) 是树的基本结构，它不包含子项目。 一般情况下，叶节点最终会完成大部分的实际工作，因为它们无法将工作指派给其他部分。 容器 (Container)——又名“组合 (Composite)”——是包含叶节点或其他容器等子项目的单位。容器不知道其子项目所属的具体类，它只通过通用的组件接口与其子项目交互。 容器接收到请求后会将工作分配给自己的子项目，处理中间结果，然后将最终结果返回给客户端。 客户端 (Client) 通过组件接口与所有项目交互。因此，客户端能以相同方式与树状结构中的简单或复杂项目交互。","s":"组合模式结构","u":"/docs/design-patterns/composite","h":"#组合模式结构","p":254},{"i":267,"t":"在本例中，我们将借助组合模式帮助你在图形编辑器中实现一系列的几何图形。 几何形状编辑器示例。 组合图形 Compound­Graphic 是一个容器，它可以由多个包括容器在内的子图形构成。组合图形与简单图形拥有相同的方法。但是，组合图形自身并不完成具体工作，而是将请求递归地传递给自己的子项目，然后“汇总”结果。 通过所有图形类所共有的接口，客户端代码可以与所有图形互动。因此，客户端不知道与其交互的是简单图形还是组合图形。客户端可以与非常复杂的对象结构进行交互，而无需与组成该结构的实体类紧密耦合。 // 组件接口会声明组合中简单和复杂对象的通用操作。 interface Graphic is method move(x, y) method draw() // 叶节点类代表组合的终端对象。叶节点对象中不能包含任何子对象。叶节点对象 // 通常会完成实际的工作，组合对象则仅会将工作委派给自己的子部件。 class Dot implements Graphic is field x, y constructor Dot(x, y) { …… } method move(x, y) is this.x += x, this.y += y method draw() is // 在坐标位置 (X,Y) 处绘制一个点。 // 所有组件类都可以扩展其他组件。 class Circle extends Dot is field radius constructor Circle(x, y, radius) { …… } method draw() is // 在坐标位置 (X,Y) 处绘制一个半径为 R 的圆。 // 组合类表示可能包含子项目的复杂组件。组合对象通常会将实际工作委派给子项 // 目，然后“汇总”结果。 class CompoundGraphic implements Graphic is field children: array of Graphic // 组合对象可在其项目列表中添加或移除其他组件（简单的或复杂的皆可）。 method add(child: Graphic) is // 在子项目数组中添加一个子项目。 method remove(child: Graphic) is // 从子项目数组中移除一个子项目。 method move(x, y) is foreach (child in children) do child.move(x, y) // 组合会以特定的方式执行其主要逻辑。它会递归遍历所有子项目，并收集和 // 汇总其结果。由于组合的子项目也会将调用传递给自己的子项目，以此类推， // 最后组合将会完成整个对象树的遍历工作。 method draw() is // 1. 对于每个子部件： // - 绘制该部件。 // - 更新边框坐标。 // 2. 根据边框坐标绘制一个虚线长方形。 // 客户端代码会通过基础接口与所有组件进行交互。这样一来，客户端代码便可同 // 时支持简单叶节点组件和复杂组件。 class ImageEditor is field all: CompoundGraphic method load() is all = new CompoundGraphic() all.add(new Dot(1, 2)) all.add(new Circle(5, 3, 10)) // …… // 将所需组件组合为复杂的组合组件。 method groupSelected(components: array of Graphic) is group = new CompoundGraphic() foreach (component in components) do group.add(component) all.remove(component) all.add(group) // 所有组件都将被绘制。 all.draw()","s":"伪代码","u":"/docs/design-patterns/composite","h":"#伪代码","p":254},{"i":269,"t":"如果你需要实现树状对象结构，可以使用组合模式。 组合模式为你提供了两种共享公共接口的基本元素类型：简单叶节点和复杂容器。容器中可以包含叶节点和其他容器。这使得你可以构建树状嵌套递归对象结构。 如果你希望客户端代码以相同方式处理简单和复杂元素，可以使用该模式。 组合模式中定义的所有元素共用同一个接口。在这一接口的帮助下，客户端不必在意其所使用的对象的具体类。 实现方式 确保应用的核心模型能够以树状结构表示。尝试将其分解为简单元素和容器。记住，容器必须能够同时包含简单元素和其他容器。 声明组件接口及其一系列方法，这些方法对简单和复杂元素都有意义。 创建一个叶节点类表示简单元素。程序中可以有多个不同的叶节点类。 创建一个容器类表示复杂元素。在该类中，创建一个数组成员变量来存储对于其子元素的引用。该数组必须能够同时保存叶节点和容器，因此请确保将其声明为组合接口类型。实现组件接口方法时，记住容器应该将大部分工作交给其子元素来完成。 最后，在容器中定义添加和删除子元素的方法。记住，这些操作可在组件接口中声明。这将会违反接口隔离原则，因为叶节点类中的这些方法为空。但是，这可以让客户端无差别地访问所有元素，即使是组成树状结构的元素。","s":"组合模式适合应用场景","u":"/docs/design-patterns/composite","h":"#组合模式适合应用场景","p":254},{"i":271,"t":"✔️ 你可以利用多态和递归机制更方便地使用复杂树结构。 ✔️ 开闭原则。无需更改现有代码，你就可以在应用中添加新元素，使其成为对象树的一部分。 ❌ 对于功能差异较大的类，提供公共接口或许会有困难。在特定情况下，你需要过度一般化组件接口，使其变得令人难以理解。","s":"组合模式优缺点","u":"/docs/design-patterns/composite","h":"#组合模式优缺点","p":254},{"i":273,"t":"桥接模式、状态模式和策略模式 (在某种程度上包括适配器模式) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。 你可以在创建复杂组合树时使用生成器模式，因为这可使其构造步骤以递归的方式运行。 责任链模式通常和组合模式结合使用。在这种情况下，叶组件接收到请求后，可以将请求沿包含全体父组件的链一直传递至对象树的底部。 你可以使用迭代器模式来遍历组合树。 你可以使用访问者模式对整个组合树执行操作。 你可以使用享元模式实现组合树的共享叶节点以节省内存。 组合和装饰模式的结构图很相似，因为两者都依赖递归组合来组织无限数量的对象。 装饰类似于组合，但其只有一个子组件。此外还有一个明显不同：装饰为被封装对象添加了额外的职责，组合仅对其子节点的结果进行了“求和”。但是，模式也可以相互合作：你可以使用装饰来扩展组合树中特定对象的行为。 大量使用组合和装饰的设计通常可从对于原型模式的使用中获益。你可以通过该模式来复制复杂结构，而非从零开始重新构造。","s":"与其他模式的关系","u":"/docs/design-patterns/composite","h":"#与其他模式的关系","p":254},{"i":275,"t":"创建型模式提供了创建对象的机制，能够提升已有代码的灵活性和可复用性。","s":"创建型模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":277,"t":"在父类中提供一个创建对象的接口以允许子类决定实例化对象的类型。","s":"📄️ 工厂方法模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":279,"t":"让你能创建一系列相关的对象，而无需指定其具体类。","s":"📄️ 抽象工厂模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":281,"t":"使你能够分步骤创建复杂对象。该模式允许你使用相同的创建代码生成不同类型和形式的对象。","s":"📄️ 生成器模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":283,"t":"让你能够复制已有对象，而又无需使代码依赖它们所属的类。","s":"📄️ 原型模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":285,"t":"让你能够保证一个类只有一个实例，并提供一个访问该实例的全局节点。","s":"📄️ 单例模式","u":"/docs/design-patterns/creational-patterns/","h":"","p":274},{"i":287,"t":"亦称：装饰者模式、装饰器模式、Wrapper、Decorator","s":"装饰模式","u":"/docs/design-patterns/decorator","h":"","p":286},{"i":289,"t":"装饰模式是一种结构型设计模式，允许你通过将对象放入包含行为的特殊封装对象中来为原对象绑定新的行为。","s":"意图","u":"/docs/design-patterns/decorator","h":"#意图","p":286},{"i":291,"t":"假设你正在开发一个提供通知功能的库，其他程序可使用它向用户发送关于重要事件的通知。 库的最初版本基于 通知器 Notifier 类，其中只有很少的几个成员变量，一个构造函数和一个 send 发送方法。该方法可以接收来自客户端的消息参数，并将该消息发送给一系列的邮箱，邮箱列表则是通过构造函数传递给通知器的。作为客户端的第三方程序仅会创建和配置通知器对象一次，然后在有重要事件发生时对其进行调用。 程序可以使用通知器类向预定义的邮箱发送重要事件通知。 此后某个时刻，你会发现库的用户希望使用除邮件通知之外的功能。许多用户会希望接收关于紧急事件的手机短信，还有些用户希望在微信上接收消息，而公司用户则希望在 QQ 上接收消息。 每种通知类型都将作为通知器的一个子类得以实现。 这有什么难的呢？首先扩展 通知器 类，然后在新的子类中加入额外的通知方法。现在客户端要对所需通知形式的对应类进行初始化，然后使用该类发送后续所有的通知消息。 但是很快有人会问：“为什么不同时使用多种通知形式呢？如果房子着火了，你大概会想在所有渠道中都收到相同的消息吧。” 你可以尝试创建一个特殊子类来将多种通知方法组合在一起以解决该问题。但这种方式会使得代码量迅速膨胀，不仅仅是程序库代码，客户端代码也会如此。 子类组合数量爆炸。 你必须找到其他方法来规划通知类的结构，否则它们的数量会在不经意之间打破吉尼斯纪录。","s":"问题","u":"/docs/design-patterns/decorator","h":"#问题","p":286},{"i":293,"t":"当你需要更改一个对象的行为时，第一个跳入脑海的想法就是扩展它所属的类。但是，你不能忽视继承可能引发的几个严重问题。 继承是静态的。你无法在运行时更改已有对象的行为，只能使用由不同子类创建的对象来替代当前的整个对象。 子类只能有一个父类。大部分编程语言不允许一个类同时继承多个类的行为。 其中一种方法是用聚合或组合，而不是继承。两者的工作方式几乎一模一样：一个对象包含指向另一个对象的引用，并将部分工作委派给引用对象；继承中的对象则继承了父类的行为，它们自己能够完成这些工作。 你可以使用这个新方法来轻松替换各种连接的“小帮手”对象，从而能在运行时改变容器的行为。一个对象可以使用多个类的行为，包含多个指向其他对象的引用，并将各种工作委派给引用对象。聚合 (或组合) 组合是许多设计模式背后的关键原则 (包括装饰在内)。记住这一点后，让我们继续关于模式的讨论。 继承与聚合的对比 封装器是装饰模式的别称，这个称谓明确地表达了该模式的主要思想。“封装器”是一个能与其他“目标”对象连接的对象。封装器包含与目标对象相同的一系列方法，它会将所有接收到的请求委派给目标对象。但是，封装器可以在将请求委派给目标前后对其进行处理，所以可能会改变最终结果。 那么什么时候一个简单的封装器可以被称为是真正的装饰呢？正如之前提到的，封装器实现了与其封装对象相同的接口。因此从客户端的角度来看，这些对象是完全一样的。封装器中的引用成员变量可以是遵循相同接口的任意对象。这使得你可以将一个对象放入多个封装器中，并在对象中添加所有这些封装器的组合行为。 比如在消息通知示例中，我们可以将简单邮件通知行为放在基类 通知器 中，但将所有其他通知方法放入装饰中。 将各种通知方法放入装饰。 客户端代码必须将基础通知器放入一系列自己所需的装饰中。因此最后的对象将形成一个栈结构。 程序可以配置由通知装饰构成的复杂栈。 实际与客户端进行交互的对象将是最后一个进入栈中的装饰对象。由于所有的装饰都实现了与通知基类相同的接口，客户端的其他代码并不在意自己到底是与“纯粹”的通知器对象，还是与装饰后的通知器对象进行交互。 我们可以使用相同方法来完成其他行为 (例如设置消息格式或者创建接收人列表)。只要所有装饰都遵循相同的接口，客户端就可以使用任意自定义的装饰来装饰对象。","s":"解决方案","u":"/docs/design-patterns/decorator","h":"#解决方案","p":286},{"i":295,"t":"穿上多件衣服将获得组合性的效果。 穿衣服是使用装饰的一个例子。觉得冷时，你可以穿一件毛衣。如果穿毛衣还觉得冷，你可以再套上一件夹克。如果遇到下雨，你还可以再穿一件雨衣。所有这些衣物都“扩展”了你的基本行为，但它们并不是你的一部分，如果你不再需要某件衣物，可以方便地随时脱掉。","s":"真实世界类比","u":"/docs/design-patterns/decorator","h":"#真实世界类比","p":286},{"i":297,"t":"部件 (Component) 声明封装器和被封装对象的公用接口。 具体部件 (Concrete Component) 类是被封装对象所属的类。它定义了基础行为，但装饰类可以改变这些行为。 基础装饰 (Base Decorator) 类拥有一个指向被封装对象的引用成员变量。该变量的类型应当被声明为通用部件接口，这样它就可以引用具体的部件和装饰。装饰基类会将所有操作委派给被封装的对象。 具体装饰类 (Concrete Decorators) 定义了可动态添加到部件的额外行为。具体装饰类会重写装饰基类的方法，并在调用父类方法之前或之后进行额外的行为。 客户端 (Client) 可以使用多层装饰来封装部件，只要它能使用通用接口与所有对象互动即可。","s":"装饰模式结构","u":"/docs/design-patterns/decorator","h":"#装饰模式结构","p":286},{"i":299,"t":"在本例中，装饰模式能够对敏感数据进行压缩和加密，从而将数据从使用数据的代码中独立出来。 加密和压缩装饰的示例。 程序使用一对装饰来封装数据源对象。这两个封装器都改变了从磁盘读写数据的方式： 当数据即将被写入磁盘前，装饰对数据进行加密和压缩。在原始类对改变毫无察觉的情况下，将加密后的受保护数据写入文件。 当数据刚从磁盘读出后，同样通过装饰对数据进行解压和解密。 装饰和数据源类实现同一接口，从而能在客户端代码中相互替换。 // 装饰可以改变组件接口所定义的操作。 interface DataSource is method writeData(data) method readData():data // 具体组件提供操作的默认实现。这些类在程序中可能会有几个变体。 class FileDataSource implements DataSource is constructor FileDataSource(filename) { …… } method writeData(data) is // 将数据写入文件。 method readData():data is // 从文件读取数据。 // 装饰基类和其他组件遵循相同的接口。该类的主要任务是定义所有具体装饰的封 // 装接口。封装的默认实现代码中可能会包含一个保存被封装组件的成员变量，并 // 且负责对其进行初始化。 class DataSourceDecorator implements DataSource is protected field wrappee: DataSource constructor DataSourceDecorator(source: DataSource) is wrappee = source // 装饰基类会直接将所有工作分派给被封装组件。具体装饰中则可以新增一些 // 额外的行为。 method writeData(data) is wrappee.writeData(data) // 具体装饰可调用其父类的操作实现，而不是直接调用被封装对象。这种方式 // 可简化装饰类的扩展工作。 method readData():data is return wrappee.readData() // 具体装饰必须在被封装对象上调用方法，不过也可以自行在结果中添加一些内容。 // 装饰必须在调用封装对象之前或之后执行额外的行为。 class EncryptionDecorator extends DataSourceDecorator is method writeData(data) is // 1. 对传递数据进行加密。 // 2. 将加密后数据传递给被封装对象 writeData（写入数据）方法。 method readData():data is // 1. 通过被封装对象的 readData（读取数据）方法获取数据。 // 2. 如果数据被加密就尝试解密。 // 3. 返回结果。 // 你可以将对象封装在多层装饰中。 class CompressionDecorator extends DataSourceDecorator is method writeData(data) is // 1. 压缩传递数据。 // 2. 将压缩后数据传递给被封装对象 writeData（写入数据）方法。 method readData():data is // 1. 通过被封装对象的 readData（读取数据）方法获取数据。 // 2. 如果数据被压缩就尝试解压。 // 3. 返回结果。 // 选项 1：装饰组件的简单示例 class Application is method dumbUsageExample() is source = new FileDataSource(\"somefile.dat\") source.writeData(salaryRecords) // 已将明码数据写入目标文件。 source = new CompressionDecorator(source) source.writeData(salaryRecords) // 已将压缩数据写入目标文件。 source = new EncryptionDecorator(source) // 源变量中现在包含： // Encryption > Compression > FileDataSource source.writeData(salaryRecords) // 已将压缩且加密的数据写入目标文件。 // 选项 2：客户端使用外部数据源。SalaryManager（工资管理器）对象并不关心 // 数据如何存储。它们会与提前配置好的数据源进行交互，数据源则是通过程序配 // 置器获取的。 class SalaryManager is field source: DataSource constructor SalaryManager(source: DataSource) { …… } method load() is return source.readData() method save() is source.writeData(salaryRecords) // ……其他有用的方法…… // 程序可在运行时根据配置或环境组装不同的装饰堆桟。 class ApplicationConfigurator is method configurationExample() is source = new FileDataSource(\"salary.dat\") if (enabledEncryption) source = new EncryptionDecorator(source) if (enabledCompression) source = new CompressionDecorator(source) logger = new SalaryManager(source) salary = logger.load() // ……","s":"伪代码","u":"/docs/design-patterns/decorator","h":"#伪代码","p":286},{"i":301,"t":"如果你希望在无需修改代码的情况下即可使用对象，且希望在运行时为对象新增额外的行为，可以使用装饰模式。 装饰能将业务逻辑组织为层次结构，你可为各层创建一个装饰，在运行时将各种不同逻辑组合成对象。由于这些对象都遵循通用接口，客户端代码能以相同的方式使用这些对象。 如果用继承来扩展对象行为的方案难以实现或者根本不可行，你可以使用该模式。 许多编程语言使用 final 最终关键字来限制对某个类的进一步扩展。复用最终类已有行为的唯一方法是使用装饰模式：用封装器对其进行封装。 实现方式 确保业务逻辑可用一个基本组件及多个额外可选层次表示。 找出基本组件和可选层次的通用方法。创建一个组件接口并在其中声明这些方法。 创建一个具体组件类，并定义其基础行为。 创建装饰基类，使用一个成员变量存储指向被封装对象的引用。该成员变量必须被声明为组件接口类型，从而能在运行时连接具体组件和装饰。装饰基类必须将所有工作委派给被封装的对象。 确保所有类实现组件接口。 将装饰基类扩展为具体装饰。具体装饰必须在调用父类方法 (总是委派给被封装对象) 之前或之后执行自身的行为。 客户端代码负责创建装饰并将其组合成客户端所需的形式。","s":"装饰模式适合应用场景","u":"/docs/design-patterns/decorator","h":"#装饰模式适合应用场景","p":286},{"i":303,"t":"✔️ 你无需创建新子类即可扩展对象的行为。 ✔️ 你可以在运行时添加或删除对象的功能。 ✔️ 你可以用多个装饰封装对象来组合几种行为。 ✔️ 单一职责原则。你可以将实现了许多不同行为的一个大类拆分为多个较小的类。 ❌ 在封装器栈中删除特定封装器比较困难。 ❌ 实现行为不受装饰栈顺序影响的装饰比较困难。 ❌ 各层的初始化配置代码看上去可能会很糟糕。","s":"装饰模式优缺点","u":"/docs/design-patterns/decorator","h":"#装饰模式优缺点","p":286},{"i":305,"t":"适配器模式可以对已有对象的接口进行修改，装饰模式则能在不改变对象接口的前提下强化对象功能。此外，装饰还支持递归组合，适配器则无法实现。 适配器能为被封装对象提供不同的接口，代理模式能为对象提供相同的接口，装饰则能为对象提供加强的接口。 责任链模式和装饰模式的类结构非常相似。两者都依赖递归组合将需要执行的操作传递给一系列对象。但是，两者有几点重要的不同之处。 责任链的管理者可以相互独立地执行一切操作，还可以随时停止传递请求。另一方面，各种装饰可以在遵循基本接口的情况下扩展对象的行为。此外，装饰无法中断请求的传递。 组合模式和装饰的结构图很相似，因为两者都依赖递归组合来组织无限数量的对象。 装饰类似于组合，但其只有一个子组件。此外还有一个明显不同：装饰为被封装对象添加了额外的职责，组合仅对其子节点的结果进行了“求和”。但是，模式也可以相互合作：你可以使用装饰来扩展组合树中特定对象的行为。 大量使用组合和装饰的设计通常可从对于原型模式的使用中获益。你可以通过该模式来复制复杂结构，而非从零开始重新构造。 装饰可让你更改对象的外表，策略模式则让你能够改变其本质。 装饰和代理有着相似的结构，但是其意图却非常不同。这两个模式的构建都基于组合原则，也就是说一个对象应该将部分工作委派给另一个对象。两者之间的不同之处在于代理通常自行管理其服务对象的生命周期，而装饰的生成则总是由客户端进行控制。","s":"与其他模式的关系","u":"/docs/design-patterns/decorator","h":"#与其他模式的关系","p":286},{"i":307,"t":"亦称：Facade","s":"外观模式","u":"/docs/design-patterns/facade","h":"","p":306},{"i":309,"t":"外观模式是一种结构型设计模式，能为程序库、框架或其他复杂类提供一个简单的接口。","s":"意图","u":"/docs/design-patterns/facade","h":"#意图","p":306},{"i":311,"t":"假设你必须在代码中使用某个复杂的库或框架中的众多对象。正常情况下，你需要负责所有对象的初始化工作、管理其依赖关系并按正确的顺序执行方法等。 最终，程序中类的业务逻辑将与第三方类的实现细节紧密耦合，使得理解和维护代码的工作很难进行。","s":"问题","u":"/docs/design-patterns/facade","h":"#问题","p":306},{"i":313,"t":"外观类为包含许多活动部件的复杂子系统提供一个简单的接口。与直接调用子系统相比，外观提供的功能可能比较有限，但它却包含了客户端真正关心的功能。 如果你的程序需要与包含几十种功能的复杂库整合，但只需使用其中非常少的功能，那么使用外观模式会非常方便， 例如，上传猫咪搞笑短视频到社交媒体网站的应用可能会用到专业的视频转换库，但它只需使用一个包含 encode­(filename, format) 方法 (以文件名与文件格式为参数进行编码的方法) 的类即可。在创建这个类并将其连接到视频转换库后，你就拥有了自己的第一个外观。","s":"解决方案","u":"/docs/design-patterns/facade","h":"#解决方案","p":306},{"i":315,"t":"电话购物。 当你通过电话给商店下达订单时，接线员就是该商店的所有服务和部门的外观。接线员为你提供了一个同购物系统、支付网关和各种送货服务进行互动的简单语音接口。","s":"真实世界类比","u":"/docs/design-patterns/facade","h":"#真实世界类比","p":306},{"i":317,"t":"外观 (Facade) 提供了一种访问特定子系统功能的便捷方式，其了解如何重定向客户端请求，知晓如何操作一切活动部件。 创建附加外观 (Additional Facade) 类可以避免多种不相关的功能污染单一外观，使其变成又一个复杂结构。客户端和其他外观都可使用附加外观。 复杂子系统 (Complex Subsystem) 由数十个不同对象构成。如果要用这些对象完成有意义的工作，你必须深入了解子系统的实现细节，比如按照正确顺序初始化对象和为其提供正确格式的数据。 子系统类不会意识到外观的存在，它们在系统内运作并且相互之间可直接进行交互。 客户端 (Client) 使用外观代替对子系统对象的直接调用。","s":"外观模式结构","u":"/docs/design-patterns/facade","h":"#外观模式结构","p":306},{"i":319,"t":"在本例中，外观模式简化了客户端与复杂视频转换框架之间的交互。 使用单个外观类隔离多重依赖的示例 你可以创建一个封装所需功能并隐藏其他代码的外观类，从而无需使全部代码直接与数十个框架类进行交互。该结构还能将未来框架升级或更换所造成的影响最小化，因为你只需修改程序中外观方法的实现即可。 // 这里有复杂第三方视频转换框架中的一些类。我们不知晓其中的代码，因此无法 // 对其进行简化。 class VideoFile // …… class OggCompressionCodec // …… class MPEG4CompressionCodec // …… class CodecFactory // …… class BitrateReader // …… class AudioMixer // …… // 为了将框架的复杂性隐藏在一个简单接口背后，我们创建了一个外观类。它是在 // 功能性和简洁性之间做出的权衡。 class VideoConverter is method convert(filename, format):File is file = new VideoFile(filename) sourceCodec = (new CodecFactory).extract(file) if (format == \"mp4\") destinationCodec = new MPEG4CompressionCodec() else destinationCodec = new OggCompressionCodec() buffer = BitrateReader.read(filename, sourceCodec) result = BitrateReader.convert(buffer, destinationCodec) result = (new AudioMixer()).fix(result) return new File(result) // 应用程序的类并不依赖于复杂框架中成千上万的类。同样，如果你决定更换框架， // 那只需重写外观类即可。 class Application is method main() is convertor = new VideoConverter() mp4 = convertor.convert(\"funny-cats-video.ogg\", \"mp4\") mp4.save()","s":"伪代码","u":"/docs/design-patterns/facade","h":"#伪代码","p":306},{"i":321,"t":"如果你需要一个指向复杂子系统的直接接口，且该接口的功能有限，则可以使用外观模式。 子系统通常会随着时间的推进变得越来越复杂。即便是应用了设计模式，通常你也会创建更多的类。尽管在多种情形中子系统可能是更灵活或易于复用的，但其所需的配置和样板代码数量将会增长得更快。为了解决这个问题，外观将会提供指向子系统中最常用功能的快捷方式，能够满足客户端的大部分需求。 如果需要将子系统组织为多层结构，可以使用外观。 创建外观来定义子系统中各层次的入口。你可以要求子系统仅使用外观来进行交互，以减少子系统之间的耦合。 让我们回到视频转换框架的例子。该框架可以拆分为两个层次：音频相关和视频相关。你可以为每个层次创建一个外观，然后要求各层的类必须通过这些外观进行交互。这种方式看上去与中介者模式非常相似。 实现方式 考虑能否在现有子系统的基础上提供一个更简单的接口。如果该接口能让客户端代码独立于众多子系统类，那么你的方向就是正确的。 在一个新的外观类中声明并实现该接口。外观应将客户端代码的调用重定向到子系统中的相应对象处。如果客户端代码没有对子系统进行初始化，也没有对其后续生命周期进行管理，那么外观必须完成此类工作。 如果要充分发挥这一模式的优势，你必须确保所有客户端代码仅通过外观来与子系统进行交互。此后客户端代码将不会受到任何由子系统代码修改而造成的影响，比如子系统升级后，你只需修改外观中的代码即可。 如果外观变得过于臃肿，你可以考虑将其部分行为抽取为一个新的专用外观类。","s":"外观模式适合应用场景","u":"/docs/design-patterns/facade","h":"#外观模式适合应用场景","p":306},{"i":323,"t":"✔️ 你可以让自己的代码独立于复杂子系统。 ❌ 外观可能成为与程序中所有类都耦合的上帝对象。","s":"外观模式优缺点","u":"/docs/design-patterns/facade","h":"#外观模式优缺点","p":306},{"i":325,"t":"外观模式为现有对象定义了一个新接口，适配器模式则会试图运用已有的接口。适配器通常只封装一个对象，外观通常会作用于整个对象子系统上。 当只需对客户端代码隐藏子系统创建对象的方式时，你可以使用抽象工厂模式来代替外观。 享元模式展示了如何生成大量的小型对象，外观则展示了如何用一个对象来代表整个子系统。 外观和中介者模式的职责类似：它们都尝试在大量紧密耦合的类中组织起合作。 外观为子系统中的所有对象定义了一个简单接口，但是它不提供任何新功能。子系统本身不会意识到外观的存在。子系统中的对象可以直接进行交流。 中介者将系统中组件的沟通行为中心化。各组件只知道中介者对象，无法直接相互交流。 外观类通常可以转换为单例模式类，因为在大部分情况下一个外观对象就足够了。 外观与代理模式的相似之处在于它们都缓存了一个复杂实体并自行对其进行初始化。代理与其服务对象遵循同一接口，使得自己和服务对象可以互换，在这一点上它与外观不同。","s":"与其他模式的关系","u":"/docs/design-patterns/facade","h":"#与其他模式的关系","p":306},{"i":327,"t":"亦称：虚拟构造函数、Virtual Constructor、Factory Method","s":"工厂方法模式","u":"/docs/design-patterns/factory-method","h":"","p":326},{"i":329,"t":"工厂方法模式是一种创建型设计模式，其在父类中提供一个创建对象的方法，允许子类决定实例化对象的类型。","s":"意图","u":"/docs/design-patterns/factory-method","h":"#意图","p":326},{"i":331,"t":"假设你正在开发一款物流管理应用。最初版本只能处理卡车运输，因此大部分代码都在位于名为 卡车 的类中。 一段时间后，这款应用变得极受欢迎。你每天都能收到十几次来自海运公司的请求，希望应用能够支持海上物流功能。 如果代码其余部分与现有类已经存在耦合关系，那么向程序中添加新类其实并没有那么容易。 这可是个好消息。但是代码问题该如何处理呢？目前，大部分代码都与 卡车 类相关。在程序中添加 轮船 类需要修改全部代码。更糟糕的是，如果你以后需要在程序中支持另外一种运输方式，很可能需要再次对这些代码进行大幅修改。 最后，你将不得不编写繁复的代码，根据不同的运输对象类，在应用中进行不同的处理。","s":"问题","u":"/docs/design-patterns/factory-method","h":"#问题","p":326},{"i":333,"t":"工厂方法模式建议使用特殊的工厂方法代替对于对象构造函数的直接调用 (即使用 new 运算符)。不用担心，对象仍将通过 new 运算符创建，只是该运算符改在工厂方法中调用罢了。工厂方法返回的对象通常被称作“产品”。 子类可以修改工厂方法返回的对象类型。 乍看之下，这种更改可能毫无意义：我们只是改变了程序中调用构造函数的位置而已。但是，仔细想一下，现在你可以在子类中重写工厂方法，从而改变其创建产品的类型。 但有一点需要注意：仅当这些产品具有共同的基类或者接口时，子类才能返回不同类型的产品，同时基类中的工厂方法还应将其返回类型声明为这一共有接口。 所有产品都必须使用同一接口。 举例来说，卡车 Truck 和 轮船 Ship 类都必须实现 运输 Transport 接口，该接口声明了一个名为 deliver 交付的方法。每个类都将以不同的方式实现该方法：卡车走陆路交付货物，轮船走海路交付货物。陆路运输 Road­Logistics 类中的工厂方法返回卡车对象，而 海路运输 Sea­Logistics 类则返回轮船对象。 只要产品类实现一个共同的接口，你就可以将其对象传递给客户代码，而无需提供额外数据。 调用工厂方法的代码 (通常被称为客户端代码) 无需了解不同子类返回实际对象之间的差别。客户端将所有产品视为抽象的 运输。客户端知道所有运输对象都提供 交付 方法，但是并不关心其具体实现方式。","s":"解决方案","u":"/docs/design-patterns/factory-method","h":"#解决方案","p":326},{"i":335,"t":"产品 (Product) 将会对接口进行声明。对于所有由创建者及其子类构建的对象，这些接口都是通用的。 具体产品 (Concrete Products) 是产品接口的不同实现。 创建者 (Creator) 类声明返回产品对象的工厂方法。该方法的返回对象类型必须与产品接口相匹配。 你可以将工厂方法声明为抽象方法，强制要求每个子类以不同方式实现该方法。或者，你也可以在基础工厂方法中返回默认产品类型。 注意，尽管它的名字是创建者，但它最主要的职责并不是创建产品。一般来说，创建者类包含一些与产品相关的核心业务逻辑。工厂方法将这些逻辑处理从具体产品类中分离出来。打个比方，大型软件开发公司拥有程序员培训部门。但是，这些公司的主要工作还是编写代码，而非生产程序员。 具体创建者 (Concrete Creators) 将会重写基础工厂方法，使其返回不同类型的产品。 注意，并不一定每次调用工厂方法都会创建新的实例。工厂方法也可以返回缓存、对象池或其他来源的已有对象。","s":"工厂方法模式结构","u":"/docs/design-patterns/factory-method","h":"#工厂方法模式结构","p":326},{"i":337,"t":"以下示例演示了如何使用工厂方法开发跨平台 UI (用户界面) 组件，并同时避免客户代码与具体 UI 类之间的耦合。 跨平台对话框示例。 基础对话框类使用不同的 UI 组件渲染窗口。在不同的操作系统下，这些组件外观或许略有不同，但其功能保持一致。Windows 系统中的按钮在 Linux 系统中仍然是按钮。 如果使用工厂方法，就不需要为每种操作系统重写对话框逻辑。如果我们声明了一个在基本对话框类中生成按钮的工厂方法，那么我们就可以创建一个对话框子类，并使其通过工厂方法返回 Windows 样式按钮。子类将继承对话框基础类的大部分代码，同时在屏幕上根据 Windows 样式渲染按钮。 如需该模式正常工作，基础对话框类必须使用抽象按钮 (例如基类或接口)，以便将其扩展为具体按钮。这样一来，无论对话框中使用何种类型的按钮，其代码都可以正常工作。 你可以使用此方法开发其他 UI 组件。不过，每向对话框中添加一个新的工厂方法，你就离抽象工厂模式更近一步。我们将在稍后谈到这个模式。 // 创建者类声明的工厂方法必须返回一个产品类的对象。创建者的子类通常会提供 // 该方法的实现。 class Dialog is // 创建者还可提供一些工厂方法的默认实现。 abstract method createButton():Button // 请注意，创建者的主要职责并非是创建产品。其中通常会包含一些核心业务 // 逻辑，这些逻辑依赖于由工厂方法返回的产品对象。子类可通过重写工厂方 // 法并使其返回不同类型的产品来间接修改业务逻辑。 method render() is // 调用工厂方法创建一个产品对象。 Button okButton = createButton() // 现在使用产品。 okButton.onClick(closeDialog) okButton.render() // 具体创建者将重写工厂方法以改变其所返回的产品类型。 class WindowsDialog extends Dialog is method createButton():Button is return new WindowsButton() class WebDialog extends Dialog is method createButton():Button is return new HTMLButton() // 产品接口中将声明所有具体产品都必须实现的操作。 interface Button is method render() method onClick(f) // 具体产品需提供产品接口的各种实现。 class WindowsButton implements Button is method render(a, b) is // 根据 Windows 样式渲染按钮。 method onClick(f) is // 绑定本地操作系统点击事件。 class HTMLButton implements Button is method render(a, b) is // 返回一个按钮的 HTML 表述。 method onClick(f) is // 绑定网络浏览器的点击事件。 class Application is field dialog: Dialog // 程序根据当前配置或环境设定选择创建者的类型。 method initialize() is config = readApplicationConfigFile() if (config.OS == \"Windows\") then dialog = new WindowsDialog() else if (config.OS == \"Web\") then dialog = new WebDialog() else throw new Exception(\"错误！未知的操作系统。\") // 当前客户端代码会与具体创建者的实例进行交互，但是必须通过其基本接口 // 进行。只要客户端通过基本接口与创建者进行交互，你就可将任何创建者子 // 类传递给客户端。 method main() is this.initialize() dialog.render()","s":"伪代码","u":"/docs/design-patterns/factory-method","h":"#伪代码","p":326},{"i":339,"t":"当你在编写代码的过程中，如果无法预知对象确切类别及其依赖关系时，可使用工厂方法。 工厂方法将创建产品的代码与实际使用产品的代码分离，从而能在不影响其他代码的情况下扩展产品创建部分代码。 例如，如果需要向应用中添加一种新产品，你只需要开发新的创建者子类，然后重写其工厂方法即可。 如果你希望用户能扩展你软件库或框架的内部组件，可使用工厂方法。 继承可能是扩展软件库或框架默认行为的最简单方法。但是当你使用子类替代标准组件时，框架如何辨识出该子类？ 解决方案是将各框架中构造组件的代码集中到单个工厂方法中，并在继承该组件之外允许任何人对该方法进行重写。 让我们看看具体是如何实现的。假设你使用开源 UI 框架编写自己的应用。你希望在应用中使用圆形按钮，但是原框架仅支持矩形按钮。你可以使用 圆形按钮 Round­Button 子类来继承标准的 按钮 Button 类。但是，你需要告诉 UI框架 UIFramework 类使用新的子类按钮代替默认按钮。 为了实现这个功能，你可以根据基础框架类开发子类 圆形按钮 UI UIWith­Round­Buttons，并且重写其 create­Button 创建按钮方法。基类中的该方法返回 按钮 对象，而你开发的子类返回 圆形按钮 对象。现在，你就可以使用 圆形按钮 UI 类代替 UI框架 类。就是这么简单！ 如果你希望复用现有对象来节省系统资源，而不是每次都重新创建对象，可使用工厂方法。 在处理大型资源密集型对象 (比如数据库连接、文件系统和网络资源) 时，你会经常碰到这种资源需求。 让我们思考复用现有对象的方法： 首先，你需要创建存储空间来存放所有已经创建的对象。 当他人请求一个对象时，程序将在对象池中搜索可用对象。 … 然后将其返回给客户端代码。 如果没有可用对象，程序则创建一个新对象 (并将其添加到对象池中)。 这些代码可不少！而且它们必须位于同一处，这样才能确保重复代码不会污染程序。 可能最显而易见，也是最方便的方式，就是将这些代码放置在我们试图重用的对象类的构造函数中。但是从定义上来讲，构造函数始终返回的是新对象，其无法返回现有实例。 因此，你需要有一个既能够创建新对象，又可以重用现有对象的普通方法。这听上去和工厂方法非常相像。 实现方式 让所有产品都遵循同一接口。该接口必须声明对所有产品都有意义的方法。 在创建类中添加一个空的工厂方法。该方法的返回类型必须遵循通用的产品接口。 在创建者代码中找到对于产品构造函数的所有引用。将它们依次替换为对于工厂方法的调用，同时将创建产品的代码移入工厂方法。你可能需要在工厂方法中添加临时参数来控制返回的产品类型。工厂方法的代码看上去可能非常糟糕。其中可能会有复杂的 switch 分支运算符，用于选择各种需要实例化的产品类。但是不要担心，我们很快就会修复这个问题。 现在，为工厂方法中的每种产品编写一个创建者子类，然后在子类中重写工厂方法，并将基本方法中的相关创建代码移动到工厂方法中。 如果应用中的产品类型太多，那么为每个产品创建子类并无太大必要，这时你也可以在子类中复用基类中的控制参数。例如，设想你有以下一些层次结构的类。基类 邮件 及其子类 航空邮件 和 陆路邮件；运输 及其子类 飞机，卡车 和 火车。航空邮件 仅使用 飞机 对象，而 陆路邮件 则会同时使用 卡车 和 火车 对象。你可以编写一个新的子类 (例如 火车邮件) 来处理这两种情况，但是还有其他可选的方案。客户端代码可以给 陆路邮件 类传递一个参数，用于控制其希望获得的产品。 如果代码经过上述移动后，基础工厂方法中已经没有任何代码，你可以将其转变为抽象类。如果基础工厂方法中还有其他语句，你可以将其设置为该方法的默认行为。","s":"工厂方法模式适合应用场景","u":"/docs/design-patterns/factory-method","h":"#工厂方法模式适合应用场景","p":326},{"i":341,"t":"✔️ 你可以避免创建者和具体产品之间的紧密耦合。 ✔️ 单一职责原则。你可以将产品创建代码放在程序的单一位置，从而使得代码更容易维护。 ✔️ 开闭原则。无需更改现有客户端代码，你就可以在程序中引入新的产品类型。 ❌ 应用工厂方法模式需要引入许多新的子类，代码可能会因此变得更复杂。最好的情况是将该模式引入创建者类的现有层次结构中。","s":"工厂方法模式优缺点","u":"/docs/design-patterns/factory-method","h":"#工厂方法模式优缺点","p":326},{"i":343,"t":"在许多设计工作的初期都会使用工厂方法模式 (较为简单，而且可以更方便地通过子类进行定制)，随后演化为使用抽象工厂模式、原型模式或生成器模式 (更灵活但更加复杂)。 抽象工厂模式通常基于一组工厂方法，但你也可以使用原型模式来生成这些类的方法。 你可以同时使用工厂方法和迭代器模式来让子类集合返回不同类型的迭代器，并使得迭代器与集合相匹配。 原型并不基于继承，因此没有继承的缺点。另一方面，原型需要对被复制对象进行复杂的初始化。工厂方法基于继承，但是它不需要初始化步骤。 工厂方法是模板方法模式的一种特殊形式。同时，工厂方法可以作为一个大型模板方法中的一个步骤。","s":"与其他模式的关系","u":"/docs/design-patterns/factory-method","h":"#与其他模式的关系","p":326},{"i":345,"t":"亦称：缓存、Cache、Flyweight","s":"享元模式","u":"/docs/design-patterns/flyweight","h":"","p":344},{"i":347,"t":"享元模式是一种结构型设计模式，它摒弃了在每个对象中保存所有数据的方式，通过共享多个对象所共有的相同状态，让你能在有限的内存容量中载入更多对象。","s":"意图","u":"/docs/design-patterns/flyweight","h":"#意图","p":344},{"i":349,"t":"假如你希望在长时间工作后放松一下，所以开发了一款简单的游戏：玩家们在地图上移动并相互射击。你决定实现一个真实的粒子系统，并将其作为游戏的特色。大量的子弹、导弹和爆炸弹片会在整个地图上穿行，为玩家提供紧张刺激的游戏体验。 开发完成后，你推送提交了最新版本的程序，并在编译游戏后将其发送给了一个朋友进行测试。尽管该游戏在你的电脑上完美运行，但是你的朋友却无法长时间进行游戏：游戏总是会在他的电脑上运行几分钟后崩溃。在研究了几个小时的调试消息记录后，你发现导致游戏崩溃的原因是内存容量不足。朋友的设备性能远比不上你的电脑，因此游戏运行在他的电脑上时很快就会出现问题。 真正的问题与粒子系统有关。每个粒子 (一颗子弹、一枚导弹或一块弹片) 都由包含完整数据的独立对象来表示。当玩家在游戏中鏖战进入高潮后的某一时刻，游戏将无法在剩余内存中载入新建粒子，于是程序就崩溃了。","s":"问题","u":"/docs/design-patterns/flyweight","h":"#问题","p":344},{"i":351,"t":"仔细观察 粒子 Particle 类，你可能会注意到颜色 (color) 和精灵图 (sprite) 这两个成员变量所消耗的内存要比其他变量多得多。更糟糕的是，对于所有的粒子来说，这两个成员变量所存储的数据几乎完全一样 (比如所有子弹的颜色和精灵图都一样)。 每个粒子的另一些状态 (坐标、移动矢量和速度) 则是不同的。因为这些成员变量的数值会不断变化。这些数据代表粒子在存续期间不断变化的情景，但每个粒子的颜色和精灵图则会保持不变。 对象的常量数据通常被称为内在状态，其位于对象中，其他对象只能读取但不能修改其数值。而对象的其他状态常常能被其他对象“从外部”改变，因此被称为外在状态。 享元模式建议不在对象中存储外在状态，而是将其传递给依赖于它的一个特殊方法。程序只在对象中保存内在状态，以方便在不同情景下重用。这些对象的区别仅在于其内在状态 (与外在状态相比，内在状态的变体要少很多)，因此你所需的对象数量会大大削减。 让我们回到游戏中。假如能从粒子类中抽出外在状态，那么我们只需三个不同的对象 (子弹、导弹和弹片) 就能表示游戏中的所有粒子。你现在很可能已经猜到了，我们将这样一个仅存储内在状态的对象称为享元。","s":"解决方案","u":"/docs/design-patterns/flyweight","h":"#解决方案","p":344},{"i":353,"t":"那么外在状态会被移动到什么地方呢？总得有类来存储它们，对不对？在大部分情况中，它们会被移动到容器对象中，也就是我们应用享元模式前的聚合对象中。 在我们的例子中，容器对象就是主要的 游戏 Game 对象，其会将所有粒子存储在名为 粒子 particles 的成员变量中。为了能将外在状态移动到这个类中，你需要创建多个数组成员变量来存储每个粒子的坐标、方向矢量和速度。除此之外，你还需要另一个数组来存储指向代表粒子的特定享元的引用。这些数组必须保持同步，这样你才能够使用同一索引来获取关于某个粒子的所有数据。 更优雅的解决方案是创建独立的情景类来存储外在状态和对享元对象的引用。在该方法中，容器类只需包含一个数组。 稍等！这样的话情景对象数量不是会和不采用该模式时的对象数量一样多吗？的确如此，但这些对象要比之前小很多。消耗内存最多的成员变量已经被移动到很少的几个享元对象中了。现在，一个享元大对象会被上千个情境小对象复用，因此无需再重复存储数千个大对象的数据。","s":"外在状态存储","u":"/docs/design-patterns/flyweight","h":"#外在状态存储","p":344},{"i":355,"t":"由于享元对象可在不同的情景中使用，你必须确保其状态不能被修改。享元类的状态只能由构造函数的参数进行一次性初始化，它不能对其他对象公开其设置器或公有成员变量。","s":"享元与不可变性","u":"/docs/design-patterns/flyweight","h":"#享元与不可变性","p":344},{"i":357,"t":"为了能更方便地访问各种享元，你可以创建一个工厂方法来管理已有享元对象的缓存池。工厂方法从客户端处接收目标享元对象的内在状态作为参数，如果它能在缓存池中找到所需享元，则将其返回给客户端；如果没有找到，它就会新建一个享元，并将其添加到缓存池中。 你可以选择在程序的不同地方放入该函数。最简单的选择就是将其放置在享元容器中。除此之外，你还可以新建一个工厂类，或者创建一个静态的工厂方法并将其放入实际的享元类中。","s":"享元工厂","u":"/docs/design-patterns/flyweight","h":"#享元工厂","p":344},{"i":359,"t":"享元模式只是一种优化。在应用该模式之前，你要确定程序中存在与大量类似对象同时占用内存相关的内存消耗问题，并且确保该问题无法使用其他更好的方式来解决。 享元 (Flyweight) 类包含原始对象中部分能在多个对象中共享的状态。同一享元对象可在许多不同情景中使用。享元中存储的状态被称为“内在状态”。传递给享元方法的状态被称为“外在状态”。 情景 (Context) 类包含原始对象中各不相同的外在状态。情景与享元对象组合在一起就能表示原始对象的全部状态。 通常情况下，原始对象的行为会保留在享元类中。因此调用享元方法必须提供部分外在状态作为参数。但你也可将行为移动到情景类中，然后将连入的享元作为单纯的数据对象。 客户端 (Client) 负责计算或存储享元的外在状态。在客户端看来，享元是一种可在运行时进行配置的模板对象，具体的配置方式为向其方法中传入一些情景数据参数。 享元工厂 (Flyweight Factory) 会对已有享元的缓存池进行管理。有了工厂后，客户端就无需直接创建享元，它们只需调用工厂并向其传递目标享元的一些内在状态即可。工厂会根据参数在之前已创建的享元中进行查找，如果找到满足条件的享元就将其返回；如果没有找到就根据参数新建享元。","s":"享元模式结构","u":"/docs/design-patterns/flyweight","h":"#享元模式结构","p":344},{"i":361,"t":"在本例中，享元模式能有效减少在画布上渲染数百万个树状对象时所需的内存。 该模式从主要的 树 Tree 类中抽取内在状态，并将其移动到享元类 树种类 Tree­Type 之中。 最初程序需要在多个对象中存储相同数据，而现在仅需在几个享元对象中保存数据，然后在作为情景的 树 对象中连入享元即可。客户端代码使用享元工厂创建树对象并封装搜索指定对象的复杂行为，并能在需要时复用对象。 // 享元类包含一个树的部分状态。这些成员变量保存的数值对于特定树而言是唯一 // 的。例如，你在这里找不到树的坐标。但这里有很多树木之间所共有的纹理和颜 // 色。由于这些数据的体积通常非常大，所以如果让每棵树都其进行保存的话将耗 // 费大量内存。因此，我们可将纹理、颜色和其他重复数据导出到一个单独的对象 // 中，然后让众多的单个树对象去引用它。 class TreeType is field name field color field texture constructor TreeType(name, color, texture) { …… } method draw(canvas, x, y) is // 1. 创建特定类型、颜色和纹理的位图。 // 2. 在画布坐标 (X,Y) 处绘制位图。 // 享元工厂决定是否复用已有享元或者创建一个新的对象。 class TreeFactory is static field treeTypes: collection of tree types static method getTreeType(name, color, texture) is type = treeTypes.find(name, color, texture) if (type == null) type = new TreeType(name, color, texture) treeTypes.add(type) return type // 情景对象包含树状态的外在部分。程序中可以创建数十亿个此类对象，因为它们 // 体积很小：仅有两个整型坐标和一个引用成员变量。 class Tree is field x,y field type: TreeType constructor Tree(x, y, type) { …… } method draw(canvas) is type.draw(canvas, this.x, this.y) // 树（Tree）和森林（Forest）类是享元的客户端。如果不打算继续对树类进行开 // 发，你可以将它们合并。 class Forest is field trees: collection of Trees method plantTree(x, y, name, color, texture) is type = TreeFactory.getTreeType(name, color, texture) tree = new Tree(x, y, type) trees.add(tree) method draw(canvas) is foreach (tree in trees) do tree.draw(canvas)","s":"伪代码","u":"/docs/design-patterns/flyweight","h":"#伪代码","p":344},{"i":363,"t":"仅在程序必须支持大量对象且没有足够的内存容量时使用享元模式。 应用该模式所获的收益大小取决于使用它的方式和情景。它在下列情况中最有效： 程序需要生成数量巨大的相似对象 这将耗尽目标设备的所有内存 对象中包含可抽取且能在多个对象间共享的重复状态。 实现方式 将需要改写为享元的类成员变量拆分为两个部分： 内在状态：包含不变的、可在许多对象中重复使用的数据的成员变量。 外在状态：包含每个对象各自不同的情景数据的成员变量 保留类中表示内在状态的成员变量，并将其属性设置为不可修改。这些变量仅可在构造函数中获得初始数值。 找到所有使用外在状态成员变量的方法，为在方法中所用的每个成员变量新建一个参数，并使用该参数代替成员变量。 你可以有选择地创建工厂类来管理享元缓存池，它负责在新建享元时检查已有的享元。如果选择使用工厂，客户端就只能通过工厂来请求享元，它们需要将享元的内在状态作为参数传递给工厂。 客户端必须存储和计算外在状态 (情景) 的数值，因为只有这样才能调用享元对象的方法。为了使用方便，外在状态和引用享元的成员变量可以移动到单独的情景类中。","s":"享元模式适合应用场景","u":"/docs/design-patterns/flyweight","h":"#享元模式适合应用场景","p":344},{"i":365,"t":"✔️ 如果程序中有很多相似对象，那么你将可以节省大量内存。 ❌ 你可能需要牺牲执行速度来换取内存，因为他人每次调用享元方法时都需要重新计算部分情景数据。 ❌ 代码会变得更加复杂。团队中的新成员总是会问：“为什么要像这样拆分一个实体的状态？”。","s":"享元模式优缺点","u":"/docs/design-patterns/flyweight","h":"#享元模式优缺点","p":344},{"i":367,"t":"你可以使用享元模式实现组合模式树的共享叶节点以节省内存。 享元展示了如何生成大量的小型对象，外观模式则展示了如何用一个对象来代表整个子系统。 如果你能将对象的所有共享状态简化为一个享元对象，那么享元就和单例模式类似了。但这两个模式有两个根本性的不同。 只会有一个单例实体，但是享元类可以有多个实体，各实体的内在状态也可以不同。 单例对象可以是可变的。享元对象是不可变的。","s":"与其他模式的关系","u":"/docs/design-patterns/flyweight","h":"#与其他模式的关系","p":344},{"i":369,"t":"设计模式是软件设计中常见问题的典型解决方案。它们就像能根据需求进行调整的预制蓝图，可用于解决代码中反复出现的设计问题。 设计模式与方法或库的使用方式不同，你很难直接在自己的程序中套用某个设计模式。模式并不是一段特定的代码，而是解决特定问题的一般性概念。你可以根据模式来实现符合自己程序实际所需的解决方案。 人们常常会混淆模式和算法，因为两者在概念上都是已知特定问题的典型解决方案。但算法总是明确定义达成特定目标所需的一系列步骤，而模式则是对解决方案的更高层次描述。同一模式在两个不同程序中的实现代码可能会不一样。 算法更像是菜谱：提供达成目标的明确步骤。而模式更像是蓝图：你可以看到最终的结果和模式的功能，但需要自己确定实现步骤。","s":"设计模式是什么？","u":"/docs/design-patterns/intro","h":"","p":368},{"i":371,"t":"大部分模式都有正规的描述方式，以便在不同情况下使用。模式的描述通常会包括以下部分： 意图部分简单描述问题和解决方案。 动机部分将进一步解释问题并说明模式会如何提供解决方案。 结构部分展示模式的每个部分和它们之间的关系。 在不同语言中的实现提供流行编程语言的代码，让读者更好地理解模式背后的思想。 部分模式介绍中还列出其他的一些实用细节，例如模式的适用性、实现步骤以及与其他模式的关系。","s":"模式包含哪些内容？","u":"/docs/design-patterns/intro","h":"#模式包含哪些内容","p":368},{"i":373,"t":"谁发明了设计模式？这是一个很好的问题，但也有点不太准确。设计模式并不是晦涩的、复杂的概念——事实恰恰相反。模式是面向对象设计中常见问题的典型解决方案。同样的解决方案在各种项目中得到了反复使用，所以最终有人给它们起了名字，并对其进行了详细描述。这基本上就是模式被发现的历程了。 模式的概念是由克里斯托佛·亚历山大在其著作《建筑模式语言》中首次提出的。本书介绍了城市设计的“语言”，而此类“语言”的基本单元就是模式。模式中可能会包含对窗户应该在多高、一座建筑应该有多少层以及一片街区应该有多大面积的植被等信息的描述。 埃里希·伽玛、约翰·弗利赛德斯、拉尔夫·约翰逊和理查德·赫尔姆这四位作者接受了模式的概念。1994 年，他们出版了《设计模式：可复用面向对象软件的基础》一书，将设计模式的概念应用到程序开发领域中。该书提供了 23 个模式来解决面向对象程序设计中的各种问题，很快便成为了畅销书。由于书名太长，人们将其简称为“四人组 (Gang of Four，GoF) 的书”，并且很快进一步简化为“GoF 的书”。 此后，人们又发现了几十种面向对象的模式。“模式方法”开始在其他程序开发领域中流行起来。如今，在面向对象设计领域之外，人们也提出了许多其他的模式。","s":"模式的历史","u":"/docs/design-patterns/intro","h":"","p":368},{"i":375,"t":"或许你已从事程序开发工作多年，却完全不知道单例模式是什么。很多人都是这样。即便如此，你可能也在不自知的情况下已经使用过一些设计模式了。所以为什么不花些时间来更进一步学习它们呢？ 设计模式是针对软件设计中常见问题的工具箱，其中的工具就是各种经过实践验证的解决方案。即使你从未遇到过这些问题，了解模式仍然非常有用，因为它能指导你如何使用面向对象的设计原则来解决各种问题。 设计模式定义了一种让你和团队成员能够更高效沟通的通用语言。你只需说“哦，这里用单例就可以了”，所有人都会理解这条建议背后的想法。只要知晓模式及其名称，你就无需解释什么是单例。","s":"为什么以及如何学习设计模式？","u":"/docs/design-patterns/intro","h":"","p":368},{"i":377,"t":"设计模式自其诞生之初似乎就饱受争议，所以让我们来看看针对模式的最常见批评吧。","s":"关于模式的争议","u":"/docs/design-patterns/intro","h":"","p":368},{"i":379,"t":"通常当所选编程语言或技术缺少必要的抽象功能时，人们才需要设计模式。在这种情况下，模式是一种可为语言提供更优功能的蹩脚解决方案。 例如，策略模式在绝大部分现代编程语言中可以简单地使用匿名 (lambda) 函数来实现。","s":"一种针对不完善编程语言的蹩脚解决方案","u":"/docs/design-patterns/intro","h":"#一种针对不完善编程语言的蹩脚解决方案","p":368},{"i":381,"t":"模式试图将已经广泛使用的方式系统化。许多人会将这样的统一化认为是某种教条，他们会“全心全意”地实施这样的模式，而不会根据项目的实际情况对其进行调整。","s":"低效的解决方案","u":"/docs/design-patterns/intro","h":"#低效的解决方案","p":368},{"i":383,"t":"如果你只有一把铁锤，那么任何东西看上去都像是钉子。 这个问题常常会给初学模式的人们带来困扰：在学习了某个模式后，他们会在所有地方使用该模式，即便是在较为简单的代码也能胜任的地方也是如此。","s":"不当使用","u":"/docs/design-patterns/intro","h":"#不当使用","p":368},{"i":385,"t":"不同设计模式的复杂程度、细节层次以及在整个系统中的应用范围等方面各不相同。我喜欢将其类比于道路的建造：如果你希望让十字路口更加安全，那么可以安装一些交通信号灯，或者修建包含行人地下通道在内的多层互通式立交桥。 最基础的、底层的模式通常被称为惯用技巧。这类模式一般只能在一种编程语言中使用。 最通用的、高层的模式是构架模式。开发者可以在任何编程语言中使用这类模式。与其他模式不同，它们可用于整个应用程序的架构设计。 此外，所有模式可以根据其意图或目的来分类。本书覆盖了三种主要的模式类别： 创建型模式提供创建对象的机制，增加已有代码的灵活性和可复用性。 结构型模式介绍如何将对象和类组装成较大的结构，并同时保持结构的灵活和高效。 行为模式负责对象间的高效沟通和职责委派。","s":"设计模式分类","u":"/docs/design-patterns/intro","h":"","p":368},{"i":387,"t":"亦称：Iterator","s":"迭代器模式","u":"/docs/design-patterns/iterator","h":"","p":386},{"i":389,"t":"迭代器模式是一种行为设计模式，让你能在不暴露集合底层表现形式 (列表、栈和树等) 的情况下遍历集合中所有的元素。","s":"意图","u":"/docs/design-patterns/iterator","h":"#意图","p":386},{"i":391,"t":"集合是编程中最常使用的数据类型之一。尽管如此，集合只是一组对象的容器而已。 各种类型的集合。 大部分集合使用简单列表存储元素。但有些集合还会使用栈、树、图和其他复杂的数据结构。 无论集合的构成方式如何，它都必须提供某种访问元素的方式，便于其他代码使用其中的元素。集合应提供一种能够遍历元素的方式，且保证它不会周而复始地访问同一个元素。 如果你的集合基于列表，那么这项工作听上去仿佛很简单。但如何遍历复杂数据结构 (例如树) 中的元素呢？例如，今天你需要使用深度优先算法来遍历树结构，明天可能会需要广度优先算法；下周则可能会需要其他方式 (比如随机存取树中的元素)。 可通过不同的方式遍历相同的集合。 不断向集合中添加遍历算法会模糊其“高效存储数据”的主要职责。此外，有些算法可能是根据特定应用订制的，将其加入泛型集合类中会显得非常奇怪。 另一方面，使用多种集合的客户端代码可能并不关心存储数据的方式。不过由于集合提供不同的元素访问方式，你的代码将不得不与特定集合类进行耦合。","s":"问题","u":"/docs/design-patterns/iterator","h":"#问题","p":386},{"i":393,"t":"迭代器模式的主要思想是将集合的遍历行为抽取为单独的迭代器对象。 迭代器可实现多种遍历算法。多个迭代器对象可同时遍历同一个集合。 除实现自身算法外，迭代器还封装了遍历操作的所有细节，例如当前位置和末尾剩余元素的数量。因此，多个迭代器可以在相互独立的情况下同时访问集合。 迭代器通常会提供一个获取集合元素的基本方法。客户端可不断调用该方法直至它不返回任何内容，这意味着迭代器已经遍历了所有元素。 所有迭代器必须实现相同的接口。这样一来，只要有合适的迭代器，客户端代码就能兼容任何类型的集合或遍历算法。如果你需要采用特殊方式来遍历集合，只需创建一个新的迭代器类即可，无需对集合或客户端进行修改。","s":"解决方案","u":"/docs/design-patterns/iterator","h":"#解决方案","p":386},{"i":395,"t":"漫步罗马的不同方式。 你计划在罗马游览数天，参观所有主要的旅游景点。但在到达目的地后，你可能会浪费很多时间绕圈子，甚至找不到罗马斗兽场在哪里。 或者你可以购买一款智能手机上的虚拟导游程序。这款程序非常智能而且价格不贵，你想在景点待多久都可以。 第三种选择是用部分旅行预算雇佣一位对城市了如指掌的当地向导。向导能根据你的喜好来安排行程，为你介绍每个景点并讲述许多激动人心的故事。这样的旅行可能会更有趣，但所需费用也会更高。 所有这些选择 (自由漫步、智能手机导航或真人向导) 都是这个由众多罗马景点组成的集合的迭代器。","s":"真实世界类比","u":"/docs/design-patterns/iterator","h":"#真实世界类比","p":386},{"i":397,"t":"迭代器 (Iterator) 接口声明了遍历集合所需的操作：获取下一个元素、获取当前位置和重新开始迭代等。 具体迭代器 (Concrete Iterators) 实现遍历集合的一种特定算法。迭代器对象必须跟踪自身遍历的进度。这使得多个迭代器可以相互独立地遍历同一集合。 集合 (Collection) 接口声明一个或多个方法来获取与集合兼容的迭代器。请注意，返回方法的类型必须被声明为迭代器接口，因此具体集合可以返回各种不同种类的迭代器。 具体集合 (Concrete Collections) 会在客户端请求迭代器时返回一个特定的具体迭代器类实体。你可能会琢磨，剩下的集合代码在什么地方呢？不用担心，它也会在同一个类中。只是这些细节对于实际模式来说并不重要，所以我们将其省略了而已。 客户端 (Client) 通过集合和迭代器的接口与两者进行交互。这样一来客户端无需与具体类进行耦合，允许同一客户端代码使用各种不同的集合和迭代器。 客户端通常不会自行创建迭代器，而是会从集合中获取。但在特定情况下，客户端可以直接创建一个迭代器 (例如当客户端需要自定义特殊迭代器时)。","s":"迭代器模式结构","u":"/docs/design-patterns/iterator","h":"#迭代器模式结构","p":386},{"i":399,"t":"在本例中，迭代器模式用于遍历一个封装了访问微信好友关系功能的特殊集合。该集合提供使用不同方式遍历档案资料的多个迭代器。 遍历社交档案的示例 “好友 (friends)”迭代器可用于遍历指定档案的好友。“同事 (colleagues)”迭代器也提供同样的功能，但仅包括与目标用户在同一家公司工作的好友。这两个迭代器都实现了同一个通用接口，客户端能在不了解认证和发送 REST 请求等实现细节的情况下获取档案。 客户端仅通过接口与集合和迭代器交互，也就不会同具体类耦合。如果你决定将应用连接到全新的社交网络，只需提供新的集合和迭代器类即可，无需修改现有代码。 // 集合接口必须声明一个用于生成迭代器的工厂方法。如果程序中有不同类型的迭 // 代器，你也可以声明多个方法。 interface SocialNetwork is method createFriendsIterator(profileId):ProfileIterator method createCoworkersIterator(profileId):ProfileIterator // 每个具体集合都与其返回的一组具体迭代器相耦合。但客户并不是这样的，因为 // 这些方法的签名将会返回迭代器接口。 class WeChat implements SocialNetwork is // ……大量的集合代码应该放在这里…… // 迭代器创建代码。 method createFriendsIterator(profileId) is return new WeChatIterator(this, profileId, \"friends\") method createCoworkersIterator(profileId) is return new WeChatIterator(this, profileId, \"coworkers\") // 所有迭代器的通用接口。 interface ProfileIterator is method getNext():Profile method hasMore():bool // 具体迭代器类。 class WeChatIterator implements ProfileIterator is // 迭代器需要一个指向其遍历集合的引用。 private field weChat: WeChat private field profileId, type: string // 迭代器对象会独立于其他迭代器来对集合进行遍历。因此它必须保存迭代器 // 的状态。 private field currentPosition private field cache: array of Profile constructor WeChatIterator(weChat, profileId, type) is this.weChat = weChat this.profileId = profileId this.type = type private method lazyInit() is if (cache == null) cache = weChat.socialGraphRequest(profileId, type) // 每个具体迭代器类都会自行实现通用迭代器接口。 method getNext() is if (hasMore()) result = cache[currentPosition] currentPosition++ return result method hasMore() is lazyInit() return currentPosition < cache.length // 这里还有一个有用的绝招：你可将迭代器传递给客户端类，无需让其拥有访问整 // 个集合的权限。这样一来，你就无需将集合暴露给客户端了。 // // 还有另一个好处：你可在运行时将不同的迭代器传递给客户端，从而改变客户端 // 与集合互动的方式。这一方法可行的原因是客户端代码并没有和具体迭代器类相 // 耦合。 class SocialSpammer is method send(iterator: ProfileIterator, message: string) is while (iterator.hasMore()) profile = iterator.getNext() System.sendEmail(profile.getEmail(), message) // 应用程序（Application）类可对集合和迭代器进行配置，然后将其传递给客户 // 端代码。 class Application is field network: SocialNetwork field spammer: SocialSpammer method config() is if working with WeChat this.network = new WeChat() if working with LinkedIn this.network = new LinkedIn() this.spammer = new SocialSpammer() method sendSpamToFriends(profile) is iterator = network.createFriendsIterator(profile.getId()) spammer.send(iterator, \"非常重要的消息\") method sendSpamToCoworkers(profile) is iterator = network.createCoworkersIterator(profile.getId()) spammer.send(iterator, \"非常重要的消息\")","s":"伪代码","u":"/docs/design-patterns/iterator","h":"#伪代码","p":386},{"i":401,"t":"当集合背后为复杂的数据结构，且你希望对客户端隐藏其复杂性时 (出于使用便利性或安全性的考虑)，可以使用迭代器模式。 迭代器封装了与复杂数据结构进行交互的细节，为客户端提供多个访问集合元素的简单方法。这种方式不仅对客户端来说非常方便，而且能避免客户端在直接与集合交互时执行错误或有害的操作，从而起到保护集合的作用。 使用该模式可以减少程序中重复的遍历代码。 重要迭代算法的代码往往体积非常庞大。当这些代码被放置在程序业务逻辑中时，它会让原始代码的职责模糊不清，降低其可维护性。因此，将遍历代码移到特定的迭代器中可使程序代码更加精炼和简洁。 如果你希望代码能够遍历不同的甚至是无法预知的数据结构，可以使用迭代器模式。 该模式为集合和迭代器提供了一些通用接口。如果你在代码中使用了这些接口，那么将其他实现了这些接口的集合和迭代器传递给它时，它仍将可以正常运行。 实现方式 声明迭代器接口。该接口必须提供至少一个方法来获取集合中的下个元素。但为了使用方便，你还可以添加一些其他方法，例如获取前一个元素、记录当前位置和判断迭代是否已结束。 声明集合接口并描述一个获取迭代器的方法。其返回值必须是迭代器接口。如果你计划拥有多组不同的迭代器，则可以声明多个类似的方法。 为希望使用迭代器进行遍历的集合实现具体迭代器类。迭代器对象必须与单个集合实体链接。链接关系通常通过迭代器的构造函数建立。 在你的集合类中实现集合接口。其主要思想是针对特定集合为客户端代码提供创建迭代器的快捷方式。集合对象必须将自身传递给迭代器的构造函数来创建两者之间的链接。 检查客户端代码，使用迭代器替代所有集合遍历代码。每当客户端需要遍历集合元素时都会获取一个新的迭代器。","s":"迭代器模式适合应用场景","u":"/docs/design-patterns/iterator","h":"#迭代器模式适合应用场景","p":386},{"i":403,"t":"✔️ 单一职责原则。通过将体积庞大的遍历算法代码抽取为独立的类，你可对客户端代码和集合进行整理。 ✔️ 开闭原则。你可实现新型的集合和迭代器并将其传递给现有代码，无需修改现有代码。 ✔️ 你可以并行遍历同一集合，因为每个迭代器对象都包含其自身的遍历状态。 ✔️ 相似的，你可以暂停遍历并在需要时继续。 ❌ 如果你的程序只与简单的集合进行交互，应用该模式可能会矫枉过正。 ❌ 对于某些特殊集合，使用迭代器可能比直接遍历的效率低。","s":"迭代器模式优缺点","u":"/docs/design-patterns/iterator","h":"#迭代器模式优缺点","p":386},{"i":405,"t":"你可以使用迭代器模式来遍历组合模式树。 你可以同时使用工厂方法模式和迭代器来让子类集合返回不同类型的迭代器，并使得迭代器与集合相匹配。 你可以同时使用备忘录模式和迭代器来获取当前迭代器的状态，并且在需要的时候进行回滚。 可以同时使用访问者模式和迭代器来遍历复杂数据结构，并对其中的元素执行所需操作，即使这些元素所属的类完全不同。","s":"与其他模式的关系","u":"/docs/design-patterns/iterator","h":"#与其他模式的关系","p":386},{"i":407,"t":"亦称：调解人、控制器、Intermediary、Controller、Mediator","s":"中介者模式","u":"/docs/design-patterns/mediator","h":"","p":406},{"i":409,"t":"中介者模式是一种行为设计模式，能让你减少对象之间混乱无序的依赖关系。该模式会限制对象之间的直接交互，迫使它们通过一个中介者对象进行合作。","s":"意图","u":"/docs/design-patterns/mediator","h":"#意图","p":406},{"i":411,"t":"假如你有一个创建和修改客户资料的对话框，它由各种控件组成，例如文本框 (Text­Field)、复选框 (Checkbox) 和按钮 (Button) 等。 用户界面中各元素间的关系会随程序发展而变得混乱。 某些表单元素可能会直接进行互动。例如，选中“我有一只狗”复选框后可能会显示一个隐藏文本框用于输入狗狗的名字。另一个例子是提交按钮必须在保存数据前校验所有输入内容。 元素间存在许多关联。因此，对某些元素进行修改可能会影响其他元素。 如果直接在表单元素代码中实现业务逻辑，你将很难在程序其他表单中复用这些元素类。例如，由于复选框类与狗狗的文本框相耦合，所以将无法在其他表单中使用它。你要么使用渲染资料表单时用到的所有类，要么一个都不用。","s":"问题","u":"/docs/design-patterns/mediator","h":"#问题","p":406},{"i":413,"t":"中介者模式建议你停止组件之间的直接交流并使其相互独立。这些组件必须调用特殊的中介者对象，通过中介者对象重定向调用行为，以间接的方式进行合作。最终，组件仅依赖于一个中介者类，无需与多个其他组件相耦合。 在资料编辑表单的例子中，对话框 (Dialog) 类本身将作为中介者，其很可能已知自己所有的子元素，因此你甚至无需在该类中引入新的依赖关系。 UI 元素必须通过中介者对象进行间接沟通。 绝大部分重要的修改都在实际表单元素中进行。让我们想想提交按钮。之前，当用户点击按钮后，它必须对所有表单元素数值进行校验。而现在它的唯一工作是将点击事件通知给对话框。收到通知后，对话框可以自行校验数值或将任务委派给各元素。这样一来，按钮不再与多个表单元素相关联，而仅依赖于对话框类。 你还可以为所有类型的对话框抽取通用接口，进一步削弱其依赖性。接口中将声明一个所有表单元素都能使用的通知方法，可用于将元素中发生的事件通知给对话框。这样一来，所有实现了该接口的对话框都能使用这个提交按钮了。 采用这种方式，中介者模式让你能在单个中介者对象中封装多个对象间的复杂关系网。类所拥有的依赖关系越少，就越易于修改、扩展或复用。","s":"解决方案","u":"/docs/design-patterns/mediator","h":"#解决方案","p":406},{"i":415,"t":"飞行器驾驶员之间不会通过相互沟通来决定下一架降落的飞机。所有沟通都通过控制塔台进行。 飞行器驾驶员们在靠近或离开空中管制区域时不会直接相互交流。但他们会与飞机跑道附近，塔台中的空管员通话。如果没有空管员，驾驶员就需要留意机场附近的所有飞机，并与数十位飞行员组成的委员会讨论降落顺序。那恐怕会让飞机坠毁的统计数据一飞冲天吧。 塔台无需管制飞行全程，只需在航站区加强管控即可，因为该区域的决策参与者数量对于飞行员来说实在太多了。","s":"真实世界类比","u":"/docs/design-patterns/mediator","h":"#真实世界类比","p":406},{"i":417,"t":"组件 (Component) 是各种包含业务逻辑的类。每个组件都有一个指向中介者的引用，该引用被声明为中介者接口类型。组件不知道中介者实际所属的类，因此你可通过将其连接到不同的中介者以使其能在其他程序中复用。 中介者 (Mediator) 接口声明了与组件交流的方法，但通常仅包括一个通知方法。组件可将任意上下文 (包括自己的对象) 作为该方法的参数，只有这样接收组件和发送者类之间才不会耦合。 具体中介者 (Concrete Mediator) 封装了多种组件间的关系。具体中介者通常会保存所有组件的引用并对其进行管理，甚至有时会对其生命周期进行管理。 组件并不知道其他组件的情况。如果组件内发生了重要事件，它只能通知中介者。中介者收到通知后能轻易地确定发送者，这或许已足以判断接下来需要触发的组件了。 对于组件来说，中介者看上去完全就是一个黑箱。发送者不知道最终会由谁来处理自己的请求，接收者也不知道最初是谁发出了请求。","s":"中介者模式结构","u":"/docs/design-patterns/mediator","h":"#中介者模式结构","p":406},{"i":419,"t":"在本例中，中介者模式可帮助你减少各种 UI 类 (按钮、复选框和文本标签) 之间的相互依赖关系。 UI 对话框类的结构 用户触发的元素不会直接与其他元素交流，即使看上去它们应该这样做。相反，元素只需让中介者知晓事件即可，并能在发出通知时同时传递任何上下文信息。 本例中的中介者是整个认证对话框。对话框知道具体元素应如何进行合作并促进它们的间接交流。当接收到事件通知后，对话框会确定负责处理事件的元素并据此重定向请求。 // 中介者接口声明了一个能让组件将各种事件通知给中介者的方法。中介者可对这 // 些事件做出响应并将执行工作传递给其他组件。 interface Mediator is method notify(sender: Component, event: string) // 具体中介者类可解开各组件之间相互交叉的连接关系并将其转移到中介者中。 class AuthenticationDialog implements Mediator is private field title: string private field loginOrRegisterChkBx: Checkbox private field loginUsername, loginPassword: Textbox private field registrationUsername, registrationPassword, registrationEmail: Textbox private field okBtn, cancelBtn: Button constructor AuthenticationDialog() is // 创建所有组件对象并将当前中介者传递给其构造函数以建立连接。 // 当组件中有事件发生时，它会通知中介者。中介者接收到通知后可自行处理， // 也可将请求传递给另一个组件。 method notify(sender, event) is if (sender == loginOrRegisterChkBx and event == \"check\") if (loginOrRegisterChkBx.checked) title = \"登录\" // 1. 显示登录表单组件。 // 2. 隐藏注册表单组件。 else title = \"注册\" // 1. 显示注册表单组件。 // 2. 隐藏登录表单组件。 if (sender == okBtn && event == \"click\") if (loginOrRegister.checked) // 尝试找到使用登录信息的用户。 if (!found) // 在登录字段上方显示错误信息。 else // 1. 使用注册字段中的数据创建用户账号。 // 2. 完成用户登录工作。 // …… // 组件会使用中介者接口与中介者进行交互。因此只需将它们与不同的中介者连接 // 起来，你就能在其他情境中使用这些组件了。 class Component is field dialog: Mediator constructor Component(dialog) is this.dialog = dialog method click() is dialog.notify(this, \"click\") method keypress() is dialog.notify(this, \"keypress\") // 具体组件之间无法进行交流。它们只有一个交流渠道，那就是向中介者发送通知。 class Button extends Component is // …… class Textbox extends Component is // …… class Checkbox extends Component is method check() is dialog.notify(this, \"check\") // ……","s":"伪代码","u":"/docs/design-patterns/mediator","h":"#伪代码","p":406},{"i":421,"t":"当一些对象和其他对象紧密耦合以致难以对其进行修改时，可使用中介者模式。 该模式让你将对象间的所有关系抽取成为一个单独的类，以使对于特定组件的修改工作独立于其他组件。 当组件因过于依赖其他组件而无法在不同应用中复用时，可使用中介者模式。 应用中介者模式后，每个组件不再知晓其他组件的情况。尽管这些组件无法直接交流，但它们仍可通过中介者对象进行间接交流。如果你希望在不同应用中复用一个组件，则需要为其提供一个新的中介者类。 如果为了能在不同情景下复用一些基本行为，导致你需要被迫创建大量组件子类时，可使用中介者模式。 由于所有组件间关系都被包含在中介者中，因此你无需修改组件就能方便地新建中介者类以定义新的组件合作方式。 实现方式 找到一组当前紧密耦合，且提供其独立性能带来更大好处的类 (例如更易于维护或更方便复用)。 声明中介者接口并描述中介者和各种组件之间所需的交流接口。在绝大多数情况下，一个接收组件通知的方法就足够了。如果你希望在不同情景下复用组件类，那么该接口将非常重要。只要组件使用通用接口与其中介者合作，你就能将该组件与不同实现中的中介者进行连接。 实现具体中介者类。该类可从自行保存其下所有组件的引用中受益。 你可以更进一步，让中介者负责组件对象的创建和销毁。此后，中介者可能会与工厂或外观类似。 组件必须保存对于中介者对象的引用。该连接通常在组件的构造函数中建立，该函数会将中介者对象作为参数传递。 修改组件代码，使其可调用中介者的通知方法，而非其他组件的方法。然后将调用其他组件的代码抽取到中介者类中，并在中介者接收到该组件通知时执行这些代码。","s":"中介者模式适合应用场景","u":"/docs/design-patterns/mediator","h":"#中介者模式适合应用场景","p":406},{"i":423,"t":"✔️ 单一职责原则。你可以将多个组件间的交流抽取到同一位置，使其更易于理解和维护。 ✔️ 开闭原则。你无需修改实际组件就能增加新的中介者。 ✔️ 你可以减轻应用中多个组件间的耦合情况。 ✔️ 你可以更方便地复用各个组件。 ❌ 一段时间后，中介者可能会演化成为上帝对象。","s":"中介者模式优缺点","u":"/docs/design-patterns/mediator","h":"#中介者模式优缺点","p":406},{"i":425,"t":"责任链模式、命令模式、中介者模式和观察者模式用于处理请求发送者和接收者之间的不同连接方式： 责任链按照顺序将请求动态传递给一系列的潜在接收者，直至其中一名接收者对请求进行处理。 命令在发送者和请求者之间建立单向连接。 中介者清除了发送者和请求者之间的直接连接，强制它们通过一个中介对象进行间接沟通。 观察者允许接收者动态地订阅或取消接收请求。 外观模式和中介者的职责类似：它们都尝试在大量紧密耦合的类中组织起合作。 外观为子系统中的所有对象定义了一个简单接口，但是它不提供任何新功能。子系统本身不会意识到外观的存在。子系统中的对象可以直接进行交流。 中介者将系统中组件的沟通行为中心化。各组件只知道中介者对象，无法直接相互交流。 中介者和观察者之间的区别往往很难记住。在大部分情况下，你可以使用其中一种模式，而有时可以同时使用。让我们来看看如何做到这一点。 中介者的主要目标是消除一系列系统组件之间的相互依赖。这些组件将依赖于同一个中介者对象。观察者的目标是在对象之间建立动态的单向连接，使得部分对象可作为其他对象的附属发挥作用。有一种流行的中介者模式实现方式依赖于观察者。中介者对象担当发布者的角色，其他组件则作为订阅者，可以订阅中介者的事件或取消订阅。当中介者以这种方式实现时，它可能看上去与观察者非常相似。当你感到疑惑时，记住可以采用其他方式来实现中介者。例如，你可永久性地将所有组件链接到同一个中介者对象。这种实现方式和观察者并不相同，但这仍是一种中介者模式。假设有一个程序，其所有的组件都变成了发布者，它们之间可以相互建立动态连接。这样程序中就没有中心化的中介者对象，而只有一些分布式的观察者。","s":"与其他模式的关系","u":"/docs/design-patterns/mediator","h":"#与其他模式的关系","p":406},{"i":427,"t":"亦称：快照、Snapshot、Memento","s":"备忘录模式","u":"/docs/design-patterns/memento","h":"","p":426},{"i":429,"t":"备忘录模式是一种行为设计模式，允许在不暴露对象实现细节的情况下保存和恢复对象之前的状态。","s":"意图","u":"/docs/design-patterns/memento","h":"#意图","p":426},{"i":431,"t":"假如你正在开发一款文字编辑器应用程序。除了简单的文字编辑功能外，编辑器中还要有设置文本格式和插入内嵌图片等功能。 后来，你决定让用户能撤销施加在文本上的任何操作。这项功能在过去几年里变得十分普遍，因此用户期待任何程序都有这项功能。你选择采用直接的方式来实现该功能：程序在执行任何操作前会记录所有的对象状态，并将其保存下来。当用户此后需要撤销某个操作时，程序将从历史记录中获取最近的快照，然后使用它来恢复所有对象的状态。 程序在执行操作前保存所有对象的状态快照，稍后可通过快照将对象恢复到之前的状态。 让我们来思考一下这些状态快照。首先，到底该如何生成一个快照呢？很可能你会需要遍历对象的所有成员变量并将其数值复制保存。但只有当对象对其内容没有严格访问权限限制的情况下，你才能使用该方式。不过很遗憾，绝大部分对象会使用私有成员变量来存储重要数据，这样别人就无法轻易查看其中的内容。 现在我们暂时忽略这个问题，假设对象都像嬉皮士一样：喜欢开放式的关系并会公开其所有状态。尽管这种方式能够解决当前问题，让你可随时生成对象的状态快照，但这种方式仍存在一些严重问题。未来你可能会添加或删除一些成员变量。这听上去很简单，但需要对负责复制受影响对象状态的类进行更改。 如何复制对象的私有状态？ 还有更多问题。让我们来考虑编辑器 (Editor) 状态的实际“快照”，它需要包含哪些数据？至少必须包含实际的文本、光标坐标和当前滚动条位置等。你需要收集这些数据并将其放入特定容器中，才能生成快照。 你很可能会将大量的容器对象存储在历史记录列表中。这样一来，容器最终大概率会成为同一个类的对象。这个类中几乎没有任何方法，但有许多与编辑器状态一一对应的成员变量。为了让其他对象能保存或读取快照，你很可能需要将快照的成员变量设为公有。无论这些状态是否私有，其都将暴露一切编辑器状态。其他类会对快照类的每个小改动产生依赖，除非这些改动仅存在于私有成员变量或方法中，而不会影响外部类。 我们似乎走进了一条死胡同：要么会暴露类的所有内部细节而使其过于脆弱；要么会限制对其状态的访问权限而无法生成快照。那么，我们还有其他方式来实现“撤销”功能吗？","s":"问题","u":"/docs/design-patterns/memento","h":"#问题","p":426},{"i":433,"t":"我们刚才遇到的所有问题都是封装“破损”造成的。一些对象试图超出其职责范围的工作。由于在执行某些行为时需要获取数据，所以它们侵入了其他对象的私有空间，而不是让这些对象来完成实际的工作。 备忘录模式将创建状态快照 (Snapshot) 的工作委派给实际状态的拥有者原发器 (Originator) 对象。这样其他对象就不再需要从“外部”复制编辑器状态了，编辑器类拥有其状态的完全访问权，因此可以自行生成快照。 模式建议将对象状态的副本存储在一个名为备忘录 (Memento) 的特殊对象中。除了创建备忘录的对象外，任何对象都不能访问备忘录的内容。其他对象必须使用受限接口与备忘录进行交互，它们可以获取快照的元数据 (创建时间和操作名称等)，但不能获取快照中原始对象的状态。 原发器拥有对备忘录的完全访问权限，负责人则只能访问元数据。 这种限制策略允许你将备忘录保存在通常被称为负责人 (Caretakers) 的对象中。由于负责人仅通过受限接口与备忘录互动，故其无法修改存储在备忘录内部的状态。同时，原发器拥有对备忘录所有成员的访问权限，从而能随时恢复其以前的状态。 在文字编辑器的示例中，我们可以创建一个独立的历史 (History) 类作为负责人。编辑器每次执行操作前，存储在负责人中的备忘录栈都会生长。你甚至可以在应用的 UI 中渲染该栈，为用户显示之前的操作历史。 当用户触发撤销操作时，历史类将从栈中取回最近的备忘录，并将其传递给编辑器以请求进行回滚。由于编辑器拥有对备忘录的完全访问权限，因此它可以使用从备忘录中获取的数值来替换自身的状态。","s":"解决方案","u":"/docs/design-patterns/memento","h":"#解决方案","p":426},{"i":436,"t":"该模式的经典实现方式依赖于许多流行编程语言 (例如 C++、C# 和 Java) 所支持的嵌套类。 原发器 (Originator) 类可以生成自身状态的快照，也可以在需要时通过快照恢复自身状态。 备忘录 (Memento) 是原发器状态快照的值对象 (value object)。通常做法是将备忘录设为不可变的，并通过构造函数一次性传递数据。 负责人 (Caretaker) 仅知道“何时”和“为何”捕捉原发器的状态，以及何时恢复状态。 负责人通过保存备忘录栈来记录原发器的历史状态。当原发器需要回溯历史状态时，负责人将从栈中获取最顶部的备忘录，并将其传递给原发器的恢复 (restoration) 方法。 在该实现方法中，备忘录类将被嵌套在原发器中。这样原发器就可访问备忘录的成员变量和方法，即使这些方法被声明为私有。另一方面，负责人对于备忘录的成员变量和方法的访问权限非常有限：它们只能在栈中保存备忘录，而不能修改其状态。","s":"基于嵌套类的实现","u":"/docs/design-patterns/memento","h":"#基于嵌套类的实现","p":426},{"i":438,"t":"另外一种实现方法适用于不支持嵌套类的编程语言 (没错，我说的就是 PHP)。 在没有嵌套类的情况下，你可以规定负责人仅可通过明确声明的中间接口与备忘录互动，该接口仅声明与备忘录元数据相关的方法，限制其对备忘录成员变量的直接访问权限。 另一方面，原发器可以直接与备忘录对象进行交互，访问备忘录类中声明的成员变量和方法。这种方式的缺点在于你需要将备忘录的所有成员变量声明为公有。","s":"基于中间接口的实现","u":"/docs/design-patterns/memento","h":"#基于中间接口的实现","p":426},{"i":440,"t":"如果你不想让其他类有任何机会通过备忘录来访问原发器的状态，那么还有另一种可用的实现方式。 这种实现方式允许存在多种不同类型的原发器和备忘录。每种原发器都和其相应的备忘录类进行交互。原发器和备忘录都不会将其状态暴露给其他类。 负责人此时被明确禁止修改存储在备忘录中的状态。但负责人类将独立于原发器，因为此时恢复方法被定义在了备忘录类中。 每个备忘录将与创建了自身的原发器连接。原发器会将自己及状态传递给备忘录的构造函数。由于这些类之间的紧密联系，只要原发器定义了合适的设置器 (setter)，备忘录就能恢复其状态。","s":"封装更加严格的实现","u":"/docs/design-patterns/memento","h":"#封装更加严格的实现","p":426},{"i":442,"t":"本例结合使用了命令模式与备忘录模式，可保存复杂文字编辑器的状态快照，并能在需要时从快照中恢复之前的状态。 保存文字编辑器状态的快照。 命令 (command) 对象将作为负责人，它们会在执行与命令相关的操作前获取编辑器的备忘录。当用户试图撤销最近的命令时，编辑器可以使用保存在命令中的备忘录来将自身回滚到之前的状态。 备忘录类没有声明任何公有的成员变量、获取器 (getter) 和设置器，因此没有对象可以修改其内容。备忘录与创建自己的编辑器相连接，这使得备忘录能够通过编辑器对象的设置器传递数据，恢复与其相连接的编辑器的状态。由于备忘录与特定的编辑器对象相连接，程序可以使用中心化的撤销栈实现对多个独立编辑器窗口的支持。 // 原发器中包含了一些可能会随时间变化的重要数据。它还定义了在备忘录中保存 // 自身状态的方法，以及从备忘录中恢复状态的方法。 class Editor is private field text, curX, curY, selectionWidth method setText(text) is this.text = text method setCursor(x, y) is this.curX = x this.curY = y method setSelectionWidth(width) is this.selectionWidth = width // 在备忘录中保存当前的状态。 method createSnapshot():Snapshot is // 备忘录是不可变的对象；因此原发器会将自身状态作为参数传递给备忘 // 录的构造函数。 return new Snapshot(this, text, curX, curY, selectionWidth) // 备忘录类保存有编辑器的过往状态。 class Snapshot is private field editor: Editor private field text, curX, curY, selectionWidth constructor Snapshot(editor, text, curX, curY, selectionWidth) is this.editor = editor this.text = text this.curX = x this.curY = y this.selectionWidth = selectionWidth // 在某一时刻，编辑器之前的状态可以使用备忘录对象来恢复。 method restore() is editor.setText(text) editor.setCursor(curX, curY) editor.setSelectionWidth(selectionWidth) // 命令对象可作为负责人。在这种情况下，命令会在修改原发器状态之前获取一个 // 备忘录。当需要撤销时，它会从备忘录中恢复原发器的状态。 class Command is private field backup: Snapshot method makeBackup() is backup = editor.createSnapshot() method undo() is if (backup != null) backup.restore() // ……","s":"伪代码","u":"/docs/design-patterns/memento","h":"#伪代码","p":426},{"i":444,"t":"当你需要创建对象状态快照来恢复其之前的状态时，可以使用备忘录模式。 备忘录模式允许你复制对象中的全部状态 (包括私有成员变量)，并将其独立于对象进行保存。尽管大部分人因为“撤销”这个用例才记得该模式，但其实它在处理事务 (比如需要在出现错误时回滚一个操作) 的过程中也必不可少。 当直接访问对象的成员变量、获取器或设置器将导致封装被突破时，可以使用该模式。 备忘录让对象自行负责创建其状态的快照。任何其他对象都不能读取快照，这有效地保障了数据的安全性。 实现方式 确定担任原发器角色的类。重要的是明确程序使用的一个原发器中心对象，还是多个较小的对象。 创建备忘录类。逐一声明对应每个原发器成员变量的备忘录成员变量。 将备忘录类设为不可变。备忘录只能通过构造函数一次性接收数据。该类中不能包含设置器。 如果你所使用的编程语言支持嵌套类，则可将备忘录嵌套在原发器中；如果不支持，那么你可从备忘录类中抽取一个空接口，然后让其他所有对象通过接口来引用备忘录。你可在该接口中添加一些元数据操作，但不能暴露原发器的状态。 在原发器中添加一个创建备忘录的方法。原发器必须通过备忘录构造函数的一个或多个实际参数来将自身状态传递给备忘录。该方法返回结果的类型必须是你在上一步中抽取的接口 (如果你已经抽取了)。实际上，创建备忘录的方法必须直接与备忘录类进行交互。 在原发器类中添加一个用于恢复自身状态的方法。该方法接受备忘录对象作为参数。如果你在之前的步骤中抽取了接口，那么可将接口作为参数的类型。在这种情况下，你需要将输入对象强制转换为备忘录，因为原发器需要拥有对该对象的完全访问权限。 无论负责人是命令对象、历史记录或其他完全不同的东西，它都必须要知道何时向原发器请求新的备忘录、如何存储备忘录以及何时使用特定备忘录来对原发器进行恢复。 负责人与原发器之间的连接可以移动到备忘录类中。在本例中，每个备忘录都必须与创建自己的原发器相连接。恢复方法也可以移动到备忘录类中，但只有当备忘录类嵌套在原发器中，或者原发器类提供了足够多的设置器并可对其状态进行重写时，这种方式才能实现。","s":"备忘录模式适合应用场景","u":"/docs/design-patterns/memento","h":"#备忘录模式适合应用场景","p":426},{"i":446,"t":"✔️ 你可以在不破坏对象封装情况的前提下创建对象状态快照。 ✔️ 你可以通过让负责人维护原发器状态历史记录来简化原发器代码。 ❌ 如果客户端过于频繁地创建备忘录，程序将消耗大量内存。 ❌ 负责人必须完整跟踪原发器的生命周期，这样才能销毁弃用的备忘录。 ❌ 绝大部分动态编程语言 (例如 PHP、Python 和 JavaScript) 不能确保备忘录中的状态不被修改。","s":"备忘录模式优缺点","u":"/docs/design-patterns/memento","h":"#备忘录模式优缺点","p":426},{"i":448,"t":"你可以同时使用命令模式和备忘录模式来实现“撤销”。在这种情况下，命令用于对目标对象执行各种不同的操作，备忘录用来保存一条命令执行前该对象的状态。 你可以同时使用备忘录和迭代器模式来获取当前迭代器的状态，并且在需要的时候进行回滚。 有时候原型模式可以作为备忘录的一个简化版本，其条件是你需要在历史记录中存储的对象的状态比较简单，不需要链接其他外部资源，或者链接可以方便地重建。","s":"与其他模式的关系","u":"/docs/design-patterns/memento","h":"#与其他模式的关系","p":426},{"i":450,"t":"亦称：事件订阅者、监听者、Event-Subscriber、Listener、Observer","s":"观察者模式","u":"/docs/design-patterns/observer","h":"","p":449},{"i":452,"t":"观察者模式是一种行为设计模式，允许你定义一种订阅机制，可在对象事件发生时通知多个“观察”该对象的其他对象。","s":"意图","u":"/docs/design-patterns/observer","h":"#意图","p":449},{"i":454,"t":"假如你有两种类型的对象：顾客 和 商店。顾客对某个特定品牌的产品非常感兴趣 (例如最新型号的 iPhone 手机)，而该产品很快将会在商店里出售。 顾客可以每天来商店看看产品是否到货。但如果商品尚未到货时，绝大多数来到商店的顾客都会空手而归。 前往商店和发送垃圾邮件 另一方面，每次新产品到货时，商店可以向所有顾客发送邮件 (可能会被视为垃圾邮件)。这样，部分顾客就无需反复前往商店了，但也可能会惹恼对新产品没有兴趣的其他顾客。 我们似乎遇到了一个矛盾：要么让顾客浪费时间检查产品是否到货，要么让商店浪费资源去通知没有需求的顾客。","s":"问题","u":"/docs/design-patterns/observer","h":"#问题","p":449},{"i":456,"t":"拥有一些值得关注的状态的对象通常被称为目标，由于它要将自身的状态改变通知给其他对象，我们也将其称为发布者 (publisher)。所有希望关注发布者状态变化的其他对象被称为订阅者 (subscribers)。 观察者模式建议你为发布者类添加订阅机制，让每个对象都能订阅或取消订阅发布者事件流。不要害怕！这并不像听上去那么复杂。实际上，该机制包括 1） 一个用于存储订阅者对象引用的列表成员变量；2） 几个用于添加或删除该列表中订阅者的公有方法。 订阅机制允许对象订阅事件通知。 现在，无论何时发生了重要的发布者事件，它都要遍历订阅者并调用其对象的特定通知方法。 实际应用中可能会有十几个不同的订阅者类跟踪着同一个发布者类的事件，你不会希望发布者与所有这些类相耦合的。此外如果他人会使用发布者类，那么你甚至可能会对其中的一些类一无所知。 因此，所有订阅者都必须实现同样的接口，发布者仅通过该接口与订阅者交互。接口中必须声明通知方法及其参数，这样发布者在发出通知时还能传递一些上下文数据。 发布者调用订阅者对象中的特定通知方法来通知订阅者。 如果你的应用中有多个不同类型的发布者，且希望订阅者可兼容所有发布者，那么你甚至可以进一步让所有发布者遵循同样的接口。该接口仅需描述几个订阅方法即可。这样订阅者就能在不与具体发布者类耦合的情况下通过接口观察发布者的状态。","s":"解决方案","u":"/docs/design-patterns/observer","h":"#解决方案","p":449},{"i":458,"t":"杂志和报纸订阅。 如果你订阅了一份杂志或报纸，那就不需要再去报摊查询新出版的刊物了。出版社 (即应用中的“发布者”) 会在刊物出版后 (甚至提前) 直接将最新一期寄送至你的邮箱中。 出版社负责维护订阅者列表，了解订阅者对哪些刊物感兴趣。当订阅者希望出版社停止寄送新一期的杂志时，他们可随时从该列表中退出。","s":"真实世界类比","u":"/docs/design-patterns/observer","h":"#真实世界类比","p":449},{"i":460,"t":"发布者 (Publisher) 会向其他对象发送值得关注的事件。事件会在发布者自身状态改变或执行特定行为后发生。发布者中包含一个允许新订阅者加入和当前订阅者离开列表的订阅构架。 当新事件发生时，发送者会遍历订阅列表并调用每个订阅者对象的通知方法。该方法是在订阅者接口中声明的。 订阅者 (Subscriber) 接口声明了通知接口。在绝大多数情况下，该接口仅包含一个 update 更新方法。该方法可以拥有多个参数，使发布者能在更新时传递事件的详细信息。 具体订阅者 (Concrete Subscribers) 可以执行一些操作来回应发布者的通知。所有具体订阅者类都实现了同样的接口，因此发布者不需要与具体类相耦合。 订阅者通常需要一些上下文信息来正确地处理更新。因此，发布者通常会将一些上下文数据作为通知方法的参数进行传递。发布者也可将自身作为参数进行传递，使订阅者直接获取所需的数据。 客户端 (Client) 会分别创建发布者和订阅者对象，然后为订阅者注册发布者更新。","s":"观察者模式结构","u":"/docs/design-patterns/observer","h":"#观察者模式结构","p":449},{"i":462,"t":"在本例中，观察者模式允许文本编辑器对象将自身的状态改变通知给其他服务对象。 将对象中发生的事件通知给其他对象。 订阅者列表是动态生成的：对象可在运行时根据程序需要开始或停止监听通知。 在本实现中，编辑器类自身并不维护订阅列表。它将工作委派给专门从事此工作的一个特殊帮手对象。你还可将该对象升级为中心化的事件分发器，允许任何对象成为发布者。 只要发布者通过同样的接口与所有订阅者进行交互，那么在程序中新增订阅者时就无需修改已有发布者类的代码。 // 发布者基类包含订阅管理代码和通知方法。 class EventManager is private field listeners: hash map of event types and listeners method subscribe(eventType, listener) is listeners.add(eventType, listener) method unsubscribe(eventType, listener) is listeners.remove(eventType, listener) method notify(eventType, data) is foreach (listener in listeners.of(eventType)) do listener.update(data) // 具体发布者包含一些订阅者感兴趣的实际业务逻辑。我们可以从发布者基类中扩 // 展出该类，但在实际情况下并不总能做到，因为具体发布者可能已经是子类了。 // 在这种情况下，你可用组合来修补订阅逻辑，就像我们在这里做的一样。 class Editor is public field events: EventManager private field file: File constructor Editor() is events = new EventManager() // 业务逻辑的方法可将变化通知给订阅者。 method openFile(path) is this.file = new File(path) events.notify(\"open\", file.name) method saveFile() is file.write() events.notify(\"save\", file.name) // …… // 这里是订阅者接口。如果你的编程语言支持函数类型，则可用一组函数来代替整 // 个订阅者的层次结构。 interface EventListener is method update(filename) // 具体订阅者会对其注册的发布者所发出的更新消息做出响应。 class LoggingListener implements EventListener is private field log: File private field message: string constructor LoggingListener(log_filename, message) is this.log = new File(log_filename) this.message = message method update(filename) is log.write(replace('%s',filename,message)) class EmailAlertsListener implements EventListener is private field email: string private field message: string constructor EmailAlertsListener(email, message) is this.email = email this.message = message method update(filename) is system.email(email, replace('%s',filename,message)) // 应用程序可在运行时配置发布者和订阅者。 class Application is method config() is editor = new Editor() logger = new LoggingListener( \"/path/to/log.txt\", \"有人打开了文件：%s\"); editor.events.subscribe(\"open\", logger) emailAlerts = new EmailAlertsListener( \"admin@example.com\", \"有人更改了文件：%s\") editor.events.subscribe(\"save\", emailAlerts)","s":"伪代码","u":"/docs/design-patterns/observer","h":"#伪代码","p":449},{"i":464,"t":"当一个对象状态的改变需要改变其他对象，或实际对象是事先未知的或动态变化的时，可使用观察者模式。 当你使用图形用户界面类时通常会遇到一个问题。比如，你创建了自定义按钮类并允许客户端在按钮中注入自定义代码，这样当用户按下按钮时就会触发这些代码。 观察者模式允许任何实现了订阅者接口的对象订阅发布者对象的事件通知。你可在按钮中添加订阅机制，允许客户端通过自定义订阅类注入自定义代码。 当应用中的一些对象必须观察其他对象时，可使用该模式。但仅能在有限时间内或特定情况下使用。 订阅列表是动态的，因此订阅者可随时加入或离开该列表。 实现方式 仔细检查你的业务逻辑，试着将其拆分为两个部分：独立于其他代码的核心功能将作为发布者；其他代码则将转化为一组订阅类。 声明订阅者接口。该接口至少应声明一个 update 方法。 声明发布者接口并定义一些接口来在列表中添加和删除订阅对象。记住发布者必须仅通过订阅者接口与它们进行交互。 确定存放实际订阅列表的位置并实现订阅方法。通常所有类型的发布者代码看上去都一样，因此将列表放置在直接扩展自发布者接口的抽象类中是显而易见的。具体发布者会扩展该类从而继承所有的订阅行为。但是，如果你需要在现有的类层次结构中应用该模式，则可以考虑使用组合的方式：将订阅逻辑放入一个独立的对象，然后让所有实际订阅者使用该对象。 创建具体发布者类。每次发布者发生了重要事件时都必须通知所有的订阅者。 在具体订阅者类中实现通知更新的方法。绝大部分订阅者需要一些与事件相关的上下文数据。这些数据可作为通知方法的参数来传递。但还有另一种选择。订阅者接收到通知后直接从通知中获取所有数据。在这种情况下，发布者必须通过更新方法将自身传递出去。另一种不太灵活的方式是通过构造函数将发布者与订阅者永久性地连接起来。 客户端必须生成所需的全部订阅者，并在相应的发布者处完成注册工作。","s":"观察者模式适合应用场景","u":"/docs/design-patterns/observer","h":"#观察者模式适合应用场景","p":449},{"i":466,"t":"✔️ 开闭原则。你无需修改发布者代码就能引入新的订阅者类 (如果是发布者接口则可轻松引入发布者类)。 ✔️ 你可以在运行时建立对象之间的联系。 ❌ 订阅者的通知顺序是随机的。","s":"观察者模式优缺点","u":"/docs/design-patterns/observer","h":"#观察者模式优缺点","p":449},{"i":468,"t":"责任链模式、命令模式、中介者模式和观察者模式用于处理请求发送者和接收者之间的不同连接方式： 责任链按照顺序将请求动态传递给一系列的潜在接收者，直至其中一名接收者对请求进行处理。 命令在发送者和请求者之间建立单向连接。 中介者清除了发送者和请求者之间的直接连接，强制它们通过一个中介对象进行间接沟通。 观察者允许接收者动态地订阅或取消接收请求。 中介者和观察者之间的区别往往很难记住。在大部分情况下，你可以使用其中一种模式，而有时可以同时使用。让我们来看看如何做到这一点。 中介者的主要目标是消除一系列系统组件之间的相互依赖。这些组件将依赖于同一个中介者对象。观察者的目标是在对象之间建立动态的单向连接，使得部分对象可作为其他对象的附属发挥作用。有一种流行的中介者模式实现方式依赖于观察者。中介者对象担当发布者的角色，其他组件则作为订阅者，可以订阅中介者的事件或取消订阅。当中介者以这种方式实现时，它可能看上去与观察者非常相似。当你感到疑惑时，记住可以采用其他方式来实现中介者。例如，你可永久性地将所有组件链接到同一个中介者对象。这种实现方式和观察者并不相同，但这仍是一种中介者模式。假设有一个程序，其所有的组件都变成了发布者，它们之间可以相互建立动态连接。这样程序中就没有中心化的中介者对象，而只有一些分布式的观察者。","s":"与其他模式的关系","u":"/docs/design-patterns/observer","h":"#与其他模式的关系","p":449},{"i":470,"t":"亦称：克隆、Clone、Prototype","s":"原型模式","u":"/docs/design-patterns/prototype","h":"","p":469},{"i":472,"t":"原型模式是一种创建型设计模式，使你能够复制已有对象，而又无需使代码依赖它们所属的类。","s":"意图","u":"/docs/design-patterns/prototype","h":"#意图","p":469},{"i":474,"t":"如果你有一个对象，并希望生成与其完全相同的一个复制品，你该如何实现呢？首先，你必须新建一个属于相同类的对象。然后，你必须遍历原始对象的所有成员变量，并将成员变量值复制到新对象中。 不错！但有个小问题。并非所有对象都能通过这种方式进行复制，因为有些对象可能拥有私有成员变量，它们在对象本身以外是不可见的。 “从外部”复制对象并非总是可行。 直接复制还有另外一个问题。因为你必须知道对象所属的类才能创建复制品，所以代码必须依赖该类。即使你可以接受额外的依赖性，那还有另外一个问题：有时你只知道对象所实现的接口，而不知道其所属的具体类，比如可向方法的某个参数传入实现了某个接口的任何对象。","s":"问题","u":"/docs/design-patterns/prototype","h":"#问题","p":469},{"i":476,"t":"原型模式将克隆过程委派给被克隆的实际对象。模式为所有支持克隆的对象声明了一个通用接口，该接口让你能够克隆对象，同时又无需将代码和对象所属类耦合。通常情况下，这样的接口中仅包含一个 克隆 方法。 所有的类对 克隆 方法的实现都非常相似。该方法会创建一个当前类的对象，然后将原始对象所有的成员变量值复制到新建的类中。你甚至可以复制私有成员变量，因为绝大部分编程语言都允许对象访问其同类对象的私有成员变量。 支持克隆的对象即为原型。当你的对象有几十个成员变量和几百种类型时，对其进行克隆甚至可以代替子类的构造。 预生成原型可以代替子类的构造。 其运作方式如下：创建一系列不同类型的对象并不同的方式对其进行配置。如果所需对象与预先配置的对象相同，那么你只需克隆原型即可，无需新建一个对象。","s":"解决方案","u":"/docs/design-patterns/prototype","h":"#解决方案","p":469},{"i":478,"t":"现实生活中，产品在得到大规模生产前会使用原型进行各种测试。但在这种情况下，原型只是一种被动的工具，不参与任何真正的生产活动。 一个细胞的分裂。 由于工业原型并不是真正意义上的自我复制，因此细胞有丝分裂 (还记得生物学知识吗？) 或许是更恰当的类比。有丝分裂会产生一对完全相同的细胞。原始细胞就是一个原型，它在复制体的生成过程中起到了推动作用。","s":"真实世界类比","u":"/docs/design-patterns/prototype","h":"#真实世界类比","p":469},{"i":481,"t":"原型 (Prototype) 接口将对克隆方法进行声明。在绝大多数情况下，其中只会有一个名为 clone 克隆的方法。 具体原型 (Concrete Prototype) 类将实现克隆方法。除了将原始对象的数据复制到克隆体中之外，该方法有时还需处理克隆过程中的极端情况，例如克隆关联对象和梳理递归依赖等等。 客户端 (Client) 可以复制实现了原型接口的任何对象。","s":"基本实现","u":"/docs/design-patterns/prototype","h":"#基本实现","p":469},{"i":483,"t":"原型注册表 (Prototype Registry) 提供了一种访问常用原型的简单方法，其中存储了一系列可供随时复制的预生成对象。最简单的注册表原型是一个 名称 → 原型 的哈希表。但如果需要使用名称以外的条件进行搜索，你可以创建更加完善的注册表版本。","s":"原型注册表实现","u":"/docs/design-patterns/prototype","h":"#原型注册表实现","p":469},{"i":485,"t":"在本例中，原型模式能让你生成完全相同的几何对象副本，同时无需代码与对象所属类耦合。 克隆一系列位于同一类层次结构中的对象。 所有形状类都遵循同一个提供克隆方法的接口。在复制自身成员变量值到结果对象前，子类可调用其父类的克隆方法。 // 基础原型。 abstract class Shape is field X: int field Y: int field color: string // 常规构造函数。 constructor Shape() is // …… // 原型构造函数。使用已有对象的数值来初始化一个新对象。 constructor Shape(source: Shape) is this() this.X = source.X this.Y = source.Y this.color = source.color // clone（克隆）操作会返回一个形状子类。 abstract method clone():Shape // 具体原型。克隆方法会创建一个新对象并将其传递给构造函数。直到构造函数运 // 行完成前，它都拥有指向新克隆对象的引用。因此，任何人都无法访问未完全生 // 成的克隆对象。这可以保持克隆结果的一致。 class Rectangle extends Shape is field width: int field height: int constructor Rectangle(source: Rectangle) is // 需要调用父构造函数来复制父类中定义的私有成员变量。 super(source) this.width = source.width this.height = source.height method clone():Shape is return new Rectangle(this) class Circle extends Shape is field radius: int constructor Circle(source: Circle) is super(source) this.radius = source.radius method clone():Shape is return new Circle(this) // 客户端代码中的某个位置。 class Application is field shapes: array of Shape constructor Application() is Circle circle = new Circle() circle.X = 10 circle.Y = 10 circle.radius = 20 shapes.add(circle) Circle anotherCircle = circle.clone() shapes.add(anotherCircle) // 变量 `anotherCircle（另一个圆）` 与 `circle（圆）` 对象的内 // 容完全一样。 Rectangle rectangle = new Rectangle() rectangle.width = 10 rectangle.height = 20 shapes.add(rectangle) method businessLogic() is // 原型是很强大的东西，因为它能在不知晓对象类型的情况下生成一个与 // 其完全相同的复制品。 Array shapesCopy = new Array of Shapes. // 例如，我们不知晓形状数组中元素的具体类型，只知道它们都是形状。 // 但在多态机制的帮助下，当我们在某个形状上调用 `clone（克隆）` // 方法时，程序会检查其所属的类并调用其中所定义的克隆方法。这样， // 我们将获得一个正确的复制品，而不是一组简单的形状对象。 foreach (s in shapes) do shapesCopy.add(s.clone()) // `shapesCopy（形状副本）` 数组中包含 `shape（形状）` 数组所有 // 子元素的复制品。","s":"伪代码","u":"/docs/design-patterns/prototype","h":"#伪代码","p":469},{"i":487,"t":"如果你需要复制一些对象，同时又希望代码独立于这些对象所属的具体类，可以使用原型模式。 这一点考量通常出现在代码需要处理第三方代码通过接口传递过来的对象时。即使不考虑代码耦合的情况，你的代码也不能依赖这些对象所属的具体类，因为你不知道它们的具体信息。 原型模式为客户端代码提供一个通用接口，客户端代码可通过这一接口与所有实现了克隆的对象进行交互，它也使得客户端代码与其所克隆的对象具体类独立开来。 如果子类的区别仅在于其对象的初始化方式，那么你可以使用该模式来减少子类的数量。别人创建这些子类的目的可能是为了创建特定类型的对象。 在原型模式中，你可以使用一系列预生成的、各种类型的对象作为原型。 客户端不必根据需求对子类进行实例化，只需找到合适的原型并对其进行克隆即可。 实现方式 创建原型接口，并在其中声明 克隆 方法。如果你已有类层次结构，则只需在其所有类中添加该方法即可。 原型类必须另行定义一个以该类对象为参数的构造函数。构造函数必须复制参数对象中的所有成员变量值到新建实体中。如果你需要修改子类，则必须调用父类构造函数，让父类复制其私有成员变量值。如果编程语言不支持方法重载，那么你可能需要定义一个特殊方法来复制对象数据。在构造函数中进行此类处理比较方便，因为它在调用 new 运算符后会马上返回结果对象。 克隆方法通常只有一行代码：使用 new 运算符调用原型版本的构造函数。注意，每个类都必须显式重写克隆方法并使用自身类名调用 new 运算符。否则，克隆方法可能会生成父类的对象。 你还可以创建一个中心化原型注册表，用于存储常用原型。你可以新建一个工厂类来实现注册表，或者在原型基类中添加一个获取原型的静态方法。该方法必须能够根据客户端代码设定的条件进行搜索。搜索条件可以是简单的字符串，或者是一组复杂的搜索参数。找到合适的原型后，注册表应对原型进行克隆，并将复制生成的对象返回给客户端。最后还要将对子类构造函数的直接调用替换为对原型注册表工厂方法的调用。","s":"原型模式适合应用场景","u":"/docs/design-patterns/prototype","h":"#原型模式适合应用场景","p":469},{"i":489,"t":"✔️ 你可以克隆对象，而无需与它们所属的具体类相耦合。 ✔️ 你可以克隆预生成原型，避免反复运行初始化代码。 ✔️ 你可以更方便地生成复杂对象。 ✔️ 你可以用继承以外的方式来处理复杂对象的不同配置。 ❌ 克隆包含循环引用的复杂对象可能会非常麻烦。","s":"原型模式优缺点","u":"/docs/design-patterns/prototype","h":"#原型模式优缺点","p":469},{"i":491,"t":"在许多设计工作的初期都会使用工厂方法模式 (较为简单，而且可以更方便地通过子类进行定制)，随后演化为使用抽象工厂模式、原型模式或生成器模式 (更灵活但更加复杂)。 抽象工厂模式通常基于一组工厂方法，但你也可以使用原型模式来生成这些类的方法。 原型可用于保存命令模式的历史记录。 大量使用组合模式和装饰模式的设计通常可从对于原型的使用中获益。你可以通过该模式来复制复杂结构，而非从零开始重新构造。 原型并不基于继承，因此没有继承的缺点。另一方面，原型需要对被复制对象进行复杂的初始化。工厂方法基于继承，但是它不需要初始化步骤。 有时候原型可以作为备忘录模式的一个简化版本，其条件是你需要在历史记录中存储的对象的状态比较简单，不需要链接其他外部资源，或者链接可以方便地重建。 抽象工厂、生成器和原型都可以用单例模式来实现。","s":"与其他模式的关系","u":"/docs/design-patterns/prototype","h":"#与其他模式的关系","p":469},{"i":493,"t":"亦称：Proxy","s":"代理模式","u":"/docs/design-patterns/proxy","h":"","p":492},{"i":495,"t":"代理模式是一种结构型设计模式，让你能够提供对象的替代品或其占位符。代理控制着对于原对象的访问，并允许在将请求提交给对象前后进行一些处理。","s":"意图","u":"/docs/design-patterns/proxy","h":"#意图","p":492},{"i":497,"t":"为什么要控制对于某个对象的访问呢？举个例子：有这样一个消耗大量系统资源的巨型对象，你只是偶尔需要使用它，并非总是需要。 数据库查询有可能会非常缓慢。 你可以实现延迟初始化：在实际有需要时再创建该对象。对象的所有客户端都要执行延迟初始代码。不幸的是，这很可能会带来很多重复代码。 在理想情况下，我们希望将代码直接放入对象的类中，但这并非总是能实现：比如类可能是第三方封闭库的一部分。","s":"问题","u":"/docs/design-patterns/proxy","h":"#问题","p":492},{"i":499,"t":"代理模式建议新建一个与原服务对象接口相同的代理类，然后更新应用以将代理对象传递给所有原始对象客户端。代理类接收到客户端请求后会创建实际的服务对象，并将所有工作委派给它。 代理将自己伪装成数据库对象，可在客户端或实际数据库对象不知情的情况下处理延迟初始化和缓存查询结果的工作。 这有什么好处呢？如果需要在类的主要业务逻辑前后执行一些工作，你无需修改类就能完成这项工作。由于代理实现的接口与原类相同，因此你可将其传递给任何一个使用实际服务对象的客户端。","s":"解决方案","u":"/docs/design-patterns/proxy","h":"#解决方案","p":492},{"i":501,"t":"信用卡和现金在支付过程中的用处相同。 信用卡是银行账户的代理，银行账户则是一大捆现金的代理。它们都实现了同样的接口，均可用于进行支付。消费者会非常满意，因为不必随身携带大量现金；商店老板同样会十分高兴，因为交易收入能以电子化的方式进入商店的银行账户中，无需担心存款时出现现金丢失或被抢劫的情况。","s":"真实世界类比","u":"/docs/design-patterns/proxy","h":"#真实世界类比","p":492},{"i":503,"t":"服务接口 (Service Interface) 声明了服务接口。代理必须遵循该接口才能伪装成服务对象。 服务 (Service) 类提供了一些实用的业务逻辑。 代理 (Proxy) 类包含一个指向服务对象的引用成员变量。代理完成其任务 (例如延迟初始化、记录日志、访问控制和缓存等) 后会将请求传递给服务对象。 通常情况下，代理会对其服务对象的整个生命周期进行管理。 客户端 (Client) 能通过同一接口与服务或代理进行交互，所以你可在一切需要服务对象的代码中使用代理。","s":"代理模式结构","u":"/docs/design-patterns/proxy","h":"#代理模式结构","p":492},{"i":505,"t":"本例演示如何使用代理模式在第三方腾讯视频 (TencentVideo，代码示例中记为 TV) 程序库中添加延迟初始化和缓存。 使用代理缓冲服务结果。 程序库提供了视频下载类。但是该类的效率非常低。如果客户端程序多次请求同一视频，程序库会反复下载该视频，而不会将首次下载的文件缓存下来复用。 代理类实现和原下载器相同的接口，并将所有工作委派给原下载器。不过，代理类会保存所有的文件下载记录，如果程序多次请求同一文件，它会返回缓存的文件。 // 远程服务接口。 interface ThirdPartyTVLib is method listVideos() method getVideoInfo(id) method downloadVideo(id) // 服务连接器的具体实现。该类的方法可以向腾讯视频请求信息。请求速度取决于 // 用户和腾讯视频的互联网连接情况。如果同时发送大量请求，即使所请求的信息 // 一模一样，程序的速度依然会减慢。 class ThirdPartyTVClass implements ThirdPartyTVLib is method listVideos() is // 向腾讯视频发送一个 API 请求。 method getVideoInfo(id) is // 获取某个视频的元数据。 method downloadVideo(id) is // 从腾讯视频下载一个视频文件。 // 为了节省网络带宽，我们可以将请求结果缓存下来并保存一段时间。但你可能无 // 法直接将这些代码放入服务类中。比如该类可能是第三方程序库的一部分或其签 // 名是 `final（最终）`。因此我们会在一个实现了服务类接口的新代理类中放入 // 缓存代码。当代理类接收到真实请求后，才会将其委派给服务对象。 class CachedTVClass implements ThirdPartyTVLib is private field service: ThirdPartyTVLib private field listCache, videoCache field needReset constructor CachedTVClass(service: ThirdPartyTVLib) is this.service = service method listVideos() is if (listCache == null || needReset) listCache = service.listVideos() return listCache method getVideoInfo(id) is if (videoCache == null || needReset) videoCache = service.getVideoInfo(id) return videoCache method downloadVideo(id) is if (!downloadExists(id) || needReset) service.downloadVideo(id) // 之前直接与服务对象交互的 GUI 类不需要改变，前提是它仅通过接口与服务对 // 象交互。我们可以安全地传递一个代理对象来代替真实服务对象，因为它们都实 // 现了相同的接口。 class TVManager is protected field service: ThirdPartyTVLib constructor TVManager(service: ThirdPartyTVLib) is this.service = service method renderVideoPage(id) is info = service.getVideoInfo(id) // 渲染视频页面。 method renderListPanel() is list = service.listVideos() // 渲染视频缩略图列表。 method reactOnUserInput() is renderVideoPage() renderListPanel() // 程序可在运行时对代理进行配置。 class Application is method init() is aTVService = new ThirdPartyTVClass() aTVProxy = new CachedTVClass(aTVService) manager = new TVManager(aTVProxy) manager.reactOnUserInput()","s":"伪代码","u":"/docs/design-patterns/proxy","h":"#伪代码","p":492},{"i":507,"t":"使用代理模式的方式多种多样，我们来看看最常见的几种。 延迟初始化 (虚拟代理)。如果你有一个偶尔使用的重量级服务对象，一直保持该对象运行会消耗系统资源时，可使用代理模式。 你无需在程序启动时就创建该对象，可将对象的初始化延迟到真正有需要的时候。 访问控制 (保护代理)。如果你只希望特定客户端使用服务对象，这里的对象可以是操作系统中非常重要的部分，而客户端则是各种已启动的程序 (包括恶意程序)，此时可使用代理模式。 代理可仅在客户端凭据满足要求时将请求传递给服务对象。 本地执行远程服务 (远程代理)。适用于服务对象位于远程服务器上的情形。 在这种情形中，代理通过网络传递客户端请求，负责处理所有与网络相关的复杂细节。 记录日志请求 (日志记录代理)。适用于当你需要保存对于服务对象的请求历史记录时。 代理可以在向服务传递请求前进行记录。 缓存请求结果 (缓存代理)。适用于需要缓存客户请求结果并对缓存生命周期进行管理时，特别是当返回结果的体积非常大时。 代理可对重复请求所需的相同结果进行缓存，还可使用请求参数作为索引缓存的键值。 智能引用。可在没有客户端使用某个重量级对象时立即销毁该对象。 代理会将所有获取了指向服务对象或其结果的客户端记录在案。代理会时不时地遍历各个客户端，检查它们是否仍在运行。如果相应的客户端列表为空，代理就会销毁该服务对象，释放底层系统资源。 代理还可以记录客户端是否修改了服务对象。其他客户端还可以复用未修改的对象。 实现方式 如果没有现成的服务接口，你就需要创建一个接口来实现代理和服务对象的可交换性。从服务类中抽取接口并非总是可行的，因为你需要对服务的所有客户端进行修改，让它们使用接口。备选计划是将代理作为服务类的子类，这样代理就能继承服务的所有接口了。 创建代理类，其中必须包含一个存储指向服务的引用的成员变量。通常情况下，代理负责创建服务并对其整个生命周期进行管理。在一些特殊情况下，客户端会通过构造函数将服务传递给代理。 根据需求实现代理方法。在大部分情况下，代理在完成一些任务后应将工作委派给服务对象。 可以考虑新建一个构建方法来判断客户端可获取的是代理还是实际服务。你可以在代理类中创建一个简单的静态方法，也可以创建一个完整的工厂方法。 可以考虑为服务对象实现延迟初始化。","s":"代理模式适合应用场景","u":"/docs/design-patterns/proxy","h":"#代理模式适合应用场景","p":492},{"i":509,"t":"✔️ 你可以在客户端毫无察觉的情况下控制服务对象。 ✔️ 如果客户端对服务对象的生命周期没有特殊要求，你可以对生命周期进行管理。 ✔️ 即使服务对象还未准备好或不存在，代理也可以正常工作。 ✔️ 开闭原则。你可以在不对服务或客户端做出修改的情况下创建新代理。 ❌ 代码可能会变得复杂，因为需要新建许多类。 ❌ 服务响应可能会延迟。","s":"代理模式优缺点","u":"/docs/design-patterns/proxy","h":"#代理模式优缺点","p":492},{"i":511,"t":"适配器模式能为被封装对象提供不同的接口，代理模式能为对象提供相同的接口，装饰模式则能为对象提供加强的接口。 外观模式与代理的相似之处在于它们都缓存了一个复杂实体并自行对其进行初始化。代理与其服务对象遵循同一接口，使得自己和服务对象可以互换，在这一点上它与外观不同。 装饰和代理有着相似的结构，但是其意图却非常不同。这两个模式的构建都基于组合原则，也就是说一个对象应该将部分工作委派给另一个对象。两者之间的不同之处在于代理通常自行管理其服务对象的生命周期，而装饰的生成则总是由客户端进行控制。","s":"与其他模式的关系","u":"/docs/design-patterns/proxy","h":"#与其他模式的关系","p":492},{"i":513,"t":"亦称：单件模式、Singleton","s":"单例模式","u":"/docs/design-patterns/singleton","h":"","p":512},{"i":515,"t":"单例模式是一种创建型设计模式，让你能够保证一个类只有一个实例，并提供一个访问该实例的全局节点。","s":"意图","u":"/docs/design-patterns/singleton","h":"#意图","p":512},{"i":517,"t":"单例模式同时解决了两个问题，所以违反了单一职责原则： 保证一个类只有一个实例。为什么会有人想要控制一个类所拥有的实例数量？最常见的原因是控制某些共享资源 (例如数据库或文件) 的访问权限。 它的运作方式是这样的：如果你创建了一个对象，同时过一会儿后你决定再创建一个新对象，此时你会获得之前已创建的对象，而不是一个新对象。 注意，普通构造函数无法实现上述行为，因为构造函数的设计决定了它必须总是返回一个新对象。 客户端甚至可能没有意识到它们一直都在使用同一个对象。 为该实例提供一个全局访问节点。还记得你 (好吧，其实是我自己) 用过的那些存储重要对象的全局变量吗？它们在使用上十分方便，但同时也非常不安全，因为任何代码都有可能覆盖掉那些变量的内容，从而引发程序崩溃。 和全局变量一样，单例模式也允许在程序的任何地方访问特定对象。但是它可以保护该实例不被其他代码覆盖。 还有一点：你不会希望解决同一个问题的代码分散在程序各处的。因此更好的方式是将其放在同一个类中，特别是当其他代码已经依赖这个类时更应该如此。 如今，单例模式已经变得非常流行，以至于人们会将只解决上文描述中任意一个问题的东西称为单例。","s":"问题","u":"/docs/design-patterns/singleton","h":"#问题","p":512},{"i":519,"t":"所有单例的实现都包含以下两个相同的步骤： 将默认构造函数设为私有，防止其他对象使用单例类的 new 运算符。 新建一个静态构建方法作为构造函数。该函数会“偷偷”调用私有构造函数来创建对象，并将其保存在一个静态成员变量中。此后所有对于该函数的调用都将返回这一缓存对象。 如果你的代码能够访问单例类，那它就能调用单例类的静态方法。无论何时调用该方法，它总是会返回相同的对象。","s":"解决方案","u":"/docs/design-patterns/singleton","h":"#解决方案","p":512},{"i":521,"t":"政府是单例模式的一个很好的示例。一个国家只有一个官方政府。不管组成政府的每个人的身份是什么，“某政府”这一称谓总是鉴别那些掌权者的全局访问节点。","s":"真实世界类比","u":"/docs/design-patterns/singleton","h":"#真实世界类比","p":512},{"i":523,"t":"单例 (Singleton) 类声明了一个名为 get­Instance 获取实例的静态方法来返回其所属类的一个相同实例。 单例的构造函数必须对客户端 (Client) 代码隐藏。调用 获取实例 方法必须是获取单例对象的唯一方式。","s":"单例模式结构","u":"/docs/design-patterns/singleton","h":"#单例模式结构","p":512},{"i":525,"t":"在本例中，数据库连接类即是一个单例。该类不提供公有构造函数，因此获取该对象的唯一方式是调用 获取实例 方法。该方法将缓存首次生成的对象，并为所有后续调用返回该对象。 // 数据库类会对 `getInstance（获取实例）` 方法进行定义以让客户端在程序各处 // 都能访问相同的数据库连接实例。 class Database is // 保存单例实例的成员变量必须被声明为静态类型。 private static field instance: Database // 单例的构造函数必须永远是私有类型，以防止使用 `new` 运算符直接调用构 // 造方法。 private constructor Database() is // 部分初始化代码（例如到数据库服务器的实际连接）。 // …… // 用于控制对单例实例的访问权限的静态方法。 public static method getInstance() is if (Database.instance == null) then acquireThreadLock() and then // 确保在该线程等待解锁时，其他线程没有初始化该实例。 if (Database.instance == null) then Database.instance = new Database() return Database.instance // 最后，任何单例都必须定义一些可在其实例上执行的业务逻辑。 public method query(sql) is // 比如应用的所有数据库查询请求都需要通过该方法进行。因此，你可以 // 在这里添加限流或缓冲逻辑。 // …… class Application is method main() is Database foo = Database.getInstance() foo.query(\"SELECT ……\") // …… Database bar = Database.getInstance() bar.query(\"SELECT ……\") // 变量 `bar` 和 `foo` 中将包含同一个对象。","s":"伪代码","u":"/docs/design-patterns/singleton","h":"#伪代码","p":512},{"i":527,"t":"如果程序中的某个类对于所有客户端只有一个可用的实例，可以使用单例模式。 单例模式禁止通过除特殊构建方法以外的任何方式来创建自身类的对象。该方法可以创建一个新对象，但如果该对象已经被创建，则返回已有的对象。 如果你需要更加严格地控制全局变量，可以使用单例模式。 单例模式与全局变量不同，它保证类只存在一个实例。除了单例类自己以外，无法通过任何方式替换缓存的实例。 请注意，你可以随时调整限制并设定生成单例实例的数量，只需修改 获取实例 方法，即 getInstance 中的代码即可实现。 实现方式 在类中添加一个私有静态成员变量用于保存单例实例。 声明一个公有静态构建方法用于获取单例实例。 在静态方法中实现“延迟初始化”。该方法会在首次被调用时创建一个新对象，并将其存储在静态成员变量中。此后该方法每次被调用时都返回该实例。 将类的构造函数设为私有。类的静态方法仍能调用构造函数，但是其他对象不能调用。 检查客户端代码，将对单例的构造函数的调用替换为对其静态构建方法的调用。","s":"单例模式适合应用场景","u":"/docs/design-patterns/singleton","h":"#单例模式适合应用场景","p":512},{"i":529,"t":"✔️ 你可以保证一个类只有一个实例。 ✔️ 你获得了一个指向该实例的全局访问节点。 ✔️ 仅在首次请求单例对象时对其进行初始化。 ❌ 违反了单一职责原则。该模式同时解决了两个问题。 ❌ 单例模式可能掩盖不良设计，比如程序各组件之间相互了解过多等。 ❌ 该模式在多线程环境下需要进行特殊处理，避免多个线程多次创建单例对象。 ❌ 单例的客户端代码单元测试可能会比较困难，因为许多测试框架以基于继承的方式创建模拟对象。由于单例类的构造函数是私有的，而且绝大部分语言无法重写静态方法，所以你需要想出仔细考虑模拟单例的方法。要么干脆不编写测试代码，或者不使用单例模式。","s":"单例模式优缺点","u":"/docs/design-patterns/singleton","h":"#单例模式优缺点","p":512},{"i":531,"t":"外观模式类通常可以转换为单例模式类，因为在大部分情况下一个外观对象就足够了。 如果你能将对象的所有共享状态简化为一个享元对象，那么享元模式就和单例类似了。但这两个模式有两个根本性的不同。 只会有一个单例实体，但是享元类可以有多个实体，各实体的内在状态也可以不同。 单例对象可以是可变的。享元对象是不可变的。 抽象工厂模式、生成器模式和原型模式都可以用单例来实现。","s":"与其他模式的关系","u":"/docs/design-patterns/singleton","h":"#与其他模式的关系","p":512},{"i":533,"t":"亦称：State","s":"状态模式","u":"/docs/design-patterns/state","h":"","p":532},{"i":535,"t":"状态模式是一种行为设计模式，让你能在一个对象的内部状态变化时改变其行为，使其看上去就像改变了自身所属的类一样。","s":"意图","u":"/docs/design-patterns/state","h":"#意图","p":532},{"i":537,"t":"状态模式与有限状态机的概念紧密相关。 有限状态机。 其主要思想是程序在任意时刻仅可处于几种有限的状态中。在任何一个特定状态中，程序的行为都不相同，且可瞬间从一个状态切换到另一个状态。不过，根据当前状态，程序可能会切换到另外一种状态，也可能会保持当前状态不变。这些数量有限且预先定义的状态切换规则被称为转移。 你还可将该方法应用在对象上。假如你有一个 文档 Document 类。文档可能会处于 草稿 Draft、审阅中 Moderation 和 已发布 Published 三种状态中的一种。文档的 publish 发布方法在不同状态下的行为略有不同： 处于 草稿 状态时，它会将文档转移到审阅中状态。 处于 审阅中 状态时，如果当前用户是管理员，它会公开发布文档。 处于 已发布 状态时，它不会进行任何操作。 文档对象的全部状态和转移。 状态机通常由众多条件运算符 (if 或 switch) 实现，可根据对象的当前状态选择相应的行为。“状态”通常只是对象中的一组成员变量值。即使你之前从未听说过有限状态机，你也很可能已经实现过状态模式。下面的代码应该能帮助你回忆起来。 class Document is field state: string // …… method publish() is switch (state) \"draft\": state = \"moderation\" break \"moderation\": if (currentUser.role == \"admin\") state = \"published\" break \"published\": // 什么也不做。 break // …… 当我们逐步在 文档 类中添加更多状态和依赖于状态的行为后，基于条件语句的状态机就会暴露其最大的弱点。为了能根据当前状态选择完成相应行为的方法，绝大部分方法中会包含复杂的条件语句。修改其转换逻辑可能会涉及到修改所有方法中的状态条件语句，导致代码的维护工作非常艰难。 这个问题会随着项目进行变得越发严重。我们很难在设计阶段预测到所有可能的状态和转换。随着时间推移，最初仅包含有限条件语句的简洁状态机可能会变成臃肿的一团乱麻。","s":"问题","u":"/docs/design-patterns/state","h":"#问题","p":532},{"i":539,"t":"状态模式建议为对象的所有可能状态新建一个类，然后将所有状态的对应行为抽取到这些类中。 原始对象被称为上下文 (context)，它并不会自行实现所有行为，而是会保存一个指向表示当前状态的状态对象的引用，且将所有与状态相关的工作委派给该对象。 文档将工作委派给一个状态对象。 如需将上下文转换为另外一种状态，则需将当前活动的状态对象替换为另外一个代表新状态的对象。采用这种方式是有前提的：所有状态类都必须遵循同样的接口，而且上下文必须仅通过接口与这些对象进行交互。 这个结构可能看上去与策略模式相似，但有一个关键性的不同——在状态模式中，特定状态知道其他所有状态的存在，且能触发从一个状态到另一个状态的转换；策略则几乎完全不知道其他策略的存在。","s":"解决方案","u":"/docs/design-patterns/state","h":"#解决方案","p":532},{"i":541,"t":"智能手机的按键和开关会根据设备当前状态完成不同行为： 当手机处于解锁状态时，按下按键将执行各种功能。 当手机处于锁定状态时，按下任何按键都将解锁屏幕。 当手机电量不足时，按下任何按键都将显示充电页面。","s":"真实世界类比","u":"/docs/design-patterns/state","h":"#真实世界类比","p":532},{"i":543,"t":"上下文 (Context) 保存了对于一个具体状态对象的引用，并会将所有与该状态相关的工作委派给它。上下文通过状态接口与状态对象交互，且会提供一个设置器用于传递新的状态对象。 状态 (State) 接口会声明特定于状态的方法。这些方法应能被其他所有具体状态所理解，因为你不希望某些状态所拥有的方法永远不会被调用。 具体状态 (Concrete States) 会自行实现特定于状态的方法。为了避免多个状态中包含相似代码，你可以提供一个封装有部分通用行为的中间抽象类。 状态对象可存储对于上下文对象的反向引用。状态可以通过该引用从上下文处获取所需信息，并且能触发状态转移。 上下文和具体状态都可以设置上下文的下个状态，并可通过替换连接到上下文的状态对象来完成实际的状态转换。","s":"状态模式结构","u":"/docs/design-patterns/state","h":"#状态模式结构","p":532},{"i":545,"t":"在本例中，状态模式将根据当前回放状态，让媒体播放器中的相同控件完成不同的行为。 使用状态对象更改对象行为的示例。 播放器的主要对象总是会连接到一个负责播放器绝大部分工作的状态对象中。部分操作会更换播放器当前的状态对象，以此改变播放器对于用户互动所作出的反应。 // 音频播放器（Audio­Player）类即为上下文。它还会维护指向状态类实例的引用， // 该状态类则用于表示音频播放器当前的状态。 class AudioPlayer is field state: State field UI, volume, playlist, currentSong constructor AudioPlayer() is this.state = new ReadyState(this) // 上下文会将处理用户输入的工作委派给状态对象。由于每个状态都以不 // 同的方式处理输入，其结果自然将依赖于当前所处的状态。 UI = new UserInterface() UI.lockButton.onClick(this.clickLock) UI.playButton.onClick(this.clickPlay) UI.nextButton.onClick(this.clickNext) UI.prevButton.onClick(this.clickPrevious) // 其他对象必须能切换音频播放器当前所处的状态。 method changeState(state: State) is this.state = state // UI 方法会将执行工作委派给当前状态。 method clickLock() is state.clickLock() method clickPlay() is state.clickPlay() method clickNext() is state.clickNext() method clickPrevious() is state.clickPrevious() // 状态可调用上下文的一些服务方法。 method startPlayback() is // …… method stopPlayback() is // …… method nextSong() is // …… method previousSong() is // …… method fastForward(time) is // …… method rewind(time) is // …… // 所有具体状态类都必须实现状态基类声明的方法，并提供反向引用指向与状态相 // 关的上下文对象。状态可使用反向引用将上下文转换为另一个状态。 abstract class State is protected field player: AudioPlayer // 上下文将自身传递给状态构造函数。这可帮助状态在需要时获取一些有用的 // 上下文数据。 constructor State(player) is this.player = player abstract method clickLock() abstract method clickPlay() abstract method clickNext() abstract method clickPrevious() // 具体状态会实现与上下文状态相关的多种行为。 class LockedState extends State is // 当你解锁一个锁定的播放器时，它可能处于两种状态之一。 method clickLock() is if (player.playing) player.changeState(new PlayingState(player)) else player.changeState(new ReadyState(player)) method clickPlay() is // 已锁定，什么也不做。 method clickNext() is // 已锁定，什么也不做。 method clickPrevious() is // 已锁定，什么也不做。 // 它们还可在上下文中触发状态转换。 class ReadyState extends State is method clickLock() is player.changeState(new LockedState(player)) method clickPlay() is player.startPlayback() player.changeState(new PlayingState(player)) method clickNext() is player.nextSong() method clickPrevious() is player.previousSong() class PlayingState extends State is method clickLock() is player.changeState(new LockedState(player)) method clickPlay() is player.stopPlayback() player.changeState(new ReadyState(player)) method clickNext() is if (event.doubleclick) player.nextSong() else player.fastForward(5) method clickPrevious() is if (event.doubleclick) player.previous() else player.rewind(5)","s":"伪代码","u":"/docs/design-patterns/state","h":"#伪代码","p":532},{"i":547,"t":"如果对象需要根据自身当前状态进行不同行为，同时状态的数量非常多且与状态相关的代码会频繁变更的话，可使用状态模式。 模式建议你将所有特定于状态的代码抽取到一组独立的类中。这样一来，你可以在独立于其他状态的情况下添加新状态或修改已有状态，从而减少维护成本。 如果某个类需要根据成员变量的当前值改变自身行为，从而需要使用大量的条件语句时，可使用该模式。 状态模式会将这些条件语句的分支抽取到相应状态类的方法中。同时，你还可以清除主要类中与特定状态相关的临时成员变量和帮手方法代码。 当相似状态和基于条件的状态机转换中存在许多重复代码时，可使用状态模式。 状态模式让你能够生成状态类层次结构，通过将公用代码抽取到抽象基类中来减少重复。 实现方式 确定哪些类是上下文。它可能是包含依赖于状态的代码的已有类；如果特定于状态的代码分散在多个类中，那么它可能是一个新的类。 声明状态接口。虽然你可能会需要完全复制上下文中声明的所有方法，但最好是仅把关注点放在那些可能包含特定于状态的行为的方法上。 为每个实际状态创建一个继承于状态接口的类。然后检查上下文中的方法并将与特定状态相关的所有代码抽取到新建的类中。在将代码移动到状态类的过程中，你可能会发现它依赖于上下文中的一些私有成员。你可以采用以下几种变通方式：- 将这些成员变量或方法设为公有。- 将需要抽取的上下文行为更改为上下文中的公有方法，然后在状态类中调用。这种方式简陋却便捷，你可以稍后再对其进行修补。- 将状态类嵌套在上下文类中。这种方式需要你所使用的编程语言支持嵌套类。 在上下文类中添加一个状态接口类型的引用成员变量，以及一个用于修改该成员变量值的公有设置器。 再次检查上下文中的方法，将空的条件语句替换为相应的状态对象方法。 为切换上下文状态，你需要创建某个状态类实例并将其传递给上下文。你可以在上下文、各种状态或客户端中完成这项工作。无论在何处完成这项工作，该类都将依赖于其所实例化的具体类。","s":"状态模式适合应用场景","u":"/docs/design-patterns/state","h":"#状态模式适合应用场景","p":532},{"i":549,"t":"✔️ 单一职责原则。将与特定状态相关的代码放在单独的类中。 ✔️ 开闭原则。无需修改已有状态类和上下文就能引入新状态。 ✔️ 通过消除臃肿的状态机条件语句简化上下文代码。 ❌ 如果状态机只有很少的几个状态，或者很少发生改变，那么应用该模式可能会显得小题大作。","s":"状态模式优缺点","u":"/docs/design-patterns/state","h":"#状态模式优缺点","p":532},{"i":551,"t":"桥接模式、状态模式和策略模式 (在某种程度上包括适配器模式) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。 状态可被视为策略的扩展。两者都基于组合机制：它们都通过将部分工作委派给“帮手”对象来改变其在不同情景下的行为。策略使得这些对象相互之间完全独立，它们不知道其他对象的存在。但状态模式没有限制具体状态之间的依赖，且允许它们自行改变在不同情景下的状态。","s":"与其他模式的关系","u":"/docs/design-patterns/state","h":"#与其他模式的关系","p":532},{"i":553,"t":"亦称：Strategy","s":"策略模式","u":"/docs/design-patterns/strategy","h":"","p":552},{"i":555,"t":"策略模式是一种行为设计模式，它能让你定义一系列算法，并将每种算法分别放入独立的类中，以使算法的对象能够相互替换。","s":"意图","u":"/docs/design-patterns/strategy","h":"#意图","p":552},{"i":557,"t":"一天，你打算为游客们创建一款导游程序。该程序的核心功能是提供美观的地图，以帮助用户在任何城市中快速定位。 用户期待的程序新功能是自动路线规划：他们希望输入地址后就能在地图上看到前往目的地的最快路线。 程序的首个版本只能规划公路路线。驾车旅行的人们对此非常满意。但很显然，并非所有人都会在度假时开车。因此你在下次更新时添加了规划步行路线的功能。此后，你又添加了规划公共交通路线的功能。 而这只是个开始。不久后，你又要为骑行者规划路线。又过了一段时间，你又要为游览城市中的所有景点规划路线。 导游代码将变得非常臃肿。 尽管从商业角度来看，这款应用非常成功，但其技术部分却让你非常头疼：每次添加新的路线规划算法后，导游应用中主要类的体积就会增加一倍。终于在某个时候，你觉得自己没法继续维护这堆代码了。 无论是修复简单缺陷还是微调街道权重，对某个算法进行任何修改都会影响整个类，从而增加在已有正常运行代码中引入错误的风险。 此外，团队合作将变得低效。如果你在应用成功发布后招募了团队成员，他们会抱怨在合并冲突的工作上花费了太多时间。在实现新功能的过程中，你的团队需要修改同一个巨大的类，这样他们所编写的代码相互之间就可能会出现冲突。","s":"问题","u":"/docs/design-patterns/strategy","h":"#问题","p":552},{"i":559,"t":"策略模式建议找出负责用许多不同方式完成特定任务的类，然后将其中的算法抽取到一组被称为策略的独立类中。 名为上下文的原始类必须包含一个成员变量来存储对于每种策略的引用。上下文并不执行任务，而是将工作委派给已连接的策略对象。 上下文不负责选择符合任务需要的算法——客户端会将所需策略传递给上下文。实际上，上下文并不十分了解策略，它会通过同样的通用接口与所有策略进行交互，而该接口只需暴露一个方法来触发所选策略中封装的算法即可。 因此，上下文可独立于具体策略。这样你就可在不修改上下文代码或其他策略的情况下添加新算法或修改已有算法了。 路线规划策略。 在导游应用中，每个路线规划算法都可被抽取到只有一个 build­Route 生成路线方法的独立类中。该方法接收起点和终点作为参数，并返回路线中途点的集合。 即使传递给每个路径规划类的参数一模一样，其所创建的路线也可能完全不同。主要导游类的主要工作是在地图上渲染一系列中途点，不会在意如何选择算法。该类中还有一个用于切换当前路径规划策略的方法，因此客户端 (例如用户界面中的按钮) 可用其他策略替换当前选择的路径规划行为。","s":"解决方案","u":"/docs/design-patterns/strategy","h":"#解决方案","p":552},{"i":561,"t":"各种前往机场的出行策略 假如你需要前往机场。你可以选择乘坐公共汽车、预约出租车或骑自行车。这些就是你的出行策略。你可以根据预算或时间等因素来选择其中一种策略。","s":"真实世界类比","u":"/docs/design-patterns/strategy","h":"#真实世界类比","p":552},{"i":563,"t":"上下文 (Context) 维护指向具体策略的引用，且仅通过策略接口与该对象进行交流。 策略 (Strategy) 接口是所有具体策略的通用接口，它声明了一个上下文用于执行策略的方法。 具体策略 (Concrete Strategies) 实现了上下文所用算法的各种不同变体。 当上下文需要运行算法时，它会在其已连接的策略对象上调用执行方法。上下文不清楚其所涉及的策略类型与算法的执行方式。 客户端 (Client) 会创建一个特定策略对象并将其传递给上下文。上下文则会提供一个设置器以便客户端在运行时替换相关联的策略。","s":"策略模式结构","u":"/docs/design-patterns/strategy","h":"#策略模式结构","p":552},{"i":565,"t":"在本例中，上下文使用了多个策略来执行不同的计算操作。 // 策略接口声明了某个算法各个不同版本间所共有的操作。上下文会使用该接口来 // 调用有具体策略定义的算法。 interface Strategy is method execute(a, b) // 具体策略会在遵循策略基础接口的情况下实现算法。该接口实现了它们在上下文 // 中的互换性。 class ConcreteStrategyAdd implements Strategy is method execute(a, b) is return a + b class ConcreteStrategySubtract implements Strategy is method execute(a, b) is return a - b class ConcreteStrategyMultiply implements Strategy is method execute(a, b) is return a * b // 上下文定义了客户端关注的接口。 class Context is // 上下文会维护指向某个策略对象的引用。上下文不知晓策略的具体类。上下 // 文必须通过策略接口来与所有策略进行交互。 private strategy: Strategy // 上下文通常会通过构造函数来接收策略对象，同时还提供设置器以便在运行 // 时切换策略。 method setStrategy(Strategy strategy) is this.strategy = strategy // 上下文会将一些工作委派给策略对象，而不是自行实现不同版本的算法。 method executeStrategy(int a, int b) is return strategy.execute(a, b) // 客户端代码会选择具体策略并将其传递给上下文。客户端必须知晓策略之间的差 // 异，才能做出正确的选择。 class ExampleApplication is method main() is 创建上下文对象。 读取第一个数。 读取最后一个数。 从用户输入中读取期望进行的行为。 if (action == addition) then context.setStrategy(new ConcreteStrategyAdd()) if (action == subtraction) then context.setStrategy(new ConcreteStrategySubtract()) if (action == multiplication) then context.setStrategy(new ConcreteStrategyMultiply()) result = context.executeStrategy(First number, Second number) 打印结果。","s":"伪代码","u":"/docs/design-patterns/strategy","h":"#伪代码","p":552},{"i":567,"t":"当你想使用对象中各种不同的算法变体，并希望能在运行时切换算法时，可使用策略模式。 策略模式让你能够将对象关联至可以不同方式执行特定子任务的不同子对象，从而以间接方式在运行时更改对象行为。 当你有许多仅在执行某些行为时略有不同的相似类时，可使用策略模式。 策略模式让你能将不同行为抽取到一个独立类层次结构中，并将原始类组合成同一个，从而减少重复代码。 如果算法在上下文的逻辑中不是特别重要，使用该模式能将类的业务逻辑与其算法实现细节隔离开来。 策略模式让你能将各种算法的代码、内部数据和依赖关系与其他代码隔离开来。不同客户端可通过一个简单接口执行算法，并能在运行时进行切换。 当类中使用了复杂条件运算符以在同一算法的不同变体中切换时，可使用该模式。 策略模式将所有继承自同样接口的算法抽取到独立类中，因此不再需要条件语句。原始对象并不实现所有算法的变体，而是将执行工作委派给其中的一个独立算法对象。 实现方式 从上下文类中找出修改频率较高的算法 (也可能是用于在运行时选择某个算法变体的复杂条件运算符)。 声明该算法所有变体的通用策略接口。 将算法逐一抽取到各自的类中，它们都必须实现策略接口。 在上下文类中添加一个成员变量用于保存对于策略对象的引用。然后提供设置器以修改该成员变量。上下文仅可通过策略接口同策略对象进行交互，如有需要还可定义一个接口来让策略访问其数据。 客户端必须将上下文类与相应策略进行关联，使上下文可以预期的方式完成其主要工作。","s":"策略模式适合应用场景","u":"/docs/design-patterns/strategy","h":"#策略模式适合应用场景","p":552},{"i":569,"t":"✔️ 你可以在运行时切换对象内的算法。 ✔️ 你可以将算法的实现和使用算法的代码隔离开来。 ✔️ 你可以使用组合来代替继承。 ✔️ 开闭原则。你无需对上下文进行修改就能够引入新的策略。 ❌ 如果你的算法极少发生改变，那么没有任何理由引入新的类和接口。使用该模式只会让程序过于复杂。 ❌ 客户端必须知晓策略间的不同——它需要选择合适的策略。 ❌ 许多现代编程语言支持函数类型功能，允许你在一组匿名函数中实现不同版本的算法。这样，你使用这些函数的方式就和使用策略对象时完全相同，无需借助额外的类和接口来保持代码简洁。","s":"策略模式优缺点","u":"/docs/design-patterns/strategy","h":"#策略模式优缺点","p":552},{"i":571,"t":"桥接模式、状态模式和策略模式 (在某种程度上包括适配器模式) 模式的接口非常相似。实际上，它们都基于组合模式——即将工作委派给其他对象，不过也各自解决了不同的问题。模式并不只是以特定方式组织代码的配方，你还可以使用它们来和其他开发者讨论模式所解决的问题。 命令模式和策略看上去很像，因为两者都能通过某些行为来参数化对象。但是，它们的意图有非常大的不同。 你可以使用命令来将任何操作转换为对象。操作的参数将成为对象的成员变量。你可以通过转换来延迟操作的执行、将操作放入队列、保存历史命令或者向远程服务发送命令等。 另一方面，策略通常可用于描述完成某件事的不同方式，让你能够在同一个上下文类中切换算法。 装饰模式可让你更改对象的外表，策略则让你能够改变其本质。 模板方法模式基于继承机制：它允许你通过扩展子类中的部分内容来改变部分算法。策略基于组合机制：你可以通过对相应行为提供不同的策略来改变对象的部分行为。模板方法在类层次上运作，因此它是静态的。策略在对象层次上运作，因此允许在运行时切换行为。 状态可被视为策略的扩展。两者都基于组合机制：它们都通过将部分工作委派给“帮手”对象来改变其在不同情景下的行为。策略使得这些对象相互之间完全独立，它们不知道其他对象的存在。但状态模式没有限制具体状态之间的依赖，且允许它们自行改变在不同情景下的状态。","s":"与其他模式的关系","u":"/docs/design-patterns/strategy","h":"#与其他模式的关系","p":552},{"i":573,"t":"结构型模式介绍如何将对象和类组装成较大的结构，并同时保持结构的灵活和高效。","s":"结构型模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":575,"t":"让接口不兼容的对象能够相互合作。","s":"📄️ 适配器模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":577,"t":"可将一个大类或一系列紧密相关的类拆分为抽象和实现两个独立的层次结构，从而能在开发时分别使用。","s":"📄️ 桥接模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":579,"t":"你可以使用它将对象组合成树状结构，并且能像使用独立对象一样使用它们。","s":"📄️ 组合模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":581,"t":"允许你通过将对象放入包含行为的特殊封装对象中来为原对象绑定新的行为。","s":"📄️ 装饰模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":583,"t":"能为程序库、框架或其他复杂类提供一个简单的接口。","s":"📄️ 外观模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":585,"t":"摒弃了在每个对象中保存所有数据的方式，通过共享多个对象所共有的相同状态，让你能在有限的内存容量中载入更多对象。","s":"📄️ 享元模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":587,"t":"让你能够提供对象的替代品或其占位符。代理控制着对于原对象的访问，并允许在将请求提交给对象前后进行一些处理。","s":"📄️ 代理模式","u":"/docs/design-patterns/structural-patterns/","h":"","p":572},{"i":589,"t":"亦称：Template Method","s":"模板方法模式","u":"/docs/design-patterns/template-method","h":"","p":588},{"i":591,"t":"模板方法模式是一种行为设计模式，它在超类中定义了一个算法的框架，允许子类在不修改结构的情况下重写算法的特定步骤。","s":"意图","u":"/docs/design-patterns/template-method","h":"#意图","p":588},{"i":593,"t":"假如你正在开发一款分析公司文档的数据挖掘程序。用户需要向程序输入各种格式 (PDF、DOC 或 CSV) 的文档，程序则会试图从这些文件中抽取有意义的数据，并以统一的格式将其返回给用户。 该程序的首个版本仅支持 DOC 文件。在接下来的一个版本中，程序能够支持 CSV 文件。一个月后，你“教会”了程序从 PDF 文件中抽取数据。 数据挖掘类中包含许多重复代码。 一段时间后，你发现这三个类中包含许多相似代码。尽管这些类处理不同数据格式的代码完全不同，但数据处理和分析的代码却几乎完全一样。如果能在保持算法结构完整的情况下去除重复代码，这难道不是一件很棒的事情吗？ 还有另一个与使用这些类的客户端代码相关的问题：客户端代码中包含许多条件语句，以根据不同的处理对象类型选择合适的处理过程。如果所有处理数据的类都拥有相同的接口或基类，那么你就可以去除客户端代码中的条件语句，转而使用多态机制来在处理对象上调用函数。","s":"问题","u":"/docs/design-patterns/template-method","h":"#问题","p":588},{"i":595,"t":"模板方法模式建议将算法分解为一系列步骤，然后将这些步骤改写为方法，最后在“模板方法”中依次调用这些方法。步骤可以是 抽象 的，也可以有一些默认的实现。为了能够使用算法，客户端需要自行提供子类并实现所有的抽象步骤。如有必要还需重写一些步骤 (但这一步中不包括模板方法自身)。 让我们考虑如何在数据挖掘应用中实现上述方案。我们可为图中的三个解析算法创建一个基类，该类将定义调用了一系列不同文档处理步骤的模板方法。 模板方法将算法分解为步骤，并允许子类重写这些步骤，而非重写实际的模板方法。 首先，我们将所有步骤声明为 抽象 类型，强制要求子类自行实现这些方法。在我们的例子中，子类中已有所有必要的实现，因此我们只需调整这些方法的签名，使之与超类的方法匹配即可。 现在，让我们看看如何去除重复代码。对于不同的数据格式，打开和关闭文件以及抽取和解析数据的代码都不同，因此无需修改这些方法。但分析原始数据和生成报告等其他步骤的实现方式非常相似，因此可将其提取到基类中，以让子类共享这些代码。 正如你所看到的那样，我们有两种类型的步骤： 抽象步骤必须由各个子类来实现 可选步骤已有一些默认实现，但仍可在需要时进行重写 还有另一种名为钩子的步骤。钩子是内容为空的可选步骤。即使不重写钩子，模板方法也能工作。钩子通常放置在算法重要步骤的前后，为子类提供额外的算法扩展点。","s":"解决方案","u":"/docs/design-patterns/template-method","h":"#解决方案","p":588},{"i":597,"t":"可对典型的建筑方案进行微调以更好地满足客户需求。 模板方法可用于建造大量房屋。标准房屋建造方案中可提供几个扩展点，允许潜在房屋业主调整成品房屋的部分细节。 每个建造步骤 (例如打地基、建造框架、建造墙壁和安装水电管线等) 都能进行微调，这使得成品房屋会略有不同。","s":"真实世界类比","u":"/docs/design-patterns/template-method","h":"#真实世界类比","p":588},{"i":599,"t":"抽象类 (Abstract­Class) 会声明作为算法步骤的方法，以及依次调用它们的实际模板方法。算法步骤可以被声明为 抽象 类型，也可以提供一些默认实现。 具体类 (Concrete­Class) 可以重写所有步骤，但不能重写模板方法自身。","s":"模板方法模式结构","u":"/docs/design-patterns/template-method","h":"#模板方法模式结构","p":588},{"i":601,"t":"本例中的模板方法模式为一款简单策略游戏中人工智能的不同分支提供“框架”。 一款简单游戏的 AI 类。 游戏中所有的种族都有几乎同类的单位和建筑。因此你可以在不同的种族上复用相同的 AI 结构，同时还需要具备重写一些细节的能力。通过这种方式，你可以重写半兽人的 AI 使其更富攻击性，也可以让人类侧重防守，还可以禁止怪物建造建筑。在游戏中新增种族需要创建新的 AI 子类，还需要重写 AI 基类中所声明的默认方法。 // 抽象类定义了一个模板方法，其中通常会包含某个由抽象原语操作调用组成的算 // 法框架。具体子类会实现这些操作，但是不会对模板方法做出修改。 class GameAI is // 模板方法定义了某个算法的框架。 method turn() is collectResources() buildStructures() buildUnits() attack() // 某些步骤可在基类中直接实现。 method collectResources() is foreach (s in this.builtStructures) do s.collect() // 某些可定义为抽象类型。 abstract method buildStructures() abstract method buildUnits() // 一个类可包含多个模板方法。 method attack() is enemy = closestEnemy() if (enemy == null) sendScouts(map.center) else sendWarriors(enemy.position) abstract method sendScouts(position) abstract method sendWarriors(position) // 具体类必须实现基类中的所有抽象操作，但是它们不能重写模板方法自身。 class OrcsAI extends GameAI is method buildStructures() is if (there are some resources) then // 建造农场，接着是谷仓，然后是要塞。 method buildUnits() is if (there are plenty of resources) then if (there are no scouts) // 建造苦工，将其加入侦查编组。 else // 建造兽族步兵，将其加入战士编组。 // …… method sendScouts(position) is if (scouts.length > 0) then // 将侦查编组送到指定位置。 method sendWarriors(position) is if (warriors.length > 5) then // 将战斗编组送到指定位置。 // 子类可以重写部分默认的操作。 class MonstersAI extends GameAI is method collectResources() is // 怪物不会采集资源。 method buildStructures() is // 怪物不会建造建筑。 method buildUnits() is // 怪物不会建造单位。","s":"伪代码","u":"/docs/design-patterns/template-method","h":"#伪代码","p":588},{"i":603,"t":"当你只希望客户端扩展某个特定算法步骤，而不是整个算法或其结构时，可使用模板方法模式。 模板方法将整个算法转换为一系列独立的步骤，以便子类能对其进行扩展，同时还可让超类中所定义的结构保持完整。 当多个类的算法除一些细微不同之外几乎完全一样时，你可使用该模式。但其后果就是，只要算法发生变化，你就可能需要修改所有的类。 在将算法转换为模板方法时，你可将相似的实现步骤提取到超类中以去除重复代码。子类间各不同的代码可继续保留在子类中。 实现方式 分析目标算法，确定能否将其分解为多个步骤。从所有子类的角度出发，考虑哪些步骤能够通用，哪些步骤各不相同。 创建抽象基类并声明一个模板方法和代表算法步骤的一系列抽象方法。在模板方法中根据算法结构依次调用相应步骤。可用 final 最终修饰模板方法以防止子类对其进行重写。 虽然可将所有步骤全都设为抽象类型，但默认实现可能会给部分步骤带来好处，因为子类无需实现那些方法。 可考虑在算法的关键步骤之间添加钩子。 为每个算法变体新建一个具体子类，它必须实现所有的抽象步骤，也可以重写部分可选步骤。","s":"模板方法模式适合应用场景","u":"/docs/design-patterns/template-method","h":"#模板方法模式适合应用场景","p":588},{"i":605,"t":"✔️ 你可仅允许客户端重写一个大型算法中的特定部分，使得算法其他部分修改对其所造成的影响减小。 ✔️ 你可将重复代码提取到一个超类中。 ❌ 部分客户端可能会受到算法框架的限制。 ❌ 通过子类抑制默认步骤实现可能会导致违反里氏替换原则。 ❌ 模板方法中的步骤越多，其维护工作就可能会越困难。","s":"模板方法模式优缺点","u":"/docs/design-patterns/template-method","h":"#模板方法模式优缺点","p":588},{"i":607,"t":"工厂方法模式是模板方法模式的一种特殊形式。同时，工厂方法可以作为一个大型模板方法中的一个步骤。 模板方法基于继承机制：它允许你通过扩展子类中的部分内容来改变部分算法。策略模式基于组合机制：你可以通过对相应行为提供不同的策略来改变对象的部分行为。模板方法在类层次上运作，因此它是静态的。策略在对象层次上运作，因此允许在运行时切换行为。","s":"与其他模式的关系","u":"/docs/design-patterns/template-method","h":"#与其他模式的关系","p":588},{"i":609,"t":"亦称：Visitor","s":"访问者模式","u":"/docs/design-patterns/visitor","h":"","p":608},{"i":611,"t":"访问者模式是一种行为设计模式，它能将算法与其所作用的对象隔离开来。","s":"意图","u":"/docs/design-patterns/visitor","h":"#意图","p":608},{"i":613,"t":"假如你的团队开发了一款能够使用巨型图像中地理信息的应用程序。图像中的每个节点既能代表复杂实体 (例如一座城市)，也能代表更精细的对象 (例如工业区和旅游景点等)。如果节点代表的真实对象之间存在公路，那么这些节点就会相互连接。在程序内部，每个节点的类型都由其所属的类来表示，每个特定的节点则是一个对象。 将图像导出为 XML。 一段时间后，你接到了实现将图像导出到 XML 文件中的任务。这些工作最初看上去非常简单。你计划为每个节点类添加导出函数，然后递归执行图像中每个节点的导出函数。解决方案简单且优雅：使用多态机制可以让导出方法的调用代码不会和具体的节点类相耦合。 但你不太走运，系统架构师拒绝批准对已有节点类进行修改。他认为这些代码已经是产品了，不想冒险对其进行修改，因为修改可能会引入潜在的缺陷。 所有节点的类中都必须添加导出至 XML 文件的方法，但如果在修改代码的过程中引入了任何缺陷，那么整个程序都会面临风险。 此外，他还质疑在节点类中包含导出 XML 文件的代码是否有意义。这些类的主要工作是处理地理数据。导出 XML 文件的代码放在这里并不合适。 还有另一个原因，那就是在此项任务完成后，营销部门很有可能会要求程序提供导出其他类型文件的功能，或者提出其他奇怪的要求。这样你很可能会被迫再次修改这些重要但脆弱的类。","s":"问题","u":"/docs/design-patterns/visitor","h":"#问题","p":608},{"i":615,"t":"访问者模式建议将新行为放入一个名为访问者的独立类中，而不是试图将其整合到已有类中。现在，需要执行操作的原始对象将作为参数被传递给访问者中的方法，让方法能访问对象所包含的一切必要数据。 如果现在该操作能在不同类的对象上执行会怎么样呢？比如在我们的示例中，各节点类导出 XML 文件的实际实现很可能会稍有不同。因此，访问者类可以定义一组 (而不是一个) 方法，且每个方法可接收不同类型的参数，如下所示： class ExportVisitor implements Visitor is method doForCity(City c) { …… } method doForIndustry(Industry f) { …… } method doForSightSeeing(SightSeeing ss) { …… } // …… 但我们究竟应该如何调用这些方法 (尤其是在处理整个图像方面) 呢？这些方法的签名各不相同，因此我们不能使用多态机制。为了可以挑选出能够处理特定对象的访问者方法，我们需要对它的类进行检查。这是不是听上去像个噩梦呢？ foreach (Node node in graph) if (node instanceof City) exportVisitor.doForCity((City) node) if (node instanceof Industry) exportVisitor.doForIndustry((Industry) node) // …… } 你可能会问，我们为什么不使用方法重载呢？就是使用相同的方法名称，但它们的参数不同。不幸的是，即使我们的编程语言 (例如 Java 和 C#) 支持重载也不行。由于我们无法提前知晓节点对象所属的类，所以重载机制无法执行正确的方法。方法会将 节点 基类作为输入参数的默认类型。 但是，访问者模式可以解决这个问题。它使用了一种名为双分派的技巧，不使用累赘的条件语句也可下执行正确的方法。与其让客户端来选择调用正确版本的方法，不如将选择权委派给作为参数传递给访问者的对象。由于该对象知晓其自身的类，因此能更自然地在访问者中选出正确的方法。它们会“接收”一个访问者并告诉其应执行的访问者方法。 // 客户端代码 foreach (Node node in graph) node.accept(exportVisitor) // 城市 class City is method accept(Visitor v) is v.doForCity(this) // …… // 工业区 class Industry is method accept(Visitor v) is v.doForIndustry(this) // …… 我承认最终还是修改了节点类，但毕竟改动很小，且使得我们能够在后续进一步添加行为时无需再次修改代码。 现在，如果我们抽取出所有访问者的通用接口，所有已有的节点都能与我们在程序中引入的任何访问者交互。如果需要引入与节点相关的某个行为，你只需要实现一个新的访问者类即可。","s":"解决方案","u":"/docs/design-patterns/visitor","h":"#解决方案","p":608},{"i":617,"t":"优秀的保险代理人总能为不同类型的团体提供不同的保单。 假如有这样一位非常希望赢得新客户的资深保险代理人。他可以拜访街区中的每栋楼，尝试向每个路人推销保险。所以，根据大楼内组织类型的不同，他可以提供专门的保单： 如果建筑是居民楼，他会推销医疗保险。 如果建筑是银行，他会推销失窃保险。 如果建筑是咖啡厅，他会推销火灾和洪水保险。","s":"真实世界类比","u":"/docs/design-patterns/visitor","h":"#真实世界类比","p":608},{"i":619,"t":"访问者 (Visitor) 接口声明了一系列以对象结构的具体元素为参数的访问者方法。如果编程语言支持重载，这些方法的名称可以是相同的，但是其参数一定是不同的。 具体访问者 (Concrete Visitor) 会为不同的具体元素类实现相同行为的几个不同版本。 元素 (Element) 接口声明了一个方法来“接收”访问者。该方法必须有一个参数被声明为访问者接口类型。 具体元素 (Concrete Element) 必须实现接收方法。该方法的目的是根据当前元素类将其调用重定向到相应访问者的方法。请注意，即使元素基类实现了该方法，所有子类都必须对其进行重写并调用访问者对象中的合适方法。 客户端 (Client) 通常会作为集合或其他复杂对象 (例如一个组合树) 的代表。客户端通常不知晓所有的具体元素类，因为它们会通过抽象接口与集合中的对象进行交互。","s":"访问者模式结构","u":"/docs/design-patterns/visitor","h":"#访问者模式结构","p":608},{"i":621,"t":"在本例中，访问者模式为几何图像层次结构添加了对于 XML 文件导出功能的支持。 通过访问者对象将各种类型的对象导出为 XML 格式文件。 // 元素接口声明了一个 `accept（接收）` 方法，它会将访问者基础接口作为一个参 // 数。 interface Shape is method move(x, y) method draw() method accept(v: Visitor) // 每个具体元素类都必须以特定方式实现 `accept` 方法，使其能调用相应元素类的 // 访问者方法。 class Dot implements Shape is // …… // 注意我们正在调用的 `visitDot（访问点）` 方法与当前类的名称相匹配。 // 这样我们能让访问者知晓与其交互的元素类。 method accept(v: Visitor) is v.visitDot(this) class Circle implements Shape is // …… method accept(v: Visitor) is v.visitCircle(this) class Rectangle implements Shape is // …… method accept(v: Visitor) is v.visitRectangle(this) class CompoundShape implements Shape is // …… method accept(v: Visitor) is v.visitCompoundShape(this) // 访问者接口声明了一组与元素类对应的访问方法。访问方法的签名能让访问者准 // 确辨别出与其交互的元素所属的类。 interface Visitor is method visitDot(d: Dot) method visitCircle(c: Circle) method visitRectangle(r: Rectangle) method visitCompoundShape(cs: CompoundShape) // 具体访问者实现了同一算法的多个版本，而且该算法能与所有具体类进行交互。 // // 访问者模式在复杂对象结构（例如组合树）上使用时能发挥最大作用。在这种情 // 况下，它可以存储算法的一些中间状态，并同时在结构中的不同对象上执行访问 // 者方法。这可能会非常有帮助。 class XMLExportVisitor implements Visitor is method visitDot(d: Dot) is // 导出点（dot）的 ID 和中心坐标。 method visitCircle(c: Circle) is // 导出圆（circle）的 ID、中心坐标和半径。 method visitRectangle(r: Rectangle) is // 导出长方形（rectangle）的 ID、左上角坐标、宽和长。 method visitCompoundShape(cs: CompoundShape) is // 导出图形（shape）的 ID 和其子项目的 ID 列表。 // 客户端代码可在不知晓具体类的情况下在一组元素上运行访问者操作。“接收”操 // 作会将调用定位到访问者对象的相应操作上。 class Application is field allShapes: array of Shapes method export() is exportVisitor = new XMLExportVisitor() foreach (shape in allShapes) do shape.accept(exportVisitor)","s":"伪代码","u":"/docs/design-patterns/visitor","h":"#伪代码","p":608},{"i":623,"t":"如果你需要对一个复杂对象结构 (例如对象树) 中的所有元素执行某些操作，可使用访问者模式。 访问者模式通过在访问者对象中为多个目标类提供相同操作的变体，让你能在属于不同类的一组对象上执行同一操作。 可使用访问者模式来清理辅助行为的业务逻辑。 该模式会将所有非主要的行为抽取到一组访问者类中，使得程序的主要类能更专注于主要的工作。 当某个行为仅在类层次结构中的一些类中有意义，而在其他类中没有意义时，可使用该模式。 你可将该行为抽取到单独的访问者类中，只需实现接收相关类的对象作为参数的访问者方法并将其他方法留空即可。 实现方式 在访问者接口中声明一组“访问”方法，分别对应程序中的每个具体元素类。 声明元素接口。如果程序中已有元素类层次接口，可在层次结构基类中添加抽象的“接收”方法。该方法必须接受访问者对象作为参数。 在所有具体元素类中实现接收方法。这些方法必须将调用重定向到当前元素对应的访问者对象中的访问者方法上。 元素类只能通过访问者接口与访问者进行交互。不过访问者必须知晓所有的具体元素类，因为这些类在访问者方法中都被作为参数类型引用。 为每个无法在元素层次结构中实现的行为创建一个具体访问者类并实现所有的访问者方法。你可能会遇到访问者需要访问元素类的部分私有成员变量的情况。在这种情况下，你要么将这些变量或方法设为公有，这将破坏元素的封装；要么将访问者类嵌入到元素类中。后一种方式只有在支持嵌套类的编程语言中才可能实现。 客户端必须创建访问者对象并通过“接收”方法将其传递给元素。","s":"访问者模式适合应用场景","u":"/docs/design-patterns/visitor","h":"#访问者模式适合应用场景","p":608},{"i":625,"t":"✔️ 开闭原则。你可以引入在不同类对象上执行的新行为，且无需对这些类做出修改。 ✔️ 单一职责原则。可将同一行为的不同版本移到同一个类中。 ✔️ 访问者对象可以在与各种对象交互时收集一些有用的信息。当你想要遍历一些复杂的对象结构 (例如对象树)，并在结构中的每个对象上应用访问者时，这些信息可能会有所帮助。 ❌ 每次在元素层次结构中添加或移除一个类时，你都要更新所有的访问者。 ❌ 在访问者同某个元素进行交互时，它们可能没有访问元素私有成员变量和方法的必要权限。","s":"访问者模式优缺点","u":"/docs/design-patterns/visitor","h":"#访问者模式优缺点","p":608},{"i":627,"t":"你可以将访问者模式视为命令模式的加强版本，其对象可对不同类的多种对象执行操作。 你可以使用访问者对整个组合模式树执行操作。 可以同时使用访问者和迭代器模式来遍历复杂数据结构，并对其中的元素执行所需操作，即使这些元素所属的类完全不同。","s":"与其他模式的关系","u":"/docs/design-patterns/visitor","h":"#与其他模式的关系","p":608},{"i":629,"t":"You have just learned the basics of Docusaurus and made some changes to the initial template. Docusaurus has much more to offer! Take a look at versioning and i18n.","s":"Congratulations!","u":"/docs/docusaurus-mdx/docusaurus-tutorial/congratulations","h":"","p":628},{"i":631,"t":"Read the official documentation Modify your site configuration with docusaurus.config.ts Add navbar and footer items with themeConfig Add a custom Design and Layout Add a search bar Find inspirations in the Docusaurus showcase Get involved in the Docusaurus Community","s":"What's next?","u":"/docs/docusaurus-mdx/docusaurus-tutorial/congratulations","h":"#whats-next","p":628},{"i":633,"t":"Docusaurus creates a page for each blog post, but also a blog index page, a tag system, an RSS feed...","s":"Create a Blog Post","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-blog-post","h":"","p":632},{"i":635,"t":"Create a file at blog/2021-02-28-greetings.md: blog/2021-02-28-greetings.md --- slug: greetings title: Greetings! authors: - name: Joel Marcey title: Co-creator of Docusaurus 1 url: https://github.com/JoelMarcey image_url: https://github.com/JoelMarcey.png - name: Sébastien Lorber title: Docusaurus maintainer url: https://sebastienlorber.com image_url: https://github.com/slorber.png tags: [greetings] --- Congratulations, you have made your first post! Feel free to play around and edit this post as much you like. A new blog post is now available at http://localhost:3000/blog/greetings.","s":"Create your first Post","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-blog-post","h":"#create-your-first-post","p":632},{"i":637,"t":"Documents are groups of pages connected through: a sidebar previous/next navigation versioning","s":"Create a Document","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-document","h":"","p":636},{"i":639,"t":"Create a Markdown file at docs/hello.md: docs/hello.md # Hello This is my **first Docusaurus document**! A new document is now available at http://localhost:3000/docs/hello.","s":"Create your first Doc","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-document","h":"#create-your-first-doc","p":636},{"i":641,"t":"Docusaurus automatically creates a sidebar from the docs folder. Add metadata to customize the sidebar label and position: docs/hello.md --- sidebar_label: 'Hi!' sidebar_position: 3 --- # Hello This is my **first Docusaurus document**! It is also possible to create your sidebar explicitly in sidebars.js: sidebars.js export default { tutorialSidebar: [ 'intro', // highlight-next-line 'hello', { type: 'category', label: 'Tutorial', items: ['tutorial-basics/create-a-document'], }, ], };","s":"Configure the Sidebar","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-document","h":"#configure-the-sidebar","p":636},{"i":643,"t":"Add Markdown or React files to src/pages to create a standalone page: src/pages/index.js → localhost:3000/ src/pages/foo.md → localhost:3000/foo src/pages/foo/bar.js → localhost:3000/foo/bar","s":"Create a Page","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-page","h":"","p":642},{"i":645,"t":"Create a file at src/pages/my-react-page.js: src/pages/my-react-page.js import React from 'react'; import Layout from '@theme/Layout'; export default function MyReactPage() { return ( <Layout> <h1>My React page</h1> <p>This is a React page</p> </Layout> ); } A new page is now available at http://localhost:3000/my-react-page.","s":"Create your first React Page","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-page","h":"#create-your-first-react-page","p":642},{"i":647,"t":"Create a file at src/pages/my-markdown-page.md: src/pages/my-markdown-page.md # My Markdown page This is a Markdown page A new page is now available at http://localhost:3000/my-markdown-page.","s":"Create your first Markdown Page","u":"/docs/docusaurus-mdx/docusaurus-tutorial/create-a-page","h":"#create-your-first-markdown-page","p":642},{"i":649,"t":"Docusaurus is a static-site-generator (also called Jamstack). It builds your site as simple static HTML, JavaScript and CSS files.","s":"Deploy your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/deploy-your-site","h":"","p":648},{"i":651,"t":"Build your site for production: npm run build The static files are generated in the build folder.","s":"Build your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/deploy-your-site","h":"#build-your-site","p":648},{"i":652,"t":"Test your production build locally: npm run serve The build folder is now served at http://localhost:3000/. You can now deploy the build folder almost anywhere easily, for free or very small cost (read the Deployment Guide).","s":"Deploy your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/deploy-your-site","h":"#deploy-your-site-1","p":648},{"i":654,"t":"Let's discover Docusaurus in less than 5 minutes.","s":"Tutorial Intro","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"","p":653},{"i":656,"t":"Get started by creating a new site. Or try Docusaurus immediately with docusaurus.new.","s":"Getting Started","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"#getting-started","p":653},{"i":658,"t":"Node.js version 18.0 or above: When installing Node.js, you are recommended to check all checkboxes related to dependencies.","s":"What you'll need","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"#what-youll-need","p":653},{"i":660,"t":"Generate a new Docusaurus site using the classic template. The classic template will automatically be added to your project after you run the command: npm init docusaurus@latest my-website classic You can type this command into Command Prompt, Powershell, Terminal, or any other integrated terminal of your code editor. The command also installs all necessary dependencies you need to run Docusaurus.","s":"Generate a new site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"#generate-a-new-site","p":653},{"i":662,"t":"Run the development server: cd my-website npm run start The cd command changes the directory you're working with. In order to work with your newly created Docusaurus site, you'll need to navigate the terminal there. The npm run start command builds your website locally and serves it through a development server, ready for you to view at http://localhost:3000/. Open docs/intro.md (this page) and edit some lines: the site reloads automatically and displays your changes.","s":"Start your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/intro","h":"#start-your-site","p":653},{"i":664,"t":"Docusaurus can manage multiple versions of your docs.","s":"Manage Docs Versions","u":"/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions","h":"","p":663},{"i":666,"t":"Release a version 1.0 of your project: npm run docusaurus docs:version 1.0 The docs folder is copied into versioned_docs/version-1.0 and versions.json is created. Your docs now have 2 versions: 1.0 at http://localhost:3000/docs/ for the version 1.0 docs current at http://localhost:3000/docs/next/ for the upcoming, unreleased docs","s":"Create a docs version","u":"/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions","h":"#create-a-docs-version","p":663},{"i":668,"t":"To navigate seamlessly across versions, add a version dropdown. Modify the docusaurus.config.ts file: docusaurus.config.ts export default { themeConfig: { navbar: { items: [ { type: 'docsVersionDropdown', }, ], }, }, }; The docs version dropdown appears in your navbar:","s":"Add a Version Dropdown","u":"/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions","h":"#add-a-version-dropdown","p":663},{"i":670,"t":"It is possible to edit versioned docs in their respective folder: versioned_docs/version-1.0/hello.md updates http://localhost:3000/docs/hello docs/hello.md updates http://localhost:3000/docs/next/hello","s":"Update an existing version","u":"/docs/docusaurus-mdx/docusaurus-tutorial/manage-docs-versions","h":"#update-an-existing-version","p":663},{"i":672,"t":"Docusaurus supports Markdown and a few additional features.","s":"Markdown Features","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"","p":671},{"i":674,"t":"Markdown documents have metadata at the top called Front Matter: my-doc.md --- id: my-doc-id title: My document title description: My document description slug: /my-custom-url --- ## Markdown heading Markdown text with [links](./hello.md)","s":"Front Matter","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#front-matter","p":671},{"i":676,"t":"Regular Markdown links are supported, using url paths or relative file paths. Let's see how to [Create a page](/create-a-page). Let's see how to [Create a page](./create-a-page.md). Result: Let's see how to Create a page.","s":"Links","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#links","p":671},{"i":678,"t":"Regular Markdown images are supported. You can use absolute paths to reference images in the static directory (static/img/docusaurus.png): ![Docusaurus logo](/img/docusaurus.png) You can reference images relative to the current file as well. This is particularly useful to colocate images close to the Markdown files using them: ![Docusaurus logo](./img/docusaurus.png)","s":"Images","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#images","p":671},{"i":680,"t":"Markdown code blocks are supported with Syntax highlighting. src/components/HelloDocusaurus.js function HelloDocusaurus() { return ( <h1>Hello, Docusaurus!</h1> ) } src/components/HelloDocusaurus.js function HelloDocusaurus() { return <h1>Hello, Docusaurus!</h1>; }","s":"Code Blocks","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#code-blocks","p":671},{"i":682,"t":"Docusaurus has a special syntax to create admonitions and callouts: My tip Use this awesome feature option Take care This action is dangerous My tip Use this awesome feature option Take care This action is dangerous","s":"Admonitions","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#admonitions","p":671},{"i":684,"t":"MDX can make your documentation more interactive and allows using any React components inside Markdown: export const Highlight = ({children, color}) => ( <span style={{ backgroundColor: color, borderRadius: '20px', color: '#fff', padding: '10px', cursor: 'pointer', }} onClick={() => { alert(`You clicked the color ${color} with label ${children}`) }}> {children} </span> ); This is <Highlight color=\"#25c2a0\">Docusaurus green</Highlight> ! This is <Highlight color=\"#1877F2\">Facebook blue</Highlight> ! This is Docusaurus green ! This is Facebook blue !","s":"MDX and React Components","u":"/docs/docusaurus-mdx/docusaurus-tutorial/markdown-features","h":"#mdx-and-react-components","p":671},{"i":686,"t":"Let's translate docs/intro.md to French.","s":"Translate your site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"","p":685},{"i":688,"t":"Modify docusaurus.config.ts to add support for the fr locale: docusaurus.config.ts export default { i18n: { defaultLocale: 'en', locales: ['en', 'fr'], }, };","s":"Configure i18n","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#configure-i18n","p":685},{"i":690,"t":"Copy the docs/intro.md file to the i18n/fr folder: mkdir -p i18n/fr/docusaurus-plugin-content-docs/current/ cp docs/intro.md i18n/fr/docusaurus-plugin-content-docs/current/intro.md Translate i18n/fr/docusaurus-plugin-content-docs/current/intro.md in French.","s":"Translate a doc","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#translate-a-doc","p":685},{"i":692,"t":"Start your site on the French locale: npm run start -- --locale fr Your localized site is accessible at http://localhost:3000/fr/ and the Getting Started page is translated. 警告 In development, you can only use one locale at a time.","s":"Start your localized site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#start-your-localized-site","p":685},{"i":694,"t":"To navigate seamlessly across languages, add a locale dropdown. Modify the docusaurus.config.ts file: docusaurus.config.ts export default { themeConfig: { navbar: { items: [ { type: 'localeDropdown', }, ], }, }, }; The locale dropdown now appears in your navbar:","s":"Add a Locale Dropdown","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#add-a-locale-dropdown","p":685},{"i":696,"t":"Build your site for a specific locale: npm run build -- --locale fr Or build your site to include all the locales at once: npm run build","s":"Build your localized site","u":"/docs/docusaurus-mdx/docusaurus-tutorial/translate-your-site","h":"#build-your-localized-site","p":685},{"i":699,"t":"Build optimized websites quickly, focus on your content using react and powered by MDX. ⚡️ Docusaurus will help you ship a beautiful documentation site in no time. 💸 Building a custom tech stack is expensive. Instead, focus on your content and just write Markdown files. 💥 Ready for more? Use advanced features like versioning, i18n, search and theme customizations. 💅 Check the best Docusaurus sites for inspiration and read some testimonials. 🧐 Docusaurus is a static-site generator. It builds a single-page application with fast client-side navigation, leveraging the full power of React to make your site interactive. It provides out-of-the-box documentation features but can be used to create any kind of site (personal website, product, blog, marketing landing pages, etc).","s":"What is Docusaurus?","u":"/docs/docusaurus-mdx/intro","h":"#what-is-docusaurus","p":697},{"i":701,"t":"MDX lets you use JSX in your markdown content. You can import components, such as interactive charts or alerts, and embed them within your content. This makes writing long-form content with components a blast. ❤️ Powerful: MDX blends markdown and JSX syntax to fit perfectly in JSX-based projects 💻 Everything is a component: Use existing components in your MDX and import other MDX files as components 🔧 Customizable: Decide which component is rendered for each markdown construct ({h1: MyHeading}) 📚 Markdown-based: The simplicity and elegance of markdown remains, you use JSX only when you want to 🔥 Blazingly blazing fast: MDX has no runtime, all compilation occurs during the build stage","s":"What is MDX?","u":"/docs/docusaurus-mdx/intro","h":"#what-is-mdx","p":697},{"i":703,"t":"In addition to the basic Markdown syntax, we have a special admonitions syntax by wrapping text with a set of 3 colons, followed by a label denoting its type. Example: :::note Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: :::tip Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: :::info Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: :::warning Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: :::danger Some **content** with _Markdown_ `syntax`. Check [this `api`](#). ::: 备注 Some content with Markdown syntax. Check this api. 提示 Some content with Markdown syntax. Check this api. 信息 Some content with Markdown syntax. Check this api. 注意 Some content with Markdown syntax. Check this api. 危险 Some content with Markdown syntax. Check this api.","s":"Admonitions","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"","p":702},{"i":705,"t":"If you use Prettier to format your Markdown files, Prettier might auto-format your code to invalid admonition syntax. To avoid this problem, add empty lines around the starting and ending directives. This is also why the examples we show here all have empty lines around the content. <!-- Prettier doesn't change this --> :::note Hello world ::: <!-- Prettier changes this --> :::note Hello world ::: <!-- to this --> ::: note Hello world:::","s":"Usage with Prettier","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#usage-with-prettier","p":702},{"i":707,"t":"You may also specify an optional title. :::note[Your Title **with** some _Markdown_ `syntax`!] Some **content** with some _Markdown_ `syntax`. ::: Your Title with some Markdown syntax! Some content with some Markdown syntax.","s":"Specifying title","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#specifying-title","p":702},{"i":709,"t":"Admonitions can be nested. Use more colons : for each parent admonition level. :::::info[Parent] Parent content ::::danger[Child] Child content :::tip[Deep Child] Deep child content ::: :::: ::::: Parent Parent content Child Child content Deep Child Deep child content","s":"Nested admonitions","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#nested-admonitions","p":702},{"i":711,"t":"You can use MDX inside admonitions too! import Tabs from '@theme/Tabs'; import TabItem from '@theme/TabItem'; :::tip[Use tabs in admonitions] <Tabs> <TabItem value=\"apple\" label=\"Apple\">This is an apple 🍎</TabItem> <TabItem value=\"orange\" label=\"Orange\">This is an orange 🍊</TabItem> <TabItem value=\"banana\" label=\"Banana\">This is a banana 🍌</TabItem> </Tabs> ::: Use tabs in admonitions Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌","s":"Admonitions with MDX","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#admonitions-with-mdx","p":702},{"i":713,"t":"Outside of Markdown, you can use the @theme/Admonition component to get the same output. MyReactPage.jsx import Admonition from '@theme/Admonition'; export default function MyReactPage() { return ( <div> <Admonition type=\"info\"> <p>Some information</p> </Admonition> </div> ); } The types that are accepted are the same as above: note, tip, danger, info, warning. Optionally, you can specify an icon by passing a JSX element or a string, or a title: MyReactPage.jsx <Admonition type=\"tip\" icon=\"💡\" title=\"Did you know...\"> Use plugins to introduce shorter syntax for the most commonly used JSX elements in your project. </Admonition> 💡Did you know... Use plugins to introduce shorter syntax for the most commonly used JSX elements in your project.","s":"Usage in JSX","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#usage-in-jsx","p":702},{"i":715,"t":"There are two kinds of customizations possible with admonitions: parsing and rendering.","s":"Customizing admonitions","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#customizing-admonitions","p":702},{"i":717,"t":"You can customize how each individual admonition type is rendered through swizzling. You can often achieve your goal through a simple wrapper. For example, in the follow example, we swap out the icon for info admonitions only. src/theme/Admonition.js import React from 'react'; import Admonition from '@theme-original/Admonition'; import MyCustomNoteIcon from '@site/static/img/info.svg'; export default function AdmonitionWrapper(props) { if (props.type !== 'info') { return <Admonition title=\"My Custom Admonition Title\" {...props} />; } return <Admonition icon={<MyCustomNoteIcon />} {...props} />; }","s":"Customizing rendering behavior","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#customizing-rendering-behavior","p":702},{"i":719,"t":"Admonitions are implemented with a Remark plugin. The plugin is designed to be configurable. To customize the Remark plugin for a specific content plugin (docs, blog, pages), pass the options through the admonitions key. docusaurus.config.ts export default { presets: [ [ '@docusaurus/preset-classic', { docs: { admonitions: { keywords: ['note', 'tip', 'info', 'warning', 'danger'], extendDefaults: true, }, }, }, ], ], }; The plugin accepts the following options: keywords: An array of keywords that can be used as the type for the admonition. extendDefaults: Should the provided options (such as keywords) be merged into the existing defaults. Defaults to true. The keyword will be passed as the type prop of the Admonition component.","s":"Customizing parsing behavior","u":"/docs/docusaurus-mdx/mdx-features/admonitions","h":"#customizing-parsing-behavior","p":702},{"i":721,"t":"Sometimes you want to link to assets (e.g. docx files, images...) directly from Markdown files, and it is convenient to co-locate the asset next to the Markdown file using it. Let's imagine the following file structure: # Your doc /website/docs/myFeature.mdx # Some assets you want to use /website/docs/assets/docusaurus-asset-example-banner.png /website/docs/assets/docusaurus-asset-example.docx","s":"Assets","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"","p":720},{"i":723,"t":"You can display images in three different ways: Markdown syntax, CJS require, or ES imports syntax. Markdown syntax CommonJS require Import statement Display images using simple Markdown syntax: ![Example banner](./assets/docusaurus-asset-example-banner.png) Display images using inline CommonJS require in JSX image tag: <img src={require('./assets/docusaurus-asset-example-banner.png').default} alt=\"Example banner\" /> Display images using ES import syntax and JSX image tag: import myImageUrl from '../assets/docusaurus-asset-example-banner.png'; <img src={myImageUrl} alt=\"Example banner\" />; All of the above result in displaying the image: 备注 If you are using @docusaurus/plugin-ideal-image, you need to use the dedicated image component, as documented.","s":"Images","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#images","p":720},{"i":725,"t":"In the same way, you can link to existing assets by require'ing them and using the returned URL in videos, a anchor links, etc. # My Markdown page <a target=\"\\_blank\" href={require('../assets/docusaurus-asset-example.docx').default}> Download this docx </a> or [Download this docx using Markdown](../assets/docusaurus-asset-example.docx) Download this docx Download this docx using Markdown Markdown links are always file paths If you use the Markdown image or link syntax, all asset paths will be resolved as file paths by Docusaurus and automatically converted to require() calls. You don't need to use require() in Markdown unless you use the JSX syntax, which you do have to handle yourself.","s":"Files","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#files","p":720},{"i":727,"t":"Docusaurus supports inlining SVGs out of the box. import DocusaurusSvg from './docusaurus.svg'; <DocusaurusSvg />; This can be useful if you want to alter the part of the SVG image via CSS. For example, you can change one of the SVG colors based on the current theme. import DocusaurusSvg from './docusaurus.svg'; <DocusaurusSvg className=\"themedDocusaurus\" />; [data-theme='light'] .themedDocusaurus [fill='#FFFF50'] { fill: greenyellow; } [data-theme='dark'] .themedDocusaurus [fill='#FFFF50'] { fill: seagreen; }","s":"Inline SVGs","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#inline-svgs","p":720},{"i":729,"t":"Docusaurus supports themed images: the ThemedImage component (included in the themes) allows you to switch the image source based on the current theme. import ThemedImage from '@theme/ThemedImage'; <ThemedImage alt=\"Docusaurus themed image\" sources={{ light: useBaseUrl('/img/docusaurus_light.svg'), dark: useBaseUrl('/img/docusaurus_dark.svg'), }} />;","s":"Themed Images","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#themed-images","p":720},{"i":731,"t":"GitHub uses its own image theming approach with path fragments, which you can easily implement yourself. To toggle the visibility of an image using the path fragment (for GitHub, it's #gh-dark-mode-only and #gh-light-mode-only), add the following to your custom CSS (you can also use your own suffix if you don't want to be coupled to GitHub): src/css/custom.css [data-theme='light'] img[src$='#gh-dark-mode-only'], [data-theme='dark'] img[src$='#gh-light-mode-only'] { display: none; } ![Docusaurus themed image](/img/docusaurus_keytar.svg#gh-light-mode-only)![Docusaurus themed image](/img/docusaurus_speed.svg#gh-dark-mode-only)","s":"GitHub-style themed images","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#github-style-themed-images","p":720},{"i":733,"t":"If a Markdown link or image has an absolute path, the path will be seen as a file path and will be resolved from the static directories. For example, if you have configured static directories to be ['public', 'static'], then for the following image: my-doc.md ![An image from the static](/img/docusaurus.png) Docusaurus will try to look for it in both static/img/docusaurus.png and public/img/docusaurus.png. The link will then be converted to a require() call instead of staying as a URL. This is desirable in two regards: You don't have to worry about the base URL, which Docusaurus will take care of when serving the asset; The image enters Webpack's build pipeline and its name will be appended by a hash, which enables browsers to aggressively cache the image and improves your site's performance. If you intend to write URLs, you can use the pathname:// protocol to disable automatic asset linking. ![banner](pathname:///img/docusaurus-asset-example-banner.png) This link will be generated as <img src=\"/img/docusaurus-asset-example-banner.png\" alt=\"banner\" />, without any processing or file existence checking.","s":"Static assets","u":"/docs/docusaurus-mdx/mdx-features/assets","h":"#static-assets","p":720},{"i":735,"t":"Code blocks within documentation are super-powered 💪.","s":"Code blocks","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"","p":734},{"i":737,"t":"You can add a title to the code block by adding a title key after the language (leave a space between them). ```jsx title=\"/src/components/HelloCodeTitle.js\" function HelloCodeTitle(props) { return <h1>Hello, {props.name}</h1>; } ``` /src/components/HelloCodeTitle.js function HelloCodeTitle(props) { return <h1>Hello, {props.name}</h1>; }","s":"Code title","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#code-title","p":734},{"i":739,"t":"Code blocks are text blocks wrapped around by strings of 3 backticks. You may check out this reference for the specifications of MDX. ```js console.log('Every repo must come with a mascot.'); ``` Use the matching language meta string for your code block, and Docusaurus will pick up syntax highlighting automatically, powered by Prism React Renderer. console.log('Every repo must come with a mascot.');","s":"Syntax highlighting","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#syntax-highlighting","p":734},{"i":741,"t":"By default, the Prism syntax highlighting theme we use is Palenight. You can change this to another theme by passing theme field in prism as themeConfig in your docusaurus.config.ts. For example, if you prefer to use the dracula highlighting theme: docusaurus.config.ts import {themes as prismThemes} from 'prism-react-renderer'; export default { themeConfig: { prism: { // highlight-next-line theme: prismThemes.dracula, }, }, }; Because a Prism theme is just a JS object, you can also write your own theme if you are not satisfied with the default. Docusaurus enhances the github and vsDark themes to provide richer highlight, and you can check our implementations for the light and dark code block themes.","s":"Theming","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#theming","p":734},{"i":743,"t":"By default, Docusaurus comes with a subset of commonly used languages. 注意 Some popular languages like Java, C#, or PHP are not enabled by default. To add syntax highlighting for any of the other Prism-supported languages, define it in an array of additional languages. 备注 Each additional language has to be a valid Prism component name. For example, Prism would map the language cs to csharp, but only prism-csharp.js exists as a component, so you need to use additionalLanguages: ['csharp']. You can look into node_modules/prismjs/components to find all components (languages) available. For example, if you want to add highlighting for the PowerShell language: docusaurus.config.ts export default { // ... themeConfig: { prism: { // highlight-next-line additionalLanguages: ['powershell'], }, // ... }, }; After adding additionalLanguages, restart Docusaurus. If you want to add highlighting for languages not yet supported by Prism, you can swizzle prism-include-languages: npm Yarn pnpm npm run swizzle @docusaurus/theme-classic prism-include-languages yarn swizzle @docusaurus/theme-classic prism-include-languages pnpm run swizzle @docusaurus/theme-classic prism-include-languages It will produce prism-include-languages.js in your src/theme folder. You can add highlighting support for custom languages by editing prism-include-languages.js: src/theme/prism-include-languages.js const prismIncludeLanguages = (Prism) => { // ... additionalLanguages.forEach((lang) => { require(`prismjs/components/prism-${lang}`); }); // highlight-next-line require('/path/to/your/prism-language-definition'); // ... }; You can refer to Prism's official language definitions when you are writing your own language definitions. When adding a custom language definition, you do not need to add the language to the additionalLanguages config array, since Docusaurus only looks up the additionalLanguages strings in languages that Prism provides. Adding the language import in prism-include-languages.js is sufficient.","s":"Supported Languages","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#supported-languages","p":734},{"i":746,"t":"You can use comments with highlight-next-line, highlight-start, and highlight-end to select which lines are highlighted. ```js function HighlightSomeText(highlight) { if (highlight) { // highlight-next-line return 'This text is highlighted!'; } return 'Nothing highlighted'; } function HighlightMoreText(highlight) { // highlight-start if (highlight) { return 'This range is highlighted!'; } // highlight-end return 'Nothing highlighted'; } ``` function HighlightSomeText(highlight) { if (highlight) { // highlight-next-line return 'This text is highlighted!'; } return 'Nothing highlighted'; } function HighlightMoreText(highlight) { if (highlight) { return 'This range is highlighted!'; } return 'Nothing highlighted'; } Supported commenting syntax: Style Syntax C-style /* ... */ and // ... JSX-style {/* ... */} Bash-style # ... HTML-style <!-- ... --> We will do our best to infer which set of comment styles to use based on the language, and default to allowing all comment styles. If there's a comment style that is not currently supported, we are open to adding them! Pull requests welcome. Note that different comment styles have no semantic difference, only their content does. You can set your own background color for highlighted code line in your src/css/custom.css which will better fit to your selected syntax highlighting theme. The color given below works for the default highlighting theme (Palenight), so if you are using another theme, you will have to tweak the color accordingly. /src/css/custom.css :root { --docusaurus-highlighted-code-line-bg: rgb(72, 77, 91); } /* If you have a different syntax highlighting theme for dark mode. */ [data-theme='dark'] { /* Color which works with dark mode syntax highlighting theme */ --docusaurus-highlighted-code-line-bg: rgb(100, 100, 100); } If you also need to style the highlighted code line in some other way, you can target on theme-code-block-highlighted-line CSS class.","s":"Highlighting with comments","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#highlighting-with-comments","p":734},{"i":748,"t":"You can also specify highlighted line ranges within the language meta string (leave a space after the language). To highlight multiple lines, separate the line numbers by commas or use the range syntax to select a chunk of lines. This feature uses the parse-number-range library and you can find more syntax on their project details. ```jsx {1,4-6,11} import React from 'react'; function MyComponent(props) { if (props.isBar) { return <div>Bar</div>; } return <div>Foo</div>; } export default MyComponent; ``` import React from 'react'; function MyComponent(props) { if (props.isBar) { return <div>Bar</div>; } return <div>Foo</div>; } export default MyComponent; prefer comments Prefer highlighting with comments where you can. By inlining highlight in the code, you don't have to manually count the lines if your code block becomes long. If you add/remove lines, you also don't have to offset your line ranges. - ```jsx {3} + ```jsx {4} function HighlightSomeText(highlight) { if (highlight) { + console.log('Highlighted text found'); return 'This text is highlighted!'; } return 'Nothing highlighted'; } ``` Below, we will introduce how the magic comment system can be extended to define custom directives and their functionalities. The magic comments would only be parsed if a highlight metastring is not present.","s":"Highlighting with metadata string","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#highlighting-with-metadata-string","p":734},{"i":750,"t":"// highlight-next-line and // highlight-start etc. are called \"magic comments\", because they will be parsed and removed, and their purposes are to add metadata to the next line, or the section that the pair of start- and end-comments enclose. You can declare custom magic comments through theme config. For example, you can register another magic comment that adds a code-block-error-line class name: docusaurus.config.ts src/css/custom.css myDoc.md export default { themeConfig: { prism: { magicComments: [ // Remember to extend the default highlight class name as well! { className: 'theme-code-block-highlighted-line', line: 'highlight', block: {start: 'highlight-start', end: 'highlight-end'}, }, { className: 'code-block-red-line', line: 'highlight-red', block: {start: 'highlight-red-start', end: 'highlight-red-end'}, }, ], }, }, }; .code-block-error-line { background-color: #ff000020; display: block; margin: 0 calc(-1 * var(--ifm-pre-padding)); padding: 0 var(--ifm-pre-padding); border-left: 3px solid #ff000080; } In JavaScript, trying to access properties on `null` will error. ```js const name = null; // highlight-red console.log(name.toUpperCase()); // Uncaught TypeError: Cannot read properties of null (reading 'toUpperCase') ``` In JavaScript, trying to access properties on null will error. const name = null; console.log(name.toUpperCase()); // Uncaught TypeError: Cannot read properties of null (reading 'toUpperCase') If you use number ranges in metastring (the {1,3-4} syntax), Docusaurus will apply the first magicComments entry's class name. This, by default, is theme-code-block-highlighted-line, but if you change the magicComments config and use a different entry as the first one, the meaning of the metastring range will change as well. You can disable the default line highlighting comments with magicComments: []. If there's no magic comment config, but Docusaurus encounters a code block containing a metastring range, it will error because there will be no class name to apply—the highlighting class name, after all, is just a magic comment entry. Every magic comment entry will contain three keys: className (required), line, which applies to the directly next line, or block (containing start and end), which applies to the entire block enclosed by the two comments. Using CSS to target the class can already do a lot, but you can unlock the full potential of this feature through swizzling. npm Yarn pnpm npm run swizzle @docusaurus/theme-classic CodeBlock/Line yarn swizzle @docusaurus/theme-classic CodeBlock/Line pnpm run swizzle @docusaurus/theme-classic CodeBlock/Line The Line component will receive the list of class names, based on which you can conditionally render different markup.","s":"Custom magic comments","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#custom-magic-comments","p":734},{"i":752,"t":"You can enable line numbering for your code block by using showLineNumbers key within the language meta string (don't forget to add space directly before the key). ```jsx {1,4-6,11} showLineNumbers import React from 'react'; function MyComponent(props) { if (props.isBar) { return <div>Bar</div>; } return <div>Foo</div>; } export default MyComponent; ``` import React from 'react'; function MyComponent(props) { if (props.isBar) { return <div>Bar</div>; } return <div>Foo</div>; } export default MyComponent;","s":"Line numbering","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#line-numbering","p":734},{"i":754,"t":"(Powered by React Live) You can create an interactive coding editor with the @docusaurus/theme-live-codeblock plugin. First, add the plugin to your package. npm Yarn pnpm npm install --save @docusaurus/theme-live-codeblock yarn add @docusaurus/theme-live-codeblock pnpm add @docusaurus/theme-live-codeblock You will also need to add the plugin to your docusaurus.config.ts. export default { // ... themes: ['@docusaurus/theme-live-codeblock'], // ... }; To use the plugin, create a code block with live attached to the language meta string. ```jsx live function Clock(props) { const [date, setDate] = useState(new Date()); useEffect(() => { const timerID = setInterval(() => tick(), 1000); return function cleanup() { clearInterval(timerID); }; }); function tick() { setDate(new Date()); } return ( <div> <h2>It is {date.toLocaleTimeString()}.</h2> </div> ); } ``` The code block will be rendered as an interactive editor. Changes to the code will reflect on the result panel live. function Clock(props) { const [date, setDate] = useState(new Date()); useEffect(() => { const timerID = setInterval(() => tick(), 1000); return function cleanup() { clearInterval(timerID); }; }); function tick() { setDate(new Date()); } return ( <div> <h2>It is {date.toLocaleTimeString()}.</h2> </div> ); }","s":"Interactive code editor","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#interactive-code-editor","p":734},{"i":756,"t":"react-live and imports It is not possible to import components directly from the react-live code editor, you have to define available imports upfront. By default, all React imports are available. If you need more imports available, swizzle the react-live scope: npm Yarn pnpm npm run swizzle @docusaurus/theme-live-codeblock ReactLiveScope -- --eject yarn swizzle @docusaurus/theme-live-codeblock ReactLiveScope --eject pnpm run swizzle @docusaurus/theme-live-codeblock ReactLiveScope --eject src/theme/ReactLiveScope/index.js import React from 'react'; const ButtonExample = (props) => ( <button {...props} style={{ backgroundColor: 'white', color: 'black', border: 'solid red', borderRadius: 20, padding: 10, cursor: 'pointer', ...props.style, }} /> ); // Add react-live imports you need here const ReactLiveScope = { React, ...React, // highlight-next-line ButtonExample, }; export default ReactLiveScope; The ButtonExample component is now available to use: function MyPlayground(props) { return ( <div> <ButtonExample onClick={() => alert('hey!')}>Click me</ButtonExample> </div> ); }","s":"Imports","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#imports","p":734},{"i":758,"t":"The noInline option should be used to avoid errors when your code spans multiple components or variables. ```jsx live noInline const project = 'Docusaurus'; const Greeting = () => <p>Hello {project}!</p>; render(<Greeting />); ``` Unlike an ordinary interactive code block, when using noInline React Live won't wrap your code in an inline function to render it. You will need to explicitly call render() at the end of your code to display the output. const project = \"Docusaurus\"; const Greeting = () => ( <p>Hello {project}!</p> ); render( <Greeting /> );","s":"Imperative Rendering (noInline)","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#imperative-rendering-noinline","p":734},{"i":760,"t":"Code block in Markdown always preserves its content as plain text, meaning you can't do something like: type EditUrlFunction = (params: { // This doesn't turn into a link (for good reason!) version: <a href=\"/docs/versioning\">Version</a>; versionDocsDirPath: string; docPath: string; permalink: string; locale: string; }) => string | undefined; If you want to embed HTML markup such as anchor links or bold type, you can use the <pre> tag, <code> tag, or <CodeBlock> component. <pre> <b>Input: </b>1 2 3 4{'\\n'} <b>Output: </b>\"366300745\"{'\\n'} </pre> Input: 1 2 3 4 Output: \"366300745\" MDX is whitespace insensitive MDX is in line with JSX behavior: line break characters, even when inside <pre>, are turned into spaces. You have to explicitly write the new line character for it to be printed out. 注意 Syntax highlighting only works on plain strings. Docusaurus will not attempt to parse code block content containing JSX children.","s":"Using JSX markup in code blocks","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#using-jsx-markup","p":734},{"i":762,"t":"With MDX, you can easily create interactive components within your documentation, for example, to display code in multiple programming languages and switch between them using a tabs component. Instead of implementing a dedicated component for multi-language support code blocks, we've implemented a general-purpose <Tabs> component in the classic theme so that you can use it for other non-code scenarios as well. The following example is how you can have multi-language code tabs in your docs. Note that the empty lines above and below each language block are intentional. This is a current limitation of MDX: you have to leave empty lines around Markdown syntax for the MDX parser to know that it's Markdown syntax and not JSX. import Tabs from '@theme/Tabs'; import TabItem from '@theme/TabItem'; <Tabs> <TabItem value=\"js\" label=\"JavaScript\"> ```js function helloWorld() { console.log('Hello, world!'); } ``` </TabItem> <TabItem value=\"py\" label=\"Python\"> ```py def hello_world(): print(\"Hello, world!\") ``` </TabItem> <TabItem value=\"java\" label=\"Java\"> ```java class HelloWorld { public static void main(String args[]) { System.out.println(\"Hello, World\"); } } ``` </TabItem> </Tabs> And you will get the following: JavaScript Python Java function helloWorld() { console.log('Hello, world!'); } def hello_world(): print(\"Hello, world!\") class HelloWorld { public static void main(String args[]) { System.out.println(\"Hello, World\"); } } If you have multiple of these multi-language code tabs, and you want to sync the selection across the tab instances, refer to the Syncing tab choices section.","s":"Multi-language support code blocks","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#multi-language-support-code-blocks","p":734},{"i":764,"t":"Displaying CLI commands in both npm and Yarn is a very common need, for example: npm Yarn pnpm npm install @docusaurus/remark-plugin-npm2yarn yarn add @docusaurus/remark-plugin-npm2yarn pnpm add @docusaurus/remark-plugin-npm2yarn Docusaurus provides such a utility out of the box, freeing you from using the Tabs component every time. To enable this feature, first install the @docusaurus/remark-plugin-npm2yarn package as above, and then in docusaurus.config.ts, for the plugins where you need this feature (doc, blog, pages, etc.), register it in the remarkPlugins option. (See docs configuration for more details on configuration format) docusaurus.config.ts export default { // ... presets: [ [ '@docusaurus/preset-classic', { docs: { remarkPlugins: [[require('@docusaurus/remark-plugin-npm2yarn'), {sync: true}]], }, pages: { // highlight-next-line remarkPlugins: [require('@docusaurus/remark-plugin-npm2yarn')], }, blog: { remarkPlugins: [[require('@docusaurus/remark-plugin-npm2yarn'), {converters: ['pnpm']}]], // ... }, }, ], ], }; And then use it by adding the npm2yarn key to the code block: ```bash npm2yarn npm install @docusaurus/remark-plugin-npm2yarn ``` Configuration​ Option Type Default Description sync boolean false Whether to sync the selected converter across all code blocks. converters array 'yarn', 'pnpm' The list of converters to use. The order of the converters is important, as the first converter will be used as the default choice.","s":"Docusaurus npm2yarn remark plugin","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#npm2yarn-remark-plugin","p":734},{"i":766,"t":"Outside of Markdown, you can use the @theme/CodeBlock component to get the same output. import CodeBlock from '@theme/CodeBlock'; export default function MyReactPage() { return ( <div> <CodeBlock language=\"jsx\" title=\"/src/components/HelloCodeTitle.js\" showLineNumbers> {`function HelloCodeTitle(props) { return <h1>Hello, {props.name}</h1>; }`} </CodeBlock> </div> ); } /src/components/HelloCodeTitle.js function HelloCodeTitle(props) { return <h1>Hello, {props.name}</h1>; } The props accepted are language, title and showLineNumbers, in the same way as you write Markdown code blocks. Although discouraged, you can also pass in a metastring prop like metastring='{1-2} title=\"/src/components/HelloCodeTitle.js\" showLineNumbers', which is how Markdown code blocks are handled under the hood. However, we recommend you use comments for highlighting lines. As previously stated, syntax highlighting is only applied when the children is a simple string.","s":"Usage in JSX","u":"/docs/docusaurus-mdx/mdx-features/code-blocks","h":"#usage-in-jsx","p":734},{"i":768,"t":"信息 Mermaid is default installed and enabled on this site. Diagrams can be rendered using Mermaid in a code block.","s":"Diagrams with Mermaid","u":"/docs/docusaurus-mdx/mdx-features/diagrams","h":"","p":767},{"i":770,"t":"Add a code block with language mermaid: Example Mermaid diagram ```mermaid graph TD; A-->B; A-->C; B-->D; C-->D; ``` See the Mermaid syntax documentation for more information on the Mermaid syntax.","s":"Usage","u":"/docs/docusaurus-mdx/mdx-features/diagrams","h":"#usage","p":767},{"i":772,"t":"Options in mermaid.options will be passed directly to mermaid.initialize. You can set themes for both light and dark mode. docusaurus.config.ts export default { themeConfig: { mermaid: { theme: {light: 'neutral', dark: 'forest'}, options: { maxTextSize: 50, }, }, }, }; See the Mermaid config documentation and the Mermaid config types for the available config options.","s":"Mermaid Config","u":"/docs/docusaurus-mdx/mdx-features/diagrams","h":"#configuration","p":767},{"i":775,"t":"Docusaurus automatically sets useful page metadata in <html>, <head> and <body> for you. It is possible to add extra metadata (or override existing ones) with the <head> tag in Markdown files: markdown-features-head-metadata.mdx --- id: head-metadata title: Head Metadata --- <head> <html className=\"some-extra-html-class\" /> <body className=\"other-extra-body-class\" /> <title>Head Metadata customized title!</title> <meta charSet=\"utf-8\" /> <meta name=\"twitter:card\" content=\"summary\" /> <link rel=\"canonical\" href=\"https://docusaurus.io/docs/mdx-features/head-metadata\" /> </head> # Head Metadata My text This <head> declaration has been added to the current Markdown doc as a demo. Open your browser DevTools and check how this page's metadata has been affected. 备注 This feature is built on top of the Docusaurus <Head> component. Refer to react-helmet for exhaustive documentation. You don't need this for regular SEO Content plugins (e.g. docs and blog) provide front matter options like description, keywords, and image, which will be automatically applied to both description and og:description, while you would have to manually declare two metadata tags when using the <head> tag.","s":"Customizing head metadata","u":"/docs/docusaurus-mdx/mdx-features/head-metadata","h":"#customizing-head-metadata","p":773},{"i":777,"t":"The Markdown pages' description metadata may be used in more places than the head metadata. For example, the docs plugin's generated category index uses the description metadata for the doc cards. By default, the description is the first content-ful line, with some efforts to convert it to plain text. For example, the following file... # Title Main content... May contain some [links](./file.mdx) or **emphasis**. ...will have the default description \"Main content... May contain some links or emphasis\". However, it's not designed to be fully functional. Where it fails to produce reasonable descriptions, you can explicitly provide one through front matter: --- description: This description will override the default. --- # Title Main content... May contain some [links](./file.mdx) or **emphasis**.","s":"Markdown page description","u":"/docs/docusaurus-mdx/mdx-features/head-metadata","h":"#markdown-page-description","p":773},{"i":779,"t":"Docusaurus uses Markdown as its main content authoring format. Learn Markdown You can learn Markdown in 10 minutes. Docusaurus uses modern tooling to help you create interactive documentation. The MDX compiler transforms Markdown files to React components, and allows you to use JSX in your Markdown content. This enables you to easily interleave React components within your content, and create delightful learning experiences. Use the MDX Playground The MDX playground is your new best friend! It is a very helpful debugging tool that shows how the MDX compiler transforms Markdown to React. Options: select the right format (MDX or CommonMark) and the following plugins Docusaurus uses: remark-gfm, remark-directive, rehype-raw.","s":"Markdown Features","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"","p":778},{"i":781,"t":"Docusaurus compiles both .md and .mdx files to React components using the MDX compiler, but the syntax can be interpreted differently depending on your settings. The MDX compiler supports 2 formats: The MDX format: a powerful parser allowing the usage of JSX The CommonMark format: a standard-compliant Markdown parser that does not allow the usage of JSX By default, Docusaurus v3 uses the MDX format for all files (including .md files) for historical reasons. We changed this by setting siteConfig.markdown.format: 'detect'. what is siteConfig.markdown.format: 'detect' The appropriate format will be selected automatically, based on file extensions: .md files will use the CommonMark format .mdx files will use the MDX format","s":"MDX vs. CommonMark","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#mdx-vs-commonmark","p":778},{"i":783,"t":"Markdown is a syntax that enables you to write formatted content in a readable syntax. ### My Doc Section Hello world message with some **bold** text, some _italic_ text, and a [link](/) ![img alt](/img/docusaurus.png) My Doc Section Hello world message with some bold text, some italic text and a link Markdown is declarative Some may assume a 1-1 correlation between Markdown and HTML, e.g., ![Preview](/img/docusaurus.png) will always become <img src=\"/img/docusaurus.png\" alt=\"Preview\" />, as-is. However, that is not the case. The Markdown syntax ![message](url) only declaratively tells Docusaurus that an image needs to be inserted here, but we may do other things like transforming a file path to URL path, so the generated markup may differ from the output of other Markdown renderers, or a naïve hand-transcription to the equivalent JSX/HTML code. In general, you should only assume the semantics of the markup (``` fences become code blocks; > becomes quotes, etc.), but not the actual compiled output.","s":"Standard features","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#standard-features","p":778},{"i":785,"t":"Hello world message with some bold text, some italic text and a link","s":"My Doc Section","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"","p":778},{"i":787,"t":"Front matter is used to add metadata to your Markdown file. All content plugins have their own front matter schema, and use the front matter to enrich the default metadata inferred from the content or other configuration. Front matter is provided at the very top of the file, enclosed by three dashes ---. The content is parsed as YAML. --- title: My Doc Title more_data: - Can be provided - as: objects or: arrays --- 信息 The API documentation of each official plugin lists the supported attributes: Docs front matter Blog front matter Pages front matter","s":"Front matter","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#front-matter","p":778},{"i":789,"t":"Markdown quotes are beautifully styled: > Easy to maintain open source documentation websites. > > — Docusaurus Easy to maintain open source documentation websites. — Docusaurus","s":"Quotes","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#quotes","p":778},{"i":791,"t":"Markdown can embed HTML elements, and details HTML elements are beautifully styled: ### Details element example <details> <summary>Toggle me!</summary> <div> <div>This is the detailed content</div> <br/> <details> <summary> Nested toggle! Some surprise inside... </summary> <div>😲😲😲😲😲</div> </details> </div> </details> Details element example Toggle me! This is the detailed content Nested toggle! Some surprise inside... 😲😲😲😲😲","s":"Details","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"#details","p":778},{"i":793,"t":"Toggle me! This is the detailed content Nested toggle! Some surprise inside... 😲😲😲😲😲","s":"Details element example","u":"/docs/docusaurus-mdx/mdx-features/intro","h":"","p":778},{"i":795,"t":"There are two ways of adding a link to another page: through a URL path and a file path. - [URL path to another document](./installation) - [file path to another document](./installation.mdx) URL paths are unprocessed by Docusaurus, and you can see them as directly rendering to <a href=\"./installation\">, i.e. it will be resolved according to the page's URL location, rather than its file-system location. If you want to reference another Markdown file included by the same plugin, you could use the relative path of the document you want to link to. Docusaurus' Markdown loader will convert the file path to the target file's URL path (and hence remove the .md extension). For example, if you are in docs/folder/doc1.md and you want to reference docs/folder/doc2.md, docs/folder/subfolder/doc3.md and docs/otherFolder/doc4.md: docs/folder/doc1.md I am referencing a [document](doc2.mdx). Reference to another [document in a subfolder](subfolder/doc3.mdx). [Relative document](../otherFolder/doc4.mdx) referencing works as well. Relative file paths are resolved against the current file's directory. Absolute file paths, on the other hand, are resolved relative to the content root, usually docs/, blog/, or localized ones like i18n/zh-Hans/plugin-content-docs/current. Absolute file paths can also be relative to the site directory. However, beware that links that begin with /docs/ or /blog/ are not portable as you would need to manually update them if you create new doc versions or localize them. You can write [links](/otherFolder/doc4.mdx) relative to the content root (`/docs/`). You can also write [links](/docs/otherFolder/doc4.mdx) relative to the site directory, but it's not recommended. Using relative file paths (with .md extensions) instead of relative URL links provides the following benefits: Links will keep working on the GitHub interface and many Markdown editors You can customize the files' slugs without having to update all the links Moving files around the folders can be tracked by your editor, and some editors may automatically update file links A versioned doc will link to another doc of the exact same version Relative URL links are very likely to break if you update the trailingSlash config 注意 Markdown file references only work when the source and target files are processed by the same plugin instance. This is a technical limitation of our Markdown processing architecture and will be fixed in the future. If you are linking files between plugins (e.g. linking to a doc page from a blog post), you have to use URL links.","s":"Markdown links","u":"/docs/docusaurus-mdx/mdx-features/links","h":"","p":794},{"i":797,"t":"信息 Math render KaTeX is default installed and enabled on this site. Mathematical equations can be rendered using KaTeX.","s":"Math Equations","u":"/docs/docusaurus-mdx/mdx-features/math-equations","h":"","p":796},{"i":799,"t":"Please read KaTeX documentation for more details.","s":"Usage","u":"/docs/docusaurus-mdx/mdx-features/math-equations","h":"#usage","p":796},{"i":801,"t":"Write inline math equations by wrapping LaTeX equations between $: Let $f\\colon[a,b]\\to\\R$ be Riemann integrable. Let $F\\colon[a,b]\\to\\R$ be $F(x)=\\int_{a}^{x} f(t)\\,dt$. Then $F$ is continuous, and at all $x$ such that $f$ is continuous at $x$, $F$ is differentiable at $x$ with $F'(x)=f(x)$. Let f ⁣:[a,b]→Rf\\colon[a,b] \\to \\Rf:[a,b]→R be Riemann integrable. Let F ⁣:[a,b]→RF\\colon[a,b]\\to\\RF:[a,b]→R be F(x)=∫axf(t) dtF(x)= \\int_{a}^{x} f(t)\\,dtF(x)=∫ax​f(t)dt. Then FFF is continuous, and at all xxx such that fff is continuous at xxx, FFF is differentiable at xxx with F′(x)=f(x)F'(x)=f(x)F′(x)=f(x).","s":"Inline","u":"/docs/docusaurus-mdx/mdx-features/math-equations","h":"#inline","p":796},{"i":803,"t":"For equation block or display mode, use line breaks and $$: $$ I = \\int_0^{2\\pi} \\sin(x)\\,dx $$ I=∫02πsin⁡(x) dxI = \\int_0^{2\\pi} \\sin(x)\\,dxI=∫02π​sin(x)dx","s":"Blocks","u":"/docs/docusaurus-mdx/mdx-features/math-equations","h":"#blocks","p":796},{"i":805,"t":"Sometimes, you may want to extend or tweak your Markdown syntax. For example: How do I embed youtube videos using the image syntax (![](https://youtu.be/yKNxeF4KMsY))? How do I style links that are on their own lines differently, e.g., as a social card? How do I make every page start with a copyright notice? And the answer is: create an MDX plugin! MDX has a built-in plugin system that can be used to customize how the Markdown files will be parsed and transformed to JSX. There are three typical use-cases of MDX plugins: Using existing remark plugins or rehype plugins; Creating remark/rehype plugins to transform the elements generated by existing MDX syntax; Creating remark/rehype plugins to introduce new syntaxes to MDX. If you play with the MDX playground, you would notice that the MDX transpilation has two intermediate steps: Markdown AST (MDAST), and Hypertext AST (HAST), before arriving at the final JSX output. MDX plugins also come in two forms: Remark: processes the Markdown AST. Rehype: processes the Hypertext AST. 提示 Use plugins to introduce shorter syntax for the most commonly used JSX elements in your project. The admonition syntax that we offer is also generated by a Remark plugin, and you could do the same for your own use case.","s":"MDX Plugins","u":"/docs/docusaurus-mdx/mdx-features/plugins","h":"","p":804},{"i":807,"t":"Docusaurus injects some default Remark plugins during Markdown processing. These plugins would: Generate the table of contents; Add anchor links to each heading; Transform images and links to require() calls. … These are all typical use-cases of Remark plugins, which can also be a source of inspiration if you want to implement your own plugin.","s":"Default plugins","u":"/docs/docusaurus-mdx/mdx-features/plugins","h":"#default-plugins","p":804},{"i":809,"t":"An MDX plugin is usually an npm package, so you install them like other npm packages using npm. Take the math plugins as an example. npm Yarn pnpm npm install --save remark-math@6 rehype-katex@7 yarn add remark-math@6 rehype-katex@7 pnpm add remark-math@6 rehype-katex@7 How are remark-math and rehype-katex different? In case you are wondering how Remark and Rehype are different, here is a good example. remark-math operates on the Markdown AST, where it sees text like $...$, and all it does is transform that to the JSX <span class=\"math math-inline\">...</span> without doing too much with the content. This decouples the extraction of math formulae from their rendering, which means you can swap KaTeX\\KaTeXKATE​X out with other math renderers, like MathJax (with rehype-mathjax), just by replacing the Rehype plugin. Next, the rehype-katex operates on the Hypertext AST where everything has been converted to HTML-like tags already. It traverses all the elements with math class and uses KaTeX\\KaTeXKATE​X to parse and render the content to actual HTML. 注意 Many official Remark/Rehype plugins are ES Modules only, a JavaScript module system, which Docusaurus supports. We recommend using an ES Modules config file to make it easier to import such packages. Next, import your plugins and add them to the plugin options through plugin or preset config in docusaurus.config.ts: docusaurus.config.ts import remarkMath from 'remark-math'; import rehypeKatex from 'rehype-katex'; export default { presets: [ [ '@docusaurus/preset-classic', { docs: { path: 'docs', remarkPlugins: [remarkMath], rehypePlugins: [rehypeKatex], }, }, ], ], };","s":"Installing plugins","u":"/docs/docusaurus-mdx/mdx-features/plugins","h":"#installing-plugins","p":804},{"i":811,"t":"Docusaurus has built-in support for MDX, which allows you to write JSX within your Markdown files and render them as React components. Check out the MDX docs to see what fancy stuff you can do with MDX. Debugging MDX The MDX format is quite strict, and you may get compilation errors. Use the MDX playground to debug them and make sure your syntax is valid.","s":"MDX and React","u":"/docs/docusaurus-mdx/mdx-features/react","h":"","p":810},{"i":813,"t":"To define any custom component within an MDX file, you have to export it: only paragraphs that start with export will be parsed as components instead of prose. export const Highlight = ({children, color}) => ( <span style={{ backgroundColor: color, borderRadius: '2px', color: '#fff', padding: '0.2rem', }}> {children} </span> ); <Highlight color=\"#25c2a0\">Docusaurus green</Highlight> and <Highlight color=\"#1877F2\">Facebook blue</Highlight> are my favorite colors. I can write **Markdown** alongside my _JSX_! Notice how it renders both the markup from your React component and the Markdown syntax: Docusaurus green and Facebook blue are my favorite colors. I can write Markdown alongside my JSX! MDX is JSX Since all doc files are parsed using MDX, anything that looks like HTML is actually JSX. Therefore, if you need to inline-style a component, follow JSX flavor and provide style objects. /* Instead of this: */ <span style=\"background-color: red\">Foo</span> /* Use this: */ <span style={{backgroundColor: 'red'}}>Foo</span>","s":"Exporting components","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#exporting-components","p":810},{"i":815,"t":"You can also import your own components defined in other files or third-party components installed via npm. <!-- Docusaurus theme component --> import TOCInline from '@theme/TOCInline'; <!-- External component --> import Button from '@mui/material/Button'; <!-- Custom component --> import BrowserWindow from '@site/src/components/BrowserWindow'; 提示 The @site alias points to your website's directory, usually where the docusaurus.config.ts file is. Using an alias instead of relative paths ('../../src/components/BrowserWindow') saves you from updating import paths when moving files around, or when versioning docs and translating. While declaring components within Markdown is very convenient for simple cases, it becomes hard to maintain because of limited editor support, risks of parsing errors, and low reusability. Use a separate .js file when your component involves complex JS logic: src/components/Highlight.js import React from 'react'; export default function Highlight({children, color}) { return ( <span style={{ backgroundColor: color, borderRadius: '2px', color: '#fff', padding: '0.2rem', }}> {children} </span> ); } markdown-file.mdx import Highlight from '@site/src/components/Highlight'; <Highlight color=\"#25c2a0\">Docusaurus green</Highlight> 提示 If you use the same component across a lot of files, you don't need to import it everywhere—consider adding it to the global scope. See below","s":"Importing components","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#importing-components","p":810},{"i":817,"t":"Apart from importing a component and exporting a component, a third way to use a component in MDX is to register it to the global scope, which will make it automatically available in every MDX file, without any import statements. For example, given this MDX file: - a - list! And some <Highlight>custom markup</Highlight>... It will be compiled to a React component containing ul, li, p, and Highlight elements. Highlight is not a native html element: you need to provide your own React component implementation for it. In Docusaurus, the MDX component scope is provided by the @theme/MDXComponents file. It's not a React component, per se, unlike most other exports under the @theme/ alias: it is a record from tag names like Highlight to their React component implementations. If you swizzle this component, you will find all tags that have been implemented, and you can further customize our implementation by swizzling the respective sub-component, like @theme/MDXComponents/Code (which is used to render Markdown code blocks). If you want to register extra tag names (like the <Highlight> tag above), you should consider wrapping @theme/MDXComponents by swizzling, so you don't have to maintain all the existing mappings. Since the swizzle CLI doesn't allow wrapping non-component files yet, you should manually create the wrapper: src/theme/MDXComponents.js import React from 'react'; // Import the original mapper import MDXComponents from '@theme-original/MDXComponents'; // highlight-next-line import Highlight from '@site/src/components/Highlight'; export default { // Re-use the default mapping ...MDXComponents, // Map the \"<Highlight>\" tag to our Highlight component // `Highlight` will receive all props that were passed to `<Highlight>` in MDX // highlight-next-line Highlight, }; And now, you can freely use <Highlight> in every page, without writing the import statement: I can conveniently use <Highlight color=\"#25c2a0\">Docusaurus green</Highlight> everywhere! I can conveniently use Docusaurus green everywhere! 注意 We use upper-case tag names like Highlight on purpose. From MDX v3+ onward (Docusaurus v3+), lower-case tag names are always rendered as native html elements, and will not use any component mapping you provide. 注意 This feature is powered by an MDXProvider. If you are importing Markdown in a React page, you have to supply this provider yourself through the MDXContent theme component. src/pages/index.js import React from 'react'; import FeatureDisplay from './_featureDisplay.mdx'; // highlight-next-line import MDXContent from '@theme/MDXContent'; export default function LandingPage() { return ( <div> <MDXContent> <FeatureDisplay /> </MDXContent> </div> ); } If you don't wrap your imported MDX with MDXContent, the global scope will not be available.","s":"MDX component scope","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#mdx-component-scope","p":810},{"i":819,"t":"Docusaurus v3 is using MDX v3. The MDX syntax is mostly compatible with CommonMark, but is much stricter because your .mdx files can use JSX and are compiled into real React components (check the playground). Some valid CommonMark features won't work with MDX (more info), notably: Indented code blocks: use triple backticks instead Autolinks (<http://localhost:3000>): use regular link syntax instead ([http://localhost:3000](http://localhost:3000)) HTML syntax (<p style=\"color: red;\">): use JSX instead (<p style={{color: 'red'}}>) Unescaped { and <: escape them with \\ instead (\\{ and \\<) Experimental CommonMark support Docusaurus v3 makes it possible to opt-in for a less strict, standard CommonMark support with the following options: The format: md front matter The .md file extension combined with the siteConfig.markdown.format: \"detect\" configuration This feature is experimental and currently has a few limitations.","s":"Markdown and JSX interoperability","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#markdown-and-jsx-interoperability","p":810},{"i":821,"t":"You can not only import a file containing a component definition, but also import any code file as raw text, and then insert it in a code block, thanks to Webpack raw-loader. In order to use raw-loader, you first need to install it in your project: npm Yarn pnpm npm install --save raw-loader yarn add raw-loader pnpm add raw-loader Now you can import code snippets from another file as it is: myMarkdownFile.mdx import CodeBlock from '@theme/CodeBlock'; import MyComponentSource from '!!raw-loader!./_myReactComponent'; <CodeBlock language=\"jsx\">{MyComponentSource}</CodeBlock> /** * Copyright (c) Facebook, Inc. and its affiliates. * * This source code is licensed under the MIT license found in the * LICENSE file in the root directory of this source tree. */ import React, {useState} from 'react'; export default function MyComponent() { const [bool, setBool] = useState(false); return ( <div> <p>MyComponent rendered !</p> <p>bool={bool ? 'true' : 'false'}</p> <p> <button onClick={() => setBool((b) => !b)}>toggle bool</button> </p> </div> ); } See using code blocks in JSX for more details of the <CodeBlock> component. 备注 You have to use <CodeBlock> rather than the Markdown triple-backtick ```, because the latter will ship out any of its content as-is, but you want to interpolate the imported text here. 注意 This feature is experimental and might be subject to breaking API changes in the future.","s":"Importing code snippets","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#importing-code-snippets","p":810},{"i":823,"t":"You can use Markdown files as components and import them elsewhere, either in Markdown files or in React pages. By convention, using the _ filename prefix will not create any doc page and means the Markdown file is a \"partial\", to be imported by other files. _markdown-partial-example.mdx <span>Hello {props.name}</span> This is text some content from `_markdown-partial-example.mdx`. someOtherDoc.mdx import PartialExample from './_markdown-partial-example.mdx'; <PartialExample name=\"Sebastien\" /> Hello Sebastien This is text some content from _markdown-partial-example.md. This way, you can reuse content among multiple pages and avoid duplicating materials. 注意 Currently, the table of contents does not contain the imported Markdown headings. This is a technical limitation that we are trying to solve (issue).","s":"Importing Markdown","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#importing-markdown","p":810},{"i":825,"t":"Within the MDX page, the following variables are available as globals: frontMatter: the front matter as a record of string keys and values; toc: the table of contents, as a tree of headings. See also Inline TOC for a more concrete use-case. contentTitle: the Markdown title, which is the first h1 heading in the Markdown text. It's undefined if there isn't one (e.g. title specified in the front matter). import TOCInline from '@theme/TOCInline'; import CodeBlock from '@theme/CodeBlock'; The table of contents for this page, serialized: <CodeBlock className=\"language-json\">{JSON.stringify(toc, null, 2)}</CodeBlock> The front matter of this page: <ul> {Object.entries(frontMatter).map(([key, value]) => <li key={key}><b>{key}</b>: {value}</li>)} </ul> <p>The title of this page is: <b>{contentTitle}</b></p> The table of contents for this page, serialized: [ { \"value\": \"Exporting components\", \"id\": \"exporting-components\", \"level\": 3 }, { \"value\": \"Importing components\", \"id\": \"importing-components\", \"level\": 3 }, { \"value\": \"MDX component scope\", \"id\": \"mdx-component-scope\", \"level\": 3 }, { \"value\": \"Markdown and JSX interoperability\", \"id\": \"markdown-and-jsx-interoperability\", \"level\": 3 }, { \"value\": \"Importing code snippets\", \"id\": \"importing-code-snippets\", \"level\": 2 }, { \"value\": \"Importing Markdown\", \"id\": \"importing-markdown\", \"level\": 2 }, { \"value\": \"Available exports\", \"id\": \"available-exports\", \"level\": 2 } ] The front matter of this page: description: Using the power of React in Docusaurus Markdown documents, thanks to MDX The title of this page is: MDX and React","s":"Available exports","u":"/docs/docusaurus-mdx/mdx-features/react","h":"#available-exports","p":810},{"i":827,"t":"信息 Tag <Tabs> and <TabItems> are default installed and enabled. Docusaurus provides the <Tabs> component that you can use in Markdown thanks to MDX: <Tabs> <TabItem value=\"apple\" label=\"Apple\" default> This is an apple 🍎 </TabItem> <TabItem value=\"orange\" label=\"Orange\"> This is an orange 🍊 </TabItem> <TabItem value=\"banana\" label=\"Banana\"> This is a banana 🍌 </TabItem> </Tabs> Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌 It is also possible to provide values and defaultValue props to Tabs: <Tabs defaultValue=\"apple\" values={[ {label: 'Apple', value: 'apple'}, {label: 'Orange', value: 'orange'}, {label: 'Banana', value: 'banana'}, ]}> <TabItem value=\"apple\">This is an apple 🍎</TabItem> <TabItem value=\"orange\">This is an orange 🍊</TabItem> <TabItem value=\"banana\">This is a banana 🍌</TabItem> </Tabs> Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌 Tabs props take precedence over the TabItem props: <Tabs defaultValue=\"apple\" values={[ {label: 'Apple 1', value: 'apple'}, {label: 'Orange 1', value: 'orange'}, {label: 'Banana 1', value: 'banana'}, ]}> <TabItem value=\"apple\" label=\"Apple 2\"> This is an apple 🍎 </TabItem> <TabItem value=\"orange\" label=\"Orange 2\"> This is an orange 🍊 </TabItem> <TabItem value=\"banana\" label=\"Banana 2\" default> This is a banana 🍌 </TabItem> </Tabs> Apple 1 Orange 1 Banana 1 This is an apple 🍎 This is an orange 🍊 This is a banana 🍌 提示 By default, all tabs are rendered eagerly during the build process, and search engines can index hidden tabs. It is possible to only render the default tab with <Tabs lazy />.","s":"Tabs and TabItem","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"","p":826},{"i":829,"t":"The first tab is displayed by default, and to override this behavior, you can specify a default tab by adding default to one of the tab items. You can also set the defaultValue prop of the Tabs component to the label value of your choice. For example, in the example above, either setting default for the value=\"apple\" tab or setting defaultValue=\"apple\" for the tabs forces the \"Apple\" tab to be open by default. Docusaurus will throw an error if a defaultValue is provided for the Tabs but it refers to a non-existing value. If you want none of the tabs to be shown by default, use defaultValue={null}.","s":"Displaying a default tab","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#displaying-a-default-tab","p":826},{"i":831,"t":"You may want choices of the same kind of tabs to sync with each other. For example, you might want to provide different instructions for users on Windows vs users on macOS, and you want to change all OS-specific instructions tabs in one click. To achieve that, you can give all related tabs the same groupId prop. Note that doing this will persist the choice in localStorage and all <Tab> instances with the same groupId will update automatically when the value of one of them is changed. Note that group IDs are globally namespaced. // highlight-next-line <Tabs groupId=\"operating-systems\"> <TabItem value=\"win\" label=\"Windows\">Use Ctrl + C to copy.</TabItem> <TabItem value=\"mac\" label=\"macOS\">Use Command + C to copy.</TabItem> </Tabs> // highlight-next-line <Tabs groupId=\"operating-systems\"> <TabItem value=\"win\" label=\"Windows\">Use Ctrl + V to paste.</TabItem> <TabItem value=\"mac\" label=\"macOS\">Use Command + V to paste.</TabItem> </Tabs> Windows macOS Use Ctrl + C to copy. Use Command + C to copy. Windows macOS Use Ctrl + V to paste. Use Command + V to paste. For all tab groups that have the same groupId, the possible values do not need to be the same. If one tab group is chosen a value that does not exist in another tab group with the same groupId, the tab group with the missing value won't change its tab. You can see that from the following example. Try to select Linux, and the above tab groups don't change. <Tabs groupId=\"operating-systems\"> <TabItem value=\"win\" label=\"Windows\"> I am Windows. </TabItem> <TabItem value=\"mac\" label=\"macOS\"> I am macOS. </TabItem> <TabItem value=\"linux\" label=\"Linux\"> I am Linux. </TabItem> </Tabs> Windows macOS Linux I am Windows. I am macOS. I am Linux. Tab choices with different group IDs will not interfere with each other: // highlight-next-line <Tabs groupId=\"operating-systems\"> <TabItem value=\"win\" label=\"Windows\">Windows in windows.</TabItem> <TabItem value=\"mac\" label=\"macOS\">macOS is macOS.</TabItem> </Tabs> // highlight-next-line <Tabs groupId=\"non-mac-operating-systems\"> <TabItem value=\"win\" label=\"Windows\">Windows is windows.</TabItem> <TabItem value=\"unix\" label=\"Unix\">Unix is unix.</TabItem> </Tabs> Windows macOS Windows in windows. macOS is macOS. Windows Unix Windows is windows. Unix is unix.","s":"Syncing tab choices","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#syncing-tab-choices","p":826},{"i":833,"t":"You might want to customize the appearance of a certain set of tabs. You can pass the string in className prop, and the specified CSS class will be added to the Tabs component: // highlight-next-line <Tabs className=\"unique-tabs\"> <TabItem value=\"Apple\">This is an apple 🍎</TabItem> <TabItem value=\"Orange\">This is an orange 🍊</TabItem> <TabItem value=\"Banana\">This is a banana 🍌</TabItem> </Tabs> Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌","s":"Customizing tabs","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#customizing-tabs","p":826},{"i":835,"t":"You can also customize each tab heading independently by using the attributes field. The extra props can be passed to the headings either through the values prop in Tabs, or props of each TabItem—in the same way as you declare label. some-doc.mdx import styles from './markdown-features-tabs-styles.module.css'; <Tabs> <TabItem value=\"apple\" label=\"Apple\" attributes={{className: styles.red}}> This is an apple 🍎 </TabItem> <TabItem value=\"orange\" label=\"Orange\" attributes={{className: styles.orange}}> This is an orange 🍊 </TabItem> <TabItem value=\"banana\" label=\"Banana\" attributes={{className: styles.yellow}}> This is a banana 🍌 </TabItem> </Tabs> styles.module.css .red { color: red; } .red[aria-selected='true'] { border-bottom-color: red; } .orange { color: orange; } .orange[aria-selected='true'] { border-bottom-color: orange; } .yellow { color: yellow; } .yellow[aria-selected='true'] { border-bottom-color: yellow; } Apple Orange Banana This is an apple 🍎 This is an orange 🍊 This is a banana 🍌 提示 className would be merged with other default class names. You may also use a custom data-value field ({'data-value': 'apple'}) paired with CSS attribute selectors: styles.module.css li[role='tab'][data-value='apple'] { color: red; }","s":"Customizing tab headings","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#customizing-tab-headings","p":826},{"i":837,"t":"It is possible to persist the selected tab into the url search parameters. This enables you to share a link to a page which pre-selects the tab - linking from your Android app to documentation with the Android tabs pre-selected. This feature does not provide an anchor link - the browser will not scroll to the tab. Use the queryString prop to enable this feature and define the search param name to use. // highlight-next-line <Tabs queryString=\"current-os\"> <TabItem value=\"android\" label=\"Android\"> Android </TabItem> <TabItem value=\"ios\" label=\"iOS\"> iOS </TabItem> </Tabs> Android iOS Android iOS As soon as a tab is clicked, a search parameter is added at the end of the url: ?current-os=android or ?current-os=ios. 提示 queryString can be used together with groupId. For convenience, when the queryString prop is true, the groupId value will be used as a fallback. // highlight-next-line <Tabs groupId=\"current-os\" queryString> <TabItem value=\"android\" label=\"Android\"> Android </TabItem> <TabItem value=\"ios\" label=\"iOS\"> iOS </TabItem> </Tabs> Android iOS Android iOS When the page loads, the tab query string choice will be restored in priority over the groupId choice (using localStorage).","s":"Query string","u":"/docs/docusaurus-mdx/mdx-features/tabs","h":"#query-string","p":826},{"i":840,"t":"You can use regular Markdown headings. ## Level 2 title ### Level 3 title #### Level 4 title Each Markdown heading will appear as a table of contents entry.","s":"Markdown headings","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#markdown-headings","p":838},{"i":842,"t":"Each heading has an ID that can be automatically generated or explicitly specified. Heading IDs allow you to link to a specific document heading in Markdown or JSX: [link](#heading-id) <Link to=\"#heading-id\">link</Link> By default, Docusaurus will generate heading IDs for you, based on the heading text. For example, ### Hello World will have ID hello-world. Generated IDs have some limitations: The ID might not look good You might want to change or translate the text without updating the existing ID A special Markdown syntax lets you set an explicit heading id: ### Hello World {#my-explicit-id} 提示 Use the write-heading-ids CLI command to add explicit IDs to all your Markdown documents. Avoid colliding IDs Generated heading IDs will be guaranteed to be unique on each page, but if you use custom IDs, make sure each one appears exactly once on each page, or there will be two DOM elements with the same ID, which is invalid HTML semantics, and will lead to one heading being unlinkable.","s":"Heading IDs","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#heading-ids","p":838},{"i":844,"t":"Each Markdown document displays a table of contents on the top-right corner. By default, this table only shows h2 and h3 headings, which should be sufficient for an overview of the page structure. In case you need to change the range of headings displayed, you can customize the minimum and maximum heading level — either per page or globally. To set the heading level for a particular page, use the toc_min_heading_level and toc_max_heading_level front matter. myDoc.md --- # Display h2 to h5 headings toc_min_heading_level: 2 toc_max_heading_level: 5 --- To set the heading level for all pages, use the themeConfig.tableOfContents option. docusaurus.config.ts export default { themeConfig: { tableOfContents: { minHeadingLevel: 2, maxHeadingLevel: 5, }, }, }; If you've set the options globally, you can still override them locally via front matter. 备注 The themeConfig option would apply to all TOC on the site, including inline TOC, but front matter options only affect the top-right TOC. You need to use the minHeadingLevel and maxHeadingLevel props to customize each <TOCInline /> component.","s":"Table of contents heading level","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#table-of-contents-heading-level","p":838},{"i":846,"t":"It is also possible to display an inline table of contents directly inside a Markdown document, thanks to MDX. The toc variable is available in any MDX document and contains all the headings of an MDX document. By default, only h2 and h3 headings are displayed in the TOC. You can change which heading levels are visible by setting minHeadingLevel or maxHeadingLevel for individual TOCInline components. import TOCInline from '@theme/TOCInline'; <TOCInline toc={toc} /> Markdown headings Heading IDs Table of contents heading level Inline table of contents Customizing table of contents generation Example Section 1 Example Subsection 1 a Example Subsection 1 b Example Subsection 1 c Example Section 2 Example Subsection 2 a Example Subsection 2 b Example Subsection 2 c Example Section 3 Example Subsection 3 a Example Subsection 3 b Example Subsection 3 c The toc global is just a list of heading items: declare const toc: { value: string; id: string; level: number; }[]; Note that the toc global is a flat array, so you can easily cut out unwanted nodes or insert extra nodes, and create a new TOC tree. import TOCInline from '@theme/TOCInline'; <TOCInline // Only show h2 and h4 headings toc={toc.filter((node) => node.level === 2 || node.level === 4)} minHeadingLevel={2} // Show h4 headings in addition to the default h2 and h3 headings maxHeadingLevel={4} /> Markdown headings Table of contents heading level Inline table of contents Customizing table of contents generation Example Section 1 Example subsubsection 1 a I Example subsubsection 1 a II Example subsubsection 1 a III Example subsubsection 1 b I Example subsubsection 1 b II Example subsubsection 1 b III Example subsubsection 1 c I Example subsubsection 1 c II Example subsubsection 1 c III Example Section 2 Example subsubsection 2 a I Example subsubsection 2 a II Example subsubsection 2 a III Example subsubsection 2 b I Example subsubsection 2 b II Example subsubsection 2 b III Example subsubsection 2 c I Example subsubsection 2 c II Example subsubsection 2 c III Example Section 3 Example subsubsection 3 a I Example subsubsection 3 a II Example subsubsection 3 a III Example subsubsection 3 b I Example subsubsection 3 b II Example subsubsection 3 b III Example subsubsection 3 c I Example subsubsection 3 c II Example subsubsection 3 c III","s":"Inline table of contents","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#inline-table-of-contents","p":838},{"i":848,"t":"The table-of-contents is generated by parsing the Markdown source with a Remark plugin. There are known edge-cases where it generates false-positives and false-negatives. Markdown headings within hideable areas will still show up in the TOC. For example, headings within Tabs and details will not be excluded. Non-Markdown headings will not show up in the TOC. This can be used to your advantage to tackle the aforementioned issue. <details> <summary>Some details containing headings</summary> <h2 id=\"#heading-id\">I'm a heading that will not show up in the TOC</h2> Some content... </details> The ability to ergonomically insert extra headings or ignore certain headings is a work-in-progress. If this feature is important to you, please report your use-case in this issue. 注意 Below is just some dummy content to have more table of contents items available on the current page.","s":"Customizing table of contents generation","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#customizing-table-of-contents-generation","p":838},{"i":850,"t":"Lorem ipsum","s":"Example Section 1","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-section-1","p":838},{"i":852,"t":"Lorem ipsum Example subsubsection 1 a I​ Example subsubsection 1 a II​ Example subsubsection 1 a III​","s":"Example Subsection 1 a","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-1-a","p":838},{"i":854,"t":"Lorem ipsum Example subsubsection 1 b I​ Example subsubsection 1 b II​ Example subsubsection 1 b III​","s":"Example Subsection 1 b","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-1-b","p":838},{"i":856,"t":"Lorem ipsum Example subsubsection 1 c I​ Example subsubsection 1 c II​ Example subsubsection 1 c III​","s":"Example Subsection 1 c","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-1-c","p":838},{"i":858,"t":"Lorem ipsum","s":"Example Section 2","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-section-2","p":838},{"i":860,"t":"Lorem ipsum Example subsubsection 2 a I​ Example subsubsection 2 a II​ Example subsubsection 2 a III​","s":"Example Subsection 2 a","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-2-a","p":838},{"i":862,"t":"Lorem ipsum Example subsubsection 2 b I​ Example subsubsection 2 b II​ Example subsubsection 2 b III​","s":"Example Subsection 2 b","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-2-b","p":838},{"i":864,"t":"Lorem ipsum Example subsubsection 2 c I​ Example subsubsection 2 c II​ Example subsubsection 2 c III​","s":"Example Subsection 2 c","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-2-c","p":838},{"i":866,"t":"Lorem ipsum","s":"Example Section 3","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-section-3","p":838},{"i":868,"t":"Lorem ipsum Example subsubsection 3 a I​ Example subsubsection 3 a II​ Example subsubsection 3 a III​","s":"Example Subsection 3 a","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-3-a","p":838},{"i":870,"t":"Lorem ipsum Example subsubsection 3 b I​ Example subsubsection 3 b II​ Example subsubsection 3 b III​","s":"Example Subsection 3 b","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-3-b","p":838},{"i":872,"t":"Lorem ipsum Example subsubsection 3 c I​ Example subsubsection 3 c II​ Example subsubsection 3 c III​","s":"Example Subsection 3 c","u":"/docs/docusaurus-mdx/mdx-features/toc","h":"#example-subsection-3-c","p":838},{"i":874,"t":"Provides the Blog feature and is the default blog plugin for Docusaurus. some features production only The feed feature works by extracting the build output, and is only active in production.","s":"📦 plugin-content-blog","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"","p":873},{"i":876,"t":"npm Yarn pnpm npm install --save @docusaurus/plugin-content-blog yarn add @docusaurus/plugin-content-blog pnpm add @docusaurus/plugin-content-blog 提示 If you use the preset @docusaurus/preset-classic, you don't need to install this plugin as a dependency. You can configure this plugin through the preset options.","s":"Installation","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#installation","p":873},{"i":878,"t":"Accepted fields: Name Type Default Description path string 'blog' Path to the blog content directory on the file system, relative to site dir. editUrl string | EditUrlFn undefined Base URL to edit your site. The final URL is computed by editUrl + relativePostPath. Using a function allows more nuanced control for each file. Omitting this variable entirely will disable edit links. editLocalizedFiles boolean false The edit URL will target the localized file, instead of the original unlocalized file. Ignored when editUrl is a function. blogTitle string 'Blog' Blog page title for better SEO. blogDescription string 'Blog' Blog page meta description for better SEO. blogSidebarCount number | 'ALL' 5 Number of blog post elements to show in the blog sidebar. 'ALL' to show all blog posts; 0 to disable. blogSidebarTitle string 'Recent posts' Title of the blog sidebar. routeBasePath string 'blog' URL route for the blog section of your site. DO NOT include a trailing slash. Use / to put the blog at root path. tagsBasePath string 'tags' URL route for the tags section of your blog. Will be appended to routeBasePath. DO NOT include a trailing slash. archiveBasePath string | null 'archive' URL route for the archive section of your blog. Will be appended to routeBasePath. DO NOT include a trailing slash. Use null to disable generation of archive. include string[] ['**/*.{md,mdx}'] Array of glob patterns matching Markdown files to be built, relative to the content path. exclude string[] See example configuration Array of glob patterns matching Markdown files to be excluded. Serves as refinement based on the include option. postsPerPage number | 'ALL' 10 Number of posts to show per page in the listing page. Use 'ALL' to display all posts on one listing page. blogListComponent string '@theme/BlogListPage' Root component of the blog listing page. blogPostComponent string '@theme/BlogPostPage' Root component of each blog post page. blogTagsListComponent string '@theme/BlogTagsListPage' Root component of the tags list page. blogTagsPostsComponent string '@theme/BlogTagsPostsPage' Root component of the \"posts containing tag\" page. blogArchiveComponent string '@theme/BlogArchivePage' Root component of the blog archive page. remarkPlugins any[] [] Remark plugins passed to MDX. rehypePlugins any[] [] Rehype plugins passed to MDX. beforeDefaultRemarkPlugins any[] [] Custom Remark plugins passed to MDX before the default Docusaurus Remark plugins. beforeDefaultRehypePlugins any[] [] Custom Rehype plugins passed to MDX before the default Docusaurus Rehype plugins. truncateMarker RegExp /<!--\\s*truncate\\s*-->/ | \\{\\/\\*\\s*truncate\\s*\\*\\/\\}/ Truncate marker marking where the summary ends. showReadingTime boolean true Show estimated reading time for the blog post. readingTime ReadingTimeFn The default reading time A callback to customize the reading time number displayed. authorsMapPath string 'authors.yml' Path to the authors map file, relative to the blog content directory. feedOptions See below {type: ['rss', 'atom']} Blog feed. feedOptions.type FeedType | FeedType[] | 'all' | null Required Type of feed to be generated. Use null to disable generation. feedOptions.createFeedItems CreateFeedItemsFn | undefined undefined An optional function which can be used to transform and / or filter the items in the feed. feedOptions.limit number | null | false 20 Limits the feed to the specified number of posts, false or null for all entries. Defaults to 20. feedOptions.title string siteConfig.title Title of the feed. feedOptions.description string `${siteConfig.title} Blog` Description of the feed. feedOptions.copyright string undefined Copyright message. feedOptions.language string (See documentation for possible values) undefined Language metadata of the feed. sortPosts 'descending' | 'ascending' 'descending' Governs the direction of blog post sorting.","s":"Configuration","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#configuration","p":873},{"i":880,"t":"EditUrlFn​ type EditUrlFunction = (params: { blogDirPath: string; blogPath: string; permalink: string; locale: string; }) => string | undefined; ReadingTimeFn​ type ReadingTimeOptions = { wordsPerMinute: number; wordBound: (char: string) => boolean; }; type ReadingTimeCalculator = (params: { content: string; frontMatter?: BlogPostFrontMatter & Record<string, unknown>; options?: ReadingTimeOptions; }) => number; type ReadingTimeFn = (params: { content: string; frontMatter: BlogPostFrontMatter & Record<string, unknown>; defaultReadingTime: ReadingTimeCalculator; }) => number | undefined; FeedType​ type FeedType = 'rss' | 'atom' | 'json'; CreateFeedItemsFn​ type CreateFeedItemsFn = (params: { blogPosts: BlogPost[]; siteConfig: DocusaurusConfig; outDir: string; defaultCreateFeedItemsFn: CreateFeedItemsFn; }) => Promise<BlogFeedItem[]>;","s":"Types","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#types","p":873},{"i":882,"t":"You can configure this plugin through preset options or plugin options. 提示 Most Docusaurus users configure this plugin through the preset options. JavaScript // Preset Options: blog // Plugin Options: @docusaurus/plugin-content-blog const config = { path: 'blog', // Simple use-case: string editUrl // editUrl: 'https://github.com/facebook/docusaurus/edit/main/website/', // Advanced use-case: functional editUrl editUrl: ({locale, blogDirPath, blogPath, permalink}) => `https://github.com/facebook/docusaurus/edit/main/website/${blogDirPath}/${blogPath}`, editLocalizedFiles: false, blogTitle: 'Blog title', blogDescription: 'Blog', blogSidebarCount: 5, blogSidebarTitle: 'All our posts', routeBasePath: 'blog', include: ['**/*.{md,mdx}'], exclude: [ '**/_*.{js,jsx,ts,tsx,md,mdx}', '**/_*/**', '**/*.test.{js,jsx,ts,tsx}', '**/__tests__/**', ], postsPerPage: 10, blogListComponent: '@theme/BlogListPage', blogPostComponent: '@theme/BlogPostPage', blogTagsListComponent: '@theme/BlogTagsListPage', blogTagsPostsComponent: '@theme/BlogTagsPostsPage', remarkPlugins: [require('./my-remark-plugin')], rehypePlugins: [], beforeDefaultRemarkPlugins: [], beforeDefaultRehypePlugins: [], truncateMarker: /<!--\\s*(truncate)\\s*-->/, showReadingTime: true, feedOptions: { type: '', title: '', description: '', copyright: '', language: undefined, createFeedItems: async (params) => { const {blogPosts, defaultCreateFeedItems, ...rest} = params; return defaultCreateFeedItems({ // keep only the 10 most recent blog posts in the feed blogPosts: blogPosts.filter((item, index) => index < 10), ...rest, }); }, }, };","s":"Example configuration","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#ex-config","p":873},{"i":884,"t":"Markdown documents can use the following Markdown front matter metadata fields, enclosed by a line --- on either side. Accepted fields: Name Type Default Description authors Authors undefined List of blog post authors (or unique author). Read the authors guide for more explanations. Prefer authors over the author_* front matter fields, even for single author blog posts. author string undefined ⚠️ Prefer using authors. The blog post author's name. author_url string undefined ⚠️ Prefer using authors. The URL that the author's name will be linked to. This could be a GitHub, Twitter, Facebook profile URL, etc. author_image_url string undefined ⚠️ Prefer using authors. The URL to the author's thumbnail image. author_title string undefined ⚠️ Prefer using authors. A description of the author. title string Markdown title The blog post title. date string File name or file creation time The blog post creation date. If not specified, this can be extracted from the file or folder name, e.g, 2021-04-15-blog-post.mdx, 2021-04-15-blog-post/index.mdx, 2021/04/15/blog-post.mdx. Otherwise, it is the Markdown file creation time. tags Tag[] undefined A list of strings or objects of two string fields label and permalink to tag to your post. draft boolean false Draft blog posts will only be available during development. unlisted boolean false Unlisted blog posts will be available in both development and production. They will be \"hidden\" in production, not indexed, excluded from sitemaps, and can only be accessed by users having a direct link. hide_table_of_contents boolean false Whether to hide the table of contents to the right. toc_min_heading_level number 2 The minimum heading level shown in the table of contents. Must be between 2 and 6 and lower or equal to the max value. toc_max_heading_level number 3 The max heading level shown in the table of contents. Must be between 2 and 6. keywords string[] undefined Keywords meta tag, which will become the <meta name=\"keywords\" content=\"keyword1,keyword2,...\"/> in <head>, used by search engines. description string The first line of Markdown content The description of your document, which will become the <meta name=\"description\" content=\"...\"/> and <meta property=\"og:description\" content=\"...\"/> in <head>, used by search engines. image string undefined Cover or thumbnail image that will be used when displaying the link to your post. slug string File path Allows to customize the blog post URL (/<routeBasePath>/<slug>). Support multiple patterns: slug: my-blog-post, slug: /my/path/to/blog/post, slug: /. type Tag = string | {label: string; permalink: string}; // An author key references an author from the global plugin authors.yml file type AuthorKey = string; type Author = { key?: AuthorKey; name: string; title?: string; url?: string; image_url?: string; }; // The front matter authors field allows various possible shapes type Authors = AuthorKey | Author | (AuthorKey | Author)[]; Example: --- title: Welcome Docusaurus authors: - slorber - yangshun - name: Joel Marcey title: Co-creator of Docusaurus 1 url: https://github.com/JoelMarcey image_url: https://github.com/JoelMarcey.png tags: [hello, docusaurus-v2] description: This is my first post on Docusaurus. image: https://i.imgur.com/mErPwqL.png hide_table_of_contents: false --- A Markdown blog post","s":"Markdown front matter","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#markdown-front-matter","p":873},{"i":886,"t":"Read the i18n introduction first.","s":"i18n","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#i18n","p":873},{"i":888,"t":"Base path: website/i18n/[locale]/docusaurus-plugin-content-blog Multi-instance path: website/i18n/[locale]/docusaurus-plugin-content-blog-[pluginId] JSON files: extracted with docusaurus write-translations Markdown files: website/i18n/[locale]/docusaurus-plugin-content-blog","s":"Translation files location","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#translation-files-location","p":873},{"i":890,"t":"website/i18n/[locale]/docusaurus-plugin-content-blog │ │ # translations for website/blog ├── authors.yml ├── first-blog-post.md ├── second-blog-post.md │ │ # translations for the plugin options that will be rendered └── options.json","s":"Example file-system structure","u":"/docs/docusaurus-mdx/plugin-contents/blog","h":"#example-file-system-structure","p":873},{"i":892,"t":"Provides the docs functionality and is the default docs plugin for Docusaurus.","s":"📦 plugin-content-docs","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"","p":891},{"i":894,"t":"npm Yarn pnpm npm install --save @docusaurus/plugin-content-docs yarn add @docusaurus/plugin-content-docs pnpm add @docusaurus/plugin-content-docs 提示 If you use the preset @docusaurus/preset-classic, you don't need to install this plugin as a dependency. You can configure this plugin through the preset options.","s":"Installation","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#installation","p":891},{"i":896,"t":"Accepted fields: Name Type Default Description path string 'docs' Path to the docs content directory on the file system, relative to site directory. editUrl string | EditUrlFunction undefined Base URL to edit your site. The final URL is computed by editUrl + relativeDocPath. Using a function allows more nuanced control for each file. Omitting this variable entirely will disable edit links. editLocalizedFiles boolean false The edit URL will target the localized file, instead of the original unlocalized file. Ignored when editUrl is a function. editCurrentVersion boolean false The edit URL will always target the current version doc instead of older versions. Ignored when editUrl is a function. routeBasePath string 'docs' URL route for the docs section of your site. DO NOT include a trailing slash. Use / for shipping docs without base path. tagsBasePath string 'tags' URL route for the tags list page of your site. It is prepended to the routeBasePath. include string[] ['**/*.{md,mdx}'] Array of glob patterns matching Markdown files to be built, relative to the content path. exclude string[] See example configuration Array of glob patterns matching Markdown files to be excluded. Serves as refinement based on the include option. sidebarPath false | string undefined Path to sidebar configuration. Use false to disable sidebars, or undefined to create a fully autogenerated sidebar. sidebarCollapsible boolean true Whether sidebar categories are collapsible by default. See also Collapsible categories sidebarCollapsed boolean true Whether sidebar categories are collapsed by default. See also Expanded categories by default sidebarItemsGenerator SidebarGenerator Omitted Function used to replace the sidebar items of type 'autogenerated' with real sidebar items (docs, categories, links...). See also Customize the sidebar items generator numberPrefixParser boolean | PrefixParser Omitted Custom parsing logic to extract number prefixes from file names. Use false to disable this behavior and leave the docs untouched, and true to use the default parser. See also Using number prefixes docsRootComponent string '@theme/DocsRoot' Parent component of all the docs plugin pages (including all versions). Stays mounted when navigation between docs pages and versions. docVersionRootComponent string '@theme/DocVersionLayout' Parent component of all docs pages of an individual version (doc pages with sidebars, tags pages). Stays mounted when navigation between pages of that specific version. docRootComponent string '@theme/DocPage' Parent component of all doc pages with sidebars (regular docs pages, category generated index pages). Stays mounted when navigation between such pages. docItemComponent string '@theme/DocItem' Main doc container, with TOC, pagination, etc. docTagsListComponent string '@theme/DocTagsListPage' Root component of the tags list page docTagDocListComponent string '@theme/DocTagDocListPage' Root component of the \"docs containing tag X\" page. docCategoryGeneratedIndexComponent string '@theme/DocCategoryGeneratedIndexPage' Root component of the generated category index page. remarkPlugins any[] [] Remark plugins passed to MDX. rehypePlugins any[] [] Rehype plugins passed to MDX. beforeDefaultRemarkPlugins any[] [] Custom Remark plugins passed to MDX before the default Docusaurus Remark plugins. beforeDefaultRehypePlugins any[] [] Custom Rehype plugins passed to MDX before the default Docusaurus Rehype plugins. showLastUpdateAuthor boolean false Whether to display the author who last updated the doc. showLastUpdateTime boolean false Whether to display the last date the doc was updated. breadcrumbs boolean true Enable or disable the breadcrumbs on doc pages. disableVersioning boolean false Explicitly disable versioning even when multiple versions exist. This will make the site only include the current version. Will error if includeCurrentVersion: false and disableVersioning: true. includeCurrentVersion boolean true Include the current version of your docs. lastVersion string First version in versions.json The version navigated to in priority and displayed by default for docs navbar items. onlyIncludeVersions string[] All versions available Only include a subset of all available versions. versions VersionsConfig {} Independent customization of each version's properties.","s":"Configuration","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#configuration","p":891},{"i":898,"t":"EditUrlFunction​ type EditUrlFunction = (params: { version: string; versionDocsDirPath: string; docPath: string; permalink: string; locale: string; }) => string | undefined; PrefixParser​ type PrefixParser = (filename: string) => { filename: string; numberPrefix?: number; }; SidebarGenerator​ type SidebarGenerator = (generatorArgs: { /** The sidebar item with type \"autogenerated\" to be transformed. */ item: {type: 'autogenerated'; dirName: string}; /** Useful metadata for the version this sidebar belongs to. */ version: {contentPath: string; versionName: string}; /** All the docs of that version (unfiltered). */ docs: { id: string; title: string; frontMatter: DocFrontMatter & Record<string, unknown>; source: string; sourceDirName: string; sidebarPosition?: number | undefined; }[]; /** Number prefix parser configured for this plugin. */ numberPrefixParser: PrefixParser; /** The default category index matcher which you can override. */ isCategoryIndex: CategoryIndexMatcher; /** * key is the path relative to the doc content directory, value is the * category metadata file's content. */ categoriesMetadata: {[filePath: string]: CategoryMetadata}; /** * Useful to re-use/enhance the default sidebar generation logic from * Docusaurus. */ defaultSidebarItemsGenerator: SidebarGenerator; // Returns an array of sidebar items — same as what you can declare in // sidebars.js, except for shorthands. See https://docusaurus.io/docs/sidebar/items }) => Promise<SidebarItem[]>; type CategoryIndexMatcher = (param: { /** The file name, without extension */ fileName: string; /** * The list of directories, from lowest level to highest. * If there's no dir name, directories is ['.'] */ directories: string[]; /** The extension, with a leading dot */ extension: string; }) => boolean; VersionsConfig​ type VersionConfig = { /** * The base path of the version, will be appended to `baseUrl` + * `routeBasePath`. */ path?: string; /** The label of the version to be used in badges, dropdowns, etc. */ label?: string; /** The banner to show at the top of a doc of that version. */ banner?: 'none' | 'unreleased' | 'unmaintained'; /** Show a badge with the version label at the top of each doc. */ badge?: boolean; /** Prevents search engines from indexing this version */ noIndex?: boolean; /** Add a custom class name to the <html> element of each doc */ className?: string; }; type VersionsConfig = {[versionName: string]: VersionConfig};","s":"Types","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#types","p":891},{"i":900,"t":"You can configure this plugin through preset options or plugin options. 提示 Most Docusaurus users configure this plugin through the preset options. JavaScript // Preset Options: docs // Plugin Options: @docusaurus/plugin-content-docs const config = { path: 'docs', breadcrumbs: true, // Simple use-case: string editUrl // editUrl: 'https://github.com/facebook/docusaurus/edit/main/website/', // Advanced use-case: functional editUrl editUrl: ({versionDocsDirPath, docPath}) => `https://github.com/facebook/docusaurus/edit/main/website/${versionDocsDirPath}/${docPath}`, editLocalizedFiles: false, editCurrentVersion: false, routeBasePath: 'docs', include: ['**/*.md', '**/*.mdx'], exclude: [ '**/_*.{js,jsx,ts,tsx,md,mdx}', '**/_*/**', '**/*.test.{js,jsx,ts,tsx}', '**/__tests__/**', ], sidebarPath: 'sidebars.js', async sidebarItemsGenerator({ defaultSidebarItemsGenerator, numberPrefixParser, item, version, docs, isCategoryIndex, }) { // Use the provided data to generate a custom sidebar slice return [ {type: 'doc', id: 'intro'}, { type: 'category', label: 'Tutorials', items: [ {type: 'doc', id: 'tutorial1'}, {type: 'doc', id: 'tutorial2'}, ], }, ]; }, numberPrefixParser(filename) { // Implement your own logic to extract a potential number prefix const numberPrefix = findNumberPrefix(filename); // Prefix found: return it with the cleaned filename if (numberPrefix) { return { numberPrefix, filename: filename.replace(prefix, ''), }; } // No number prefix found return {numberPrefix: undefined, filename}; }, docLayoutComponent: '@theme/DocPage', docItemComponent: '@theme/DocItem', remarkPlugins: [require('./my-remark-plugin')], rehypePlugins: [], beforeDefaultRemarkPlugins: [], beforeDefaultRehypePlugins: [], showLastUpdateAuthor: false, showLastUpdateTime: false, disableVersioning: false, includeCurrentVersion: true, lastVersion: undefined, versions: { current: { label: 'Android SDK v2.0.0 (WIP)', path: 'android-2.0.0', banner: 'none', }, '1.0.0': { label: 'Android SDK v1.0.0', path: 'android-1.0.0', banner: 'unmaintained', }, }, onlyIncludeVersions: ['current', '1.0.0', '2.0.0'], };","s":"Example configuration","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#ex-config","p":891},{"i":902,"t":"Markdown documents can use the following Markdown front matter metadata fields, enclosed by a line --- on either side. Accepted fields: Name Type Default Description id string file path (including folders, without the extension) A unique document ID. title string Markdown title or id The text title of your document. Used for the page metadata and as a fallback value in multiple places (sidebar, next/previous buttons...). Automatically added at the top of your doc if it does not contain any Markdown title. pagination_label string sidebar_label or title The text used in the document next/previous buttons for this document. sidebar_label string title The text shown in the document sidebar for this document. sidebar_position number Default ordering Controls the position of a doc inside the generated sidebar slice when using autogenerated sidebar items. See also Autogenerated sidebar metadata. sidebar_class_name string undefined Gives the corresponding sidebar label a special class name when using autogenerated sidebars. sidebar_custom_props object undefined Assign custom props to the sidebar item referencing this doc displayed_sidebar string undefined Force the display of a given sidebar when browsing the current document. Read the multiple sidebars guide for details. hide_title boolean false Whether to hide the title at the top of the doc. It only hides a title declared through the front matter, and have no effect on a Markdown title at the top of your document. hide_table_of_contents boolean false Whether to hide the table of contents to the right. toc_min_heading_level number 2 The minimum heading level shown in the table of contents. Must be between 2 and 6 and lower or equal to the max value. toc_max_heading_level number 3 The max heading level shown in the table of contents. Must be between 2 and 6. pagination_next string | null Next doc in the sidebar The ID of the documentation you want the \"Next\" pagination to link to. Use null to disable showing \"Next\" for this page. pagination_prev string | null Previous doc in the sidebar The ID of the documentation you want the \"Previous\" pagination to link to. Use null to disable showing \"Previous\" for this page. parse_number_prefixes boolean numberPrefixParser plugin option Whether number prefix parsing is disabled on this doc. See also Using number prefixes. custom_edit_url string | null Computed using the editUrl plugin option The URL for editing this document. Use null to disable showing \"Edit this page\" for this page. keywords string[] undefined Keywords meta tag for the document page, for search engines. description string The first line of Markdown content The description of your document, which will become the <meta name=\"description\" content=\"...\"/> and <meta property=\"og:description\" content=\"...\"/> in <head>, used by search engines. image string undefined Cover or thumbnail image that will be used when displaying the link to your post. slug string File path Allows to customize the document URL (/<routeBasePath>/<slug>). Support multiple patterns: slug: my-doc, slug: /my/path/myDoc, slug: /. tags Tag[] undefined A list of strings or objects of two string fields label and permalink to tag to your docs. draft boolean false Draft documents will only be available during development. unlisted boolean false Unlisted documents will be available in both development and production. They will be \"hidden\" in production, not indexed, excluded from sitemaps, and can only be accessed by users having a direct link. last_update FileChange undefined Allows overriding the last updated author and/or date. Date can be any parsable date string. type Tag = string | {label: string; permalink: string}; type FileChange = {date: string; author: string}; Example: --- id: doc-markdown title: Docs Markdown Features hide_title: false hide_table_of_contents: false sidebar_label: Markdown sidebar_position: 3 pagination_label: Markdown features custom_edit_url: https://github.com/facebook/docusaurus/edit/main/docs/api-doc-markdown.md description: How do I find you when I cannot solve this problem keywords: - docs - docusaurus image: https://i.imgur.com/mErPwqL.png slug: /myDoc last_update: date: 1/1/2000 author: custom author name --- # Markdown Features My Document Markdown content","s":"Markdown front matter","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#markdown-front-matter","p":891},{"i":904,"t":"Read the i18n introduction first.","s":"i18n","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#i18n","p":891},{"i":906,"t":"Base path: website/i18n/[locale]/docusaurus-plugin-content-docs Multi-instance path: website/i18n/[locale]/docusaurus-plugin-content-docs-[pluginId] JSON files: extracted with docusaurus write-translations Markdown files: website/i18n/[locale]/docusaurus-plugin-content-docs/[versionName]","s":"Translation files location","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#translation-files-location","p":891},{"i":908,"t":"website/i18n/[locale]/docusaurus-plugin-content-docs │ │ # translations for website/docs ├── current │ ├── api │ │ └── config.md │ └── getting-started.md ├── current.json │ │ # translations for website/versioned_docs/version-1.0.0 ├── version-1.0.0 │ ├── api │ │ └── config.md │ └── getting-started.md └── version-1.0.0.json","s":"Example file-system structure","u":"/docs/docusaurus-mdx/plugin-contents/docs","h":"#example-file-system-structure","p":891},{"i":910,"t":"The functionalities of the most three contents blog, docs and pages are provided by docusaurus. These contents plugins are responsible for loading your site's content, and creating pages for your theme to render. plugin-content-docs plugin-content-blog plugin-content-pages","s":"Plugin Contents","u":"/docs/docusaurus-mdx/plugin-contents/intro","h":"","p":909},{"i":912,"t":"Front matter is used to add metadata to your Markdown file. All content plugins have their own front matter schema, and use the front matter to enrich the default metadata inferred from the content or other configuration. Front matter is provided at the very top of the file, enclosed by three dashes ---. The content is parsed as YAML. --- title: My Doc Title more_data: - Can be provided - as: objects or: arrays --- The API documentation of each official plugin lists the supported attributes.","s":"Front Matter","u":"/docs/docusaurus-mdx/plugin-contents/intro","h":"#front-matter","p":909},{"i":914,"t":"The default pages plugin for Docusaurus. The classic template ships with this plugin with default configurations. This plugin provides creating pages functionality.","s":"📦 plugin-content-pages","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"","p":913},{"i":916,"t":"npm Yarn pnpm npm install --save @docusaurus/plugin-content-pages yarn add @docusaurus/plugin-content-pages pnpm add @docusaurus/plugin-content-pages 提示 If you use the preset @docusaurus/preset-classic, you don't need to install this plugin as a dependency. You can configure this plugin through the preset options.","s":"Installation","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#installation","p":913},{"i":918,"t":"Accepted fields: Name Type Default Description path string 'src/pages' Path to data on filesystem relative to site dir. Components in this directory will be automatically converted to pages. routeBasePath string '/' URL route for the pages section of your site. DO NOT include a trailing slash. include string[] ['**/*.{js,jsx,ts,tsx,md,mdx}'] Matching files will be included and processed. exclude string[] See example configuration No route will be created for matching files. mdxPageComponent string '@theme/MDXPage' Component used by each MDX page. remarkPlugins [] any[] Remark plugins passed to MDX. rehypePlugins [] any[] Rehype plugins passed to MDX. beforeDefaultRemarkPlugins any[] [] Custom Remark plugins passed to MDX before the default Docusaurus Remark plugins. beforeDefaultRehypePlugins any[] [] Custom Rehype plugins passed to MDX before the default Docusaurus Rehype plugins.","s":"Configuration","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#configuration","p":913},{"i":920,"t":"You can configure this plugin through preset options or plugin options. 提示 Most Docusaurus users configure this plugin through the preset options. JavaScript // Preset Options: pages // Plugin Options: @docusaurus/plugin-content-pages const config = { path: 'src/pages', routeBasePath: '', include: ['**/*.{js,jsx,ts,tsx,md,mdx}'], exclude: [ '**/_*.{js,jsx,ts,tsx,md,mdx}', '**/_*/**', '**/*.test.{js,jsx,ts,tsx}', '**/__tests__/**', ], mdxPageComponent: '@theme/MDXPage', remarkPlugins: [require('./my-remark-plugin')], rehypePlugins: [], beforeDefaultRemarkPlugins: [], beforeDefaultRehypePlugins: [], };","s":"Example configuration","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#ex-config","p":913},{"i":922,"t":"Markdown pages can use the following Markdown front matter metadata fields, enclosed by a line --- on either side. Accepted fields: Name Type Default Description title string Markdown title The blog post title. description string The first line of Markdown content The description of your page, which will become the <meta name=\"description\" content=\"...\"/> and <meta property=\"og:description\" content=\"...\"/> in <head>, used by search engines. keywords string[] undefined Keywords meta tag, which will become the <meta name=\"keywords\" content=\"keyword1,keyword2,...\"/> in <head>, used by search engines. image string undefined Cover or thumbnail image that will be used when displaying the link to your post. wrapperClassName string Class name to be added to the wrapper element to allow targeting specific page content. hide_table_of_contents boolean false Whether to hide the table of contents to the right. draft boolean false Draft pages will only be available during development. unlisted boolean false Unlisted pages will be available in both development and production. They will be \"hidden\" in production, not indexed, excluded from sitemaps, and can only be accessed by users having a direct link. Example: --- title: Markdown Page description: Markdown page SEO description wrapperClassName: markdown-page hide_table_of_contents: false draft: true --- Markdown page content","s":"Markdown front matter","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#markdown-front-matter","p":913},{"i":924,"t":"Read the i18n introduction first.","s":"i18n","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#i18n","p":913},{"i":926,"t":"Base path: website/i18n/[locale]/docusaurus-plugin-content-pages Multi-instance path: website/i18n/[locale]/docusaurus-plugin-content-pages-[pluginId] JSON files: extracted with docusaurus write-translations Markdown files: website/i18n/[locale]/docusaurus-plugin-content-pages","s":"Translation files location","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#translation-files-location","p":913},{"i":928,"t":"website/i18n/[locale]/docusaurus-plugin-content-pages │ │ # translations for website/src/pages ├── first-markdown-page.md └── second-markdown-page.md","s":"Example file-system structure","u":"/docs/docusaurus-mdx/plugin-contents/pages","h":"#example-file-system-structure","p":913},{"i":930,"t":"在实际中，采集的数据往往不完整、不一致，并可能包含许多错误。数据预处理 (Data Preprocessing) 是一种数据挖掘技术，对原始数据进行处理以便进一步分析。 本文介绍分类数据 (Categorical Data) 的处理。","s":"分类数据的预处理","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"","p":929},{"i":932,"t":"在处理分类数据时，需要区分定类 (nominal) 特征和定序 (ordinal) 特征。 定类特征：不同类别，相互间比较没有意义。如姓名，性别，水果等。 定序特征：不同类别，相互间可以比较排序。如非常满意/一般满意/不满意，小型/中型/大型等。和数字特征不同，两者之差一般没有意义。 以下的 df 变量代表了 T 恤的一些特征： >>> import pandas as pd >>> df = pd.DataFrame([ ... ['green', 'M', 10.1, 'class1'], ... ['red', 'L', 13.5, 'class2'], ... ['blue', 'XL', 15.3, 'class1']]) >>> df.columns = ['color', 'size', 'price', 'classlabel'] >>> df color size price classlabel 0 green M 10.1 class1 1 red L 13.5 class2 2 blue XL 15.3 class1 其中包括定类特征 color（颜色）、定序特征 size（尺码） 和数字特征 price（价格）。最后一列为分类类别 label。","s":"定类和定序","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#nominal-and-ordinal","p":929},{"i":934,"t":"为了确保学习算法能够识别定序特征，需要手动将分类字符串映射 (Mapping) 为整型。 如上例的 T 恤尺码，假设已知排序 XL>L>MXL > L > MXL>L>M，可以进行如下转换： >>> size_mapping = { ... 'XL': 3, ... 'L': 2, ... 'M': 1} >>> df['size'] = df['size'].map(size_mapping) >>> df color size price classlabel 0 green 1 10.1 class1 1 red 2 13.5 class2 2 blue 3 15.3 class1 对于反向转换，创建反向词典然后进行 map 即可： >>> inv_size_mapping = {v: k for k, v in size_mapping.items()} >>> df['size'].map(inv_size_mapping) 0 M 1 L 2 XL Name: size, dtype: object","s":"定序特征的映射","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#mapping-of-ordinal-features","p":929},{"i":936,"t":"许多机器学习库要求类标签编码 (Encoding) 为整数值；虽然 scikit-learn 已默认集成了此处理机制，但是建议养成手动转换的习惯。 类标签的数字大小没有任何意义，因此可以直接使用枚举进行标签转换： >>> import numpy as np >>> class_mapping = {label:idx for idx,label in ... enumerate(np.unique(df['classlabel']))} >>> class_mapping {'class1': 0, 'class2': 1} 将类标签编码为整数： >>> df['classlabel'] = df['classlabel'].map(class_mapping) >>> df color size price classlabel 0 green 1 10.1 0 1 red 2 13.5 1 2 blue 3 15.3 0 反向转换： >>> inv_class_mapping = {v: k for k, v in class_mapping.items()} >>> df['classlabel'] = df['classlabel'].map(inv_class_mapping) >>> df color size price classlabel 0 green 1 10.1 class1 1 red 2 13.5 class2 2 blue 3 15.3 class1 通过 sklearn.preprocessing.LabelEncoder 可以更简便地将类标签编码为整数： >>> from sklearn.preprocessing import LabelEncoder >>> class_le = LabelEncoder() >>> y = class_le.fit_transform(df['classlabel'].values) >>> y array([0, 1, 0]) 反向转换： >>> class_le.inverse_transform(y) array(['class1', 'class2', 'class1'], dtype=object)","s":"类标签的编码","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#encoding-of-class-labels","p":929},{"i":939,"t":"在介绍独热编码 (One-Hot Encoding) 之前，先说明一下为什么不用之前章节的编码方式。 如果按照之前的方式进行编码： >>> X = df[['color', 'size', 'price']].values >>> color_le = LabelEncoder() >>> X[:, 0] = color_le.fit_transform(X[:, 0]) >>> X array([[1, 1, 10.1], [2, 2, 13.5], [0, 3, 15.3]], dtype=object) 编码结果为： blue = 0 green = 1 red = 2 如果把上述数据提供给分类器，则会发生处理分类数据的最常见错误之一：虽然我们知道 0、1、2 这些数字不代表大小，但是算法并不知道。因此算法在学习过程中，会默认将其关联起来，即假定 red > green > blue。这样处理后，算法仍然能产生一定的结果，但其性能会受影响。 独热编码的思想为为每一个值创建一个新的特征。对于上述的例子，可以把颜色特征转换为三个新的特征：blue、green 和 red，然后使用二进制值标记。对于 blue 样本而言，编码为 blue=1, green=0, red=0。","s":"独热编码的原理","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#onehot-encoding-principle","p":929},{"i":941,"t":"使用 sklearn.preprocessing.OneHotEncoder 对特征 color 进行编码，返回一个稀疏矩阵： >>> from sklearn.preprocessing import OneHotEncoder >>> ohe = OneHotEncoder(categorical_features=[0]) >>> ohe.fit_transform(X).toarray() array([[ 0. , 1. , 0. , 1. , 10.1], [ 0. , 0. , 1. , 2. , 13.5], [ 1. , 0. , 0. , 3. , 15.3]]) 另一个更方便的独热编码方法是 pandas 中的 get_dummies 方法，转换 DataFrame 的指定字符串列，其他列保持不变： >>> pd.get_dummies(df[['price', 'color', 'size']]) price size color_blue color_green color_red 0 10.1 1 0 1 0 1 13.5 2 0 0 1 2 15.3 3 1 0 0","s":"独热编码的实现","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#onehot-encoding-implementation","p":929},{"i":943,"t":"当使用热门的编码数据集时，必须记住它引入了多重共线性，即某个变量可以由其他变量线性预测得到 (如上面的矩阵，若已知 blue、green、red 中的任意两个，可以得到最后一个)。这会对某些操作 (如矩阵求逆) 造成影响。 为了减少变量之间的相关性，我们可以简单地从独热编码数组中删除一个特征列。 sklearn.preprocessing.OneHotEncoder 不提供特征列删除方法，需要转换为 numpy 数组后进行切片： >>> ohe = OneHotEncoder(categorical_features=[0]) >>> ohe.fit_transform(X).toarray()[:, 1:] array([[ 1. , 0. , 1. , 10.1], [ 0. , 1. , 2. , 13.5], [ 0. , 0. , 3. , 15.3]]) pandas 中的 get_dummies 提供参数 drop_first，可以很方便地删除首个特征列： >>> pd.get_dummies(df[['price', 'color', 'size']], ... drop_first=True) price size color_green color_red 0 10.1 1 1 0 1 13.5 2 0 1 2 15.3 3 0 0","s":"独热编码的相关性","u":"/docs/machine-learning/data-preprocessing/categorical-data","h":"#onehot-encoding-correlation","p":929},{"i":945,"t":"特征缩放 (Feature Scaling) 是将不同特征的值量化到同一区间的方法，也是预处理中容易忽视的关键步骤之一。除了极少数算法 (如决策树和随机森林) 之外，大部分机器学习和优化算法采用特征缩放后会表现更优。 特征缩放方法可分为包含归一化 (Normalization) 和标准化 (Standardization)。不同领域对这两个术语的定义可能不同，本文只对常用的定义进行介绍。","s":"特征缩放","u":"/docs/machine-learning/data-preprocessing/feature-scaling","h":"","p":944},{"i":947,"t":"一般来说，归一化是指将特征重新缩放到 [0，1][0，1][0，1] 的范围，属于极值缩放 (Min-Max Scaling) 的一种情况。其数学表达如下： xnorm(i)=x(i)−xminxmax−xmin\\begin{align} x_{norm}^{(i)} = \\cfrac {x^{(i)} - x_{min}} {x_{max} - x_{min}} \\end{align}xnorm(i)​=xmax​−xmin​x(i)−xmin​​​​ 其中，x(i)x^{(i)}x(i) 和 xnorm(i)x_{norm}^{(i)}xnorm(i)​ 分别表示第 iii 个样本归一化前后的特征值，xmaxx_{max}xmax​ 和 xminx_{min}xmin​ 分别表示该特征的最大值和最小值。 在 scikit-learn 中，可通过 sklearn.preprocessing.MinMaxScaler 实现： >>> from sklearn.preprocessing import MinMaxScaler >>> mms = MinMaxScaler() >>> X_train_norm = mms.fit_transform(X_train) >>> X_test_norm = mms.transform(X_test)","s":"归一化","u":"/docs/machine-learning/data-preprocessing/feature-scaling","h":"#normalization","p":944},{"i":949,"t":"标准化是将对特征缩放为服从正态分布，即平均值为 0、方差为 1。与归一化相比，标准化更适用于大部分学习算法。 以梯度下降法为例，如下左子图 (标准化前的收敛) 和右子图 (标准化后的收敛)： 其数学表达如下： xstd(i)=x(i)−μxσx\\begin{align} x_{std}^{(i)} = \\cfrac {x^{(i)} - \\mu_x} {\\sigma_x} \\end{align}xstd(i)​=σx​x(i)−μx​​​​ 其中，x(i)x^{(i)}x(i) 和 xstd(i)x_{std}^{(i)}xstd(i)​ 分别表示第 iii 个样本标准化前后的特征值，μx\\mu_xμx​ 和 σx\\sigma_xσx​ 分别表示该特征的平均值和标准差。 在 scikit-learn 中，可通过 sklearn.preprocessing.StandardScaler 实现： >>> from sklearn.preprocessing import StandardScaler >>> stdsc = StandardScaler() >>> X_train_std = stdsc.fit_transform(X_train) >>> X_test_std = stdsc.transform(X_test)","s":"标准化","u":"/docs/machine-learning/data-preprocessing/feature-scaling","h":"#standardization","p":944},{"i":951,"t":"评估指标 (Evaluation Metrics) 除了准确率 (Accuracy) 之外，还有其他的一些指标，如精确率 (Precision)、召回率 (Recall) 和 F1 分数 (F1 Score) 等。它们是混淆矩阵中的评估指标。","s":"混淆矩阵","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"","p":950},{"i":953,"t":"在介绍不同评分指标的评估指标之前，先介绍混淆矩阵 (Confusion Matrix)： TP (True Positives)：预测为正、实际为正的样本数 FN (False Negatives)：预测为负、实际为正的样本数 FP (False Positives)：预测为正、实际为负的样本数 TN (True Negatives)：预测为负、实际为负的样本数 混淆矩阵的形式为 True/False + Positive/Negative (Positive/Negative 是对于预测的类标签而言)。","s":"混淆矩阵的概念","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#confusion-matrix-concept","p":950},{"i":955,"t":"以 wdbc 数据集为例进行说明。先进行导入及预处理： import pandas as pd from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.svm import SVC from sklearn.pipeline import make_pipeline df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.iloc[:, 2:] y = df.iloc[:, 1] le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, stratify=y, random_state=1 ) pipe_svc = make_pipeline(StandardScaler(), SVC(random_state=1)) 通过 sklearn.metrics.confusion_matrix 计算混淆矩阵： from sklearn.metrics import confusion_matrix pipe_svc.fit(X_train, y_train) y_pred = pipe_svc.predict(X_test) confmat = confusion_matrix(y_true=y_test, y_pred=y_pred) print(confmat) 上面的函数打印出了 pipe_svc 在测试集上的混淆矩阵： 需要注意的是，scikit-learn 的混淆矩阵排列方式为 [[TN，FP]，[FN，TP]]。 [[71 1] [ 2 40]] 为了更直观地说明，通过 matplotlib 绘图如下： import matplotlib.pyplot as plt fig, ax = plt.subplots(figsize=(2.5, 2.5)) ax.matshow(confmat, cmap=plt.cm.Blues, alpha=0.3) for i in range(confmat.shape[0]): for j in range(confmat.shape[1]): ax.text(x=j, y=i, s=confmat[i, j], va=\"center\", ha=\"center\") plt.xlabel(\"predicted label\") plt.ylabel(\"true label\") plt.show() 这个数据集的类标签为病情恶性或者良性，通过 LabelEncoder 进行分类标签编码，恶性为 1 (正)，良性为 0 (负)。 左上：TN，预测为良性且预测正确的样本数。 右上：FP，预测为恶性且预测错误 (实际上为良性) 的样本数。 左下：FN，预测为良性且预测错误 (实际上为恶性) 的样本数。 右下：TP，预测为恶性且预测正确的样本数。 虽然大部分情况下比较关注分类正确 (TN + TP) 的表现。但是对于一些实际问题而言，FP 和 FN 是不一样的。以上述的 wdbc 数据而言，如果把良性病情预测恶性 (FP)，患者很有可能再后续再进行复查；但是如果把恶性病情预测成良性 (FN)，可能会让患者掉以轻心以拖延治疗，相比 FP 而言会带来更严重的后果。这也是需要制定不同评估指标的原因。 为了便于记忆，FP 也称 false alarm，可以理解为报警铃的误报；FN 也称 miss，应该报警但是实际没有报警。","s":"混淆矩阵的 scikit-learn 演示","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#confusion-matrix-using-sklearn","p":950},{"i":957,"t":"下图来自 Wikipedia - Confusion matrix： 下面介绍其中一些重要的评估指标，其中 P=TP+FNP = TP + FNP=TP+FN 表示实际为正的样本数，N=TN+FPN = TN + FPN=TN+FP 表示实际为负的样本数。","s":"评估指标介绍","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#evaluation-metrics-introduction","p":950},{"i":959,"t":"ACC (Accuracy) 代表准确率，ERR (Error) 代表错误率： ACC=TP+TNP+N=TP+TNTP+TN+FP+FNERR=FP+FNP+N=FP+FNTP+TN+FP+FN=1−ACC\\begin{align} ACC & = \\frac {TP + TN} {P + N} = \\frac {TP + TN} {TP + TN + FP + FN} \\\\ ERR & = \\frac {FP + FN} {P + N} = \\frac {FP + FN} {TP + TN + FP + FN} = 1 - ACC \\end{align}ACCERR​=P+NTP+TN​=TP+TN+FP+FNTP+TN​=P+NFP+FN​=TP+TN+FP+FNFP+FN​=1−ACC​​ scikit-learn 实现如下： from sklearn.metrics import accuracy_score accuracy = accuracy_score(y_true=y_test, y_pred=y_pred)","s":"准确率","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#accuracy","p":950},{"i":961,"t":"召回率 (Recall) 即 TPR (True Positive Rate)，表示实际为正的样本中正确预测的概率，也称敏感度 (Sensitivity) 或命中率 (Hit Rate)： Recall=TPR=TPP=TPTP+FN\\begin{align} Recall = TPR = \\frac {TP} {P} = \\frac {TP} {TP + FN} \\end{align}Recall=TPR=PTP​=TP+FNTP​​​ scikit-learn 实现如下： from sklearn.metrics import recall_score recall = recall_score(y_true=y_test, y_pred=y_pred)","s":"召回率","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#recall","p":950},{"i":963,"t":"精准率 (Precision) 即 PPV (Positive Predictive Value)，表示预测为正的样本中正确预测的概率： Precision=PPV=TPTP+FP\\begin{align} Precision = PPV = \\frac {TP} {TP + FP} \\end{align}Precision=PPV=TP+FPTP​​​ scikit-learn 实现如下： from sklearn.metrics import precision_score precision = precision_score(y_true=y_test, y_pred=y_pred)","s":"精准率","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#precision","p":950},{"i":965,"t":"F1 分数 (F1 Score) 是召回率和精准率的调和平均值： F1=21Recall+1Precision=2Recall×PrecisionRecall+Precision\\begin{align} F_1 = \\cfrac 2 {\\cfrac 1 {Recall} + \\cfrac 1 {Precision}} = 2 \\frac {Recall \\times Precision} {Recall + Precision} \\end{align}F1​=Recall1​+Precision1​2​=2Recall+PrecisionRecall×Precision​​​ scikit-learn 实现如下： from sklearn.metrics import f1_score f1 = f1_score(y_true=y_test, y_pred=y_pred)","s":"F1 分数","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#f1-score","p":950},{"i":967,"t":"马修斯相关系数 (Matthews Correlation Coefficient，MCC) 对多个指标进行综合打分： MCC=TP×TN−FP×FN(TP+FP)(TP+FN)(TN+FP)(TN+FN)\\begin{align} MCC = \\frac {TP \\times TN - FP \\times FN} {\\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}} \\end{align}MCC=(TP+FP)(TP+FN)(TN+FP)(TN+FN)​TP×TN−FP×FN​​​ scikit-learn 实现如下： from sklearn.metrics import matthews_corrcoef mcc = matthews_corrcoef(y_true=y_test, y_pred=y_pred)","s":"马修斯相关系数","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#matthews-correlation-coefficient","p":950},{"i":969,"t":"需要注意的是，scikit-learn 中大多数算法默认使用 accuracy_score 作为评估指标。另外，其中正类认为是的标签为 1 的类。 通过 sklearn.metrics.make_scorer 可以替换评估指标和正类的类标签： from sklearn.metrics import make_scorer, f1_score scorer = make_scorer(f1_score, pos_label=0) gs = GridSearchCV(estimator=pipe_svc, param_grid=param_grid, scoring=scorer, cv=10) gs = gs.fit(X_train, y_train) print(gs.best_score_) # Output: 0.986202145696 >>> print(gs.best_params_) # Output: {'svc__C': 10.0, 'svc__gamma': 0.01, 'svc__kernel': 'rbf'} 有关评估指标的更多内容，请参见 Wikipedia - Confusion matrix 和 sklearn.metrics。","s":"替换 scikit-learn 的评估指标","u":"/docs/machine-learning/evaluation-metrics/confusion-matrix","h":"#replace-evaluation-metrics-in-sklearn","p":950},{"i":971,"t":"在信号检测理论中，接收者操作特征 (Receiver Operating Characteristic，ROC) 曲线是是一种坐标图式的分析工具，通过计算 ROC 的曲线下面积 (Area Under Curve，AUC) 可以对分类模型进行评估。ROC 分析的是二分分类模型。 ROC 曲线通过绘制采用不同分类阈值时的 TPR (True Positive Rate) 与 FPR (False Positive Rate) 来选择模型。它展示了在不同分类阈值下，模型的性能表现。ROC 曲线的对角线可以被解释为随机猜测 (如丢硬币、正反面出现概率预测均是 50%)，并且落在对角线上方的分类模型优于随机猜测，落在对角线下方的分类模型比随机猜测更差。 AUC 是 ROC 曲线下的面积，即 ROC 曲线和横轴之间的面积。AUC 值的范围在 0 到 1 之间，其中 0.5 表示模型的预测性能等于随机猜测，而 1 表示完美分类器。AUC 值越接近 1，表示模型的性能越好。 下文将实现分类器的 ROC 曲线绘制，该分类器仅使用 wdbc 数据集中的两个特征来预测肿瘤是良性还是恶性。","s":"ROC 和 AUC","u":"/docs/machine-learning/evaluation-metrics/roc-and-auc","h":"","p":970},{"i":973,"t":"import pandas as pd import numpy as np import matplotlib.pyplot as plt from sklearn.model_selection import StratifiedKFold from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA from sklearn.linear_model import LogisticRegression from sklearn.pipeline import make_pipeline df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.loc[:, 2:].values y = df.loc[:, 1].values le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.20, stratify=y, random_state=1 )","s":"数据导入和预处理","u":"/docs/machine-learning/evaluation-metrics/roc-and-auc","h":"#data-loading-and-preprocessing","p":970},{"i":975,"t":"使用逻辑回归 pipeline，并采用折叠数为 3 的 StratifiedKFold，如下代码： from sklearn.metrics import roc_curve, auc from scipy import interp pipe_lr = make_pipeline( StandardScaler(), PCA(n_components=2), LogisticRegression(penalty=\"l2\", random_state=1, C=100.0), ) X_train2 = X_train[:, [4, 14]] cv = list(StratifiedKFold(n_splits=3, random_state=1).split(X_train, y_train)) fig = plt.figure(figsize=(7, 5)) mean_tpr = 0.0 mean_fpr = np.linspace(0, 1, 100) all_tpr = [] for i, (train, test) in enumerate(cv): probas = pipe_lr.fit(X_train2[train], y_train[train]).predict_proba(X_train2[test]) fpr, tpr, thresholds = roc_curve(y_train[test], probas[:, 1], pos_label=1) mean_tpr += interp(mean_fpr, fpr, tpr) mean_tpr[0] = 0.0 roc_auc = auc(fpr, tpr) plt.plot(fpr, tpr, label=\"ROC fold {} (area = {:.2f}\".format(i + 1, roc_auc)) plt.plot([0, 1], [0, 1], linestyle=\"--\", color=(0.6, 0.6, 0.6), label=\"random guessing\") mean_tpr /= len(cv) mean_tpr[-1] = 1.0 mean_auc = auc(mean_fpr, mean_tpr) plt.plot( mean_fpr, mean_tpr, \"k--\", label=\"mean ROC (area = {:.2f}\".format(mean_auc), lw=2 ) 上面的代码通过从 SciPy 导入的 interp 函数插入了三次折叠的平均 ROC 曲线，并通过 auc 函数计算曲线下面积。 三次绘制的 ROC 曲线表明不同折叠之间存在一定程度的变化，并且 ROC AUC 的平均值 (0.76) 落在完美预测 (1.0) 和随机猜测 (0.5) 之间： 如果只需要用到 ROC AUC 分数，也可以直接导入 sklearn.metrics.roc_auc_score 函数。ROC AUC 分数可以对样本数量不平均的二分分类模型进行评估。","s":"ROC 曲线的 scikit-learn 实现","u":"/docs/machine-learning/evaluation-metrics/roc-and-auc","h":"#roc-plotting-in-sklearn","p":970},{"i":977,"t":"线性判别分析 (Linear Discriminant Analysis，LDA) 作为一种特征提取技术，可以提高计算效率，防止由于维数灾难而导致的过拟合。LDA 与 PCA 类似，不同之处在于 PCA 的目标是找到数据集中最大方差的正交分量轴，而 LDA 的目标是找到优化类可分性的特征子空间。 LDA 和 PCA 都是线性变换技术，可用于减少数据集中的维数。区别在于 LDA 是监督算法，而 PCA 是无监督算法。 LDA 旨在找到对应最多投影的线性判别，如下图所示，其中圆形和十字分别表示两类的正态分布样本： xxx 轴 (LD1) 所示的线性判别可以很好地分类；而尽管 yyy 轴 (LD2) 所示的线性判别拥有更大的投影方差，但是无法捕获任何分类信息。 LDA 中假设数据是正态分布的。此外，我们假设类的协方差矩阵相同，并且特征之间互不相关。","s":"线性判别分析","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"","p":976},{"i":979,"t":"LDA 的算法流程的简单介绍如下： 对输入的 ddd 维数据集 X\\boldsymbol XX 进行标准化。 计算每个类的 ddd 维均值向量，构造类内散布矩阵 SW\\boldsymbol S_WSW​ 和类间散布矩阵 SB\\boldsymbol S_BSB​。 计算矩阵 SW−1SB\\boldsymbol S_W^{-1} \\boldsymbol S_BSW−1​SB​ 的特征向量和特征值。 对特征值进行降序排序，对相应的特征向量进行排序。 提取 kkk 个最大特征值对应的特征向量，其中 kkk (k≤dk \\le dk≤d) 是新特征子空间的维数。 使用提取的 kkk 个特征向量构造投影矩阵 W\\boldsymbol WW。 使用投影矩阵 W\\boldsymbol WW 对 X\\boldsymbol XX 进行变换，得到新的 kkk 维特征子空间。 LDA 与 PCA 非常相似，通过将矩阵分解成特征值和特征向量，然后通过投影矩阵得到新的低维特征空间。其不同点在于 LDA 将类标签考虑在内 (步骤 2)。","s":"算法思想","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#algorithm-principle","p":976},{"i":981,"t":"导入 Wine 数据集，第 1 列为其分类标签，第 2~14 列为特征。分割数据集为 70% 的训练集和 30% 的测试集： import pandas as pd from sklearn.model_selection import train_test_split df_wine = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data\", header=None, ) X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=0, stratify=y ) 对训练集和测试集进行标准化： from sklearn.preprocessing import StandardScaler sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test)","s":"数据导入和标准化","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#data-load-and-standardization","p":976},{"i":984,"t":"计算均值向量，后面将用它来构造类内散布矩阵和类间散布矩阵。在第 iii 类样本的均值向量为 mi\\boldsymbol m_imi​中，存储了该类样本特征的平均值 μm\\mu_mμm​： mi=1ni∑x∈Dicxm\\begin{align} \\boldsymbol m_i = \\frac 1 {n_i} \\sum_{x \\in D_i}^c \\boldsymbol x_m \\end{align}mi​=ni​1​x∈Di​∑c​xm​​​ 得到三个均值向量： mi=[μi,alcoholμi,malic acid⋮μi,proline]\\begin{align} \\boldsymbol m_i = \\begin{bmatrix} \\mu_{i,alcohol} \\\\ \\mu_{i,malic \\ acid} \\\\ \\vdots \\\\ \\mu_{i,proline} \\end{bmatrix} \\end{align}mi​=​μi,alcohol​μi,malic acid​⋮μi,proline​​​​​ np.set_printoptions(precision=4) mean_vecs = [] for label in range(1, 4): mean_vecs.append(np.mean(X_train_std[y_train == label], axis=0)) print(\"MV {}: {}\\n\".format(label, mean_vecs[label - 1])) # Output: # MV 1: [ 0.9066 -0.3497 0.3201 -0.7189 0.5056 0.8807 0.9589 -0.5516 0.5416 # 0.2338 0.5897 0.6563 1.2075] # MV 2: [-0.8749 -0.2848 -0.3735 0.3157 -0.3848 -0.0433 0.0635 -0.0946 0.0703 # -0.8286 0.3144 0.3608 -0.7253] # MV 3: [ 0.1992 0.866 0.1682 0.4148 -0.0451 -1.0286 -1.2876 0.8287 -0.7795 # 0.9649 -1.209 -1.3622 -0.4013]","s":"均值向量","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#mean-vector","p":976},{"i":986,"t":"类内散布矩阵 SW\\boldsymbol S_WSW​ 的计算如下，其中 Si\\boldsymbol S_iSi​ 为第 iii 类的散布矩阵。 SW=∑i=1cSiSi:=1niSi=1ni∑x∈Dic(x−mi)(x−mi)T=Σi\\begin{align} \\boldsymbol S_W & = \\sum_{i=1}^c \\boldsymbol S_i \\\\ \\boldsymbol S_i & := \\frac 1 {n_i} \\boldsymbol S_i = \\frac 1 {n_i} \\sum_{x \\in D_i}^c (\\boldsymbol x - \\boldsymbol m_i) (\\boldsymbol x - \\boldsymbol m_i)^T = \\boldsymbol \\Sigma_i \\end{align}SW​Si​​=i=1∑c​Si​:=ni​1​Si​=ni​1​x∈Di​∑c​(x−mi​)(x−mi​)T=Σi​​​ 由于 LDA 假设是训练集中的类别标签是均匀分布的，这里将散列矩阵 Si\\boldsymbol S_iSi​ 缩放至 1ni\\frac 1 {n_i}ni​1​，缩放后恰好为协方差矩阵。 d = 13 # number of features S_W = np.zeros((d, d)) for label, mv in zip(range(1, 4), mean_vecs): class_scatter = np.cov(X_train_std[y_train == label].T) S_W += class_scatter print(\"Scaled within-class scatter matrix: {}x{}\".format(S_W.shape[0], S_W.shape[1])) # Output: Scaled within-class scatter matrix: 13x13","s":"类内散布矩阵","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#intra-class-scatter-matrix","p":976},{"i":988,"t":"类间散布矩阵 SB\\boldsymbol S_BSB​ 的计算如下，其中 m\\boldsymbol mm 为所有样本的均值向量： SB=∑i=1cni(mi−m)(mi−m)T\\begin{align} \\boldsymbol S_B = \\sum_{i=1}^cn_i (\\boldsymbol m_i - \\boldsymbol m) (\\boldsymbol m_i - \\boldsymbol m)^T \\end{align}SB​=i=1∑c​ni​(mi​−m)(mi​−m)T​​ mean_overall = np.mean(X_train_std, axis=0) d = 13 # number of features S_B = np.zeros((d, d)) for i, mean_vec in enumerate(mean_vecs): n = X_train[y_train == i + 1, :].shape[0] mean_vec = mean_vec.reshape(d, 1) # make column vector mean_overall = mean_overall.reshape(d, 1) S_B += n * (mean_vec - mean_overall).dot((mean_vec - mean_overall).T) print(\"Between-class scatter matrix: {}x{}\".format(S_B.shape[0], S_B.shape[1])) # Output: Between-class scatter matrix: 13x13","s":"类间散布矩阵","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#inter-class-scatter-matrix","p":976},{"i":990,"t":"计算矩阵 SW−1SB\\boldsymbol S_W^{-1} \\boldsymbol S_BSW−1​SB​ 的特征值和特征向量，按照特征值降序对相应的特征向量进行排序： eigen_vals, eigen_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B)) eigen_pairs = [ (np.abs(eigen_vals[i]), eigen_vecs[:, i]) for i in range(len(eigen_vals)) ] eigen_pairs.sort(key=lambda k: k[0], reverse=True) 在 LDA 中，线性判别式的数目至多为 c−1c-1c−1，其中 ccc 为类标签的数量。","s":"特征值和特征向量","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#eigenvalues-and-eigenvectors","p":976},{"i":992,"t":"为了衡量线性判别式 (特征向量) 捕获多少类别鉴别信息，对不同的线性判别式的辨别能力 (discriminability) 进行绘图： import matplotlib.pyplot as plt tot = sum(eigen_vals.real) discr = [(i / tot) for i in sorted(eigen_vals.real, reverse=True)] cum_discr = np.cumsum(discr) plt.bar( range(1, 14), discr, alpha=0.5, align=\"center\", label='individual \"discriminability\"', ) plt.step(range(1, 14), cum_discr, where=\"mid\", label='cumulative \"discriminability\"') plt.ylabel('\"discriminability\" ratio') plt.xlabel(\"Linear Discriminants\") plt.ylim([-0.1, 1.1]) plt.legend(loc=\"best\") plt.show()","s":"线性判别式的辨别能力","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#discrimination-ability-of-linear-discriminant","p":976},{"i":994,"t":"使用投影矩阵转换原始数据集： x′=xW↓X′=XW\\begin{align} \\boldsymbol x' & = \\boldsymbol x \\boldsymbol W \\\\ & \\downarrow \\\\ \\boldsymbol X' & = \\boldsymbol X \\boldsymbol W \\end{align}x′X′​=xW↓=XW​​ w = np.hstack( (eigen_pairs[0][1][:, np.newaxis].real, eigen_pairs[1][1][:, np.newaxis].real) ) X_train_lda = X_train_std.dot(w) colors = [\"r\", \"b\", \"g\"] markers = [\"s\", \"x\", \"o\"] for l, c, m in zip(np.unique(y_train), colors, markers): plt.scatter( X_train_lda[y_train == l, 0], X_train_lda[y_train == l, 1] * (-1), c=c, label=l, marker=m, ) plt.xlabel(\"LD 1\") plt.ylabel(\"LD 2\") plt.legend(loc=\"lower right\") plt.show() 代码绘图结果如下，类别在新的特征子空间中线性可分：","s":"特征提取","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#feature-extraction","p":976},{"i":996,"t":"边界绘图函数 plot_decision_regions 见之前的文章。 通过 sklearn.discriminant_analysis.LinearDiscriminantAnalysis 将测试集和训练集降至二维，然后使用逻辑回归对降维后的测试集进行线性分类： from sklearn.linear_model import LogisticRegression from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA lda = LDA(n_components=2) lr = LogisticRegression() X_train_lda = lda.fit_transform(X_train_std, y_train) X_test_lda = lda.transform(X_test_std) lr.fit(X_train_lda, y_train) plot_decision_regions(X_train_lda, y_train, classifier=lr) plt.xlabel(\"LD 1\") plt.ylabel(\"LD 2\") plt.legend(loc=\"lower left\") plt.show() 在降维空间绘制已通过训练得到的决策边界，观察是否能够进行很好地分类： plot_decision_regions(X_test_lda, y_test, classifier=lr) plt.xlabel(\"LD 1\") plt.ylabel(\"LD 2\") plt.legend(loc=\"lower left\") plt.show() 可以看到逻辑回归在新的二维子空间上表现很好，在测试数据集上只有很少样本分类错误。","s":"Scikit-learn 实现","u":"/docs/machine-learning/feature-selection/feature-extraction-lda","h":"#sklearn-implementation","p":976},{"i":998,"t":"与特征选择类似，我们可以使用特征提取 (Feature Extraction) 来减少数据集中特征的数量。其区别在于，特征选择保留原始特征，而特征提取则将数据转换或投影到新的特征空间。本文介绍主成分分析 (Principal Component Analysis，PCA)，它是一种无监督的线性变换技术，主要特点是特征提取和降维。","s":"主成分分析","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"","p":997},{"i":1000,"t":"PCA 广泛应用于不同领域，帮助我们根据特征之间的相关性来识别数据中的模式。其原理是找到高维数据中最大方差的方向，并将其投影到与原始维数相同或更少维数的新的正交空间上。 新的子空间的正交轴 (即主成分) 可以被解释为在新的特征轴彼此正交的约束下的最大方差的方向，如下图所示： 在上图中，x1x_1x1​ 和 x2x_2x2​ 是原始特征轴，PC1 和 PC2 是数据集的第一主成分和第二主成分。 PCA 构造了一个维度变换矩阵 W\\boldsymbol WW，将高维空间向量 x\\boldsymbol xx 映射到低维空间向量 z\\boldsymbol zz： x=[x1,x2,⋯ ,xd],x∈Rd↓xW,W∈Rd×kz=[z1,z2,⋯ ,zk],z∈Rk\\begin{align} \\boldsymbol x & = [x_1, x_2, \\cdots, x_d], x \\in R^d \\\\ & \\downarrow \\boldsymbol x \\boldsymbol W, \\boldsymbol W \\in R^{d \\times k} \\\\ \\boldsymbol z & = [z_1, z_2, \\cdots, z_k], z \\in R^k \\end{align}xz​=[x1​,x2​,⋯,xd​],x∈Rd↓xW,W∈Rd×k=[z1​,z2​,⋯,zk​],z∈Rk​​ 维度变换后，第一主成分将具有最大的方差，第二主成分将具有第二大的方差，以此类推。这些主成分必须均不相关 (即使输入特征之间有相关性)，数学表示为主成分向量之间两两正交。 需要注意的是，PCA 方向对数据缩放非常敏感。举例来说，假设一个特征在 [-100,100] 之间平均分布，另外一个特征在 [-1,1] 之间平均分布，PCA 会认为前一个特征重要得多。因此在运用 PCA 时，需要使用标准化将输入特征缩放到相同的尺度。 PCA 的算法流程的简单介绍如下： 对输入的 ddd 维数据集 X\\boldsymbol XX 进行标准化。 构造协方差矩阵。 计算协方差矩阵的特征向量和特征值。 对特征值进行降序排序，对相应的特征向量进行排序。 提取 kkk 个最大特征值对应的特征向量，其中 kkk (k≤dk \\le dk≤d) 是新特征子空间的维数。 使用提取的 kkk 个特征向量构造投影矩阵 W\\boldsymbol WW。 使用投影矩阵 W\\boldsymbol WW 对 X\\boldsymbol XX 进行变换，得到新的 kkk 维特征子空间。","s":"算法思想","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#algorithm-principle","p":997},{"i":1002,"t":"导入 Wine 数据集，第 1 列为其分类标签，第 2~14 列为特征。分割数据集为 70% 的训练集和 30% 的测试集： import pandas as pd from sklearn.model_selection import train_test_split df_wine = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data\", header=None, ) X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=0, stratify=y ) 对训练集和测试集进行标准化： from sklearn.preprocessing import StandardScaler sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test)","s":"数据导入和标准化","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#data-load-and-standardization","p":997},{"i":1004,"t":"接下来引入协方差矩阵。对于 nnn 的两个特征向量 (机器学习中通常用列向量表示) xj\\boldsymbol x_jxj​ 和 xk\\boldsymbol x_kxk​，其协方差如下： σjk=σkj=1n∑i=1n(xj(i)−μj)(xk(i)−μk)\\begin{align} \\sigma_{jk} = \\sigma_{kj} = {\\frac 1 n} \\sum_{i=1}^n (x_j^{(i)} - \\mu_j)(x_k^{(i)} - \\mu_k) \\end{align}σjk​=σkj​=n1​i=1∑n​(xj(i)​−μj​)(xk(i)​−μk​)​​ 其中 μj\\mu_jμj​ 和 μk\\mu_kμk​ 分别代表 xj\\boldsymbol x_jxj​ 和 xk\\boldsymbol x_kxk​ 平均值。对于 PCA 的样本，在标准化后这两个平均值都为 0。 协方差 σjk\\sigma_{jk}σjk​ 可以表示 xj\\boldsymbol x_jxj​ 和 xk\\boldsymbol x_kxk​ 的相关程度： 若 σjk\\sigma_{jk}σjk​ 大于 0，表明这两个特征正相关，即一个特征随另外一个特征的变大而变大。 若 σjk\\sigma_{jk}σjk​ 大于 0，表明这两个特征负相关，即一个特征随另外一个特征的变大而变小。 若 σjk\\sigma_{jk}σjk​ 等于 0，表明这两个特征不相关，即一个特征变化不受另外一个特征的变化影响。此时这两个特征向量两两正交。 接下来构建协方差矩阵 Σ\\boldsymbol \\SigmaΣ(这是大写的希腊字母 Sigma，不要与求和符号 ∑\\sum∑ 混淆)。以 3 个特征为例，其协方差矩阵如下： Σ=[σ12σ12σ13σ21σ22σ23σ31σ32σ32]\\begin{align} \\boldsymbol \\Sigma = \\begin{bmatrix} \\sigma_1^2 & \\sigma_{12} & \\sigma_{13} \\\\ \\sigma_{21} & \\sigma_2^2 & \\sigma_{23} \\\\ \\sigma_{31} & \\sigma_{32} & \\sigma_3^2 \\end{bmatrix} \\end{align}Σ=​σ12​σ21​σ31​​σ12​σ22​σ32​​σ13​σ23​σ32​​​​​ 协方差矩阵 Σ\\boldsymbol \\SigmaΣ 是实对称矩阵，矩阵对角线为特征的方差，其余为特征之间的协方差。Σ\\boldsymbol \\SigmaΣ 的特征向量表示主成分 (即具有最大方差的方向)，对应的特征值为主成分的大小。 Wine 数据集有 13 个特征，我们将从 13×13 维协方差矩阵中获得 13 个特征向量和特征值。","s":"协方差矩阵的构造","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#construct-covariance-matrix","p":997},{"i":1006,"t":"求解矩阵的特征值 λ\\lambdaλ 和特征向量 v\\boldsymbol vv，使其满足条件： Σv=λv\\begin{align} {\\boldsymbol \\Sigma} {\\boldsymbol v} = \\lambda {\\boldsymbol v} \\end{align}Σv=λv​​ 矩阵特征值和特征向量的数学计算较为繁琐，这里不作过多介绍。 使用 numpy 内置的 linalg.eig 函数可以方便地计算特征值和特征向量： import numpy as np cov_mat = np.cov(X_train_std.T) eigen_vals, eigen_vecs = np.linalg.eig(cov_mat) 上面通过 numpy.cov 创建协方差矩阵，然后通过 numpy.linalg.eig 对其进行特征分解，产生由 13 个特征值组成的向量 eigen_vals 和 13 个特征向量 (列向量) 组成的矩阵 eigen_vecs。","s":"特征值和特征向量","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#eigenvalues-and-eigenvectors","p":997},{"i":1008,"t":"把 ddd 维空间压缩到 kkk 维空间，需要从中挑选包含信息最多 (方差最大) 的 kkk 个特征向量 (主成分)。特征值反映了特征向量的大小，需要降序排序特征值，然后提取前 kkk 个特征值对应的特征向量。 在提取特征之前，为了观察特征的方差之间的差异，这里先对特征值的解释方差占比 (explained variance ratio) 进行绘图： import matplotlib.pyplot as plt tot = sum(eigen_vals) var_exp = [(i / tot) for i in sorted(eigen_vals, reverse=True)] cum_var_exp = np.cumsum(var_exp) plt.bar( range(1, 14), var_exp, alpha=0.5, align=\"center\", label=\"individual explained variance\", ) plt.step(range(1, 14), cum_var_exp, where=\"mid\", label=\"cumulative explained variance\") plt.ylabel(\"Explained variance ratio\") plt.xlabel(\"Principal component index\") plt.legend(loc=\"best\") plt.show() 可以看到，第一主成分大约占了方差的 40%，第二主成分大约占了总方差的 20%，这两个特征值解释了接近 60% 的数据集方差。 需要注意的是，整个过程中没有使用 y_train。PCA 属于无监督学习，在分析和提取主成分的过程中从来不使用类的标签。","s":"解释方差占比","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#explained-variance-ratio","p":997},{"i":1010,"t":"本节以 Wine 数据集进行演示特征提取的最后几个步骤： 提取 kkk 个最大特征值对应的特征向量，其中 kkk (k≤dk \\le dk≤d) 是新特征子空间的维数。 使用提取的 kkk 个特征向量构造投影矩阵 W\\boldsymbol WW， 使用投影矩阵 W\\boldsymbol WW 对 X\\boldsymbol XX 进行变换，得到新的 kkk 维特征子空间。 简单来说，就是按照特征值降序将特征向量进行排序，从特征向量中构造投影矩阵，并使用投影矩阵将数据转换到低维子空间。 特征向量排序： # Make a list of (eigenvalue, eigenvector) tuples eigen_pairs = [ (np.abs(eigen_vals[i]), eigen_vecs[:, i]) for i in range(len(eigen_vals)) ] # Sort the (eigenvalue, eigenvector) tuples from high to low eigen_pairs.sort(key=lambda k: k[0], reverse=True) 以两个主成分为例，构造投影矩阵： 注意，为了后面的绘制二维散点图，因此这里只挑选了两个主成分。实际中应该根据效率性能的平衡来确定主成分的个数。 w = np.hstack((eigen_pairs[0][1][:, np.newaxis], eigen_pairs[1][1][:, np.newaxis])) 使用投影矩阵转换原始数据集： x′=xW↓X′=XW\\begin{align} \\boldsymbol x' & = \\boldsymbol x \\boldsymbol W \\\\ & \\downarrow \\\\ \\boldsymbol X' & = \\boldsymbol X \\boldsymbol W \\end{align}x′X′​=xW↓=XW​​ 其中 X\\boldsymbol XX 为原始数据集，x\\boldsymbol xx 为其中的单个样本；X‘\\boldsymbol X‘X‘ 为变换后的数据集， x’\\boldsymbol x’x’ 为其中的单个样本。 X_train_pca = X_train_std.dot(w) 原始的 Wine 数据集有 13 维，通过特征矩阵 W∈R13×2\\boldsymbol W \\in R^{13 \\times 2}W∈R13×2 后降为 2 维，对降维后的数据集进行绘图： colors = [\"r\", \"b\", \"g\"] markers = [\"s\", \"x\", \"o\"] for l, c, m in zip(np.unique(y_train), colors, markers): plt.scatter( X_train_pca[y_train == l, 0], X_train_pca[y_train == l, 1], c=c, label=l, marker=m, ) plt.xlabel(\"PC 1\") plt.ylabel(\"PC 2\") plt.legend(loc=\"lower left\") plt.show() 从下图可以看到，数据沿着 xxx 轴 (第一主成分) 比沿着 yyy 轴 (第二主成分) 更加分散，与上节中第一主成分的方差较大相吻合。另外，降维后的分类数据仍保留其特征，可以用线性分类器进行分类。 需要再次强调，PCA 是一种无监督的技术，在整个 PCA 过程中不使用任何类标签信息。","s":"特征提取","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#feature-extraction","p":997},{"i":1012,"t":"边界绘图函数 plot_decision_regions 见之前的文章。 通过 sklearn.decomposition.PCA 将测试集和训练集降至二维，然后使用逻辑回归对降维后的测试集进行线性分类： from sklearn.linear_model import LogisticRegression from sklearn.decomposition import PCA pca = PCA(n_components=2) lr = LogisticRegression() X_train_pca = pca.fit_transform(X_train_std) X_test_pca = pca.transform(X_test_std) lr.fit(X_train_pca, y_train) plot_decision_regions(X_train_pca, y_train, classifier=lr) plt.xlabel(\"PC 1\") plt.ylabel(\"PC 2\") plt.legend(loc=\"lower left\") plt.show() 在降维空间绘制已通过训练得到的决策边界，观察是否能够进行很好地分类： plot_decision_regions(X_test_pca, y_test, classifier=lr) plt.xlabel(\"PC1\") plt.ylabel(\"PC2\") plt.legend(loc=\"lower left\") plt.show() 可以看到逻辑回归在新的二维子空间上表现很好，在测试数据集上只有很少样本分类错误。 关于数据集的解释方差占比，可以设置 PCA 的参数 n_components 为 None，对测试集进行变换后通过 explained_variance_ratio_ 属性得到： pca = PCA(n_components=None) X_train_pca = pca.fit_transform(X_train_std) print(pca.explained_variance_ratio_)","s":"Scikit-learn 实现","u":"/docs/machine-learning/feature-selection/feature-extraction-pca","h":"#sklearn-implementation","p":997},{"i":1014,"t":"避免过拟合的方法中，有一种称为特征选择 (Feature Selection)，即选择最重要的特征、同时舍弃不重要的特征。本文以 Wine 数据集为例，使用随机森林演示了特征重要性评估和选择方法。","s":"特征的重要性","u":"/docs/machine-learning/feature-selection/feature-importance","h":"","p":1013},{"i":1016,"t":"Wine 数据集是对意大利同一地区种植的葡萄酒进行化学分析的结果，但起源于三种不同的品种。 第一列为其分类标签 (即葡萄酒产地)，其余 13 列为特征。 import pandas as pd df_wine = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data\", header=None, ) df_wine.columns = [ \"Class label\", \"Alcohol\", \"Malic acid\", \"Ash\", \"Alcalinity of ash\", \"Magnesium\", \"Total phenols\", \"Flavanoids\", \"Nonflavanoid phenols\", \"Proanthocyanins\", \"Color intensity\", \"Hue\", \"OD280/OD315 of diluted wines\", \"Proline\", ] print(df_wine.head()) 按分类标签分割数据集为 70% 的训练数据集和 30% 的测试数据集： from sklearn.model_selection import train_test_split X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=0, stratify=y )","s":"Wine 数据集","u":"/docs/machine-learning/feature-selection/feature-importance","h":"#wine-dataset","p":1013},{"i":1018,"t":"scikit-learn 中的 sklearn.ensemble.RandomForestClassifier 已经集成了特征的重要性排序，实现如下： from sklearn.ensemble import RandomForestClassifier feat_labels = df_wine.columns[1:] forest = RandomForestClassifier(n_estimators=500, random_state=1) forest.fit(X_train, y_train) importances = forest.feature_importances_ indices = np.argsort(importances)[::-1] for f in range(X_train.shape[1]): print(\"{:2d}) {:30}{:f} \".format(f + 1, feat_labels[f], importances[f])) 特征的重要性排序如下： 1) Proline 0.179927 2) Color intensity 0.153158 3) Flavanoids 0.146123 4) Alcohol 0.138224 5) OD280/OD315 of diluted wines 0.114818 6) Hue 0.077525 7) Total phenols 0.058236 8) Malic acid 0.030856 9) Alcalinity of ash 0.030000 10) Proanthocyanins 0.025713 11) Magnesium 0.025135 12) Nonflavanoid phenols 0.011548 13) Ash 0.008738 对特征重要性进行绘图： import matplotlib.pyplot as plt plt.title(\"Feature Importance\") plt.bar(range(X_train.shape[1]), importances[indices], align=\"center\") plt.xticks(range(X_train.shape[1]), feat_labels, rotation=90) plt.xlim([-1, X_train.shape[1]]) plt.tight_layout() plt.show() 需要提到的是，scikit-learn 还实现了一个 SelectFromModel 对象，它在模型拟合之后根据用户指定的阈值选择特征，并且可以将不同估计器 (Estimator) 与其连接。 以随机森林为例，以使用以下代码将特征阈值设置为 0.1，可以筛选出最重要的五个特征： from sklearn.feature_selection import SelectFromModel sfm = SelectFromModel(forest, threshold=0.1, prefit=True) X_selected = sfm.transform(X_train) print(\"Number of samples that meet this criterion:\", X_selected.shape[0]) for f in range(X_selected.shape[1]): print( \"{:2d}) {:30}{:f} \".format( f + 1, feat_labels[indices[f]], importances[indices[f]] ) ) 输出如下： Number of samples that meet this criterion: 124 1) Proline 0.179927 2) Color intensity 0.153158 3) Flavanoids 0.146123 4) Alcohol 0.138224 5) OD280/OD315 of diluted wines 0.114818","s":"特征重要性的 Scikit-learn 实现","u":"/docs/machine-learning/feature-selection/feature-importance","h":"#feature-importance-using-sklearn","p":1013},{"i":1021,"t":"我应该用自顶向下的方法还是自底向上的方法学习机器学习相关知识？ 自顶向下 自顶向下学习方法从整体或高层次的概念、理论或问题开始，然后逐步细化、深入和扩展。它强调整体观念和宏观理解，并通过逐渐分解、归纳和推演形成更具体的细节。 自底向上 相比之下，自底向上学习方法从具体的细节、实例或基本要素开始，然后逐步组合、归纳和抽象形成更高层次的概念、理论或问题。它强调逐步建立对细节的理解和掌握，并通过将细节逐步整合和推广来形成整体认知。","s":"如何学习","u":"/docs/machine-learning/ml-basics/how-to-learn","h":"","p":1020},{"i":1023,"t":"您需要快速熟悉或者重温机器学习中使用先决知识，例如： 数学 线性代数 概率与统计 数值优化 微积分 Python 编程基础 在开始学习机器学习所需的数学基础知识时，您需要使用自底向上的方法。数学知识和 Python 基础是一套系统性的知识，因此自底向上更合适。 学到什么程度合适？每个算法的原理和数学建模是不一样的，不是说数学知识掌握 100 分才能进行机器学习。建议同步进行。","s":"先决知识：自底向上","u":"/docs/machine-learning/ml-basics/how-to-learn","h":"#how-to-learn-prerequisite","p":1020},{"i":1025,"t":"假设您需要开始学习机器学习，从高级概念开始，然后逐步深入。 如果您自学，那么在学习机器学习时使用自顶向下的方法更有意义，否则你可能会在不重要的概念上浪费很多时间。 例如，您可能想运行一个基于 CNN 的图像识别，这样您就可以建立一定程度的好奇心，例如 CNN 是如何工作的？如果你有一个已完成的 demo，你就会更有动力去寻找答案。正如在编程中，我们从 hello world 开始学习而不是从汇编开始学习一样。 因此，我建议在学习先决条件 (数学、Python) 时使用自底向上的方法。然后在学习机器学习本身时，使用自顶向下的方法。这两个步骤可以同步进行。","s":"机器学习知识：自顶向下","u":"/docs/machine-learning/ml-basics/how-to-learn","h":"#how-to-learn-ml","p":1020},{"i":1027,"t":"进入 21 世纪，你所考虑的不应该是“我没有学习资料”：学习资料网上随处可见，而且未来会越来越多。 这是我建议的学习方法： 对于初学者：遵循“自顶向下”的方法，首先学习 python，然后按照在线教程或者进行编码。在小型数据集上构建您的第一个机器学习模型。 对于中级开发人员：遵循“自底向上”的方法，阅读官方文档、机器学习书籍，并尝试解决 kaggle 数据集上的一些问题。选择您感兴趣的一个或一些类别，并了解该算法为何有效，了解其数学原理。 对于高级开发人员：我认为高级开发人员不太需要阅读本文；如果实在有什么建议，建议多读论文和代码，多问“为什么”和“怎么做”。","s":"在哪里学习","u":"/docs/machine-learning/ml-basics/how-to-learn","h":"#where-to-learn","p":1020},{"i":1029,"t":"本文介绍机器学习的三大类型：监督式学习、非监督式学习和强化学习。 机器学习在近 30 多年已发展为一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、计算复杂性理论等多门学科。机器学习理论主要是设计和分析一些让计算机可以自动“学习”的算法。机器学习算法是一类从数据中自动分析获得规律，并利用规律对未知数据进行预测的算法。机器学习已广泛应用于数据挖掘、计算机视觉、自然语言处理、生物特征识别、搜索引擎、医学诊断、检测信用卡欺诈、证券市场分析、DNA 序列测序、语音和手写识别、战略游戏和机器人等领域。","s":"机器学习三大类型","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"","p":1028},{"i":1031,"t":"监督式学习，是一个机器学习中的方法，可以由训练资料中学到或建立一个模式，并依此模式推测新的实例。训练资料是由输入物件 (通常是向量) 和预期输出所组成。函数的输出可以是一个连续的值 (称为回归分析)，或是预测一个分类标签 (称为分类)。","s":"监督式学习 (Supervised Learning)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#supervised-learning","p":1028},{"i":1033,"t":"在分类中，函数的输出是一个分类标签。常见的例子有垃圾邮件识别和手写数字识别。","s":"分类 (Classification)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#classification","p":1028},{"i":1035,"t":"在回归中，函数的输出可以是一个连续的值，通常是一个数学函数。例如，对于某一职位，员工薪水和工龄之间的关系。","s":"回归 (Regression)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#regression","p":1028},{"i":1037,"t":"另一种类型的机器学习是强化学习。在强化学习中，目标是开发一种基于与环境交互来改善其性能的代理。由于存在反馈机制，因此可以认为强化学习和监督式学习相关。然而，在强化学习中，这种反馈不是正确标签，而是强调如何基于环境而行动，以取得最大化的预期利益。 一个普遍的例子是象棋引擎。在这里，代理根据棋盘状态 (环境) 决定一系列动作，反馈可以在游戏结束时定义为胜或负。","s":"强化学习 (Reinforcement Learning)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#reinforcement-learning","p":1028},{"i":1039,"t":"在无监督学习中，我们处理的是未标记的数据或未知结构的数据。使用无监督的学习技术，我们能够探索我们的数据的结构，以提取有意义的信息。常见的非监督式学习方法有聚类分析和降维。","s":"非监督式学习 (Unsupervised Learning)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#unsupervised-learning","p":1028},{"i":1041,"t":"聚类是一种探索性数据分析技术，能够在不知道输入对象的任何先验知识的情况下，将其分成不同的集群。每个集群包含一定程度相似的对象，但是与其他集群中的对象不相似。例如营销人员将客户分类成不同的客户群。","s":"聚类 (Clustering)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#clustering","p":1028},{"i":1043,"t":"通常，我们正在处理高维度的数据，这对于有限的存储空间和机器学习算法的计算性能是很大的挑战。降维是指在某些限定条件下，降低随机变量的维度，得到一组“不相关”的主变量，同时保留大部分有效信息。","s":"降维 (Dimensionality Reduction)","u":"/docs/machine-learning/ml-basics/machine-learning-major-types","h":"#dimensionality-reduction","p":1028},{"i":1046,"t":"信息 在这个网站中，python 默认为 python3，因为 python2 不再维护。 近年来，Python 已成为世界上最流行的编程语言之一。它用于从机器学习到构建网站和软件测试的各个方面。它可供开发人员和非开发人员使用。 在后面的文章中，我们假设您了解 python 的基本知识并且在您的计算机上安装了 python。我们建议您使用 Anaconda 安装，这样您就不需要再安装 python。 如果你确实想只安装 Python，请参阅下面的链接： Python Source Releases for Linux Python Releases for Windows Python Releases for macOS 对于那些刚接触 Python 的人，请查看 Python 教程。","s":"什么是 Python？","u":"/docs/machine-learning/ml-basics/python-environment-installation","h":"#what-is-python","p":1044},{"i":1048,"t":"信息 在这个网站中，Anaconda 是 python3 版本的 Anaconda3。 Anaconda 是用于科学计算 (数据科学、机器学习应用、大规模数据处理、预测分析等) 的 Python 和 R 编程语言的发行版，旨在简化包管理和部署。该发行版包括适用于 Windows、Linux 和 macOS 的数据科学包。 您可以从 Anaconda Archive 下载 Anaconda 并按照以下指南进行安装。 在 Linux 上安装 Anaconda 在 Windows 上安装 Anaconda 在 macOS 上安装 Anaconda 如果您想了解 Anaconda 中包含哪些软件包，请查看此链接。","s":"什么是 Anaconda？","u":"/docs/machine-learning/ml-basics/python-environment-installation","h":"#what-is-anaconda","p":1044},{"i":1050,"t":"Jupyter Notebook 和 Jupyter Lab 都是交互式计算环境，使用户能够在基于 Web 的界面中处理代码、数据和多媒体内容。与传统的 Jupyter Notebook 相比，Jupyter Lab 提供了增强的现代化界面以及附加的特性和功能。 在 Anaconda 中，Jupyter Notebook 和 Jupyter Lab 默认已经安装。 启动 Jupyter Lab： jupyter lab 或者启动 Jupyter Notebook： jupyter notebook","s":"什么是 Jupyter？","u":"/docs/machine-learning/ml-basics/python-environment-installation","h":"#what-is-jupyter","p":1044},{"i":1052,"t":"机器学习主要包括预处理、训练、评估和预测阶段。本文演示了如何使用 scikit-learn 进行分类。","s":"入门：基于 Iris 数据集","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"","p":1051},{"i":1054,"t":"原始数据很少呈现为学习算法的最佳性能所需的形式和形状。因此，数据的预处理是任何机器学习应用程序中最关键的步骤之一。以鸢尾花数据集为例，我们可以将原始数据看作一系列花图，从中我们可以提取有意义的特征，如花的颜色，花萼和花瓣的长度和宽度。 许多机器学习算法还要求能够将所有特征在同一数量级，这通常通过归一化或者正态分布等特征变换方法来实现。部分特征可能是高度相关的，特征可能存在冗余。在这种情况下，降维可以减少所需的存储空间，并且算法可以学习得更快。 为了确定机器学习算法是否不仅在训练集上表现良好的同时，能很好地预测到新的数据，我们将数据集随机分为相互独立的训练集和测试集。训练集用于训练和优化我们的机器学习模型，测试集用于最终评估最终模型。 在开始加载数据之前，按照常用约定导入这些库： import pandas as pd import numpy as np import matplotlib.pyplot as plt","s":"预处理","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#preprocessing","p":1051},{"i":1056,"t":"您可以在此处下载 iris.csv。 names = [\"sepal-length\", \"sepal-width\", \"petal-length\", \"petal-width\", \"class\"] dataset = read_csv(\"iris.csv\", names=names)","s":"加载数据","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#load-data","p":1051},{"i":1058,"t":"打印 dataset 的形状： print(dataset.shape) # (150, 5) 打印 dataset 的前几行 (head() 默认打印 5 行)： print(dataset.head()) # sepal-length sepal-width petal-length petal-width class # 0 5.1 3.5 1.4 0.2 Iris-setosa # 1 4.9 3.0 1.4 0.2 Iris-setosa # 3 4.6 3.1 1.5 0.2 Iris-setosa # 2 4.7 3.2 1.3 0.2 Iris-setosa # 4 5.0 3.6 1.4 0.2 Iris-setosa 打印 dataset 的 class 和每个 class 的数量： print(dataset.groupby(\"class\").size()) # class # Iris-setosa 50 # Iris-versicolor 50 # Iris-virginica 50 # dtype: int64 打印 dataset 的统计数据： print(dataset.describe()) # sepal-length sepal-width petal-length petal-width # count 150.000000 150.000000 150.000000 150.000000 # mean 5.843333 3.054000 3.758667 1.198667 # std 0.828066 0.433594 1.764420 0.763161 # min 4.300000 2.000000 1.000000 0.100000 # 25% 5.100000 2.800000 1.600000 0.300000 # 50% 5.800000 3.000000 4.350000 1.300000 # 75% 6.400000 3.300000 5.100000 1.800000 # max 7.900000 4.400000 6.900000 2.500000","s":"探索性数据分析","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#exploratory-data-analysis","p":1051},{"i":1060,"t":"有些文章将 train-test-split 作为数据预处理过程，有些文章认为这是一个训练过程。 在我看来，它是数据预处理和训练之间的桥梁。 将原始数据随机分成 80% 的训练集和 20% 的测试集： from sklearn.model_selection import train_test_split array = dataset.values X = array[:, 0:4] y = array[:, 4] X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.20, shuffle=True, random_state=1 ) 备注 random_state 是用于分割的随机种子。设置后，将在不同的计算机上生成相同的训练数据集和测试数据集，以便重现结果。 print(X_train.shape, X_test.shape, y_train.shape, y_test.shape) # (120, 4) (30, 4) (120,) (30,)","s":"测试集训练集划分","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#test-train-split","p":1051},{"i":1062,"t":"目前已有许多不同的机器学习算法，用于解决不同的问题任务。每个分类算法都有其固有的偏差，在实践中，比较几个不同的算法然后从中选出最优算法，对于训练和选择最佳性能模型至关重要。一个常用的算法度量指标是分类准确率，即正确分类数据的比重。 另外，我们可以使用不同的交叉验证技术，其中将训练数据集进一步分为训练和验证子集，以估计模型的泛化性能。 最后，算法的默认参数对于实际问题往往不会具有最佳表现。因此，我们可以使用超参数优化技术，通过调节算法参数，我们可以提高算法的性能。 在训练之前，我们需要知道我们面临什么样的问题：这是一个多类分类监督问题。我们可以使用 DecisionTreeClassifier 分类器。 from sklearn.tree import DecisionTreeClassifier tree_model = DecisionTreeClassifier() tree_model.fit(X_train, Y_train)","s":"训练","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#training","p":1051},{"i":1064,"t":"在选择了模型并使用训练集进行训练之后，我们可以使用测试集来来估计泛化误差。 如果我们对其性能感到满意，可以使用这个模型来预测新的未来数据。 需要注意的是，训练的参数 (如特征缩放和降维) 仅从训练数据集中获得，在测试数据上测量的性能可能是过拟合的。 进行评估： print(f\"Score of tree_model: {tree_model.score(X_validation, Y_validation)}\") # Score of tree_model: 0.9666666666666667 对新的未知数据进行分类： print( f\"Prediction of [6.0, 3.1, 5.1, 1.9]: {tree_model.predict([[6.0, 3.1, 5.1, 1.9]])[0]}\" ) # Prediction of [6.0, 3.1, 5.1, 1.9]: Iris-virginica","s":"评估和预测","u":"/docs/machine-learning/ml-basics/start-with-iris-dataset","h":"#evaluation-and-prediction","p":1051},{"i":1066,"t":"欠拟合 (Underfitting) 和过拟合 (Overfitting) 是机器学习中的重要概念和常见问题。本文就这两个概念进行简单说明。","s":"欠拟合和过拟合","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"","p":1065},{"i":1068,"t":"机器学习的目的，是利用已知数据 (训练数据) 训练出机器学习的模型，然后将该模型应用到未知数据 (测试数据) 中。 从已知数据归纳总结，然后对未知数据的预测称为泛化 (Generalize)。 泛化能力好的机器学习模型，在使用训练数据进行训练后，对没有见过的数据可以进行准确预测。反之，泛化能力差的模型不能对未知数据进行准确预测。","s":"泛化","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"#generalization","p":1065},{"i":1070,"t":"过拟合和欠拟合都会导致模型没有良好的泛化能力。 以二维数据的二分分类为例，如下图： 左子图：对已知数据欠缺拟合，存在高偏差 (high bias) 右子图：对已知数据过度拟合，存在高方差 (high variance) 中间子图：对已知数据良好拟合，可以概括出已知数据的特征","s":"拟合","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"#fitting","p":1065},{"i":1072,"t":"欠拟合的模型存在高偏差，对于已知数据和未知数据都表现不佳。 在机器学习中一般较少讨论欠拟合。一般而言，增加模型复杂度即可解决欠拟合问题。","s":"欠拟合","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"#underfitting","p":1065},{"i":1074,"t":"过拟合的模型存在高方差，对已知数据表现良好，但是对未知数据表现不佳。 过拟合表示对已知数据进行了过度解读，包括其中的噪音和细节，导致训练出来的模型不能很好地适用于未知数据。 样本数量少、噪音数据多、模型参数过多和复杂度过高等原因，都会导致过拟合。","s":"过拟合","u":"/docs/machine-learning/ml-basics/underfitting-and-overfitting","h":"#overfitting","p":1065},{"i":1076,"t":"网格搜索 (Grid Search) 是一种通过遍历给定的超参数组合来优化模型表现的方法。 机器学习算法中有两类参数：一类是从训练集中学习到的参数，比如逻辑回归中的权重参数和偏差参数，另一类是超参数 (Hyperparameter)，也就是需要人工设定的参数，比如正则项系数或者决策树的深度。 网格搜索通过寻找最佳的超参数组合，可以进一步帮助提高模型的性能。","s":"网格搜索","u":"/docs/machine-learning/model-selection/grid-search","h":"","p":1075},{"i":1078,"t":"网格搜索的思想非常简单，属于暴力 (Brute Force) 算法：穷尽每个超参数的组合来评估对应的模型性能，然后挑选模型性能的超参数。","s":"算法思想","u":"/docs/machine-learning/model-selection/grid-search","h":"#algorithm-principle","p":1075},{"i":1080,"t":"import pandas as pd from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.iloc[:, 2:] y = df.iloc[:, 1] le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, stratify=y, random_state=1 )","s":"数据导入和预处理","u":"/docs/machine-learning/model-selection/grid-search","h":"#data-load-and-preprocessing","p":1075},{"i":1082,"t":"创建管道对象： from sklearn.preprocessing import StandardScaler from sklearn.svm import SVC from sklearn.pipeline import make_pipeline pipe_svc = make_pipeline(StandardScaler(), SVC(random_state=1)) 通过网格搜索所有超参数组合 (下面是 8 + 64 = 72 个) 中的准确率最高的一个： from sklearn.model_selection import GridSearchCV param_range = [0.0001, 0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0] param_grid = [ {\"svc__C\": param_range, \"svc__kernel\": [\"linear\"]}, {\"svc__C\": param_range, \"svc__gamma\": param_range, \"svc__kernel\": [\"rbf\"]}, ] gs = GridSearchCV(estimator=pipe_svc, param_grid=param_grid, scoring=\"accuracy\", cv=10) gs.fit(X_train, y_train) 网格搜索得到的最优模型的准确率、参数、以及模型调用如下： print(gs.best_score_) # Output: 0.984615384615 print(gs.best_params_) # Output: {'svc__C': 100.0, 'svc__gamma': 0.001, 'svc__kernel': 'rbf'} clf = gs.best_estimator_ clf.fit(X_train, y_train) print(\"Test accuracy: {:.3f}\".format(clf.score(X_test, y_test))) # Output: Test accuracy: 0.974","s":"基于 Scikit-learn 的网格搜索","u":"/docs/machine-learning/model-selection/grid-search","h":"#grid-search-using-sklearn","p":1075},{"i":1084,"t":"Holdout 验证 (Holdout Validation) 是一种广泛使用的模型验证方法，将数据集划分为不同的集合，一部分用于训练，另一部分用于测试。","s":"Holdout 验证","u":"/docs/machine-learning/model-selection/holdout","h":"","p":1083},{"i":1086,"t":"对于评估机器学习模型的泛化性能，一种经典和普遍的方法是 holdout 交叉验证。holdout 方法将初始数据集分成单独的训练集 (Training Set) 和测试集 (Test Set)，前者用于模型训练，后者用于评估模型的泛化性能。在典型的机器学习程序中，人们会对超参数进行不断调整和比较，以进一步提高对不可见数据进行预测的性能。这个过程被称为模型选择 (Model Selection)，尝试将超参数调整至最优。 但是，如果在模型选择过程中重复使用相同的测试集，那么这个测试集就不是真正意义上的测试集。真正的测试集应该是不可见的。如果一直尝试对测试集拟合，这个测试集实际上就是训练集的一部分。 尽管如此，许多人仍然将数据集分为测试集和训练集，然后按照测试集的表现来进行模型选择。这不是一个良好的机器学习方法。","s":"数据集划分：训练集和测试集","u":"/docs/machine-learning/model-selection/holdout","h":"#数据集划分训练集和测试集","p":1083},{"i":1088,"t":"一种更好的模型选择方法是将数据分成三部分：训练集、验证集 (Validation Set) 和测试集。训练集用于拟合不同的模型，然后根据模型在验证集上的表现来进行模型选择。在整个训练过程中，测试集是不可见的，不会对测试集过拟合。 下图说明了保持交叉验证的概念，使用训练集和验证集进行反复训练并将超参数调整至较优水平，再使用测试集来评估模型的泛化性能： Holdout 方法的缺点是算法评估对数据划分比较敏感，对于不同的数据划分比例和不同的分布，评估结果可能会有较大差异。","s":"数据集划分：训练集、验证集和测试集","u":"/docs/machine-learning/model-selection/holdout","h":"#数据集划分训练集验证集和测试集","p":1083},{"i":1090,"t":"K 折交叉验证 (K-Fold Cross-Validation) 是一种模型选择 (Model Selection) 方法，将初始样本分为 K 个折叠 (Fold)，一个折叠作为数据集、其余 K-1 个折叠作为训练集，反复重复上述步骤 K 次并将得到的结果综合起来，得到最终的评估结果。K 折交叉验证在一定程度上解决了 holdout 只划分数据一次的缺点。","s":"K 折交叉验证","u":"/docs/machine-learning/model-selection/k-fold-cross-validation","h":"","p":1089},{"i":1092,"t":"K 折交叉验证的步骤是，随机地将训练数据集分成 K 次折叠。其中 K-1 次折叠用于模型训练、另外一个折叠用于性能评估，上述步骤重复 K 次 (每次抽取不同的折叠)，获得 K 个模型的性能评估结果。 K 折交叉验证可以得到令人满意的泛化性能的最优超参数值，具有更高的准确率和鲁棒性。K 折交叉验证表现好的原因在于其拥有更多的训练样本，且每个训练样本都恰好验证一次，这样可以产生较低的方差。 下图说明了详细的 K 折交叉验证 (K = 10) 的流程，其中 test fold 实际上发挥的是验证集的作用： 根据以往研究人员的经验，超参数 K 一般推荐采用 10。如果 K 太小，方差会较高，如果 K 太大，模型的训练时间会变长。对于大型数据集，可以适当降低 K 的值 (如 K = 5)。 一种特殊的 K 折交叉验证为留一验证 (Leave-One-Out Cross-Validation，LOOCV)，K = n (n 为数据集的样本数量)，每折只有一个样本，可以用于处理小数据集。","s":"K 折交叉验证原理","u":"/docs/machine-learning/model-selection/k-fold-cross-validation","h":"#kfold-cross-validation-principle","p":1089},{"i":1094,"t":"分层 K 折交叉验证 (Stratified K-Fold Cross-Validation) 是对 K 折交叉验证的改进，分层的意思是每一个折叠中的分类比例都与原始数据集相同，能更好地适用于不同分类的样本数差异较大的情况。下面基于 scikit-learn 中的进行说明。 先做好交叉验证之前的前提工作，其中 pipe_lr 是管道对象，封装了标准化、PCA 和逻辑回归： import pandas as pd from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA from sklearn.linear_model import LogisticRegression from sklearn.pipeline import make_pipeline df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.loc[:, 2:].values y = df.loc[:, 1].values le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.20, stratify=y, random_state=1 ) pipe_lr = make_pipeline( StandardScaler(), PCA(n_components=2), LogisticRegression(random_state=1) ) 使用 sklearn.model_selection.StratifiedKFold 进行 K 折分层交叉验证： import numpy as np from sklearn.model_selection import StratifiedKFold kfold = StratifiedKFold(n_splits=10, random_state=1).split(X_train, y_train) scores = [] for k, (train, test) in enumerate(kfold): pipe_lr.fit(X_train[train], y_train[train]) score = pipe_lr.score(X_train[test], y_train[test]) scores.append(score) print('Fold: {:2d}, Class dist.: {}, Acc: {:.3f}'.format(k + 1, np.bincount(y_train[train]), score) 将样本分为 n_splits=10 个折叠，在每一次循环中使用管道对象 pipe_lr 对测试集进行训练，然后观察训练后的模型在验证集上的准确率。运行结果如下： Fold: 1, Class dist.: [256 153], Acc: 0.935 Fold: 2, Class dist.: [256 153], Acc: 0.935 Fold: 3, Class dist.: [256 153], Acc: 0.957 Fold: 4, Class dist.: [256 153], Acc: 0.957 Fold: 5, Class dist.: [256 153], Acc: 0.935 Fold: 6, Class dist.: [257 153], Acc: 0.956 Fold: 7, Class dist.: [257 153], Acc: 0.978 Fold: 8, Class dist.: [257 153], Acc: 0.933 Fold: 9, Class dist.: [257 153], Acc: 0.956 Fold: 10, Class dist.: [257 153], Acc: 0.956 计算 10 次训练的准确率的平均值和方差： print(\"CV accuracy: {:.3f} +/- {:.3f}\".format(np.mean(scores), np.std(scores))) # Output: CV accuracy: 0.950 +/- 0.014 上面是通过具体实现流程说明交叉验证的工作流程，也可以通过 sklearn.model_selection.cross_val_score 实现模型评估： scores = cross_val_score(estimator=pipe_lr, X=X_train, y=y_train, cv=10, n_jobs=1) print(\"CV accuracy scores: {}\".format(scores)) print(\"CV accuracy: {:.3f} +/- {:.3f}\".format(np.mean(scores), np.std(scores))) 其中 cv 为折叠数量，n_jobs 是代码运行使用 CPU 核心的数量，结果如下： CV accuracy scores: [ 0.93478261 0.93478261 0.95652174 0.95652174 0.93478261 0.95555556 0.97777778 0.93333333 0.95555556 0.95555556] CV accuracy: 0.950 +/- 0.014 结果与之前一致，采用 cross_val_score 可以非常便捷地对交叉验证模型进行评估。","s":"分层 K 折交叉验证的 scikit-learn 实现","u":"/docs/machine-learning/model-selection/k-fold-cross-validation","h":"#stratified-kfold-cross-validation-using-sklearn","p":1089},{"i":1096,"t":"嵌套交叉验证 (Nested Cross-Validation) 算法具有更稳定的性能，在训练集上的结果相对于测试集几乎是无偏的。 其思想是先使用 K 折交叉验证将数据分为训练折叠和测试折叠，然后在训练折叠内部使用 K 折交叉验证后用于测试折叠，以选择最优模型。如下为 5×2 折叠交叉验证的示意图： 基于 SVM 的 5×2 折叠交叉验证，实现如下： gs = GridSearchCV(estimator=pipe_svc, param_grid=param_grid, scoring=\"accuracy\", cv=2) scores = cross_val_score(gs, X_train, y_train, scoring=\"accuracy\", cv=5) print(\"CV accuracy: {:.3f} +/- {:.3f}\".format(np.mean(scores), np.std(scores))) # Output: CV accuracy: 0.974 +/- 0.015 基于决策树的 5×2 折叠交叉验证，实现如下： from sklearn.tree import DecisionTreeClassifier gs = GridSearchCV( estimator=DecisionTreeClassifier(om_state=0), param_grid=[{\"max_depth\": [1, 2, 3, 4, 5, 6, 7, None]}], scoring=\"accuracy\", cv=2, ) scores = cross_val_score(gs, X_train, y_train, scoring=\"accuracy\", cv=5) print(\"CV accuracy: %.3f +/- %.3f\" % (np.mean(scores), np.std(scores))) # Output: CV accuracy: 0.934 +/- 0.016 可以看到，基于 SVM 模型的嵌套交叉验证相比于基于决策树的交叉验证更优。","s":"嵌套交叉验证","u":"/docs/machine-learning/model-selection/k-fold-cross-validation","h":"#nested-cross-validation","p":1089},{"i":1098,"t":"绘制模型的学习曲线 (Learning Curve) 和验证曲线 (Validation Curve) 是常用的调试手段，能够从中直观看到模型在测试集和验证集上的表现，以及判断是否有过拟合或欠拟合问题。","s":"学习曲线和验证曲线","u":"/docs/machine-learning/model-selection/learning-and-validation-curve","h":"","p":1097},{"i":1100,"t":"通过曲线可以容易看出模型是否存在高偏差或高偏差，以及判断否能够通过增加样本数目解决这些问题。 常见的学习曲线如下图所示： 左上子图：学习曲线和验证曲线都很差，高偏差、欠拟合。 右上子图：学习曲线很好但验证曲线很差，高方差、过拟合 右下子图：在拥有一定数量样本的情况下，具有良好的方差 - 偏差权衡 (bias-variance tradeoff) 和拟合程度。","s":"方差 - 偏差权衡","u":"/docs/machine-learning/model-selection/learning-and-validation-curve","h":"#variance-bias-tradeoff","p":1097},{"i":1102,"t":"绘制学习曲线时，自变量为样本数，因变量为评价指标。 读取 wdbc 数据集，并将其分为 80% 的训练集和 20% 的测试集： import pandas as pd from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA from sklearn.linear_model import LogisticRegression from sklearn.pipeline import make_pipeline df = pd.read_csv( \"https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data\", header=None, ) X = df.loc[:, 2:].values y = df.loc[:, 1].values le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.20, stratify=y, random_state=1 ) 使用 sklearn.model_selection.learning_curve 生成学习曲线的值，然后通过 pyplot 绘制模型对于训练集和验证集的准确率： pipe_lr：scikit-learn 管道对象 train_sizes：测试集为数据集 X_train 的比例 (这里为 10%、20%、…、100%) cv：分层交叉验证的折叠数 K n_jobs：使用的 CPU 核心数 train_scores 和 test_scores：共有 len(train_sizes) 行，每行有 cv 个交叉验证的分数，因此均值标准差都是按行计算 axis=1 plt.fill_between：通过标准差绘制数据的离散程度 import numpy as np import matplotlib.pyplot as plt from sklearn.model_selection import learning_curve pipe_lr = make_pipeline(StandardScaler(), LogisticRegression(random_state=1)) train_sizes, train_scores, test_scores = learning_curve( estimator=pipe_lr, X=X_train, y=y_train, train_sizes=np.linspace(0.1, 1.0, 10), cv=10, n_jobs=1, ) train_mean = np.mean(train_scores, axis=1) train_std = np.std(train_scores, axis=1) test_mean = np.mean(test_scores, axis=1) test_std = np.std(test_scores, axis=1) plt.plot( train_sizes, train_mean, color=\"blue\", marker=\"o\", markersize=5, label=\"training accuracy\", ) plt.fill_between( train_sizes, train_mean + train_std, train_mean - train_std, alpha=0.15, color=\"blue\", ) plt.plot( train_sizes, test_mean, color=\"green\", linestyle=\"--\", marker=\"s\", markersize=5, label=\"validation accuracy\", ) plt.fill_between( train_sizes, test_mean + test_std, test_mean - test_std, alpha=0.15, color=\"green\" ) plt.grid() plt.xlabel(\"Number of training samples\") plt.ylabel(\"Accuracy\") plt.legend(loc=\"lower right\") plt.ylim([0.8, 1.03]) plt.show() 得到模型的准确率随样本数变化的曲线： 若训练集的样本数小于 250，训练集的准确率很高，但是测试集的准确率相对较低，模型存在过拟合问题。若训练集的样本数大于 250，则模型在训练集和验证集上的表现都非常好。","s":"学习曲线","u":"/docs/machine-learning/model-selection/learning-and-validation-curve","h":"#learning-curve","p":1097},{"i":1104,"t":"和学习曲线不同，验证曲线的因变量往往是模型的参数值，如逻辑回归中的参数 C。 使用 sklearn.model_selection.validation_curve 生成学习曲线的值，然后通过 pyplot 绘制模型对于训练集和验证集的准确率： pipe_lr：scikit-learn 管道对象 logisticregression__C：逻辑回归的超参数 C，正则化系数的倒数 param_range：超参数的取值范围 from sklearn.model_selection import validation_curve param_range = [0.001, 0.01, 0.1, 1.0, 10.0, 100.0] train_scores, test_scores = validation_curve( estimator=pipe_lr, X=X_train, y=y_train, param_name=\"logisticregression__C\", param_range=param_range, cv=10, ) train_mean = np.mean(train_scores, axis=1) train_std = np.std(train_scores, axis=1) test_mean = np.mean(test_scores, axis=1) test_std = np.std(test_scores, axis=1) plt.plot( param_range, train_mean, color=\"blue\", marker=\"o\", markersize=5, label=\"training accuracy\", ) plt.fill_between( param_range, train_mean + train_std, train_mean - train_std, alpha=0.15, color=\"blue\", ) plt.plot( param_range, test_mean, color=\"green\", linestyle=\"--\", marker=\"s\", markersize=5, label=\"validation accuracy\", ) plt.fill_between( param_range, test_mean + test_std, test_mean - test_std, alpha=0.15, color=\"green\" ) plt.grid() plt.xscale(\"log\") plt.legend(loc=\"lower right\") plt.xlabel(\"Parameter C\") plt.ylabel(\"Accuracy\") plt.ylim([0.8, 1.03]) plt.show() 得到模型的准确率随逻辑回归参数 C 变化的曲线： 在正则化强度较大 (C 小于 0.01) 时，模型有一定程度的欠拟合 (高偏差)，但在正则化强度较小 (C 大于 10) 时，模型又会出现过拟合 (高方差)。超参数 C 的取值在 0.01 和 0.1 之间时，模型性能最优。","s":"验证曲线","u":"/docs/machine-learning/model-selection/learning-and-validation-curve","h":"#validation-curve","p":1097},{"i":1106,"t":"本文介绍了基于梯度下降法 (Gradient Descent，GD) 的自适应线性神经元 (Adaptive Linear Neuron，Adaline)，以及对应的算法实现。","s":"Adaline 和梯度下降法","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"","p":1105},{"i":1108,"t":"Adaline 是 1960 年由 Bernard Widrow 和 Tedd Hoff 提出的，被认为是对 Rosenblatt 感知器的改进。Adaline 算法定义了最小化成本函数的核心概念，为之后一些更先进的机器学习算法 (如逻辑回归和支持向量机) 奠定了基础。 Adaline 规则和 Rosenblatt 感知器的不同之处在于在调整权重的激活函数不同，前者采用线性函数，后者采用单位阶跃函数。在 Adaline 中，ϕ(wTx)=wTx\\phi(w^T x)= w^T xϕ(wTx)=wTx。 Adaline 在使用线性激活函数更新权重之外，采用单位阶跃的量化器来预测类标签，如下图所示：","s":"Adaline 原理","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#adaline-principle","p":1105},{"i":1110,"t":"定义在学习过程中需要优化的目标函数，是监督式学习的关键步骤。目标函数通常是需要最小化的成本函数。对于 Adaline，我们定义权重的成本函数 JJJ 为预测类标签和实际类标签之间的方差总和 (Sum of Squared Errors，SSE)。 J(w)=12Σi(y(i)−ϕ(z(i)))2\\begin{align} J(w) = {\\frac 1 2} \\Sigma_i(y^{(i)} - \\phi(z^{(i)}))^2 \\end{align}J(w)=21​Σi​(y(i)−ϕ(z(i)))2​​ 线性激活函数的优点是，成本函数可微并且是凸函数 (局部最小值为全局最小值)。 ∂J(w)∂wj=12Σi(y(i)−ϕ(z(i)))2∂z∂z∂wj=−Σi(y(i)−ϕ(z(i)))xj(i)\\begin{align} {\\frac {\\partial J(w)} {\\partial w_j}} &= {\\frac 1 2} {\\frac {\\Sigma_i(y^{(i)} - \\phi(z^{(i)}))^2} {\\partial z}} {\\frac {\\partial z} {\\partial w_j}} \\\\ &= -{\\Sigma_i(y^{(i)} - \\phi(z^{(i)}))} x_j^{(i)} \\end{align}∂wj​∂J(w)​​=21​∂zΣi​(y(i)−ϕ(z(i)))2​∂wj​∂z​=−Σi​(y(i)−ϕ(z(i)))xj(i)​​​ 这里采用一种称为梯度下降的算法来找出最小化成本函数对应的权重，以便对 Iris 数据子集的样本进行分类。如下图所示，可以将梯度下降类比成下山的过程，直到达到局部最小值。每次训练相当于在斜坡上行走一步，其中步长由学习率和斜率决定： 梯度下降法的思想是，如果函数在某点可微且有定义，那么函数在该点沿着梯度相反的方向下降最快，下降系数用学习率 η\\etaη 表示： Δwj=−ηΔJ(w)\\begin{align} \\Delta w_j = -\\eta \\Delta J(w) \\end{align}Δwj​=−ηΔJ(w)​​ 每次训练后，权重更新为： wj:=wj+Δwj=wj−ηΔJ(w)\\begin{align} w_j := w_j + \\Delta w_j = w_j - \\eta \\Delta J(w) \\end{align}wj​:=wj​+Δwj​=wj​−ηΔJ(w)​​ 权重的每次更新是基于训练集中的所有样本 (而并非单个样本)，因此这种最原始的梯度下降法也被称为批量梯度下降法 (Batch Gradient Descent，BGD)。","s":"批量梯度下降法","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#batch-gradient-descent","p":1105},{"i":1112,"t":"下面代码中，采用了面向对象的方法，定义 Adaline 为 Python 类。 import numpy as np class AdalineGD(object): def __init__(self, eta=0.01, n_iter=50, random_state=1): self.eta = eta self.n_iter = n_iter self.random_state = random_state def fit(self, X, y): rgen = np.random.RandomState(self.random_state) self.w_ = rgen.normal(loc=0.0, scale=0.01, size=1 + X.shape[1]) self.cost_ = [] for i in range(self.n_iter): net_input = self.net_input(X) output = self.activation(net_input) errors = y - output self.w_[1:] += self.eta * X.T.dot(errors) self.w_[0] += self.eta * errors.sum() cost = (errors**2).sum() / 2.0 self.cost_.append(cost) return self def net_input(self, X): return np.dot(X, self.w_[1:]) + self.w_[0] def activation(self, X): return X def predict(self, X): return np.where(self.activation(X) >= 0.0, 1, -1) 对算法训练过程进行绘图： import pandas as pd import matplotlib.pyplot as plt df = pd.read_csv( \"https://archive.ics.uci.edu/ml/achine-learning-databases/iris/iris.data\", header=None, ) X = df.iloc[:100, [0, 2]].values y = df.iloc[:100, 4].values y = np.where(y == \"Iris-setosa\", -1, 1) fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(8, 4)) ada1 = AdalineGD(n_iter=10, eta=0.01).fit(X, y) ax[0].plot(range(1, len(ada1.cost_) + 1), np.log10(ada1.cost_), marker=\"o\") ax[0].set_xlabel(\"Epochs\") ax[0].set_ylabel(\"log(Sum-squared-error)\") ax[0].set_title(\"Adaline - Learning rate 0.01\") ada2 = AdalineGD(n_iter=10, eta=0.0001).fit(X, y) ax[1].plot(range(1, len(ada2.cost_) + 1), ada2.cost_, marker=\"o\") ax[1].set_xlabel(\"Epochs\") ax[1].set_ylabel(\"Sum-squared-error\") ax[1].set_title(\"Adaline - Learning rate 0.0001\") plt.tight_layout() plt.show() 从上图中的左子图可以观察到，如果学习率太大，由于每次训练都越过了局部最小值，成本函数得不到最小化，反而错误会在学习过程中一直增加。右子图中，成本函数能够逐渐降低，但由于选择了非常小的学习率 η=0.0001\\eta = 0.0001η=0.0001 ，以至于算法需要很长时间才能收敛。 下图中的左子图说明了成本函数随权重的调整而最小化，右子图说明了学习率太大所带来的问题： 许多机器学习算法需要某些方法才能实现最佳性能，梯度下降法是从特征缩放 (feature scaling) 中受益的许多算法之一。这里我们将使用一种称为标准化 (standardization) 的特征缩放方法，能够将数据变换成服从标准正态分布 (平均值为 0，标准差为 1)。 例如，对第 jjj 个特征，只需要对每个训练样本减去样本均值 μj\\mu_jμj​ ，并除以标准差 σj\\sigma_jσj​ ： xj′=xj−μjσj\\begin{align} x_j^{'} = {\\frac {x_j - \\mu_j} {\\sigma_j}} \\end{align}xj′​=σj​xj​−μj​​​​ 标准化可以通过 NumPy 的方法轻松实现： X_std = np.copy(X) X_std[:, 0] = (X[:, 0] - X[:, 0].mean()) / X[:, 0].std() X_std[:, 1] = (X[:, 1] - X[:, 1].mean()) / X[:, 1].std() 标准化后，再次使用 Adaline 进行训练，可以看到在学习率 η=0.01\\eta = 0.01η=0.01 上可以收敛： ada = AdalineGD(n_iter=15, eta=0.01) ada.fit(X_std, y) plot_decision_regions(X_std, y, classifier=ada) plt.title(\"Adaline - Gradient Descent\") plt.xlabel(\"sepal length [standardized]\") plt.ylabel(\"petal length [standardized]\") plt.legend(loc=\"upper left\") plt.tight_layout() plt.show() plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker=\"o\") plt.xlabel(\"Epochs\") plt.ylabel(\"Sum-squared-error\") plt.tight_layout() plt.show() 上图显示成本函数 SSE 随着训练次数的增加而逐渐变小，样本正确分类时，成本函数得到最小化，但并不为 0。","s":"基于批量梯度下降法的 Adaline 实现","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#adaline-implementation-based-on-batch-gradient-descent","p":1105},{"i":1114,"t":"批量梯度下降法在每次训练时，都需要使用到所有样本。假设有一个百万数量级的数据集 (这在机器学习中并不罕见)，使用批量梯度下降法会带来极大的计算成本，其权重的更新如下： Δw=ηΣi(y(i)−ϕ(z(i)))x(i)\\begin{align} \\Delta w = \\eta {\\Sigma_i(y^{(i)} - \\phi(z^{(i)}))} x^{(i)} \\end{align}Δw=ηΣi​(y(i)−ϕ(z(i)))x(i)​​ 一种流行替代方法是随机梯度下降法 (Stochastic Gradient Descent，SGD)，有时也称为迭代 (Iterative) 梯度下降法或在线 (On-line) 梯度下降法，每次使用单个训练样本对权重进行更新： Δw=η(y(i)−ϕ(z(i)))x(i)\\begin{align} \\Delta w = \\eta (y^{(i)} - \\phi(z^{(i)})) x^{(i)} \\end{align}Δw=η(y(i)−ϕ(z(i)))x(i)​​ 相对于批量梯度下下降法，随机梯度下降法的权重的更新频率更快，通常收敛也会更快。由于单个样本有很大的随机性 (即噪音较大)，每次迭代方向并不是都朝着局部最优解方向，算法准确率会相对下降一些。但随着训练次数增加，通常能够收敛到局部最优解附近。采用随机梯度下降法时，在每个训练时期都需要对样本进行洗牌，以获得随机样本。 在随机梯度下降法的实现中，固定学习率 η\\etaη 经常被随着时间的推移而减少的自适应学习率来代替，如 num1niter+num2{\\frac {num1} {n_{iter} + num2}}niter​+num2num1​, 其中 num1num1num1 和 num2num2num2 是常数。 随机梯度下降法的另一个优点是在线学习 (On-line Learning)。每当获取新的样本数据之后，都可以对模型进行训练。这能够适用于持续输入大量数据 (如网络应用中的用户数据) 的情况，另外每次训练后可以丢弃样本以防止数据累积造成的空间不足。 小批量梯度下降法 (Mini-batch Gradient Descent，MBGD) 是批量梯度下降法和随机梯度下降法思想的融合，每次训练采用小批量的样本 (例如样本总数为 1000，每次训练采用其中随机 10 个)，可以克制 BGD 训练较慢和 SGD 噪音较大的问题。","s":"随机梯度下降法","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#stochastic-gradient-descent","p":1105},{"i":1116,"t":"对上节的代码进行调整，添加权重的在线学习函数 partial_fit、训练样本洗牌函数 _shuffle、权重初始化函数 _initialize_weights 和权重调节函数 _update_weights，实现基于随机梯度下降的 Adaline。 import numpy as np class AdalineSGD(object): def __init__(self, eta=0.01, n_iter=10, shuffle=True, random_state=None): self.eta = eta self.n_iter = n_iter self.w_initialized = False self.shuffle = shuffle self.random_state = random_state def fit(self, X, y): self._initialize_weights(X.shape[1]) self.cost_ = [] for i in range(self.n_iter): if self.shuffle: X, y = self._shuffle(X, y) cost = [] for xi, target in zip(X, y): cost.append(self._update_weights(xi, target)) avg_cost = sum(cost) / len(y) self.cost_.append(avg_cost) return self def partial_fit(self, X, y): if not self.w_initialized: self._initialize_weights(X.shape[1]) if y.ravel().shape[0] > 1: for xi, target in zip(X, y): self._update_weights(xi, target) else: self._update_weights(X, y) return self def _shuffle(self, X, y): r = self.rgen.permutation(len(y)) return X[r], y[r] def _initialize_weights(self, m): \"\"\"Initialize weights to small random numbers\"\"\" self.rgen = np.random.RandomState(self.random_state) self.w_ = self.rgen.normal(loc=0.0, scale=0.01, size=1 + m) self.w_initialized = True def _update_weights(self, xi, target): output = self.activation(self.net_input(xi)) error = target - output self.w_[1:] += self.eta * xi.dot(error) self.w_[0] += self.eta * error cost = 0.5 * error**2 return cost def net_input(self, X): return np.dot(X, self.w_[1:]) + self.w_[0] def activation(self, X): return X def predict(self, X): return np.where(self.activation(self.net_input(X)) >= 0.0, 1, -1) 对算法训练过程进行绘图： ada = AdalineSGD(n_iter=15, eta=0.01, random_state=1) ada.fit(X_std, y) plot_decision_regions(X_std, y, classifier=ada) plt.title(\"Adaline - Stochastic Gradient Descent\") plt.xlabel(\"sepal length [standardized]\") plt.ylabel(\"petal length [standardized]\") plt.legend(loc=\"upper left\") plt.tight_layout() plt.show() plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker=\"o\") plt.xlabel(\"Epochs\") plt.ylabel(\"Average Cost\") plt.tight_layout() plt.show() 从上图可以看到，随机梯度下降法每次使用单个样本训练，成本函数 SSE 也可以快速收敛。对于在线学习的场景，对单个样本调用 ada.partial_fit(X_std[0, :], y[0]) 即可对训练模型进行更新。","s":"基于随机梯度下降法的 Adaline 实现","u":"/docs/machine-learning/neural-network/adaline-and-gradient-descent","h":"#adaline-implementation-based-on-stochastic-gradient-descent","p":1105},{"i":1118,"t":"Scikit-learn 的名字源于 SciKit (SciPy Toolkit)，即 SciPy 的第三方扩展工具包。经过历年的发展，Scikit-learn 已成为最流行的机器学习库之一。本文以 Iris 数据集的分类为例，对其进行简介。 如官方网站所介绍，以下是 scikit-learn 的特征： 简单高效的数据挖掘和数据分析工具 可供任何人使用，可在任何环境中重复使用 基于 NumPy，SciPy，以及 matplotlib 开放源码，可用作商业用途 (需遵循 BSD 许可证) 关于 scikit-learn 的安装，请参照这份文档。","s":"Scikit-learn 简介：使用感知器","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"","p":1117},{"i":1120,"t":"从 scikit-learn 加载 Iris 数据集，其中第三列表示花瓣长度 petal length，第四列表示花瓣宽度 petal width。这些类已经转换为整数标签，其中 0 = 山鸢尾 Iris-Setosa，1 = 变色鸢尾 Iris-Versicolor，2 = 维吉尼亚鸢尾 Iris-Verginica。 from sklearn import datasets import numpy as np iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target print(\"Class labels:\", np.unique(y)) # output: Class labels: [0 1 2]","s":"数据导入","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#load-data","p":1117},{"i":1122,"t":"通过函数 sklearn.model_selection.train_test_split 将 150 个数据集分为 70% 的训练集和 30% 的测试集： from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) 这里 stratify=y 表示按照标签值将数据集划分，划分后训练集和测试集的标签具有相同的比例，可以用 np.bincount 打印其中每类标签的个数： print(\"Labels counts in y:\", np.bincount(y)) # output: Labels counts in y: [50 50 50] print( \"Labels counts in y_train:\", np.bincount(y_train) ) # output: Labels counts in y_train: [35 35 35] print( \"Labels counts in y_test:\", np.bincount(y_test) ) # output: Labels counts in y_test: [15 15 15] 通过函数 sklearn.preprocessing.StandardScaler 对特征进行标准化： from sklearn.preprocessing import StandardScaler sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test)","s":"预处理","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#preprocessing","p":1117},{"i":1124,"t":"使用神经元模型 sklearn.linear_model.Perceptron，对训练集进行训练 fit： from sklearn.linear_model import Perceptron ppn = Perceptron(max_iter=40, eta0=0.1, random_state=0) ppn.fit(X_train_std, y_train)","s":"模型训练","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#model-training","p":1117},{"i":1126,"t":"训练完成后，对测试集进行预测 predict，并打印出其中错误预测的样本数量： y_pred = ppn.predict(X_test_std) print( \"Misclassified samples: %d\" % (y_test != y_pred).sum() ) # output: Misclassified samples: 3 训练准确率可以通过 sklearn.metrics.accuracy_score 得到： from sklearn.metrics import accuracy_score print(\"Accuracy: %.2f\" % accuracy_score(y_test, y_pred)) # output: Accuracy: 0.93 scikit-learn 中的每种分类函数都有计算准确率的方法 score，执行时会计算 accuracy_score 并返回，输出结果相同： print(\"Accuracy: %.2f\" % ppn.score(X_test_std, y_test)) # output: Accuracy: 0.93","s":"模型评估","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#model-evaluation","p":1117},{"i":1128,"t":"对算法训练过程进行绘图： from matplotlib.colors import ListedColormap import matplotlib.pyplot as plt def plot_decision_regions(X, y, classifier, test_idx=None, resolution=0.02): markers = (\"s\", \"x\", \"o\", \"^\", \"v\") colors = (\"red\", \"blue\", \"lightgreen\", \"gray\", \"cyan\") cmap = ListedColormap(colors[: len(np.unique(y))]) x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1 x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1 xx1, xx2 = np.meshgrid( np.arange(x1_min, x1_max, resolution), np.arange(x2_min, x2_max, resolution) ) Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T) Z = Z.reshape(xx1.shape) plt.contourf(xx1, xx2, Z, alpha=0.3, cmap=cmap) plt.xlim(xx1.min(), xx1.max()) plt.ylim(xx2.min(), xx2.max()) for idx, cl in enumerate(np.unique(y)): plt.scatter( x=X[y == cl, 0], y=X[y == cl, 1], alpha=0.8, c=colors[idx], marker=markers[idx], label=cl, edgecolor=\"black\", ) if test_idx: X_test, y_test = X[test_idx, :], y[test_idx] plt.scatter( X_test[:, 0], X_test[:, 1], c=\"\", edgecolor=\"black\", alpha=1.0, linewidth=1, marker=\"o\", s=100, label=\"test set\", ) X_combined_std = np.vstack((X_train_std, X_test_std)) y_combined = np.hstack((y_train, y_test)) plot_decision_regions( X=X_combined_std, y=y_combined, classifier=ppn, test_idx=range(105, 150) ) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show() 绘制边界如下，其中测试集用黑色圆圈标出：","s":"绘制分类边界","u":"/docs/machine-learning/neural-network/introduction-to-sklearn-with-perceptron","h":"#plot-decistion-boundary","p":1117},{"i":1130,"t":"逻辑回归 (Logistic Regression) 是一种非常容易实现的分类模型，对于线性可分的情况有很好的表现。与之前文章中的感知器和 Adaline 类似，本文中的逻辑回归也是二元分类的线性模型。","s":"逻辑回归","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"","p":1129},{"i":1132,"t":"为了解释逻辑回归模型背后的思想，先介绍一个概念：比值比 (Odds ratio，OR)。 比值比的数学表示为 p1−p\\cfrac p {1-p}1−pp​，其中 ppp 为某事件可能发生的几率。 在此基础上，定义 logit 函数，即比值比的对数 (计算机科学中 log⁡\\loglog 表示自然对数)： logit(p)=log⁡p1−plogit(p) = \\log {\\cfrac p {1-p}}logit(p)=log1−pp​ logit 的作用是将范围为 (0,1)(0,1)(0,1) 的变量，映射到整个实数集。 对于给定的 xxx： y=1y=1y=1 的概率 p(y=1∣x)p(y=1 | x)p(y=1∣x) 在 (0,1)(0,1)(0,1) 之间。 基于神经元模型，输出的概率是由净输入 z=∑i=0mwixi=wTxz = \\sum_{i=0}^m w_i x_i = w^T xz=∑i=0m​wi​xi​=wTx 得到的。 基于以上逻辑，建立 p(y=1∣x)→zp(y=1 \\mid x) \\rightarrow zp(y=1∣x)→z 的 logit 映射： logit(p(y=1∣x))=z\\begin{align} logit(p(y=1 \\mid x)) = z \\end{align}logit(p(y=1∣x))=z​​ 因此，logit 的反函数即为 z→p(y=1∣x)z \\rightarrow p(y=1 \\mid x)z→p(y=1∣x) 的映射： ϕ(z)=11+e−z=p(y=1∣x)\\begin{align} \\phi (z) = \\cfrac 1 {1+e^{-z}} = p(y=1 \\mid x) \\end{align}ϕ(z)=1+e−z1​=p(y=1∣x)​​ 这里 ϕ(z)=11+e−z\\phi (z) = \\cfrac 1 {1+e^{-z}}ϕ(z)=1+e−z1​ 称为 logistic sigmoid 函数，通常简称为 sigmoid 函数。(sigmoid 意为 S-shaped，即 S 形状的曲线。) import matplotlib.pyplot as plt import numpy as np def sigmoid(z): return 1.0 / (1.0 + np.exp(-z)) z = np.arange(-7, 7, 0.1) phi_z = sigmoid(z) plt.plot(z, phi_z) plt.axvline(0.0, color=\"k\") plt.ylim(-0.1, 1.1) plt.xlabel(\"z\") plt.ylabel(\"$\\phi (z)$\") plt.yticks([0.0, 0.5, 1.0]) ax = plt.gca() ax.yaxis.grid(True) plt.show()","s":"算法思想","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#idea-of-algorithm","p":1129},{"i":1134,"t":"Adaline 和逻辑回归的差异，如下图所示： Adaline： 激活函数：线性函数 ϕ(z)=z\\phi (z) = zϕ(z)=z 阈值函数：阶跃函数 y^={1if ϕ(z)≥00otherwise\\hat y = \\begin{cases} 1 & if \\ \\phi (z) \\ge 0 \\\\[2ex] 0 & otherwise \\end{cases}y^​=⎩⎨⎧​10​if ϕ(z)≥0otherwise​ 逻辑回归： 激活函数：sigmoid 函数 ϕ(z)=11+e−z\\phi (z) = \\cfrac 1 {1+e^{-z}}ϕ(z)=1+e−z1​ 阈值函数：阶跃函数 y^={1if ϕ(z)≥0.50otherwise\\hat y = \\begin{cases} 1 & if \\ \\phi (z) \\ge 0.5 \\\\[2ex] 0 & otherwise \\end{cases}y^​=⎩⎨⎧​10​if ϕ(z)≥0.5otherwise​ 需要注意的是，逻辑回归中的条件 ϕ(z)≥0.5\\phi (z) \\ge 0.5ϕ(z)≥0.5，等价于 z≥0z \\ge 0z≥0。","s":"算法模型","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#algorithm-model","p":1129},{"i":1136,"t":"定义损失函数 (Loss Function) 和成本函数 (Cost Function)，以训练权重参数 www。 损失函数用于单个样本，代表预测输出 y^(i)\\hat y^{(i)}y^​(i) 和实际输出 y(i)y^{(i)}y(i) 之间的误差。 L(y^(i),y(i))=−[y(i)log⁡(y^(i))+(1−y(i))log⁡(1−y^(i))]={−log⁡(y^(i))if y(i)=1−log⁡(1−y^(i))if y(i)=0\\begin{align} L(\\hat y^{(i)}, y^{(i)}) & = -[y^{(i)} \\log (\\hat y^{(i)}) + (1 - y^{(i)}) \\log (1 - \\hat y^{(i)})] \\\\ & = \\begin{cases} -\\log (\\hat y^{(i)}) & \\text{if} \\ y^{(i)} = 1 \\\\[2ex] -\\log (1 - \\hat y^{(i)}) & \\text{if} \\ y^{(i)} = 0\\end{cases} \\end{align}L(y^​(i),y(i))​=−[y(i)log(y^​(i))+(1−y(i))log(1−y^​(i))]=⎩⎨⎧​−log(y^​(i))−log(1−y^​(i))​if y(i)=1if y(i)=0​​​ 当 y(i)=1y^{(i)} = 1y(i)=1 时，最小化 LLL 等价于 y^(i)\\hat y^{(i)}y^​(i) 接近于 1。 当 y(i)=0y^{(i)} = 0y(i)=0 时，最小化 LLL 等价于 y^(i)\\hat y^{(i)}y^​(i) 接近于 0。 成本函数是整个训练集的损失函数的平均值。最小化成本函数，可以得到最优的参数 www。 J(w)=1m∑i=1mL(y^(i),y(i))=−1m∑i=1m[y(i)log⁡(y^(i))+(1−y(i))log⁡(1−y^(i))]\\begin{align} J(w) & = {\\frac 1 m} \\sum _{i=1}^m L(\\hat y^{(i)}, y^{(i)}) \\\\ & = -{\\frac 1 m} \\sum _{i=1}^m [y^{(i)} \\log (\\hat y^{(i)}) + (1 - y^{(i)}) \\log (1 - \\hat y^{(i)})] \\end{align}J(w)​=m1​i=1∑m​L(y^​(i),y(i))=−m1​i=1∑m​[y(i)log(y^​(i))+(1−y(i))log(1−y^​(i))]​​","s":"损失函数和成本函数","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#loss-function-and-cost-function","p":1129},{"i":1138,"t":"逻辑回归的实现如下，使用梯度下降法进行参数训练： import numpy as np class LogisticRegressionGD(object): def __init__(self, eta=0.05, n_iter=100, random_state=1): self.eta = eta self.n_iter = n_iter self.random_state = random_state def fit(self, X, y): rgen = np.random.RandomState(self.random_state) self.w_ = rgen.normal(loc=0.0, scale=0.01, size=1 + X.shape[1]) self.cost_ = [] for i in range(self.n_iter): net_input = self.net_input(X) output = self.activation(net_input) errors = y - output self.w_[1:] += self.eta * X.T.dot(errors) self.w_[0] += self.eta * errors.sum() cost = -(y.dot(np.log(output)) + ((1 - y).dot(np.log(1 - output)))) / X.shape[0] self.cost_.append(cost) return self def net_input(self, X): return np.dot(X, self.w_[1:]) + self.w_[0] def activation(self, z): return 1.0 / (1.0 + np.exp(-np.clip(z, -250, 250))) def predict(self, X): return np.where(self.net_input(X) >= 0.0, 1, 0)","s":"Python 实现","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#python-implementation","p":1129},{"i":1140,"t":"以 Iris-setosa (标签 0) and Iris-versicolor (标签 1) 为例，采用逻辑回归分类，绘制决策边界如下， import matplotlib.pyplot as plt from plot_decision_regions import plot_decision_regions from sklearn import datasets from sklearn.model_selection import train_test_split iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=1, stratify=y) X_train_01_subset = X_train[(y_train == 0) | (y_train == 1)] y_train_01_subset = y_train[(y_train == 0) | (y_train == 1)] lrgd = LogisticRegressionGD(eta=0.05,n_iter=1000,random_state=1) lrgd.fit(X_train_01_subset,y_train_01_subset) plot_decision_regions(X=X_train_01_subset,y=y_train_01_subset,classifier=lrgd) plt.xlabel('petal length [standardized]') plt.ylabel('petal width [standardized]') plt.legend(loc='upper left') plt.show()","s":"绘制图像","u":"/docs/machine-learning/neural-network/logistic-regression-implementation","h":"#plotting","p":1129},{"i":1142,"t":"本文介绍了逻辑回归 (Logistic Regression) 相关的数学知识，重点在于参数和变量的向量化。","s":"逻辑回归的向量化","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"","p":1141},{"i":1144,"t":"二元分类，是将示例归类为两个类别中的一类。 例如，有 1000 张 64 x 64 像素的图片，已知其中哪些是猫、哪些不是。在这个基础上，给一张新的 64 x 64 像素的图片，需要判断是不是猫。 这种基础的图像识别问题，可以归为二元分类。","s":"二元分类","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#binary-classification","p":1141},{"i":1146,"t":"训练样本数和测试样本数 m=mtrain=1000mtest=1\\begin{align} m = m_{train} & = 1000 \\\\ m_{test} & = 1 \\end{align}m=mtrain​mtest​​=1000=1​​ 单个样本的特征数 n=nx=64×64×3\\begin{align} n = n_x = 64 \\times 64 \\times 3 \\end{align}n=nx​=64×64×3​​ 单个样本的输入和输出 x(i)=[x1(i)x2(i)⋮xn(i)]∈Rn,y(i)∈{0,1}⊂R1\\begin{align} x^{(i)} = \\begin{bmatrix} x^{(i)}_1 \\\\x^{(i)}_2 \\\\ \\vdots \\\\ x^{(i)}_n \\end{bmatrix} \\in R^{n}, \\quad y^{(i)} \\in \\{0,1\\} \\subset R^1 \\end{align}x(i)=​x1(i)​x2(i)​⋮xn(i)​​​∈Rn,y(i)∈{0,1}⊂R1​​ 总样本的输入和输出 X=[x(1)x(2)⋯x(m)]∈Rn×mY=[y(1)y(2)⋯y(m)]∈R1×m\\begin{align} X & = \\begin{bmatrix} x^{(1)} & x^{(2)} & \\cdots & x^{(m)} \\end{bmatrix} \\in R^{n \\times m} \\\\ Y & = \\begin{bmatrix} y^{(1)} & y^{(2)} & \\cdots & y^{(m)} \\end{bmatrix} \\in R^{1 \\times m} \\end{align}XY​=[x(1)​x(2)​⋯​x(m)​]∈Rn×m=[y(1)​y(2)​⋯​y(m)​]∈R1×m​​","s":"数学建模","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#modeling-in-math","p":1141},{"i":1148,"t":"逻辑回归是一种学习算法，适用于输出为 0 或 1 的情况。逻辑回归的目标是最小化其预测输出 y^\\hat yy^​ 和实际输出 yyy 的误差。 Given x, y^=P(y=1∣x),where 0≤y^≤1\\begin{align} Given \\ x, \\ \\hat y = P(y =1 \\mid x), \\quad where \\ 0 \\leq \\hat y \\leq 1 \\end{align}Given x, y^​=P(y=1∣x),where 0≤y^​≤1​​ 对于单个样本，逻辑回归使用的参数如下： 输入：x∈Rnx \\in R^nx∈Rn 实际输出：y∈0,1y \\in {0,1}y∈0,1 权重：w∈Rnw \\in R^nw∈Rn 阈值/偏置：b∈R1b \\in R^1b∈R1 净输入/加权输入：z=wTx+bz = w^T x + bz=wTx+b 预测输出：y^=σ(z)=σ(wTx+b)\\hat y = \\sigma (z) = \\sigma (w^T x + b)y^​=σ(z)=σ(wTx+b) 将输入 zzz 映射到输出 y^\\hat yy^​ 的函数称为激活函数 (Activation Function)。这里激活函数使用 Sigmoid 函数σ(z)\\sigma (z)σ(z)，可以将输出映射到 [0,1][0,1][0,1] 的范围内： σ(z)=11+e−z\\begin{align} \\sigma (z) = \\frac 1 {1 + e^{-z}} \\end{align}σ(z)=1+e−z1​​​ 如果 zzz 很大，那么 y^\\hat yy^​ 接近于 1；反之则接近于 0。","s":"逻辑回归","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#logistic-regression","p":1141},{"i":1150,"t":"定义损失函数 (Loss Function) 和成本函数 (Cost Function)，以训练参数 www 和 bbb。 损失函数用于单个样本，代表预测输出 y^(i)\\hat y^{(i)}y^​(i) 和实际输出 y(i)y^{(i)}y(i) 之间的误差。 L(y^(i),y(i))=−[y(i)log⁡(y^(i))+(1−y(i))log⁡(1−y^(i))]\\begin{align} L(\\hat y^{(i)}, y^{(i)}) = -[y^{(i)} \\log (\\hat y^{(i)}) + (1 - y^{(i)}) \\log (1 - \\hat y^{(i)})] \\end{align}L(y^​(i),y(i))=−[y(i)log(y^​(i))+(1−y(i))log(1−y^​(i))]​​ 若 y(i)=1y^{(i)} = 1y(i)=1，则 L(y^(i)，y(i))=−log⁡(y^(i))L (\\hat y^{(i)}，y^{(i)}) = -\\log (\\hat y^{(i)})L(y^​(i)，y(i))=−log(y^​(i))，最小化 LLL 等价于 y^(i)\\hat y^{(i)}y^​(i) 接近于 1。 若 y(i)=0y^{(i)} = 0y(i)=0，则 L(y^(i)，y(i))=−log⁡(1−y^(i))L (\\hat y^{(i)}，y^{(i)}) = -\\log (1 - \\hat y^{(i)})L(y^​(i)，y(i))=−log(1−y^​(i))，最小化 LLL 等价于 y^(i)\\hat y^{(i)}y^​(i) 接近于 0。 成本函数是整个训练集的损失函数的平均值。最小化成本函数，可以得到最优的参数 www 和 bbb。 J(w,b)=1m∑i=1mL(y^(i),y(i))=−1m∑i=1m[y(i)log⁡(y^(i))+(1−y(i))log⁡(1−y^(i))]\\begin{align} J(w, b) & = {\\frac 1 m} \\sum _{i=1}^m L(\\hat y^{(i)}, y^{(i)}) \\\\ & = -{\\frac 1 m} \\sum _{i=1}^m [y^{(i)} \\log (\\hat y^{(i)}) + (1 - y^{(i)}) \\log (1 - \\hat y^{(i)})] \\end{align}J(w,b)​=m1​i=1∑m​L(y^​(i),y(i))=−m1​i=1∑m​[y(i)log(y^​(i))+(1−y(i))log(1−y^​(i))]​​","s":"函数定义","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#function-definition","p":1141},{"i":1152,"t":"梯度下降法的定义为，如果实值函数 F(x)F(x)F(x) 在点 aaa 处可微且有定义，那么函数 F(x)F(x)F(x) 在点 aaa 沿着梯度相反的方向下降最快。这里使用梯度下降法最小化成本函数 J(w，b)J(w，b)J(w，b)，以得到最优的参数 www 和 bbb，其中 α\\alphaα 为学习率 (learning rate)。 wj:=wj−α∂J∂wj,where j=1,2,⋯ ,nb:=b−α∂J∂b\\begin{align} w_j & := w_j - \\alpha \\frac {\\partial J} {\\partial w_j}, \\quad where \\ j = 1,2,\\cdots,n \\\\ b & := b - \\alpha \\frac {\\partial J} {\\partial b} \\end{align}wj​b​:=wj​−α∂wj​∂J​,where j=1,2,⋯,n:=b−α∂b∂J​​​ 记 a(i)=y^(i)=σ(z(i))a^{(i)} = \\hat y^{(i)} = \\sigma (z^{(i)})a(i)=y^​(i)=σ(z(i))： {∂J∂L=1m∂L∂a(i)=−y(i)a(i)+1−y(i)1−a(i)∂a(i)∂z(i)=e−z(i)(1+e−z(i))2=a(i)(1−a(i))⇒∂J∂z(i)=∂J∂L∂L∂a(i)∂a(i)∂z(i)=1m(a(i)−y(i))\\left \\lbrace \\begin{align} \\frac {\\partial J} {\\partial L} & = \\frac 1 m \\\\ \\frac {\\partial L} {\\partial a^{(i)}} & = - {\\frac {y^{(i)}} {a^{(i)}}} + {\\frac {1 - y^{(i)}} {1 - a^{(i)}}} \\\\ \\frac {\\partial a^{(i)}} {\\partial z^{(i)}} & = \\frac {e^{-z^{(i)}}} {(1 + e^{-z^{(i)}})^2} = a^{(i)}(1 - a^{(i)}) \\\\ \\end{align} \\right . \\\\ \\Rightarrow \\frac {\\partial J} {\\partial z^{(i)}} = {\\frac {\\partial J} {\\partial L}} {\\frac {\\partial L} {\\partial a^{(i)}}} {\\frac {\\partial a^{(i)}} {\\partial z^{(i)}}} = {\\frac 1 m} (a^{(i)} - y^{(i)})⎩⎨⎧​∂L∂J​∂a(i)∂L​∂z(i)∂a(i)​​=m1​=−a(i)y(i)​+1−a(i)1−y(i)​=(1+e−z(i))2e−z(i)​=a(i)(1−a(i))​​⇒∂z(i)∂J​=∂L∂J​∂a(i)∂L​∂z(i)∂a(i)​=m1​(a(i)−y(i)) 由于 z(i)=w1x1(i)+w2x2(i)+⋯+wnxn(i)+bz^{(i)} = w_1 x^{(i)} _1 + w_2 x^{(i)} _2 + \\cdots + w_n x^{(i)} _n + bz(i)=w1​x1(i)​+w2​x2(i)​+⋯+wn​xn(i)​+b，因此有： ∂J∂wj=∑i=1m∂J∂z(i)∂z(i)∂wj=∑i=1mxj(i)∂J∂z(i)∂J∂b=∑i=1m∂J∂z(i)∂z(i)∂b=∑i=1m∂J∂z(i)\\begin{align} \\frac {\\partial J} {\\partial w_j} & = \\sum_{i=1}^m {\\frac {\\partial J} {\\partial z^{(i)}}} {\\frac {\\partial z^{(i)}} {\\partial w_j}} = \\sum_{i=1}^m x_j^{(i)} {\\frac {\\partial J} {\\partial z^{(i)}}} \\\\ \\frac {\\partial J} {\\partial b} & = \\sum_{i=1}^m {\\frac {\\partial J} {\\partial z^{(i)}}} {\\frac {\\partial z^{(i)}} {\\partial b}} = \\sum_{i=1}^m {\\frac {\\partial J} {\\partial z^{(i)}}} \\end{align}∂wj​∂J​∂b∂J​​=i=1∑m​∂z(i)∂J​∂wj​∂z(i)​=i=1∑m​xj(i)​∂z(i)∂J​=i=1∑m​∂z(i)∂J​∂b∂z(i)​=i=1∑m​∂z(i)∂J​​​","s":"梯度下降法","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#梯度下降法","p":1141},{"i":1154,"t":"以 z=wTx+bz = w^T x + bz=wTx+b 为例，原始输入输出为： z(1)=w1x1(1)+w2x2(1)+⋯+wnxn(1)+bz(2)=w1x1(2)+w2x2(2)+⋯+wnxn(2)+b⋮z(m)=w1x1(m)+w2x2(m)+⋯+wnxn(m)+b\\begin{align} z^{(1)} & = w_1 x^{(1)}_1 + w_2 x^{(1)}_2 + \\cdots + w_n x^{(1)}_n + b \\\\ z^{(2)} & = w_1 x^{(2)}_1 + w_2 x^{(2)}_2 + \\cdots + w_n x^{(2)}_n + b \\\\ & \\vdots \\\\ z^{(m)} & = w_1 x^{(m)}_1 + w_2 x^{(m)}_2 + \\cdots + w_n x^{(m)}_n + b \\end{align}z(1)z(2)z(m)​=w1​x1(1)​+w2​x2(1)​+⋯+wn​xn(1)​+b=w1​x1(2)​+w2​x2(2)​+⋯+wn​xn(2)​+b⋮=w1​x1(m)​+w2​x2(m)​+⋯+wn​xn(m)​+b​​ 向量化之后为： [z(1)z(2)⋮z(m)]T=[w1w2⋮wn]T[x1(1)x1(2)⋯x1(m)x2(1)x2(2)⋯x2(m)⋮⋮⋱⋮xn(1)xn(2)⋯xn(m)]+[bb⋮b]T⇓Z=WTX+B\\begin{align} {\\begin{bmatrix} z^{(1)} \\\\ z^{(2)} \\\\ \\vdots \\\\ z^{(m)} \\end{bmatrix}}^T & = {\\begin{bmatrix} w_1 \\\\ w_2 \\\\ \\vdots \\\\ w_n \\end{bmatrix}}^T \\begin{bmatrix} x^{(1)}_1 & x^{(2)}_1 & \\cdots & x^{(m)}_1 \\\\ x^{(1)}_2 & x^{(2)}_2 & \\cdots & x^{(m)}_2 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ x^{(1)}_n & x^{(2)}_n & \\cdots & x^{(m)}_n \\end{bmatrix} + {\\begin{bmatrix} b \\\\ b \\\\ \\vdots \\\\ b \\end{bmatrix}}^T \\\\ & \\Downarrow \\\\ Z & = W^T X + B \\end{align}​z(1)z(2)⋮z(m)​​TZ​=​w1​w2​⋮wn​​​T​x1(1)​x2(1)​⋮xn(1)​​x1(2)​x2(2)​⋮xn(2)​​⋯⋯⋱⋯​x1(m)​x2(m)​⋮xn(m)​​​+​bb⋮b​​T⇓=WTX+B​​ 向量化之后，对整个训练样本进行单次训练，描述如下： Z=WTX+BA=σ(Z)dZ=∂J∂Z=1m(A−Y)dW=∂J∂W=X⋅[dZ]Tdb=∑i=1mdZiW:=W−α⋅dWb:=b−α⋅db\\begin{align} Z & = W^T X + B \\\\ A & = \\sigma (Z) \\\\ dZ & = \\frac {\\partial J} {\\partial Z} = {\\frac 1 m} (A - Y) \\\\ dW & = \\frac {\\partial J} {\\partial W} = X \\cdot [dZ]^T \\\\ db & = \\sum_{i=1}^m dZ_i \\\\ W & := W - \\alpha \\cdot dW \\\\ b & := b - \\alpha \\cdot db \\end{align}ZAdZdWdbWb​=WTX+B=σ(Z)=∂Z∂J​=m1​(A−Y)=∂W∂J​=X⋅[dZ]T=i=1∑m​dZi​:=W−α⋅dW:=b−α⋅db​​ 以上可以使用 Python Numpy 进行实现。","s":"向量化","u":"/docs/machine-learning/neural-network/logistic-regression-mathmatics-and-vectorization","h":"#向量化","p":1141},{"i":1156,"t":"本文介绍了 MCP 神经元和感知器，以及对应的算法实现。","s":"MCP 神经元和感知器","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","h":"","p":1155},{"i":1158,"t":"Warren McCullock 和 Walter Pitts 通过研究大脑，于 1943 年提出了第一个人工智能模型：MCP 神经元。神经元是涉及化学和电信号处理和传输的大脑中相互联系的神经细胞，如下图所示： MCP 神经元为具有二进制输出的简单逻辑门。多个信号从树突传入细胞体中，如果累积输入信号超过一定阈值，则从轴突传出输出信号。 Frank Rosenblatt 于 1957 年发表了基于 MCP 神经元模型的感知器学习规则，提出了一种自动学习最佳权重系数的算法，然后与输入特征相乘，从而决定是否触发神经元。这种算法可以用于监督式学习中的分类。 感知器采用输入向量 xxx 和权重向量 www，净输入 zzz 为这二者的线性组合 (z=w1x1+…+wmxmz = w_1 x_1 + \\ldots + w_m x_mz=w1​x1​+…+wm​xm​)： w=[w1w2⋮wm],x=[x1x2⋮xm]w = \\begin{bmatrix} w_1 \\\\ w_2 \\\\ \\vdots \\\\ w_m \\\\ \\end{bmatrix}, x = \\begin{bmatrix} x_1 \\\\ x_2 \\\\ \\vdots \\\\ x_m \\\\ \\end{bmatrix}w=​w1​w2​⋮wm​​​,x=​x1​x2​⋮xm​​​ 激活函数采用阶跃函数 ϕ(z)\\phi(z)ϕ(z), θ\\thetaθ 为神经元的触发阈值： ϕ(z)={1,if z≥θ−1,if z<θ\\phi(z) = \\begin{cases} 1, &\\text{if } z \\geq \\theta \\\\[2ex] -1, &\\text{if } z \\lt \\theta \\end{cases}ϕ(z)=⎩⎨⎧​1,−1,​if z≥θif z<θ​ 通过设定 x0=1x_0 = 1x0​=1 和 w0=−θw_0 = -\\thetaw0​=−θ，将 θ\\thetaθ 集成到 zzz 中，可以让上式更整齐： z=w0x0+w1x1+w2x2+…+wmxm=wTxz = w_0 x_0 + w_1 x_1 + w_2 x_2 + \\ldots + w_m x_m = w^T xz=w0​x0​+w1​x1​+w2​x2​+…+wm​xm​=wTxϕ(z)={1,if z≥0−1,if z<0\\phi(z) = \\begin{cases} 1, &\\text{if } z \\geq 0 \\\\[2ex] -1, &\\text{if } z \\lt 0 \\end{cases}ϕ(z)=⎩⎨⎧​1,−1,​if z≥0if z<0​ 下图为通过 z=wTxz = w^T xz=wTx 得到 1 或 -1 的激活函数 (左子图)，以及其用于区分两个线性可分的类 (右子图)： MCP 神经元和 Rosenblatt 阈值感知器模型的思想为简化模拟大脑单个神经元的工作原理，即输入是否达到触发条件。 Rosenblatt 感知器规则非常简单： 将权重初始化为 0 或较小的随机数。 对于每个训练样本 x(i)x^{(i)}x(i)，执行以下步骤： 计算输出值 y^\\hat yy^​。 更新权重。 权重 wjw_jwj​ 的更新可以表示为： wj:=wj+Δwjw_j := w_j + \\Delta w_jwj​:=wj​+Δwj​ 用于更新权重向量中的第 jjj 个权重 Δwj\\Delta w_jΔwj​ 可由感知器学习规则计算得到： Δwj=η(y(i)−y^(i))xj(i)\\Delta w_j = \\eta (y^{(i)} - \\hat y^{(i)}) x_j^{(i)}Δwj​=η(y(i)−y^​(i))xj(i)​ 其中 η\\etaη 是学习率 (介于 0 和 1 之间)，y(i)y^{(i)}y(i) 是第 iii 次训练的实际类标签，y^(i)\\hat y^{(i)}y^​(i) 是第 iii 次训练的预测类标签。需要注意，权重向量中的所有权重的更新是同时的，更新权重之后才会更新下一次的 y^(i)\\hat y^{(i)}y^​(i)。 例如，二维数据的权重更新如下： Δw0=η(y(i)−output(i))Δw1=η(y(i)−output(i))x1(i)Δw2=η(y(i)−output(i))x2(i)\\begin{align} \\Delta w_0 &= \\eta (y^{(i)} - \\text{output}^{(i)}) \\\\ \\Delta w_1 &= \\eta (y^{(i)} - \\text{output}^{(i)}) x_1^{(i)} \\\\ \\Delta w_2 &= \\eta (y^{(i)} - \\text{output}^{(i)}) x_2^{(i)} \\end{align}Δw0​Δw1​Δw2​​=η(y(i)−output(i))=η(y(i)−output(i))x1(i)​=η(y(i)−output(i))x2(i)​​​ 在感知器预测正确类标签的情况下，权重保持不变： Δwj=η(−1(i)−−1(i))xj(i)=0Δwj=η(1(i)−1(i))xj(i)=0\\begin{align} \\Delta w_j &= \\eta (-1^{(i)} - -1^{(i)}) x_j^{(i)} = 0 \\\\ \\Delta w_j &= \\eta (1^{(i)} - 1^{(i)}) x_j^{(i)} = 0 \\end{align}Δwj​Δwj​​=η(−1(i)−−1(i))xj(i)​=0=η(1(i)−1(i))xj(i)​=0​​ 在感知器预测错误类标签的情况下，权重朝正确类标签的方向更新： 2Δwj=η(1(i)−−1(i))xj(i)=η(2)xj(i)Δwj=η(−1(i)−1(i))xj(i)=η(−2)xj(i)\\begin{align}{2} \\Delta w_j &= \\eta (1^{(i)} - -1^{(i)}) x_j^{(i)} = \\eta (2) x_j^{(i)} \\\\ \\Delta w_j &= \\eta (-1^{(i)} - 1^{(i)}) x_j^{(i)} = \\eta (-2) x_j^{(i)} \\end{align}2Δwj​Δwj​​=η(1(i)−−1(i))xj(i)​=η(2)xj(i)​=η(−1(i)−1(i))xj(i)​=η(−2)xj(i)​​​ 为了更好地理解上述表达式中乘数因子 xj(i)x_j^{(i)}xj(i)​ 的作用，这里按照以下条件来举例说明： y(i)=1,y^(i)=−1,η=1y^{(i)} = 1, \\hat y^{(i)} = -1, \\eta = 1y(i)=1,y^​(i)=−1,η=1 如果有样本 xj(i)=0.5x_j^{(i)} = 0.5xj(i)​=0.5，但是被错误分类为 -1，对应的 Δwj\\Delta w_jΔwj​ 为： Δwj(i)=1×(1−(−1))×0.5=1\\Delta w_j^{(i)} = 1 \\times (1 - (-1)) \\times 0.5 = 1Δwj(i)​=1×(1−(−1))×0.5=1 如果有另外一个样本为 xj(i)=2x_j^{(i)} = 2xj(i)​=2，但是被错误分类为 -1，会产生更大的 Δwj\\Delta w_jΔwj​，以便下次能正确分类： Δwj(i)=1×(1−(−1))×2=4\\Delta w_j^{(i)} = 1 \\times (1 - (-1)) \\times 2 = 4Δwj(i)​=1×(1−(−1))×2=4 注意，感知器只有在类线性可分且学习率足够小才能收敛。如果类之间不是线性可分的，需要设置最大训练次数或者设置可容忍的错误分类数量，否则感知器会一直更新权重： 下图简单描述了感知器的原理： 在输入阶段，感知器接收样本 xxx 的输入并和权重 www 来计算净输入，然后将净输入传递到激活函数 (这里采用单位阶跃函数)，该函数生成输出预测类标签 -1 或 +1。在学习阶段，该输出用于计算预测误差并更新权重。","s":"MCP 神经元和感知器原理","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","h":"#mcp-neuron-and-perceptron-priciple","p":1155},{"i":1160,"t":"下面代码中，采用了面向对象的方法，定义感知器为 Python 类。 import numpy as np class Perceptron(object): def __init__(self, eta=0.01, n_iter=50, random_state=1): self.eta = eta self.n_iter = n_iter self.random_state = random_state def fit(self, X, y): rgen = np.random.RandomState(self.random_state) self.w_ = rgen.normal(loc=0.0, scale=0.01, size=1 + X.shape[1]) self.errors_ = [] for _ in range(self.n_iter): errors = 0 for xi, target in zip(X, y): errors += int(self.predict(xi) != target) update = self.eta * (target - self.predict(xi)) self.w_[1:] += update * xi self.w_[0] += update self.errors_.append(errors) return self def net_input(self, X): return np.dot(X, self.w_[1:]) + self.w_[0] def predict(self, X): return np.where(self.net_input(X) >= 0.0, 1, -1) 通过上述实现，可以通过指定学习速率 eta 和训练次数 n_iter 来初始化感知器对象。fit 方法可以初始化一个全 0 权重向量 self.w_，包含权重 w0w_0w0​ ~ wmw_mwm​ 。 在权重初始化后，使用感知器的学习规则更新权重。fit 传入已知样本和对应标签，用于训练阶段得到算法参数；predict 用于预测任何样本 (通常使用未知样本以观察算法性能) 的对应标签，用于验证阶段。 另外，这里定义了错误分类的样本数目 self.errors_，以观察算法在每次训练后的表现。","s":"Rosenblatt 感知器的 Python 实现","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","h":"#python-implementation-of-perceptron","p":1155},{"i":1162,"t":"加载 Iris 数据集​ Iris 数据集可以看做矩阵 R150×4R^{150 \\times 4}R150×4，具有 150 个样本，4 个特征 (花萼长度 sepal length、花萼宽度 sepal width、花瓣长度 petal length、花瓣宽度 petal width)，可分成 3 个分类 (山鸢尾 Setosa、变色鸢尾 Versicolor、维吉尼亚鸢尾 Verginica)。 从 UCI Machine Learning Repository 读取 Iris 数据集，并打印最后五行： import pandas as pd df = pd.read_csv( \"https://archive.ics.uci.edu/ml/achine-learning-databases/iris/iris.data\", header=None, ) df.tail() Iris 数据子集绘图​ 为了简单演示训练流程，我们只挑选 Sepal Length 和 Petal Length 这两个特征，另外只挑选 Setosa 和 Versicolor 这两类。 我们提取前 100 个样本的类标签 (依次对应 50 个 Setosa 和 50 个 Versicolor)，并将类标签转换为整数类标签 -1 (Setosa) 和 1 (Versicolor)，用 pandas.DataFrame 表示。然后提取这 100 个样本的第一个特征列 Sepal Length 和第三个特征列 Petal Length，将它们分配给特征矩阵 X 并通过二维散点图可视化： import pandas as pd import matplotlib.pyplot as plt df = pd.read_csv( \"https://archive.ics.uci.edu/ml/achine-learning-databases/iris/iris.data\", header=None, ) X = df.iloc[:100, [0, 2]].values y = df.iloc[:100, 4].values y = np.where(y == \"Iris-setosa\", -1, 1) plt.scatter(X[:50, 0], X[:50, 1], color=\"red\", marker=\"o\", label=\"setosa\") plt.scatter(X[50:100, 0], X[50:100, 1], color=\"blue\", marker=\"x\", label=\"versicolor\") plt.xlabel(\"sepal length [cm]\") plt.ylabel(\"petal length [cm]\") plt.legend(loc=\"upper left\") plt.tight_layout() plt.show() 感知器模型训练​ 接下来在提取的 Iris 数据子集上训练我们的感知器算法，同时，我们将绘制每次训练后的分类错误以检查算法是否收敛，并找到分离两个花类的决策边界： ppn = Perceptron(eta=0.1, n_iter=10) ppn.fit(X, y) plt.plot(range(1, len(ppn.errors_) + 1), ppn.errors_, marker=\"o\") plt.xlabel(\"Epochs\") plt.ylabel(\"Number of updates\") plt.tight_layout() plt.show() 从上图可以观察到在六次训练后，样本错误分类数目为 0，算法得到收敛。 决策边界绘图​ 定义决策边界绘图函数如下： from matplotlib.colors import ListedColormap def plot_decision_regions(X, y, classifier, resolution=0.02): # setup marker generator and color map markers = (\"s\", \"x\", \"o\", \"^\", \"v\") colors = (\"red\", \"blue\", \"lightgreen\", \"gray\", \"cyan\") cmap = ListedColormap(colors[: len(np.unique(y))]) # plot the decision surface x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1 x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1 xx1, xx2 = np.meshgrid( np.arange(x1_min, x1_max, resolution), np.arange(x2_min, x2_max, resolution) ) Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T) Z = Z.reshape(xx1.shape) plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap) plt.xlim(xx1.min(), xx1.max()) plt.ylim(xx2.min(), xx2.max()) # plot class samples for idx, cl in enumerate(np.unique(y)): plt.scatter( x=X[y == cl, 0], y=X[y == cl, 1], alpha=0.8, c=cmap(idx), edgecolor=\"black\", marker=markers[idx], label=cl, ) 对上一节中的样本进行绘图： plot_decision_regions(X, y, classifier=ppn) plt.xlabel(\"sepal length [cm]\") plt.ylabel(\"petal length [cm]\") plt.legend(loc=\"upper left\") plt.tight_layout() plt.show() 通过学习，感知器生成了将 Iris 训练子集完全分类的决策边界。 备注 虽然本例中感知器能够完全分类两种花卉，但收敛仍是感知器最重要的问题之一。如果两个类线性可分，感知器算法就能够收敛。然而对于无法线性可分的类，除非我们手动设置最大训练次数，否则权重永远不会停止更新。","s":"基于 Iris 数据集的感知器模型训练","u":"/docs/machine-learning/neural-network/mcp-neuron-and-perceptron","h":"#perceptron-model-training-based-on-iris-dataset","p":1155},{"i":1164,"t":"信息 NumPy 是用于 Python 中多维数组计算的软件库。 本文部分内容翻译自斯坦福大学文档 CS231n - Python NumPy Tutorial。","s":"NumPy 快速入门","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"","p":1163},{"i":1166,"t":"NumPy 是 Python 中科学计算的基础包。它是一个 Python 库，提供多维数组对象、各种派生对象 (例如数组和矩阵) 以及各种用于快速数组操作的例程，包括数学、逻辑、形状操作、排序、选择、I/O、离散傅里叶变换、基本线性代数、基本统计运算、随机模拟等等。 NumPy 包的核心是 ndarray 对象。它封装了同构数据类型的 n 维数组，许多操作在编译代码中执行以提高性能。NumPy 数组和标准 Python 序列之间有几个重要的区别： 与 Python 列表 (可以动态增长) 不同，NumPy 数组在创建时大小是固定的。更改 ndarray 的大小将创建一个新数组并删除原始数组。 NumPy 数组中的元素都必须具有相同的数据类型，因此在内存中的大小也相同。例外：可以拥有 (Python，包括 NumPy) 对象的数组，从而允许不同大小元素的数组。 NumPy 数组有助于对大量数据进行高级数学和其他类型的运算。通常，与使用 Python 的内置序列相比，此类操作的执行效率更高，并且代码更少。 越来越多的基于 Python 的科学和数学包正在使用 NumPy 数组；尽管这些通常支持 Python 序列输入，但它们在处理之前将此类输入转换为 NumPy 数组，并且通常输出 NumPy 数组。换句话说，为了有效地使用当今大部分 (甚至是大多数) 基于 Python 的科学/数学软件，仅仅知道如何使用 Python 的内置序列类型是不够的 - 还需要知道如何使用 NumPy 数组。 关于序列大小和速度的问题在科学计算中尤为重要。作为一个简单的示例，考虑将一维序列中的每个元素与相同长度的另一个序列中的相应元素相乘的情况。如果数据存储在两个 Python 列表 a 和 b 中，我们可以迭代每个元素： c = [] for i in range(len(a)): c.append(a[i] * b[i]) 这会产生正确的答案，但如果 a 和 b 各自包含数百万个数字，我们将为 Python 中的循环效率低下付出代价。我们可以通过编写 C 语言更快地完成相同的任务 (为了清楚起见，我们忽略了变量声明和初始化、内存分配等) for (i = 0; i < rows; i++) { c[i] = a[i]*b[i]; } 这节省了解释 Python 代码和操作 Python 对象所涉及的所有开销，但代价是牺牲了从 Python 编码中获得的好处。此外，所需的编码工作随着数据维度的增加而增加。例如，在二维数组的情况下，C 代码 (如前所述) 扩展为 for (i = 0; i < rows; i++) { for (j = 0; j < columns; j++) { c[i][j] = a[i][j]*b[i][j]; } } NumPy 为我们提供了两全其美的功能：当涉及 ndarray 时，逐元素操作是“默认模式”，但逐元素操作可以通过预编译的 C 代码快速执行。在 NumPy 中可以用 c = a * b 执行前面示例的操作，速度接近 C 语言，同时代码简单，符合我们基于 Python 的期望。","s":"什么是 NumPy","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#what-is-numpy","p":1163},{"i":1168,"t":"矢量化的代码没有任何显式循环、索引等 - 当然，这些事情实际上是在优化的预编译 C 代码中被处理了。矢量化代码具有许多优点，其中包括： 矢量化代码更简洁，更容易阅读 更少的代码行通常意味着更少的错误 代码更类似于标准数学符号 (通常更容易正确编码数学结构) 矢量化会产生更多符合 Python 风格的代码；如果没有矢量化，我们的代码将充斥着低效且难以阅读的 for 循环","s":"为什么 NumPy 很快？","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#why-numpy-fast","p":1163},{"i":1170,"t":"Numpy 是 Python 中科学计算的核心库。它提供了一个高性能的多维数组对象，以及使用这些数组的工具。","s":"使用 Numpy","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#use-numpy","p":1163},{"i":1172,"t":"Numpy 的核心功能是 ndarray (即 n-dimensional array，多维数组) 数据结构。这是一个表示多维度、同质并且固定大小的数组对象。维数是数组的秩 rank；数组的形状 shape 是一个整数元组，表示沿着每个维度的数组大小。 我们可以从嵌套的 Python 列表初始化 Numpy 数组，并使用方括号来访问元素： import numpy as np a = np.array([1, 2, 3]) # Create a rank 1 array print type(a) # Prints \"<type 'numpy.ndarray'>\" print a.shape # Prints \"(3,)\" print a[0], a[1], a[2] # Prints \"1 2 3\" a[0] = 5 # Change an element of the array print a # Prints \"[5, 2, 3]\" b = np.array([[1,2,3],[4,5,6]]) # Create a rank 2 array print b.shape # Prints \"(2, 3)\" print b[0, 0], b[0, 1], b[1, 0] # Prints \"1 2 4\" Numpy 还提供许多创建数组的函数： import numpy as np a = np.zeros((2,2)) # Create an array of all zeros print a # Prints \"[[ 0. 0.] # [ 0. 0.]]\" b = np.ones((1,2)) # Create an array of all ones print b # Prints \"[[ 1. 1.]]\" c = np.full((2,2), 7) # Create a constant array print c # Prints \"[[ 7. 7.] # [ 7. 7.]]\" d = np.eye(2) # Create a 2x2 identity matrix print d # Prints \"[[ 1. 0.] # [ 0. 1.]]\" e = np.random.random((2,2)) # Create an array filled with random values print e # Might print \"[[ 0.91940167 0.08143941] # [ 0.68744134 0.87236687]]\" 你可以在这份文档中阅读关于数组创建的其他方法。","s":"数组","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#arrays","p":1163},{"i":1174,"t":"Numpy 提供了多种索引到数组的方法。 切片：与 Python 列表类似，可以对 Numpy 数组进行切片。由于数组可能是多维的，因此必须为数组的每个维度指定一个切片： import numpy as np # Create the following rank 2 array with shape (3, 4) # [[ 1 2 3 4] # [ 5 6 7 8] # [ 9 10 11 12]] a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]]) # Use slicing to pull out the subarray consisting of the first 2 rows # and columns 1 and 2; b is the following array of shape (2, 2): # [[2 3] # [6 7]] b = a[:2, 1:3] # A slice of an array is a view into the same data, so modifying it # will modify the original array. print a[0, 1] # Prints \"2\" b[0, 0] = 77 # b[0, 0] is the same piece of data as a[0, 1] print a[0, 1] # Prints \"77\" 你还可以将整数索引与片段索引进行混合。但是，这样做会产生比原始数组更低的数组： import numpy as np # Create the following rank 2 array with shape (3, 4) # [[ 1 2 3 4] # [ 5 6 7 8] # [ 9 10 11 12]] a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]]) # Two ways of accessing the data in the middle row of the array. # Mixing integer indexing with slices yields an array of lower rank, # while using only slices yields an array of the same rank as the # original array: row_r1 = a[1, :] # Rank 1 view of the second row of a row_r2 = a[1:2, :] # Rank 2 view of the second row of a print row_r1, row_r1.shape # Prints \"[5 6 7 8] (4,)\" print row_r2, row_r2.shape # Prints \"[[5 6 7 8]] (1, 4)\" # We can make the same distinction when accessing columns of an array: col_r1 = a[:, 1] col_r2 = a[:, 1:2] print col_r1, col_r1.shape # Prints \"[ 2 6 10] (3,)\" print col_r2, col_r2.shape # Prints \"[[ 2] # [ 6] # [10]] (3, 1)\" 整数数组索引：当你使用切片索引到 Numpy 数组时，生成的数组视图将始终是原始数组的子数组。相反，整数数组索引允许你使用另一个数组的数据来构造任意数组。例如： import numpy as np a = np.array([[1,2], [3, 4], [5, 6]]) # An example of integer array indexing. # The returned array will have shape (3,) and print a[[0, 1, 2], [0, 1, 0]] # Prints \"[1 4 5]\" # The above example of integer array indexing is equivalent to this: print np.array([a[0, 0], a[1, 1], a[2, 0]]) # Prints \"[1 4 5]\" # When using integer array indexing, you can reuse the same # element from the source array: print a[[0, 0], [1, 1]] # Prints \"[2 2]\" # Equivalent to the previous integer array indexing example print np.array([a[0, 1], a[0, 1]]) # Prints \"[2 2]\" 一个有用的整数数组索引技巧，是从矩阵的每一行中选择一个元素： import numpy as np # Create a new array from which we will select elements a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]]) print a # prints \"array([[ 1, 2, 3], # [ 4, 5, 6], # [ 7, 8, 9], # [10, 11, 12]])\" # Create an array of indices b = np.array([0, 2, 0, 1]) # Select one element from each row of a using the indices in b print a[np.arange(4), b] # Prints \"[ 1 6 7 11]\" # Mutate one element from each row of a using the indices in b a[np.arange(4), b] += 10 print a # prints \"array([[11, 2, 3], # [ 4, 5, 16], # [17, 8, 9], # [10, 21, 12]]) 布尔数组索引：布尔数组索引可以让你选择数组的任意元素。通常，这种类型的索引用于选择满足某些条件的数组的元素。例如： import numpy as np a = np.array([[1,2], [3, 4], [5, 6]]) bool_idx = (a > 2) # Find the elements of a that are bigger than 2; # this returns a numpy array of Booleans of the same # shape as a, where each slot of bool_idx tells # whether that element of a is > 2. print bool_idx # Prints \"[[False False] # [ True True] # [ True True]]\" # We use boolean array indexing to construct a rank 1 array # consisting of the elements of a corresponding to the True values # of bool_idx print a[bool_idx] # Prints \"[3 4 5 6]\" # We can do all of the above in a single concise statement: print a[a > 2] # Prints \"[3 4 5 6]\" 为了简洁起见，我们省略了很多有关 Numpy 数组索引的细节；如果你想了解更多，请阅读这份文档。","s":"数组索引","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#array-indexing","p":1163},{"i":1176,"t":"每个 Numpy 数组都是相同类型元素的网格。Numpy 提供了大量可用于构造数组的数值数据类型。创建数组时，Numpy 会尝试猜测数据类型，但构造数组的函数通常还包含一个可选参数来显式指定数据类型。下面是一个例子： import numpy as np x = np.array([1, 2]) # Let numpy choose the datatype print(x.dtype) # Prints \"int64\" x = np.array([1.0, 2.0]) # Let numpy choose the datatype print(x.dtype) # Prints \"float64\" x = np.array([1, 2], dtype=np.int64) # Force a particular datatype print(x.dtype) # Prints \"int64\" 你可以在这份文档中查看 Numpy 支持的数据类型。","s":"数据类型","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#datatypes","p":1163},{"i":1178,"t":"基本的数学函数在数组上按元素运算，并且可以作为运算符重载和 numpy 模块中的函数使用： import numpy as np x = np.array([[1,2],[3,4]], dtype=np.float64) y = np.array([[5,6],[7,8]], dtype=np.float64) # Elementwise sum; both produce the array # [[ 6.0 8.0] # [10.0 12.0]] print x + y print np.add(x, y) # Elementwise difference; both produce the array # [[-4.0 -4.0] # [-4.0 -4.0]] print x - y print np.subtract(x, y) # Elementwise product; both produce the array # [[ 5.0 12.0] # [21.0 32.0]] print x * y print np.multiply(x, y) # Elementwise division; both produce the array # [[ 0.2 0.33333333] # [ 0.42857143 0.5 ]] print x / y print np.divide(x, y) # Elementwise square root; produces the array # [[ 1. 1.41421356] # [ 1.73205081 2. ]] print np.sqrt(x) 请注意，* 是元素乘法，而不是矩阵乘法。如需使用矩阵乘法，请使用函数 dot。dot 可用作 Numpy 模块中的函数，也可用作数组对象的实例方法： import numpy as np x = np.array([[1,2],[3,4]]) y = np.array([[5,6],[7,8]]) v = np.array([9,10]) w = np.array([11, 12]) # Inner product of vectors; both produce 219 print v.dot(w) print np.dot(v, w) # Matrix / vector product; both produce the rank 1 array [29 67] print x.dot(v) print np.dot(x, v) # Matrix / matrix product; both produce the rank 2 array # [[19 22] # [43 50]] print x.dot(y) print np.dot(x, y) Numpy 提供了许多有用的矩阵计算函数；其中最重要的函数之一是 sum： import numpy as np x = np.array([[1,2],[3,4]]) print np.sum(x) # Compute sum of all elements; prints \"10\" print np.sum(x, axis=0) # Compute sum of each column; prints \"[4 6]\" print np.sum(x, axis=1) # Compute sum of each row; prints \"[3 7]\" 你可以在这份文档中找到 numpy 提供的数学函数完整列表。 除了使用数组计算数学函数之外，我们经常需要重新整形或以其他方式处理数组中的数据。这种类型的操作的最简单的例子是转置矩阵；要转置矩阵，只需使用数组对象的 T 属性： import numpy as np x = np.array([[1,2], [3,4]]) print x # Prints \"[[1 2] # [3 4]]\" print x.T # Prints \"[[1 3] # [2 4]]\" # Note that taking the transpose of a rank 1 array does nothing: v = np.array([1,2,3]) print v # Prints \"[1 2 3]\" print v.T # Prints \"[1 2 3]\" Numpy 提供了更多的功能来操作数组；你可以在这份文档中看到完整列表。","s":"数组计算","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#array-math","p":1163},{"i":1180,"t":"广播是一种强大的机制，允许 Numpy 在执行算术运算时使用不同形状的数组。通常我们有一个更小的数组和一个更大的数组，我们想要使用较小的数组多次来对较大的数组执行一些操作。 例如，假设我们要为矩阵的每一行添加一个常量向量。我们可以这样做： import numpy as np # We will add the vector v to each row of the matrix x, # storing the result in the matrix y x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]]) v = np.array([1, 0, 1]) y = np.empty_like(x) # Create an empty matrix with the same shape as x # Add the vector v to each row of the matrix x with an explicit loop for i in range(4): y[i, :] = x[i, :] + v # Now y is the following # [[ 2 2 4] # [ 5 5 7] # [ 8 8 10] # [11 11 13]] print y 这种方法是可以的；然而，当矩阵 x 非常大时，Python 循环可能会运行很长时间。实际上，将向量 v 添加到矩阵 x 的每一行，等价于通过创建垂直堆叠 v 的矩阵 vv，然后执行 x 和 vv 的元素求和。我们可以这样实现这个方法： import numpy as np # We will add the vector v to each row of the matrix x, # storing the result in the matrix y x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]]) v = np.array([1, 0, 1]) vv = np.tile(v, (4, 1)) # Stack 4 copies of v on top of each other print vv # Prints \"[[1 0 1] # [1 0 1] # [1 0 1] # [1 0 1]]\" y = x + vv # Add x and vv elementwise print y # Prints \"[[ 2 2 4 # [ 5 5 7] # [ 8 8 10] # [11 11 13]]\" Numpy 广播允许我们在不创建 v 的多个副本的情况下执行这个计算。以上情况下，我们可以使用广播： import numpy as np # We will add the vector v to each row of the matrix x, # storing the result in the matrix y x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]]) v = np.array([1, 0, 1]) y = x + v # Add v to each row of x using broadcasting print y # Prints \"[[ 2 2 4] # [ 5 5 7] # [ 8 8 10] # [11 11 13]]\" 即使 x 具有形状 (4, 3) 且 v 具有形状 (3,)，行 y = x + v 可以正常执行；工作原理是由于广播，v 仿佛有形状 (4, 3)，其中每行都是 v 的副本，然后按元素进行求和。 两个数组间的广播遵循以下规则： 如果阵列不具有相同的秩，则对较小秩的阵列进行预处理，直到两个形状都具有相同的长度。 如果两个数组在某一维度的大小相等，或者其中一个数组在该维度的大小为 1，则称两个数组在这个维度上兼容。 如果两个数组在所有维度上都兼容，则可以进行广播。 广播后，每个数组形状等同于较大的数组形状。 如果在某一维度，其中一个数组大小等于 1 并且另一个数组大小大于 1，则前者沿着此维度复制自身。 如果感到困惑，请尝试阅读这份文档或这份说明。 支持广播的函数被称为通用函数。你可以在这份文档中找到所有通用函数的列表。 以下是广播的一些应用： import numpy as np # Compute outer product of vectors v = np.array([1,2,3]) # v has shape (3,) w = np.array([4,5]) # w has shape (2,) # To compute an outer product, we first reshape v to be a column # vector of shape (3, 1); we can then broadcast it against w to yield # an output of shape (3, 2), which is the outer product of v and w: # [[ 4 5] # [ 8 10] # [12 15]] print np.reshape(v, (3, 1)) * w # Add a vector to each row of a matrix x = np.array([[1,2,3], [4,5,6]]) # x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3), # giving the following matrix: # [[2 4 6] # [5 7 9]] print x + v # Add a vector to each column of a matrix # x has shape (2, 3) and w has shape (2,). # If we transpose x then it has shape (3, 2) and can be broadcast # against w to yield a result of shape (3, 2); transposing this result # yields the final result of shape (2, 3) which is the matrix x with # the vector w added to each column. Gives the following matrix: # [[ 5 6 7] # [ 9 10 11]] print (x.T + w).T # Another solution is to reshape w to be a column vector of shape (2, 1); # we can then broadcast it directly against x to produce the same # output. print x + np.reshape(w, (2, 1)) # Multiply a matrix by a constant: # x has shape (2, 3). NumPy treats scalars as arrays of shape (); # these can be broadcast together to shape (2, 3), producing the # following array: # [[ 2 4 6] # [ 8 10 12]] print x * 2 广播通常会使你的代码更加简洁快捷，因此你应尽可能地使用它。","s":"广播","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#broadcasting","p":1163},{"i":1182,"t":"这个简短的概述已经涉及到大部分 Numpy 的重要功能，但仍有许多地方未涉及。查看 Numpy 参考文档以了解更多关于 Numpy 的信息。","s":"Numpy 文档","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#numpy-documentation","p":1163},{"i":1184,"t":"Numpy 提供了一个高性能的多维数组和基本的工具来计算和操纵这些数组。Scipy 建立在此基础之上，并提供了大量功能，可以运行在 Numpy 数组上，并且可用于不同类型的科学和工程应用。 熟悉 Scipy 的最佳方法是浏览这份文档。","s":"Scipy","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#scipy","p":1163},{"i":1186,"t":"Scipy 提供了一些基本功能来处理图像。例如，它具有从磁盘读取图像到 Numpy 数组，将 Numpy 数组写入磁盘作为图像并调整图像大小的功能。下面的示例中展示了这些功能： from scipy.misc import imread, imsave, imresize # Read an JPEG image into a numpy array img = imread('assets/cat.jpg') print img.dtype, img.shape # Prints \"uint8 (400, 248, 3)\" # We can tint the image by scaling each of the color channels # by a different scalar constant. The image has shape (400, 248, 3); # we multiply it by the array [1, 0.95, 0.9] of shape (3,); # numpy broadcasting means that this leaves the red channel unchanged, # and multiplies the green and blue channels by 0.95 and 0.9 # respectively. img_tinted = img * [1, 0.95, 0.9] # Resize the tinted image to be 300 by 300 pixels. img_tinted = imresize(img_tinted, (300, 300)) # Write the tinted image back to disk imsave('assets/cat_tinted.jpg', img_tinted)","s":"图像操作","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#image-operations","p":1163},{"i":1188,"t":"Scipy 定义了一些有用的函数，用于计算点集合之间的距离。 函数 scipy.spatial.distance.pdist 计算给定单个集合中所有点之间的距离： import numpy as np from scipy.spatial.distance import pdist, squareform # Create the following array where each row is a point in 2D space: # [[0 1] # [1 0] # [2 0]] x = np.array([[0, 1], [1, 0], [2, 0]]) print x # Compute the Euclidean distance between all rows of x. # d[i, j] is the Euclidean distance between x[i, :] and x[j, :], # and d is the following array: # [[ 0. 1.41421356 2.23606798] # [ 1.41421356 0. 1. ] # [ 2.23606798 1. 0. ]] d = squareform(pdist(x, 'euclidean')) print d 你可以在这份文档中阅读有关此功能的所有详细信息。 类似的函数 (scipy.spatial.distance.cdist) 能够计算不同集合内所有点之间的距离；你可以阅读这份文档。","s":"点的距离","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#distance-between-points","p":1163},{"i":1190,"t":"Matplotlib 是一个绘图库。本节简要介绍了 matplotlib.pyplot 模块，该模块提供了与 MATLAB 类似的绘图系统。","s":"Matplotlib","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#matplotlib","p":1163},{"i":1192,"t":"Matplotlib 中最重要的函数是 plot，它可以绘制二维数据。这是一个简单的例子： import numpy as np import matplotlib.pyplot as plt # Compute the x and y coordinates for points on a sine curve x = np.arange(0, 3 * np.pi, 0.1) y = np.sin(x) # Plot the points using matplotlib plt.plot(x, y) plt.show() # You must call plt.show() to make graphics appear. 运行此代码，会生成以下图形： 只需一点额外的工作，我们可以轻松地绘制多行，并添加标题，图例和轴标签： import numpy as np import matplotlib.pyplot as plt # Compute the x and y coordinates for points on sine and cosine curves x = np.arange(0, 3 * np.pi, 0.1) y_sin = np.sin(x) y_cos = np.cos(x) # Plot the points using matplotlib plt.plot(x, y_sin) plt.plot(x, y_cos) plt.xlabel(\"x axis label\") plt.ylabel(\"y axis label\") plt.title(\"Sine and Cosine\") plt.legend([\"Sine\", \"Cosine\"]) plt.show() 关于 plot 函数的更多信息，你可以阅读这份文档。","s":"绘图","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#plotting","p":1163},{"i":1194,"t":"你可以使用 subplot 函数在同一图中绘制不同子图。例如： import numpy as np import matplotlib.pyplot as plt # Compute the x and y coordinates for points on sine and cosine curves x = np.arange(0, 3 * np.pi, 0.1) y_sin = np.sin(x) y_cos = np.cos(x) # Set up a subplot grid that has height 2 and width 1, # and set the first such subplot as active. plt.subplot(2, 1, 1) # Make the first plot plt.plot(x, y_sin) plt.title(\"Sine\") # Set the second subplot as active, and make the second plot. plt.subplot(2, 1, 2) plt.plot(x, y_cos) plt.title(\"Cosine\") # Show the figure. plt.show() 关于 subplot 函数的更多信息，你可以阅读这份文档。","s":"绘制子图","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#subplots","p":1163},{"i":1196,"t":"你可以使用 imshow 功能来显示图像。例如： import numpy as np from scipy.misc import imread, imresize import matplotlib.pyplot as plt img = imread(\"assets/cat.jpg\") img_tinted = img * [1, 0.95, 0.9] # Show the original image plt.subplot(1, 2, 1) plt.imshow(img) # Show the tinted image plt.subplot(1, 2, 2) # A slight gotcha with imshow is that it might give strange results # if presented with data that is not uint8. To work around this, we # explicitly cast the image to uint8 before displaying it. plt.imshow(np.uint8(img_tinted)) plt.show()","s":"图像","u":"/docs/machine-learning/numpy-pandas/numpy-quickstart","h":"#images","p":1163},{"i":1198,"t":"套袋算法 (Bagging) 是一种集成学习技术，与 MajorityVoteClassifier 相似，不同之处在于 bagging 不是每次使用相同的训练集来拟合单个分类器，而是对初始训练集进行 bootstrap 抽样。这也是 bagging 称为引导聚合 (Bootstrap Aggregating) 的原因。","s":"Bagging","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","h":"","p":1197},{"i":1200,"t":"Bagging 的概念如下图： 为了更具体说明 bagging 分类器如何工作，参见下图中的示例。图中有 n = 7 个训练实例 (以索引 1 - 7 表示)，在每轮 bagging 中进行有放回地抽样 k 次，然后使用这 k 次的聚合样本 (允许包含重复的样本) 来拟合分类器。如果聚合样本中的样本数等于实例，则称为 bootstrap 抽样。 bagging 一般使用在较弱的分类器中使用 (如未修剪的决策树)，以降低其过拟合的问题。在对每个分类器进行拟合后，通过多数投票方法来对结果进行预测。","s":"基本概念","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","h":"#基本概念","p":1197},{"i":1202,"t":"为了对 bagging 方法进行说明，这里使用 Wine 数据集，并提取值为 2 和 3 的分类标签、特征为 Alcohol 和 OD280/OD315 的样本： import pandas as pd df_wine = pd.read_csv( \"https://archive.ics.uci.edu/ml/\" \"machine-learning-databases/wine/wine.data\", header=None, ) df_wine.columns = [ \"Class label\", \"Alcohol\", \"Malic acid\", \"Ash\", \"Alcalinity of ash\", \"Magnesium\", \"Total phenols\", \"Flavanoids\", \"Nonflavanoid phenols\", \"Proanthocyanins\", \"Color intensity\", \"Hue\", \"OD280/OD315 of diluted wines\", \"Proline\", ] df_wine = df_wine[df_wine[\"Class label\"] != 1] y = df_wine[\"Class label\"].values X = df_wine[[\"Alcohol\", \"OD280/OD315 of diluted wines\"]].values 将标签进行编码，并将样本分为 80% 的训练集和 20% 的测试集： from sklearn.preprocessing import LabelEncoder from sklearn.model_selection import train_test_split le = LabelEncoder() y = le.fit_transform(y) X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, random_state=1, stratify=y )","s":"数据导入及预处理","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","h":"#数据导入及预处理","p":1197},{"i":1204,"t":"使用 sklearn.ensemble.BaggingClassifier 进行 bagging。 这里使用未修剪的决策树作为基础分类器，并建立 500 个由不同 bootstrap 样本得到的决策树的集合： from sklearn.ensemble import BaggingClassifier from sklearn.tree import DecisionTreeClassifier tree = DecisionTreeClassifier(criterion=\"entropy\", max_depth=None, random_state=1) bag = BaggingClassifier( base_estimator=tree, n_estimators=500, max_samples=1.0, max_features=1.0, bootstrap=True, bootstrap_features=False, n_jobs=1, random_state=1, ) 接下来，计算训练集和测试集中的预测准确性，以比较 bagging 分类器与单个未裁剪决策树的表现： from sklearn.metrics import accuracy_score tree = tree.fit(X_train, y_train) y_train_pred = tree.predict(X_train) y_test_pred = tree.predict(X_test) tree_train = accuracy_score(y_train, y_train_pred) tree_test = accuracy_score(y_test, y_test_pred) print(\"Decision tree train/test accuracies %.3f/%.3f\" % (tree_train, tree_test)) bag = bag.fit(X_train, y_train) y_train_pred = bag.predict(X_train) y_test_pred = bag.predict(X_test) bag_train = accuracy_score(y_train, y_train_pred) bag_test = accuracy_score(y_test, y_test_pred) print(\"Bagging train/test accuracies %.3f/%.3f\" % (bag_train, bag_test)) 得到结果如下： Decision tree train/test accuracies 1.000/0.833 Bagging train/test accuracies 1.000/0.917 尽管 bagging 和决策树对于训练集的预测准确率均为 100%，但在测试集上 bagging 的准确率要高于测试集，泛化能力更优。 对 bagging 和决策树的决策边界分别绘图。 import numpy as np import matplotlib.pyplot as plt x_min = X_train[:, 0].min() - 1 x_max = X_train[:, 0].max() + 1 y_min = X_train[:, 1].min() - 1 y_max = X_train[:, 1].max() + 1 xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1), np.arange(y_min, y_max, 0.1)) f, axarr = plt.subplots(nrows=1, ncols=2, sharex=\"col\", sharey=\"row\", figsize=(8, 3)) for idx, clf, tt in zip([0, 1], [tree, bag], [\"Decision tree\", \"Bagging\"]): clf.fit(X_train, y_train) Z = clf.predict(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) axarr[idx].contourf(xx, yy, Z, alpha=0.3) axarr[idx].scatter( X_train[y_train == 0, 0], X_train[y_train == 0, 1], c=\"blue\", marker=\"^\" ) axarr[idx].scatter( X_train[y_train == 1, 0], X_train[y_train == 1, 1], c=\"green\", marker=\"o\" ) axarr[idx].set_title(tt) axarr[0].set_ylabel(\"Alcohol\", fontsize=12) plt.text( 10.2, -0.5, s=\"OD280/OD315 of diluted wines\", ha=\"center\", va=\"center\", fontsize=12 ) plt.tight_layout() # plt.savefig('images/07_08.png', dpi=300, bbox_inches='tight') plt.show() 从上图可以看出，bagging 的决策边界相比决策树更为平滑。 在实践中，bagging 往往用于解决由于解决分类器模型的过拟合问题，降低模型的方差。需要注意的是，bagging 无法减少模型偏差 (如某些模型太简单，无法很好地捕捉数据中的趋势)。因此 bagging 更适用于低偏差的模型，如未修剪的决策树。","s":"bagging 的 scikit-learn 实现","u":"/docs/machine-learning/traditional-ml-algorithms/bagging","h":"#bagging-的-scikit-learn-实现","p":1197},{"i":1206,"t":"决策树 (Decision Tree) 是一种特殊的树结构，代表的是样本特征与样本标签之间的一种映射关系。 决策树举例如下，分叉路径则代表某个可能的属性值，而终结节点代表最终决策：","s":"决策树和随机森林","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"","p":1205},{"i":1209,"t":"为了引入决策树分类的算法，先介绍决策树学习中的重要概念：信息增益 (Information Gain)。 这个指标可以衡量分类给数据中带来信息的程度。若分类带来的信息增益越大，就越能减少数据的无序度。 信息增益的表示如下，为父节点和子节点中的不纯度 (Inpurity) 差值： IG(Dp,f)=I(Dp)−∑j=1mNiNpI(Dj)\\begin{align} IG(D_p, f) = I(D_p) - \\sum_{j=1}^m \\cfrac {N_i} {N_p} I(D_j) \\end{align}IG(Dp​,f)=I(Dp​)−j=1∑m​Np​Ni​​I(Dj​)​​ 其中 fff 代表对应的特征，DpD_pDp​ 和 DjD_jDj​ 分别表示父节点的数据和第 jjj 个子节点的数据集，NpN_pNp​ 和 NiN_iNi​ 分别表示父节点的数据和第 jjj 个子节点的样本数量，I()I()I() 代表不纯度的函数。 不纯度的计算有以下几种方法： 熵 (Entropy)：IH(t)=−∑j=1cp(i∣t)⋅log⁡2p(i∣t)I_H(t) = -\\sum_{j=1}^c p(i \\mid t) \\cdot \\log_2 p(i \\mid t)IH​(t)=−∑j=1c​p(i∣t)⋅log2​p(i∣t) Gini 不纯度 (Gini Impurity)：IG(t)=1−∑j=1cp(i∣t)2I_G(t) = 1- \\sum_{j=1}^c p(i \\mid t)^2IG​(t)=1−∑j=1c​p(i∣t)2 分类错误 (Classification Error)：IE(t)=1−max⁡p(i∣t)I_E(t) = 1- \\max p(i \\mid t)IE​(t)=1−maxp(i∣t) 在实际应用中，熵和 Gini 不纯度的结果非常相似，不必纠结于这两个计算标准的选择。而分类错误对节点概率的变化较不敏感，不推荐在决策树增长时使用。","s":"定义","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#定义","p":1205},{"i":1211,"t":"以如下决策树演示不纯度的计算，其中 (a，b)(a，b)(a，b) 代表节点中所属分类的样本数量。 例如父节点，包含 40 个属于类 1 的样本、40 个属于类 2 的样本；其他节点同理。 决策树 A 的熵： IH(Dp)=−(12log⁡12+12log⁡12)=1IH(Dleft)=−(34log⁡34+14log⁡14)=0.81IH(Dright)=−(14log⁡14+34log⁡34)=0.81IGH=1−120.81−120.81=0.19\\begin{align} I_H(D_p) & = -({\\cfrac 1 2} \\log{\\cfrac 1 2} + {\\cfrac 1 2} \\log{\\cfrac 1 2}) = 1 \\\\ I_H(D_{left}) & = -({\\cfrac 3 4} \\log{\\cfrac 3 4} + {\\cfrac 1 4} \\log{\\cfrac 1 4}) = 0.81 \\\\ I_H(D_{right}) & = -({\\cfrac 1 4} \\log{\\cfrac 1 4} + {\\cfrac 3 4} \\log{\\cfrac 3 4}) = 0.81 \\\\ IG_H & = 1 - {\\cfrac 1 2} 0.81 - {\\cfrac 1 2} 0.81 = 0.19 \\end{align}IH​(Dp​)IH​(Dleft​)IH​(Dright​)IGH​​=−(21​log21​+21​log21​)=1=−(43​log43​+41​log41​)=0.81=−(41​log41​+43​log43​)=0.81=1−21​0.81−21​0.81=0.19​​ 决策树 B 的熵： IH(Dp)=−(12log⁡12+12log⁡12)=1IH(Dleft)=−(13log⁡13+23log⁡23)=0.92IH(Dright)=0IGH=1−340.92−0=0.31\\begin{align} I_H(D_p) & = -({\\cfrac 1 2} \\log{\\cfrac 1 2} + {\\cfrac 1 2} \\log{\\cfrac 1 2}) = 1 \\\\ I_H(D_{left}) & = -({\\cfrac 1 3} \\log{\\cfrac 1 3} + {\\cfrac 2 3} \\log{\\cfrac 2 3}) = 0.92 \\\\ I_H(D_{right}) & = 0 \\\\ IG_H & = 1 - {\\cfrac 3 4} 0.92 - 0 = 0.31 \\end{align}IH​(Dp​)IH​(Dleft​)IH​(Dright​)IGH​​=−(21​log21​+21​log21​)=1=−(31​log31​+32​log32​)=0.92=0=1−43​0.92−0=0.31​​ 决策树 A 的 Gini 不纯度： IG(Dp)=1−(12)2−(12)2=12IG(Dleft)=1−(34)2−(14)2=38IG(Dright)=1−(14)2−(34)2=38IGG=1−12⋅38−12⋅38=0.125\\begin{align} I_G(D_p) & = 1 - ({\\cfrac 1 2})^2 - ({\\cfrac 1 2})^2 = \\cfrac 1 2 \\\\ I_G(D_{left}) & = 1 - ({\\cfrac 3 4})^2 - ({\\cfrac 1 4})^2 = \\cfrac 3 8 \\\\ I_G(D_{right}) & = 1 - ({\\cfrac 1 4})^2 - ({\\cfrac 3 4})^2 = \\cfrac 3 8 \\\\ IG_G & = 1 - {\\cfrac 1 2} \\cdot {\\cfrac 3 8} - {\\cfrac 1 2} \\cdot {\\cfrac 3 8} = 0.125 \\end{align}IG​(Dp​)IG​(Dleft​)IG​(Dright​)IGG​​=1−(21​)2−(21​)2=21​=1−(43​)2−(41​)2=83​=1−(41​)2−(43​)2=83​=1−21​⋅83​−21​⋅83​=0.125​​ 决策树 B 的 Gini 不纯度： IG(Dp)=1−(12)2−(12)2=12IG(Dleft)=1−(23)2−(13)2=49IG(Dright)=1−12−02=0IGG=12−34⋅49−0=0.167\\begin{align} I_G(D_p) & = 1 - ({\\cfrac 1 2})^2 - ({\\cfrac 1 2})^2 = \\cfrac 1 2 \\\\ I_G(D_{left}) & = 1 - ({\\cfrac 2 3})^2 - ({\\cfrac 1 3})^2 = \\cfrac 4 9 \\\\ I_G(D_{right}) & = 1 - 1^2 - 0^2 = 0 \\\\ IG_G & = \\cfrac 1 2 - {\\cfrac 3 4} \\cdot {\\cfrac 4 9} - 0 = 0.167 \\end{align}IG​(Dp​)IG​(Dleft​)IG​(Dright​)IGG​​=1−(21​)2−(21​)2=21​=1−(32​)2−(31​)2=94​=1−12−02=0=21​−43​⋅94​−0=0.167​​ 决策树 A 的分类错误： IE(Dp)=1−12=12IE(Dleft)=1−34=14IE(Dright)=1−34=14IGE=12−12⋅14−12⋅14=0.25\\begin{align} I_E(D_p) & = 1 - {\\cfrac 1 2} = \\cfrac 1 2 \\\\ I_E(D_{left}) & = 1 - {\\cfrac 3 4} = \\cfrac 1 4 \\\\ I_E(D_{right}) & = 1 - {\\cfrac 3 4} = \\cfrac 1 4 \\\\ IG_E & = {\\cfrac 1 2} - {\\cfrac 1 2} \\cdot {\\cfrac 1 4} - {\\cfrac 1 2} \\cdot {\\cfrac 1 4} = 0.25 \\end{align}IE​(Dp​)IE​(Dleft​)IE​(Dright​)IGE​​=1−21​=21​=1−43​=41​=1−43​=41​=21​−21​⋅41​−21​⋅41​=0.25​​ 决策树 B 的分类错误： IE(Dp)=1−12=12IE(Dleft)=1−13=13IE(Dright)=1−1=0IGE=12−34⋅13−0=0.25\\begin{align} I_E(D_p) & = 1 - {\\cfrac 1 2} = \\cfrac 1 2 \\\\ I_E(D_{left}) & = 1 - {\\cfrac 1 3} = \\cfrac 1 3 \\\\ I_E(D_{right}) & = 1 - 1 = 0 \\\\ IG_E & = {\\cfrac 1 2} - {\\cfrac 3 4} \\cdot {\\cfrac 1 3} - 0 = 0.25 \\end{align}IE​(Dp​)IE​(Dleft​)IE​(Dright​)IGE​​=1−21​=21​=1−31​=31​=1−1=0=21​−43​⋅31​−0=0.25​​ 为了更直观的比较三种信息增益计算方法的差异，对平均分布 [0,1][0,1][0,1] 的样本应用并绘图： import matplotlib.pyplot as plt import numpy as np def gini(p): return (p) * (1 - (p)) + (1 - p) * (1 - (1 - p)) def entropy(p): return -p * np.log2(p) - (1 - p) * np.log2((1 - p)) def error(p): return 1 - np.max([p, 1 - p]) x = np.arange(0.0, 1.0, 0.01) ent = [entropy(p) if p != 0 else None for p in x] sc_ent = [e * 0.5 if e else None for e in ent] err = [error(i) for i in x] ax = plt.subplot(111) for ( i, lab, ls, c, ) in zip( [ent, sc_ent, gini(x), err], [\"Entropy\", \"Entropy (scaled)\", \"Gini Impurity\", \"Misclassification Error\"], [\"-\", \"-\", \"--\", \"-.\"], [\"black\", \"lightgray\", \"red\", \"green\", \"cyan\"], ): line = ax.plot(x, i, label=lab, linestyle=ls, lw=2, color=c) ax.legend( loc=\"upper center\", bbox_to_anchor=(0.5, 1.15), ncol=5, fancybox=True, shadow=False ) ax.axhline(y=0.5, linewidth=1, color=\"k\", linestyle=\"--\") ax.axhline(y=1.0, linewidth=1, color=\"k\", linestyle=\"--\") plt.ylim([0, 1.1]) plt.xlabel(\"p(i=1)\") plt.ylabel(\"Impurity Index\") plt.show()","s":"计算示例","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#计算示例","p":1205},{"i":1214,"t":"决策树分类的思想是，从树根开始将特征上的数据分割成最大的信息增益，然后在子节点重复这个拆分过程。 在实践中，这可能会导致一个有很多节点的很深的树，很容易导致过度拟合。因此通常要通过设置树的最大深度限制来修剪树。 以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (其中决策边界绘制函数 plot_decision_regions 请参见之前的文章)： import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.tree import DecisionTreeClassifier iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) tree = DecisionTreeClassifier(criterion=\"gini\", max_depth=4, random_state=1) tree.fit(X_train, y_train) X_combined = np.vstack((X_train, X_test)) y_combined = np.hstack((y_train, y_test)) plot_decision_regions(X_combined, y_combined, classifier=tree, test_idx=range(105, 150)) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show()","s":"代码实现","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#代码实现","p":1205},{"i":1216,"t":"Windows 下的 Graphviz 需要： 下载并安装 Graphviz Windows 安装包 graphviz-2.xx.msi 将 C:\\Program Files (x86)\\Graphviz2.xx\\bin\\; 添加到环境变量 Path (计算机——属性——高级系统设置——环境变量) Pip 安装软件包：pip install pydotplus graphviz pyparsing 对上节生成的 tree 进行绘图： from pydotplus import graph_from_dot_data from sklearn.tree import export_graphviz dot_data = export_graphviz( tree, filled=True, rounded=True, class_names=[\"Setosa\", \"Versicolor\", \"Virginica\"], feature_names=[\"petal length\", \"petal width\"], out_file=None, ) graph = graph_from_dot_data(dot_data) graph.write_png(\"tree.png\")","s":"Graphviz 绘图","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#graphviz-绘图","p":1205},{"i":1218,"t":"随机森林是一个包含多个决策树的分类器，并且其输出的分类标签是由每个树的的分类标签的众数而定。 从已知的样本集合 (样本数 MMM，特征数 NNN) 中，有放回地随机取 nnn 个 bootstrap 样本 (n<Nn < Nn<N)。 对取得的 bootstrap 的样本生成决策树：a。无放回地随机选择其中 mmm 个特征 (m<<Mm << Mm<<M)。b。根据目标函数提供的最佳分割特征 (如最大化信息增益) 来分割节点。 重复步骤 1-2 若干次数。 汇总每棵树的预测标签，把其中数量最多的作为随机森林的分类标签。 import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.ensemble import RandomForestClassifier iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) forest = RandomForestClassifier( criterion=\"gini\", n_estimators=25, random_state=1, n_jobs=2 ) forest.fit(X_train, y_train) X_combined = np.vstack((X_train, X_test)) y_combined = np.hstack((y_train, y_test)) plot_decision_regions( X_combined, y_combined, classifier=forest, test_idx=range(105, 150) ) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show() 上面通过 n_estimators 参数从 25 个决策树中训练了一个随机森林，并使用 Gini 不纯度作为分割节点的标准。n_jobs 参数表示可以使用计算机的多个核心 (这里是两个核心) 来并行化训练。","s":"随机森林","u":"/docs/machine-learning/traditional-ml-algorithms/decision-tree","h":"#随机森林","p":1205},{"i":1220,"t":"集合 (Ensemble) 方法的目标是将不同的分类器组合到一起，相比每个单独的分类器具有更好的泛化性能。","s":"使用集合的投票分类方法","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","h":"","p":1219},{"i":1222,"t":"如果 10 位专家的预测分别如下，集合方法可以将其预测结果结合起来，从而得出比每位专家的预测更精确和更稳健的预测： 一致 (Unanimity)：预测情况一致 绝对多数投票 (Majority Voting)：预测情况不同，取高于 50% 的预测结果，适用于二元分类 相对多数投票 (Plurality Voting)：预测情况不同，取其中相对最高的预测结果，适用于多元分类 投票算法用于分类器时，可以取 m 个不同的分类器，然后使用不同的分类算法 (决策树、SVM、逻辑回归等) 构建集合；也可以使用相同的分类算法对不同的测试集进行评估。 以下为使用多数投票的集合方法实例，其中有 m 个分类器 C1，C2，⋯，CmC_1，C_2， \\cdots，C_mC1​，C2​，⋯，Cm​ 以及其评估结果： 记 x\\boldsymbol xx 为输入，y^\\hat yy^​ 为预测的众数： y^=mode{C1(x),C2(x),⋯ ,Cm(x)}\\begin{align} \\hat y = mode \\{C_1(\\boldsymbol x), C_2(\\boldsymbol x), \\cdots, C_m(\\boldsymbol x) \\} \\end{align}y^​=mode{C1​(x),C2​(x),⋯,Cm​(x)}​​ 在统计学中，使用 modemodemode 代表众数，即出现次数最多的元素。","s":"算法描述","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","h":"#算法描述","p":1219},{"i":1224,"t":"接下来阐述为什么集合在绝大多数情况下能够比单个分类器具有更好的表现。 以二元分类为例，假设单个分类器的错误率 \\varepsilon=0.25，使用 11 个分类器 (假设其互不相关、且每个分类器的错误率相同) 的集合错误率显著降低： ERR=∑k=611Ck11εk(1−ε)11−k=0.034\\begin{align} ERR = \\sum_{k=6}^{11} C_k^{11} \\varepsilon^k (1 - \\varepsilon)^{11 - k} = 0.034 \\end{align}ERR=k=6∑11​Ck11​εk(1−ε)11−k=0.034​​ 其中 CknC_k^nCkn​ 为二项式系数 n！k！(n−k)！\\cfrac {n！} {k！(n-k)！}k！(n−k)！n！​。 上述的数学表达式在 python 中实现如下： from scipy.misc import comb import math def ensemble_error(n_classifier, error): k_start = int(math.ceil(n_classifier / 2)) probs = [ comb(n_classifier, k) * error**k * (1 - error) ** (n_classifier - k) for k in range(k_start, n_classifier + 1) ] return sum(probs) print(ensemble_error(11, 0.25)) # Output: 0.034327507019042969 集合错误率和单个分类器错误率之前的关系绘图如下： import numpy as np import matplotlib.pyplot as plt error_range = np.arange(0.0, 1.01, 0.01) ens_errors = [ensemble_error(n_classifier=11, error=err) for err in error_range] plt.plot(error_range, ens_errors, label=\"Ensemble Error\", linewidth=2) plt.plot(error_range, error_range, linestyle=\"--\", label=\"Base Error\", linewidth=2) plt.xlabel(\"Base error\") plt.ylabel(\"Base/Ensemble error\") plt.legend(loc=\"upper left\") plt.show() 可以看的，只要单个分类器错误率小于 0.5 (二元分类可以轻易达到这个水平)，那么使用集合能够模型提高模型的预测能力。","s":"算法思想","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","h":"#算法思想","p":1219},{"i":1226,"t":"加权相对多数分类器的结果如下，其中 jjj 代表第 jjj 个分类器，iii 代表类标签： y^=arg⁡max⁡i∑j=1mwjpij\\begin{align} \\hat y = \\arg \\max_i \\sum_{j=1}^m w_j p_{ij} \\end{align}y^​=argimax​j=1∑m​wj​pij​​​ 为进行说明，假设有二元分类 (类标签 iii 为 0 或 1)，使用三个分类器的集合进行加权评估，每个分类器对于给定输入 x\\boldsymbol xx 的概率和权重如下： 第一个分类器预测为 0 和 1 和概率分别为 C1(x)=[0.9，0.1]C_1 (\\boldsymbol x) = [0.9，0.1]C1​(x)=[0.9，0.1]，权重为 0.2。 第二个分类器预测为 0 和 1 和概率分别为 C1(x)=[0.8，0.2]C_1 (\\boldsymbol x) = [0.8，0.2]C1​(x)=[0.8，0.2]，权重为 0.2。 第三个分类器预测为 0 和 1 和概率分别为 C1(x)=[0.4，0.6]C_1 (\\boldsymbol x) = [0.4，0.6]C1​(x)=[0.4，0.6]，权重为 0.6。 预测为类 0 和类 1 的概率分别为： p(i=0∣x)=0.9×0.2+0.8×0.2+0.4×0.2=0.58p(i=1∣x)=0.1×0.2+0.2×0.2+0.6×0.2=0.42\\begin{align} p(i = 0 \\mid \\boldsymbol x) & = 0.9 \\times 0.2 + 0.8 \\times 0.2 + 0.4 \\times 0.2 = 0.58 \\\\ p(i = 1 \\mid \\boldsymbol x) & = 0.1 \\times 0.2 + 0.2 \\times 0.2 + 0.6 \\times 0.2 = 0.42 \\end{align}p(i=0∣x)p(i=1∣x)​=0.9×0.2+0.8×0.2+0.4×0.2=0.58=0.1×0.2+0.2×0.2+0.6×0.2=0.42​​ 最终的预测分类为 0： y^=arg⁡max⁡i[p(i=0∣x),p(i=1∣x)]=0\\begin{align} \\hat y = \\arg \\max_i [p(i = 0 \\mid \\boldsymbol x), p(i = 1 \\mid \\boldsymbol x)] = 0 \\end{align}y^​=argimax​[p(i=0∣x),p(i=1∣x)]=0​​ ex = np.array([[0.9, 0.1], [0.8, 0.2], [0.4, 0.6]]) p = np.average(ex, axis=0, weights=[0.2, 0.2, 0.6]) print(p) # Output: array([ 0.58, 0.42]) print(np.argmax(p)) # Output: 0 scikit-learn 中实现了投票分类，请参见 sklearn.ensemble.VotingClassifier。","s":"加权相对多数分类器","u":"/docs/machine-learning/traditional-ml-algorithms/ensemble-voting-classifer","h":"#加权相对多数分类器","p":1219},{"i":1228,"t":"本文介绍懒惰学习的一个典型示例：K-近邻 (K-Nearest Neighbors，KNN) 算法。之所以称为懒惰，是因为它不从训练样本中学习判别函数，而是在记住已有的样本数据集的基础上对新样本进行分类。","s":"K-近邻","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","h":"","p":1227},{"i":1230,"t":"机器学习算法可以被分为两大类，参数模型和变参模型： 参数模型：学习时更新参数然后将其用于预测，如感知器、逻辑回归、线性 SVM 变参模型：参数不固定，如决策树/随机森林、使用核技巧的 SVM KNN 属于变参模型的一个子类：基于实例的学习 (instance-based learning)，在训练过程中记住整个训练集。懒惰学习是基于实例的学习的特例，在整个学习过程中不涉及损失函数的概念。 KNN 算法非常简单，步骤及图示如下： 确定 kkk 的大小和距离度量。 对于测试集中的一个样本，找到训练集中和它最近的 kkk 个样本。 将这 kkk 个样本的投票结果作为测试样本的类别。","s":"算法思想","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","h":"#算法思想","p":1227},{"i":1232,"t":"以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (设置 k=5k = 5k=5)： from sklearn.neighbors import KNeighborsClassifier knn = KNeighborsClassifier(n_neighbors=5, p=2, metric=\"minkowski\") knn.fit(X_train, y_train) X_combined = np.vstack((X_train, X_test)) y_combined = np.hstack((y_train, y_test)) plot_decision_regions(X_combined, y_combined, classifier=knn, test_idx=range(105, 150)) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show() kkk 的选择对于 KNN 模型来说至关重要，另外一个重要参数为距离度量。 上述代码使用的是 minkowski 距离： d(x(i),x(j))=∑k∣xk(i)−xk(j)∣pp\\begin{align} \\displaystyle d(x^{(i)},x^{(j)}) = \\sqrt[p] {\\sum_k |x^{(i)}_k - x^{(j)}_k|^p} \\end{align}d(x(i),x(j))=p​k∑​∣xk(i)​−xk(j)​∣p​​​ 若 p=2p=2p=2，则代表欧几里得距离；若 p=1p=1p=1，则代表曼哈顿距离。","s":"算法实现","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","h":"#算法实现","p":1227},{"i":1234,"t":"如果特征空间维度非常高，空间中最相似的两个点也可能距离很远，KNN 算法很容易过拟合。 在这种情况下，建议通过特征选择和降维等方法来避免维度问题。","s":"算法的维度问题","u":"/docs/machine-learning/traditional-ml-algorithms/k-nearest-neighbors","h":"#算法的维度问题","p":1227},{"i":1236,"t":"支持向量机 (Support Vector Machine，SVM) 是一种监督式学习方法，其学习策略为最大化样本与超平面 (即决策边界) 之间的间隔。本文介绍线性 SVM 的原理及实现。 间隔被定义为分离超平面与最靠近这个超平面的训练样本之间的距离。 这些影响边界的特殊样本称为支持向量，也是算法称为支持向量机的原因。","s":"线性 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-linear","h":"","p":1235},{"i":1238,"t":"为了得到边缘最大化，与决策边界平行的正负超平面可以用数学表示如下： w0+wTxpos=1w0+wTxneg=−1\\begin{align} w_0 + {\\boldsymbol w^T} {\\boldsymbol {x_{pos}}} & = 1 \\\\ w_0 + {\\boldsymbol w^T} {\\boldsymbol {x_{neg}}} & = -1 \\end{align}w0​+wTxpos​w0​+wTxneg​​=1=−1​​ 相减得到： wT(xpos−xneg)=2\\begin{align} {\\boldsymbol w^T} (\\boldsymbol {x_{pos}} - \\boldsymbol {x_{neg}}) = 2 \\end{align}wT(xpos​−xneg​)=2​​ 对上式中的 wT\\boldsymbol w^TwT 进行向量归一化： wT∣∣w∣∣(xpos−xneg)=2∣∣w∣∣,where ∣∣w∣∣=∑j=1m(wj)2\\begin{align} \\frac {\\boldsymbol w^T} {||\\boldsymbol w||} (\\boldsymbol {x_{pos}} - \\boldsymbol {x_{neg}}) = \\frac 2 {||\\boldsymbol w||}, \\quad where \\ ||\\boldsymbol w|| = \\sum_{j=1}^m (w_j)^2 \\end{align}∣∣w∣∣wT​(xpos​−xneg​)=∣∣w∣∣2​,where ∣∣w∣∣=j=1∑m​(wj​)2​​ 这两个超平面之间的距离是 2∣∣w∣∣\\cfrac 2 {||\\boldsymbol w||}∣∣w∣∣2​，要使两平面间的距离最大，我们需要最小化 ∣∣w∣∣||\\boldsymbol w||∣∣w∣∣。 同时为了使得样本数据点都在超平面的间隔区以外，我们需要保证对于所有的 iii 满足以下条件之一： w0+wTx(i)≥1,if y(i)=1w0+wTx(i)≤−1,if y(i)=−1\\begin{align} w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}} & \\ge 1, \\quad if \\ y^{(i)} = 1 \\\\ w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}} & \\le -1, \\quad if \\ y^{(i)} = -1 \\end{align}w0​+wTx(i)w0​+wTx(i)​≥1,if y(i)=1≤−1,if y(i)=−1​​ 上式等同于： y(i)(w0+wTx(i))≥1,∀i\\begin{align} y^{(i)}(w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}}) \\ge 1, \\quad \\forall i \\end{align}y(i)(w0​+wTx(i))≥1,∀i​​ 硬间隔 SVM 的目标是在上式约束条件下，最小化 ∣∣w∣∣||\\boldsymbol w||∣∣w∣∣；在实际中，一般是最小化 12∣∣w∣∣2\\cfrac 1 2 ||\\boldsymbol w||^221​∣∣w∣∣2。","s":"硬间隔 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-linear","h":"#硬间隔-svm","p":1235},{"i":1240,"t":"SVM 在软间隔分类器中引入了松弛变量 ξ\\xiξ，它允许分类器对一些样本犯错，允许一些样本不满足硬间隔约束条件。 这样做可以避免 SVM 分类器过拟合，于是也就避免了模型过于复杂，降低了模型对噪声点的敏感性，提升了模型的泛化性能。 带松弛变量的分类器约束条件如下： w0+wTx(i)≥1−ξ(i),if y(i)=1w0+wTx(i)≤−1+ξ(i),if y(i)=−1\\begin{align} w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}} & \\ge 1 - \\xi ^{(i)}, \\quad if \\ y^{(i)} = 1 \\\\ w_0 + {\\boldsymbol w^T} {\\boldsymbol x^{(i)}} & \\le -1 + \\xi ^{(i)}, \\quad if \\ y^{(i)} = -1 \\end{align}w0​+wTx(i)w0​+wTx(i)​≥1−ξ(i),if y(i)=1≤−1+ξ(i),if y(i)=−1​​ 软间隔 SVM 的目标是最小化 12∣∣w∣∣2+C(∑iξ(i))\\cfrac 1 2 ||\\boldsymbol w||^2 + C (\\sum_i \\xi ^{(i)})21​∣∣w∣∣2+C(∑i​ξ(i))。 参数 CCC 可以平衡偏差和方差。CCC 越大，算法分类越严格，方差越高，过大的 CCC 可能会引起过拟合；反之同理。 以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (其中决策边界绘制函数 plot_decision_regions 请参见之前的文章)： import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.svm import SVC from sklearn.preprocessing import StandardScaler iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test) X_combined_std = np.vstack((X_train_std, X_test_std)) y_combined = np.hstack((y_train, y_test)) svm = SVC(kernel=\"linear\", C=1.0, random_state=1) svm.fit(X_train_std, y_train) plot_decision_regions( X_combined_std, y_combined, classifier=svm, test_idx=range(105, 150) ) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show()","s":"软间隔 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-linear","h":"#软间隔-svm","p":1235},{"i":1242,"t":"在原始 SVM 只支持线性样本的基础上，引入核技巧 (Kernel Trick) 可以对非线性的样本进行分类。算法思想为将输入向量映射到高维空间，然后用超平面划分。本文中有举例说明。","s":"核技巧和非线性 SVM","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","h":"","p":1241},{"i":1244,"t":"下图描述了 SVM 如何将低维非线性可分的问题转换为高维度线性可分。 如图所示，原始的内环 (红色样本) 和外环 (蓝色样本) 不能线性分割。 通过非线性变换 ϕ(x)\\phi (x)ϕ(x)，将原始二维数据集映射到新的三维特征空间，如右上子图。 ϕ(x1,x2)=(z1,z2,z3)=(x1,x2,x12+x22)\\begin{align} \\phi (x_1, x_2) = (z_1, z_2, z_3) = (x_1, x_2, x_1^2 + x_2^2) \\end{align}ϕ(x1​,x2​)=(z1​,z2​,z3​)=(x1​,x2​,x12​+x22​)​​ 将分离样本的线性超平面 z3=cz_3 = cz3​=c 其投影回原始特征空间，则得到原始二维空间的非线性决策边界 x12+x22=cx_1^2 + x_2^2 = cx12​+x22​=c。","s":"核技巧原理","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","h":"#核技巧原理","p":1241},{"i":1246,"t":"核技巧的数学描述如下： k(x(i),x(j))=ϕ(x(i))Tϕ(x(j))\\begin{align} k(\\boldsymbol x^{(i)}, \\boldsymbol x^{(j)}) = \\phi(\\boldsymbol x^{(i)})^T \\phi(\\boldsymbol x^{(j)}) \\end{align}k(x(i),x(j))=ϕ(x(i))Tϕ(x(j))​​ 以常见的 (高斯) 径向基函数 (Radial Basis Function，RBF) 为例，核函数为： k(x(i),x(j))=exp⁡(−∣∣x(i)−x(j)∣∣22σ2)\\begin{align} k(\\boldsymbol x^{(i)}, \\boldsymbol x^{(j)}) = \\exp \\left(- \\cfrac {||\\boldsymbol x^{(i)} - \\boldsymbol x^{(j)}||^2} {2\\sigma^2} \\right) \\end{align}k(x(i),x(j))=exp(−2σ2∣∣x(i)−x(j)∣∣2​)​​ 上式通常简化为： k(x(i),x(j))=exp⁡(−γ∣∣x(i)−x(j)∣∣2)\\begin{align} k(\\boldsymbol x^{(i)}, \\boldsymbol x^{(j)}) = \\exp \\left(- \\gamma {||\\boldsymbol x^{(i)} - \\boldsymbol x^{(j)}||^2} \\right) \\end{align}k(x(i),x(j))=exp(−γ∣∣x(i)−x(j)∣∣2)​​ 其中 γ=12σ2\\gamma = \\cfrac 1 {2\\sigma^2}γ=2σ21​ 为需要优化的超参数。","s":"数学表达","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","h":"#数学表达","p":1241},{"i":1248,"t":"以 Iris 数据集为例，基于 Scikit-learn 的实现如下 (其中决策边界绘制函数 plot_decision_regions 请参见之前的文章)： import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.svm import SVC from sklearn.preprocessing import StandardScaler iris = datasets.load_iris() X = iris.data[:, [2, 3]] y = iris.target X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.3, random_state=1, stratify=y ) sc = StandardScaler() sc.fit(X_train) X_train_std = sc.transform(X_train) X_test_std = sc.transform(X_test) X_combined_std = np.vstack((X_train_std, X_test_std)) y_combined = np.hstack((y_train, y_test)) svm = SVC(kernel=\"rbf\", random_state=1, gamma=0.2, C=1.0) svm.fit(X_train_std, y_train) plot_decision_regions( X_combined_std, y_combined, classifier=svm, test_idx=range(105, 150) ) plt.xlabel(\"petal length [standardized]\") plt.ylabel(\"petal width [standardized]\") plt.legend(loc=\"upper left\") plt.show() 上图的决策边界是较为合理的曲线。 将 SVC 的超参数 γ\\gammaγ 增大至 100100100，观察决策边界的变化： svm = SVC(kernel=\"rbf\", random_state=1, gamma=100.0, C=1.0) 可以看到，类 1 和类 2 的边界非常紧凑，样本空间远远小于类 3 的样本空间。 当 γ\\gammaγ 较大时，容易出现过拟合情况，在实际应用中需要控制 γ\\gammaγ 的大小在合理范围。","s":"非线性 SVM 实现","u":"/docs/machine-learning/traditional-ml-algorithms/svm-nonlinear","h":"#非线性-svm-实现","p":1241},{"i":1252,"t":"嵌入层：Embedding 输入嵌入层 Input Embedding 输出嵌入层 Output Embedding 位置编码层：Positional Encoding 堆叠层 注意力层： Multi-Head 注意力机制 Mask 注意力机制 前馈神经网络 其他 參差网络 Residual Add 层归一化 Layer Normalization 预测词输出 Linear & SoftMax","s":"分层设计","u":"/docs/machine-learning/transformer/transformer-architecture","h":"#分层设计","p":1249},{"i":1257,"t":"简单来说，注意力就是我们关注的重点。 以上图的柴犬为例，人类的视觉注意力可以聚焦于图像的某个 (或者某些) 区域，同时忽略其余的区域。","s":"人类的图像注意力","u":"/docs/machine-learning/transformer/transformer-attention","h":"#人类的图像注意力","p":1254},{"i":1259,"t":"类似的，在文本中也有注意力机制，在阅读某一个词的时候，我们会去同时关注其他某些相关的词。","s":"人类的文本注意力","u":"/docs/machine-learning/transformer/transformer-attention","h":"#人类的文本注意力","p":1254},{"i":1261,"t":"Transformer 的注意力机制是 Transformer 架构的核心。","s":"Transformer 的注意力机制","u":"/docs/machine-learning/transformer/transformer-attention","h":"#transformer-的注意力机制","p":1254},{"i":1263,"t":"毫不夸张的说，QQQ、KKK、VVV 是天才设计。也是大模型的基石。如何理解 QQQ、KKK、VVV？ 以爬山为例，假设您想要估算当前的海拔高度，但没有直接获得这个信息。相反，您使用望远镜观察到周围有若干个碑石： 离你最近的上方碑石的信息：海拔 2000 米；离你较远 离你最近的下方碑石的信息：海拔 1800 米；离你较近 我们预测当前的海拔高度为：2000∗0.7+1800∗0.3=19402000 * 0.7 + 1800 * 0.3 = 19402000∗0.7+1800∗0.3=1940 (米)。 现在，让我们将这个过程解释为注意力机制的步骤： QQQ：当前状态，作为查询 KKK：观测到的碑石状态 (键值) VVV：碑石存储的数值信息 QKTQK^TQKT 是点积。SoftMax 让其概率为之和为 1。 为了解决维度过高带来的影响，Transformer 设计的时候，使用了缩放的点积。","s":"理解注意力机制的 QQQ / KKK / VVV","u":"/docs/machine-learning/transformer/transformer-attention","h":"#理解注意力机制的-q--k--v","p":1254},{"i":1265,"t":"我们看一下 QQQ 和 KTK^TKT： Q=(q1q2⋮),K=(k1k2⋮)Q = \\begin{pmatrix} q_1 \\\\ q_2 \\\\ \\vdots \\\\ \\end{pmatrix}, K = \\begin{pmatrix} k_1 \\\\ k_2 \\\\ \\vdots \\\\ \\end{pmatrix}Q=​q1​q2​⋮​​,K=​k1​k2​⋮​​ 其中 qiq_iqi​ 和 kjk_jkj​ 是多维向量，维度为嵌入向量的维度 d_modeld\\_modeld_model。 QKTQK^TQKT 的结果为： (q1k1q1k2⋯q2k1q2k2⋯⋮⋮⋱)\\begin{pmatrix} q_1k_1 & q_1k_2 & \\cdots \\\\ q_2k_1 & q_2k_2 & \\cdots \\\\ \\vdots & \\vdots & \\ddots \\\\ \\end{pmatrix}​q1​k1​q2​k1​⋮​q1​k2​q2​k2​⋮​⋯⋯⋱​​ 上面的 qikjq_ik_jqi​kj​ 是向量的点积结果，用于表征查询 qiq_iqi​ 和键值 kjk_jkj​ 之间的匹配程度。","s":"理解 QKTQK^TQKT","u":"/docs/machine-learning/transformer/transformer-attention","h":"#理解-qkt","p":1254},{"i":1267,"t":"注意力机制为查询和目标之间的注意力，比如在翻译任务中，源语言和翻译的目标语言是不同的。 在查询为目标本身的时候，为注意力的一种特殊形式：自注意力。 自注意力可以分为两种情况： 前向关注 (关注这个 token，和之前的其余 tokens) 双向关注 (关注这个 token，和之前以及之后的 tokens)","s":"自注意力机制","u":"/docs/machine-learning/transformer/transformer-attention","h":"#自注意力机制","p":1254},{"i":1269,"t":"在自注意力相关性中，mask 代表关注的程度。由于矩阵天然具有前后双向关注的特性，如果我们只需要关注于之前的 tokens，则需要添加屏蔽之后 attention 的 mask。 通常来说，前向关注的注意力机制也称为因果注意力 (casual attention)。 在因果注意力中，为了保持自回归性质，注意力机制会限制每个位置只能注意到其之前的位置，而不是整个输入序列。 在代码实现中，可以在计算 QKTQK^TQKT 或者计算 QKTdk\\cfrac{QK^T}{\\sqrt{d_k}}dk​​QKT​ 后，将右上部分 (不包含对角线) 设置成负无穷大或者一个非常大的负值 (如 1e-9)，这样在经过 SoftMax 之后，对应位置的 attention score 接近为 0。","s":"自注意力中的 mask","u":"/docs/machine-learning/transformer/transformer-attention","h":"#自注意力中的-mask","p":1254},{"i":1272,"t":"#!/usr/bin/env python3 \"\"\" Implementation of Transformer: Attention Is All You Need References: - [Paper arXiv: Attention Is All You Need](https://arxiv.org/abs/1706.03762) - [Blog Post: The Illustrated Transformer](http://jalammar.github.io/illustrated-transformer/) - [YouTube Video: The Illustrated Transformer](https://youtu.be/ISNdQcPhsts?si=VyFfVKoITGOV78OA) \"\"\" import argparse import math import os import sys import torch import torch.nn as nn import torch.optim as optim from torchinfo import summary class PositionalEncoding(nn.Module): def __init__(self, d_model, max_seq_length): super(PositionalEncoding, self).__init__() pe = torch.zeros(max_seq_length, d_model) position = torch.arange(0, max_seq_length, dtype=torch.float).unsqueeze(1) div_term = torch.exp( torch.arange(0, d_model, 2).float() * -(math.log(10000.0) / d_model) ) pe[:, 0::2] = torch.sin(position * div_term) pe[:, 1::2] = torch.cos(position * div_term) self.register_buffer(\"pe\", pe.unsqueeze(0)) def forward(self, x): return x + self.pe[:, : x.size(1)] class MultiHeadAttention(nn.Module): def __init__(self, d_model, num_heads): super(MultiHeadAttention, self).__init__() # Ensure that the model dimension (d_model) is divisible by the number of heads assert d_model % num_heads == 0, \"d_model must be divisible by num_heads\" # Initialize dimensions self.d_model = d_model # Model's dimension self.num_heads = num_heads # Number of attention heads self.d_k = ( d_model // num_heads ) # Dimension of each head's key, query, and value # Linear layers for transforming inputs self.W_q = nn.Linear(d_model, d_model) # Query transformation self.W_k = nn.Linear(d_model, d_model) # Key transformation self.W_v = nn.Linear(d_model, d_model) # Value transformation self.W_o = nn.Linear(d_model, d_model) # Output transformation def scaled_dot_product_attention(self, Q, K, V, mask=None): # Calculate attention scores attn_scores = torch.matmul(Q, K.transpose(-2, -1)) / math.sqrt(self.d_k) # Apply mask if provided (useful for preventing attention to certain parts like padding) if mask is not None: attn_scores = attn_scores.masked_fill(mask == 0, -1e9) # Softmax is applied to obtain attention probabilities attn_probs = torch.softmax(attn_scores, dim=-1) # Multiply by values to obtain the final output output = torch.matmul(attn_probs, V) return output def split_heads(self, x): # Reshape the input to have num_heads for multi-head attention batch_size, seq_length, d_model = x.size() return x.view(batch_size, seq_length, self.num_heads, self.d_k).transpose(1, 2) def combine_heads(self, x): # Combine the multiple heads back to original shape batch_size, _, seq_length, d_k = x.size() return x.transpose(1, 2).contiguous().view(batch_size, seq_length, self.d_model) def forward(self, Q, K, V, mask=None): # Apply linear transformations and split heads Q = self.split_heads(self.W_q(Q)) K = self.split_heads(self.W_k(K)) V = self.split_heads(self.W_v(V)) # Perform scaled dot-product attention attn_output = self.scaled_dot_product_attention(Q, K, V, mask) # Combine heads and apply output transformation output = self.W_o(self.combine_heads(attn_output)) return output class EncoderLayer(nn.Module): def __init__(self, d_model, num_heads, d_ff, dropout): super(EncoderLayer, self).__init__() self.self_attn = MultiHeadAttention(d_model, num_heads) self.feed_forward = PositionWiseFeedForward(d_model, d_ff) self.norm1 = nn.LayerNorm(d_model) self.norm2 = nn.LayerNorm(d_model) self.dropout = nn.Dropout(dropout) def forward(self, x, mask): attn_output = self.self_attn(x, x, x, mask) x = self.norm1(x + self.dropout(attn_output)) ff_output = self.feed_forward(x) x = self.norm2(x + self.dropout(ff_output)) return x class DecoderLayer(nn.Module): def __init__(self, d_model, num_heads, d_ff, dropout): super(DecoderLayer, self).__init__() self.self_attn = MultiHeadAttention(d_model, num_heads) self.cross_attn = MultiHeadAttention(d_model, num_heads) self.feed_forward = PositionWiseFeedForward(d_model, d_ff) self.norm1 = nn.LayerNorm(d_model) self.norm2 = nn.LayerNorm(d_model) self.norm3 = nn.LayerNorm(d_model) self.dropout = nn.Dropout(dropout) def forward(self, x, enc_output, src_mask, tgt_mask): attn_output = self.self_attn(x, x, x, tgt_mask) x = self.norm1(x + self.dropout(attn_output)) attn_output = self.cross_attn(x, enc_output, enc_output, src_mask) x = self.norm2(x + self.dropout(attn_output)) ff_output = self.feed_forward(x) x = self.norm3(x + self.dropout(ff_output)) return x class PositionWiseFeedForward(nn.Module): def __init__(self, d_model, d_ff): super(PositionWiseFeedForward, self).__init__() self.fc1 = nn.Linear(d_model, d_ff) self.fc2 = nn.Linear(d_ff, d_model) self.relu = nn.ReLU() def forward(self, x): return self.fc2(self.relu(self.fc1(x))) class Transformer(nn.Module): def __init__( self, src_vocab_size, tgt_vocab_size, d_model, num_heads, num_layers, d_ff, max_seq_length, dropout, ): super(Transformer, self).__init__() self.encoder_embedding = nn.Embedding(src_vocab_size, d_model) self.decoder_embedding = nn.Embedding(tgt_vocab_size, d_model) self.positional_encoding = PositionalEncoding(d_model, max_seq_length) self.encoder_layers = nn.ModuleList( [EncoderLayer(d_model, num_heads, d_ff, dropout) for _ in range(num_layers)] ) self.decoder_layers = nn.ModuleList( [DecoderLayer(d_model, num_heads, d_ff, dropout) for _ in range(num_layers)] ) self.fc = nn.Linear(d_model, tgt_vocab_size) self.dropout = nn.Dropout(dropout) def generate_mask(self, src, tgt): src_mask = (src != 0).unsqueeze(1).unsqueeze(2) tgt_mask = (tgt != 0).unsqueeze(1).unsqueeze(3) seq_length = tgt.size(1) nopeak_mask = ( 1 - torch.triu(torch.ones(1, seq_length, seq_length), diagonal=1) ).bool() tgt_mask = tgt_mask & nopeak_mask return src_mask, tgt_mask def forward(self, src, tgt): src_mask, tgt_mask = self.generate_mask(src, tgt) src_embedded = self.dropout( self.positional_encoding(self.encoder_embedding(src)) ) tgt_embedded = self.dropout( self.positional_encoding(self.decoder_embedding(tgt)) ) enc_output = src_embedded for enc_layer in self.encoder_layers: enc_output = enc_layer(enc_output, src_mask) dec_output = tgt_embedded for dec_layer in self.decoder_layers: dec_output = dec_layer(dec_output, enc_output, src_mask, tgt_mask) output = self.fc(dec_output) return output def main(args): transformer = Transformer( args.src_vocab_size, args.tgt_vocab_size, args.d_model, args.num_heads, args.num_layers, args.d_ff, args.max_seq_length, args.dropout, ) # Generate random sample data src_data = torch.randint( 1, args.src_vocab_size, (64, args.max_seq_length) ) # (batch_size, seq_length) tgt_data = torch.randint( 1, args.tgt_vocab_size, (64, args.max_seq_length) ) # (batch_size, seq_length) print(summary(transformer, input_data=[src_data, tgt_data], device=\"cpu\")) criterion = nn.CrossEntropyLoss(ignore_index=0) optimizer = optim.Adam( transformer.parameters(), lr=0.0001, betas=(0.9, 0.98), eps=1e-9 ) transformer.train() for epoch in range(10): optimizer.zero_grad() output = transformer(src_data, tgt_data[:, :-1]) loss = criterion( output.contiguous().view(-1, args.tgt_vocab_size), tgt_data[:, 1:].contiguous().view(-1), ) loss.backward() optimizer.step() print(f\"Epoch: {epoch+1}, Loss: {loss.item()}\") transformer.eval() # Generate random sample validation data val_src_data = torch.randint( 1, args.src_vocab_size, (64, args.max_seq_length) ) # (batch_size, seq_length) val_tgt_data = torch.randint( 1, args.tgt_vocab_size, (64, args.max_seq_length) ) # (batch_size, seq_length) with torch.no_grad(): val_output = transformer(val_src_data, val_tgt_data[:, :-1]) val_loss = criterion( val_output.contiguous().view(-1, args.tgt_vocab_size), val_tgt_data[:, 1:].contiguous().view(-1), ) print(f\"Validation Loss: {val_loss.item()}\") if __name__ == \"__main__\": parser = argparse.ArgumentParser( formatter_class=argparse.ArgumentDefaultsHelpFormatter ) parser.add_argument( \"--src_vocab_size\", type=int, default=5000, help=\"source vocabulary size\" ) parser.add_argument( \"--tgt_vocab_size\", type=int, default=5000, help=\"target vocabulary size\" ) parser.add_argument( \"--d_model\", type=int, default=512, help=\"dimensionality of model's input and output\", ) parser.add_argument( \"--num_heads\", type=int, default=8, help=\"number of attention heads in multi-head attention\", ) parser.add_argument( \"--num_layers\", type=int, default=6, help=\"number of layers for both the encoder and the decoder\", ) parser.add_argument( \"--d_ff\", type=int, default=2048, help=\"dimensionality of the inner layer in the feed-forward network\", ) parser.add_argument( \"--max_seq_length\", type=int, default=100, help=\"the maximum length of the sequence\", ) parser.add_argument( \"--dropout\", type=float, default=0.1, help=\"dropout rate for regularization\", ) try: args = parser.parse_args() main(args) except KeyboardInterrupt: print(\"Interrupted\") try: sys.exit(0) except SystemExit: os._exit(0)","s":"PyTorch 代码实现","u":"/docs/machine-learning/transformer/transformer-code-implementation","h":"#pytorch-代码实现","p":1270},{"i":1274,"t":"总体来看，Transformer 模型主要由两个块组成： Encoder (左侧)：编码器接收输入并构建其表示 (其特征)。这意味着对模型进行了优化，以从输入中获得理解。 Decoder (右侧)：解码器使用编码器的表示 (特征) 以及其他输入来生成目标序列。这意味着该模型已针对生成输出进行了优化。 编码组件是若干个 encoder 堆叠而成，解码组件也是若干个 decoder 堆叠而成的。层数是一个超参数，在原始论文中设置为 6。","s":"编码器和解码器","u":"/docs/machine-learning/transformer/transformer-encoders-decoders","h":"","p":1273},{"i":1276,"t":"编码器和解码器实际上是寻找 token 的内在特征。 举例来说： This pear is delicious. The orange is yummy. That watermelon tastes terrible. 假设我们现在对“pear”，“delicious”，“orange”，“yummy”，“watermelon”，“terrible”进行 one-hot 编码： 1 0 0 0 0 0 # pear 0 1 0 0 0 0 # delicious 0 0 1 0 0 0 # orange 0 0 0 1 0 0 # yummy 0 0 0 0 1 0 # watermelon 0 0 0 0 0 1 # terrible 但是这种编码不能代表词语之间的内在联系，因此有了 Word2Vec 编码，比如对于上面的单词，我们编码成二维： 第一维：水果属性 第二维：好吃程度 [64, 0] # pear [0, 80] # delicious [57, 0] # orange [0, 96] # yummy [83, 0] # watermelon [0, -77] # terrible 这种编码格式更符合人们的直觉。但是在实际情况中，语言编码的复杂性非常高： 由于几万个单词，有很多维度，人工编码不可行。 固定的编码不能很好的表征其含义，在不同语境下，相同的单词可能有不同的意义。 Transformer 的解码器和编码器，在翻译任务中，可以理解为 token 的特征提取器。解码器和编码器会自动提取源语言和目标语言中的 token 的特征。","s":"理解编码器和解码器","u":"/docs/machine-learning/transformer/transformer-encoders-decoders","h":"#理解编码器和解码器","p":1273},{"i":1278,"t":"Transformer 是一种采用自注意力机制 (self-attention) 的深度学习模型架构，这一机制可以按输入数据各部分重要性的不同而分配不同的权重。该模型由 Google 机器翻译团队于 2017 年发表于论文 Attention is all you need 中，为 OpenAI 开发的 ChatGPT、Google 的 Gemini、Meta 的 LLaMA 等大语言模型的核心基础架构。 Transformer 模型是迄今发明出最新且最强大的模型之一。","s":"Transformer 概览","u":"/docs/machine-learning/transformer/transformer-overview","h":"","p":1277},{"i":1280,"t":"什么是自然语言处理 (Natural Language Processing，NLP)？NLP 是语言学和机器学习交叉领域，专注于理解与人类语言相关的一切。NLP 任务的目标不仅是单独理解单个单词，而且是能够理解这些单词的上下文。 以下是常见 NLP 任务的列表，每个任务都有一些示例： 对整个句子进行分类：获取评论的情绪，检测电子邮件是否为垃圾邮件，确定句子在语法上是否正确或两个句子在逻辑上是否相关。 对句子中的每个词进行分类：识别句子的语法成分 (名词、动词、形容词) 或命名实体 (人、地点、组织)。 生成文本内容：用自动生成的文本完成提示，用屏蔽词填充文本中的空白 从文本中提取答案：给定问题和上下文，根据上下文中提供的信息提取问题的答案。 从输入文本生成新句子：将文本翻译成另一种语言，总结文本。 NLP 不仅限于书面文本。它还解决了语音识别和计算机视觉中的复杂挑战，例如音频生成、图像识别、图像描述等。 在 Transformer 发明之前，机器学习中 NLP 的任务处理基本是通过 RNN 或者其变体 GRU、LSTM 建模的。相比于这些模型，Transformer 具有以下优势： 并行计算。RNN 和 LSTM 需要顺序处理序列数据，因此很难进行并行计算。而 Transformer 的自注意力机制允许同时处理整个序列，从而可以充分利用 GPU 的并行计算能力，大大提高模型训练和推理的速度。 更好的长期依赖。RNN 在处理长序列时面临梯度消失或梯度爆炸的问题，导致难以建模长期依赖关系。相比之下，Transformer 使用了自注意力机制，能够直接建模序列中不同位置之间的依赖关系，从而更好地捕捉长期依赖关系。 灵活性：Transformer 架构具有很高的灵活性，可以很容易地进行修改和扩展。例如，BERT、GPT 等知名模型都是基于 Transformer 架构的，它们在各种自然语言处理任务中取得了前所未有的成绩。","s":"自然语言处理","u":"/docs/machine-learning/transformer/transformer-overview","h":"#自然语言处理","p":1277},{"i":1281,"t":"我们先将整个模型视为黑盒。 在机器翻译中，接收一种语言的句子作为输入，然后将其翻译成其他语言输出。 Transformer 设计之初就是为了解决 NLP 中的翻译问题。","s":"Transformer 概览","u":"/docs/machine-learning/transformer/transformer-overview","h":"#transformer-概览-1","p":1277},{"i":1284,"t":"对于任何一门语言，单词在句子中的位置以及排列顺序是非常重要的，它们不仅是一个句子的语法结构的组成部分，更是表达语义的重要概念。 Transformer 模型抛弃了 RNN、LSTM、GRU 作为序列学习的基本模型。我们知道，RNN 本身就是一种顺序结构，天生就包含了词在序列中的位置信息。当抛弃 RNN 结构，完全采用 Attention 取而代之，这些词序信息就会丢失。","s":"为什么需要位置编码","u":"/docs/machine-learning/transformer/transformer-positional-encoding","h":"#为什么需要位置编码","p":1282},{"i":1286,"t":"最简单的位置编码是：第一个 token 编码为 0，第一个 token 编码为 1，以此类推。这种方法带来的问题是，不仅这些数值会变得非常大，而且模型也会遇到一些比训练中的所有句子都要长的句子。此外，数据集中不一定在所有数值上都会包含相对应长度的句子，也就是模型很有可能没有看到过任何一个这样的长度的样本句子，这会严重影响模型的泛化能力。 因此，一种好的位置编码方案需要满足以下几条要求： 能够为每个时间步输出一个独一无二的编码 给定任意一个位置，编码的值必须是确定性的 (而不是需要在机器学习中的超参数) 固定步长的两个位置的编码，应该存在一定的关系 模型应该能泛化到更长的句子","s":"怎么实现位置编码","u":"/docs/machine-learning/transformer/transformer-positional-encoding","h":"#怎么实现位置编码","p":1282},{"i":1288,"t":"Transformer 的位置编码为： PE(pos,2i)=sin(pos100002i/dmodel),PE(pos,2i+1)=cos(pos100002i/dmodel).\\begin{aligned} \\text{PE}_{(pos,2i)}=sin\\left(\\frac{pos}{10000^{2i/d_{model}}}\\right), \\\\ \\text{PE}_{(pos,2i+1)}=cos\\left(\\frac{pos}{10000^{2i/d_{model}}}\\right). \\end{aligned}PE(pos,2i)​=sin(100002i/dmodel​pos​),PE(pos,2i+1)​=cos(100002i/dmodel​pos​).​ 其中 pospospos 为位置编号，iii 是维度编号。 为什么采用这种编码？我们看一下说明： We chose this function because we hypothesized it would allow the model to easily learn to attend by relative positions, since for any fixed offset kkk, PEpos+kPE_{pos+k}PEpos+k​ can be represented as a linear function of PEposPE_{pos}PEpos​. 这句话的意思是，上面的编码能够让模型轻松关注相对位置。给定距离为 kkk 的两个位置，其编码 PEpos+kPE_{pos+k}PEpos+k​ 和 PEposPE_{pos}PEpos​ 存在固定的线性变换关系。 从结果来看，Transformer 的位置编码能够有效泛化到更长的句子。 需要明确的是，这不代表其为唯一可行的位置编码方案。","s":"Transformer 的位置编码","u":"/docs/machine-learning/transformer/transformer-positional-encoding","h":"#transformer-的位置编码","p":1282},{"i":1290,"t":"下图为对 20 个位置编码为的示例，其中每个位置编码为 512 维的向量。左半部分是维度为 2i2i2i 的正弦编码，右半部分是是维度为 2i2i2i 的余弦编码。 将它们交叉连接，就是 Transformer 使用的位置编码向量。","s":"Transformer 编码的可视化","u":"/docs/machine-learning/transformer/transformer-positional-encoding","h":"#transformer-编码的可视化","p":1282},{"i":1292,"t":"论文通过添加一种称为“多头”注意力的机制进一步细化了自注意力。它扩展了模型关注不同位置的能力。 比如对于以下语句：“The animal didn’t cross the street because it was too tired” 在语义不同的时候，可以有不同的注意力，比如“it”关注于指代的东西时候，对“animal”有很高的权重；“it”关注于其当前形容词的时候，对“tired”有很高的权重。 如下图所示，原始论文中使用了 8 个注意力头，每个注意力头都有自己的 QQQ / KKK / VVV 矩阵。 这可以理解为有 8 个不同的特征子空间，每个子空间可以提取不同的特征表示，最终嵌入 (投影) 到同一个向量中。 对于这个合成的嵌入向量再做一次矩阵变换，得到最终的注意力矩阵 ZZZ。","s":"分割的多头注意力机制","u":"/docs/machine-learning/transformer/transformer-split-multi-head-attention","h":"","p":1291},{"i":1295,"t":"Informer 在论文 Informer：Beyond Efficient Transformer for Long Sequence Time-Series Forecasting 中提出，对经典的 Transformer 提出了一些改进，用于长时间序列预测 (Long sequence time-series forecasting，LSTF) 任务，包括： ProbSparse 自注意力机制，其时间复杂度和内存使用量达到 O(LlogL)O(LlogL)O(LlogL) ，并且在序列的依赖性对齐方面具有相近的性能； 自注意力蒸馏通过将级联层输入减半来突出主导注意力，并有效处理极长的输入序列； 在生成式的解码器中，通过一次前向操作而不是一步一步的方式来预测长时间序列，大大提高了长序列预测的推理速度。 Informer 源码开源在 GitHub - Informer2020。","s":"Informer","u":"/docs/machine-learning/transformer/transformer-variants","h":"#informer","p":1293},{"i":1297,"t":"除了输入 embedding 和位置编码外，informer 还引入了时间维度的 embedding：","s":"Informer 的 Embedding 层","u":"/docs/machine-learning/transformer/transformer-variants","h":"#informer-的-embedding-层","p":1293},{"i":1299,"t":"在注意力机制矩阵中，不是每一列都是有 attention 作用的，因此选择 QQQ 矩阵中贡献率最高的 top-uuu 行，其中 uuu 取值 c∗lnLc * lnLc∗lnL，ccc 是常数。 ProbSparse 通过计算 KL 散度 (Kullback-Leibler divergence) 来得到不同行注意力的贡献率。KL 散度在统计模型中可以反映信息增益，当两个分布差异较大的时候，KL 散度结果数值会越高。 通过计算每一行实际的 attention 和均匀分布 attention 的 KL 散度，可以近似衡量这一行对注意力的贡献。 但是这样计算后，内存使用并没有减少。所以作者又提出了随机选择 lnLlnLlnL 行。 经过以上处理，模型的注意力矩阵内存和时间复杂度都从 O(L2)O(L^2)O(L2) 减少到 O(LlogL)O(LlogL)O(LlogL)。 这里需要注意的是，原始论文中计算 QKTQK^TQKT 后，在经典的 Transformer 的基础上，把 Informer 中没有参与计算的位置，使用平均权重填充。因此第一层注意力层的输出的形状和经典的 Transformer 保持一致。","s":"ProbSparse 自注意力机制","u":"/docs/machine-learning/transformer/transformer-variants","h":"#probsparse-自注意力机制","p":1293},{"i":1301,"t":"原始的注意力层的输出结果数据尺寸不会变化，但是 Informer 中会进行池化减半操作。减小了计算量和训练时间。 这里的减半操作是使用卷积神经网络中步长为 2 的最大池化 (MaxPooling)。","s":"卷积池化减半","u":"/docs/machine-learning/transformer/transformer-variants","h":"#卷积池化减半","p":1293},{"i":1303,"t":"经典的 Transformer 用于 NLP，很多时候每个输出结果和之前的单词具有语义上的紧密联系，因此按照一步一步的输出比较适合。 在 Informer 中，由于预测未来某一些时刻的指标，这些指标之前没有类似于 NLP 中前后强关联的语义关系，因此可以采用单次输出所需要的序列，极大的提高了推理速度。","s":"单次解码器设计","u":"/docs/machine-learning/transformer/transformer-variants","h":"#单次解码器设计","p":1293},{"i":1307,"t":"gdb lldb (gdb) backtrace (gdb) bt (lldb) thread backtrace (lldb) bt","s":"回溯当前线程调用栈","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#回溯当前线程调用栈","p":1304},{"i":1309,"t":"gdb lldb (gdb) thread apply all bt (lldb) thread backtrace all (lldb) bt all","s":"回溯所有线程调用栈","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#回溯所有线程调用栈","p":1304},{"i":1311,"t":"gdb lldb (gdb) bt 5 (lldb) thread backtrace -c 5 (lldb) bt 5","s":"回溯当前线程调用栈的 backtrace 的前几帧","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#回溯当前线程调用栈的-backtrace-的前几帧","p":1304},{"i":1314,"t":"gdb lldb (gdb) disassemble (gdb) disas (lldb) disassemble --frame (lldb) di -f","s":"反汇编当前栈帧函数","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#反汇编当前栈帧函数","p":1304},{"i":1316,"t":"gdb lldb (gdb) disassemble main (lldb) disassemble --name main (lldb) di -n main","s":"反汇编任何名为 main 的函数","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#反汇编任何名为-main-的函数","p":1304},{"i":1318,"t":"gdb lldb (gdb) disassemble 0x1eb8 0x1ec3 (lldb) disassemble --start-address 0x1eb8 --end-address 0x1ec3 (lldb) di -s 0x1eb8 -e 0x1ec3","s":"反汇编某个地址范围","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#反汇编某个地址范围","p":1304},{"i":1320,"t":"gdb lldb (gdb) x/20i 0x1eb8 (lldb) disassemble --start-address 0x1eb8 --count 20 (lldb) di -s 0x1eb8 -c 20","s":"从给定地址反汇编若干条指令","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#从给定地址反汇编若干条指令","p":1304},{"i":1322,"t":"gdb lldb (lldb) disassemble --frame --mixed (lldb) di -f -m","s":"同时显示当前函数的源代码和反汇编代码","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#同时显示当前函数的源代码和反汇编代码","p":1304},{"i":1324,"t":"gdb lldb (lldb) disassemble --frame --bytes (lldb) di -f -b","s":"反汇编当前函数","u":"/docs/modern-cpp/gdb-lldb/backtrace-and-disassemble","h":"#反汇编当前函数","p":1304},{"i":1328,"t":"gdb lldb (gdb) break main (lldb) breakpoint set --name main (lldb) br s -n main (lldb) b main # or breakpoint on C++ method: (lldb) breakpoint set --method main (lldb) br s -M main","s":"根据函数名或者方法名设置断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#根据函数名或者方法名设置断点","p":1325},{"i":1330,"t":"gdb lldb (gdb) break test.c:12 (gdb) b test.c:12 (lldb) breakpoint set --file test.c --line 12 (lldb) br s -f test.c -l 12 (lldb) b test.c:12","s":"根据源文件行号设置断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#根据源文件行号设置断点","p":1325},{"i":1332,"t":"gdb lldb (gdb) break foo if strcmp(y,\"hello\") == 0 (lldb) breakpoint set --name foo --condition '(int)strcmp(y,\"hello\") == 0' (lldb) br s -n foo -c '(int)strcmp(y,\"hello\") == 0'","s":"设置条件断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#设置条件断点","p":1325},{"i":1334,"t":"gdb lldb (gdb) delete 1 # or delete all breakpoints at current line (gdb) clear (lldb) breakpoint delete 1 (lldb) br del 1","s":"删除某个断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#删除某个断点","p":1325},{"i":1336,"t":"禁用断点 gdb lldb (gdb) disable 1 (lldb) breakpoint disable 1 (lldb) br dis 1 启用断点 gdb lldb (gdb) enable 1 (lldb) breakpoint enable 1 (lldb) br en 1","s":"禁用/启用断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#禁用启用断点","p":1325},{"i":1338,"t":"通过正则表达式匹配函数，来设置断点 gdb lldb (gdb) rbreak [REGULAR EXPRESSION] (lldb) breakpoint set --func-regex [REGULAR EXPRESSION] (lldb) br s -r [REGULAR EXPRESSION] 通过正则表达式匹配源文件内容，来设置断点 gdb lldb (gdb) shell grep -e -n [REGULAR EXPRESSION] [SOURCE FILE] (gdb) break source-file:line-number (lldb) breakpoint set --source-pattern [REGULAR EXPRESSION] --file [SOURCE FILE] (lldb) br s -p [REGULAR EXPRESSION] -f [SOURCE FILE]","s":"通过正则表达式设置断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#通过正则表达式设置断点","p":1325},{"i":1340,"t":"gdb lldb (gdb) info break (lldb) breakpoint list (lldb) br l","s":"列出所有断点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#列出所有断点","p":1325},{"i":1343,"t":"gdb lldb (gdb) watch global_var (lldb) watchpoint set variable global_var (lldb) wa s v global_var","s":"监控进程中某个变量的值","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控进程中某个变量的值","p":1325},{"i":1345,"t":"如果未指定 -x byte_size，则要监视的区域的大小默认为指针大小。 该命令采用原始输入，计算为表达式，返回指向区域开头的无符号整数，位于 -- 选项终止符之后。 gdb lldb (gdb) watch -location g_char_ptr (lldb) watchpoint set expression -- my_ptr (lldb) wa s e -- my_ptr","s":"监控进程中的某块内存","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#监控进程中的某块内存","p":1325},{"i":1347,"t":"gdb lldb (lldb) watch set var global (lldb) watchpoint modify -c '(global==5)' (lldb) c ... (lldb) bt * thread #1: tid = 0x1c03, 0x0000000100000ef5 a.out`modify + 21 at main.cpp:16, stop reason = watchpoint 1 frame #0: 0x0000000100000ef5 a.out`modify + 21 at main.cpp:16 frame #1: 0x0000000100000eac a.out`main + 108 at main.cpp:25 frame #2: 0x00007fff8ac9c7e1 libdyld.dylib`start + 1 (lldb) frame var global (int32_t) global = 5","s":"设置监控的条件","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#设置监控的条件","p":1325},{"i":1349,"t":"gdb lldb (gdb) delete 1 (lldb) watchpoint delete 1 (lldb) watch del 1","s":"删除监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#删除监控点","p":1325},{"i":1351,"t":"gdb lldb (gdb) info break (lldb) watchpoint list (lldb) watch l","s":"列出所有的监控点","u":"/docs/modern-cpp/gdb-lldb/breakpoints-and-watchpoints","h":"#列出所有的监控点","p":1325},{"i":1353,"t":"形式：x/count fmt size address count：整数，默认为 1 fmt: a | Address 地址 i | Instruction 指令 t | Binary 二进制 o | Octal 八进制 h/x | Hex 十六进制 z | Hex，zero padded 十六进制，填充 0 对齐 d | Decimal 十进制 u | Unsigned decimal 无符号十进制 f | Float 浮点 c | Char 字符 s | String 字符串 size: b | 8 bits - byte h | 16 bits - halfword w | 32 bits - word g | 64 bits - giant","s":"检查内存地址的数据","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"","p":1352},{"i":1355,"t":"gdb lldb (gdb) x [ADDRESS] (lldb) memory read [ADDRESS] (lldb) x [ADDRESS]","s":"读取内存","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#读取内存","p":1352},{"i":1357,"t":"gdb lldb (gdb) x/4xw 0xbffff3c0 (lldb) memory read --size 4 --format x --count 4 0xbffff3c0 (lldb) me r -s4 -fx -c4 0xbffff3c0 (lldb) x -s4 -fx -c4 0xbffff3c0 # LLDB now supports the GDB shorthand format syntax but there can’t be space after the command: (lldb) memory read/4xw 0xbffff3c0 (lldb) x/4xw 0xbffff3c0 (lldb) memory read --gdb-format 4xw 0xbffff3c0","s":"读取若干十六进制的内存","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#读取若干十六进制的内存","p":1352},{"i":1359,"t":"gdb lldb (gdb) set logging on (gdb) set logging file /tmp/mem.txt (gdb) x/512bx 0xbffff3c0 (gdb) set logging off (lldb) memory read --outfile /tmp/mem.txt --count 512 0xbffff3c0 (lldb) me r -o/tmp/mem.txt -c512 0xbffff3c0 (lldb) x/512bx -o/tmp/mem.txt 0xbffff3c0","s":"从内存指定地址读取若干字节，并保存到本地文件","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#从内存指定地址读取若干字节并保存到本地文件","p":1352},{"i":1361,"t":"gdb lldb (gdb) dump memory /tmp/mem.bin 0x1000 0x2000 (lldb) memory read --outfile /tmp/mem.bin --binary 0x1000 0x2000 (lldb) me r -o /tmp/mem.bin -b 0x1000 0x2000","s":"从内存指定地址范围读取字节，并保存到本地文件","u":"/docs/modern-cpp/gdb-lldb/check-data-in-memory-address","h":"#从内存指定地址范围读取字节并保存到本地文件","p":1352},{"i":1364,"t":"gdb lldb (gdb) info shared (lldb) image list","s":"列出可执行文件和所有依赖的共享库","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#列出可执行文件和所有依赖的共享库","p":1362},{"i":1366,"t":"gdb lldb (gdb) info symbol 0x1ec4 (lldb) image lookup --address 0x1ec4 (lldb) im loo -a 0x1ec4","s":"查找可执行文件或任何共享库中原始地址信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#查找可执行文件或任何共享库中原始地址信息","p":1362},{"i":1368,"t":"gdb lldb (gdb) info function <FUNC_REGEX> # This one finds debug symbols: (lldb) image lookup -r -n <FUNC_REGEX> # This one finds non-debug symbols: (lldb) image lookup -r -s <FUNC_REGEX> # Provide a list of binaries as arguments to limit the search.","s":"在二进制文件中查找与正则表达式匹配的函数","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#在二进制文件中查找与正则表达式匹配的函数","p":1362},{"i":1370,"t":"gdb lldb (gdb) info line 0x1ec4 (lldb) image lookup -v --address 0x1ec4 # look for the LineEntry line, which will have the full source path and line range information.","s":"查找完整的源代码行信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#查找完整的源代码行信息","p":1362},{"i":1372,"t":"gdb lldb (lldb) image lookup --address 0x1ec4 a.out (lldb) im loo -a 0x1ec4 a.out","s":"仅在 a.out 中查找地址信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#仅在-aout-中查找地址信息","p":1362},{"i":1374,"t":"gdb lldb (gdb) ptype Point (lldb) image lookup --type Point (lldb) im loo -t Point","s":"按名称查找类型 Point 的信息","u":"/docs/modern-cpp/gdb-lldb/check-executable-and-libraries","h":"#按名称查找类型-point-的信息","p":1362},{"i":1378,"t":"gdb lldb (gdb) p bar (gdb) p/x bar (lldb) p bar (lldb) p/x bar","s":"显示变量的内容","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示变量的内容","p":1375},{"i":1380,"t":"gdb lldb (gdb) info args (gdb) info locals (lldb) frame variable (lldb) fr v # add '-no-args' to disable args (lldb) frame variable --no-args (lldb) fr v -a","s":"显示当前栈帧的参数和局部变量","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前栈帧的参数和局部变量","p":1375},{"i":1382,"t":"gdb lldb (gdb) p *ptr@10 (lldb) parray 10 ptr","s":"检查数组","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#检查数组","p":1375},{"i":1385,"t":"gdb lldb (gdb) info registers (lldb) register read","s":"显示当前线程的通用寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程的通用寄存器","p":1375},{"i":1387,"t":"gdb lldb (gdb) info all-registers (lldb) register read --all (lldb) re r -a","s":"显示当前线程的所有寄存器","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程的所有寄存器","p":1375},{"i":1389,"t":"gdb lldb (gdb) info all-registers rax rsp rbp (lldb) register read rax rsp rbp","s":"显示当前线程中指定寄存器的值","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程中指定寄存器的值","p":1375},{"i":1391,"t":"gdb lldb (gdb) p/t $rax (lldb) register read --format binary rax (lldb) re r -f b rax # LLDB now supports the GDB shorthand format syntax but there can’t be space after the command (lldb) register read/t rax (lldb) p/t $rax","s":"显示当前线程中指定寄存器的值，格式为二进制","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#显示当前线程中指定寄存器的值格式为二进制","p":1375},{"i":1393,"t":"gdb lldb (gdb) set print object 1 (gdb) p someCPPObjectPtrOrReference (Only works for C++ objects) (lldb) expr -d 1 -- [SomeClass returnAnObject] (lldb) expr -d 1 -- someCPPObjectPtrOrReference # or set dynamic type printing to be the default: (lldb) settings set target.prefer-dynamic run-target","s":"打印表达式结果的动态类型 (C++)","u":"/docs/modern-cpp/gdb-lldb/check-variables-and-registers","h":"#打印表达式结果的动态类型-c","p":1375},{"i":1395,"t":"GEF 是对 GDB 的增强，使用 Python API 为 GDB 提供附加功能，在动态分析和漏洞开发过程中提供更容易理解的二进制布局，并且安装简单，无外部依赖。 除了 GEF 外，也有其他的 GDB 增强工具，如： pwndbg peda gdbgui gdb-dashboard 不同的 GDB 增强工具可能有冲突，同一时间只建议安装一种工具。","s":"GEF - GDB 增强工具","u":"/docs/modern-cpp/gdb-lldb/gef","h":"","p":1394},{"i":1397,"t":"$ bash -c \"$(curl -fsSL https://gef.blah.cat/sh)\" 安装后会修改 ~/.gdbinit 文件，其中内容是包含新增的 ~/.gef-.py 文件，从而达到对 GDB 的 hacking。","s":"安装","u":"/docs/modern-cpp/gdb-lldb/gef","h":"#安装","p":1394},{"i":1399,"t":"context / ctx：查看上下文信息 aliases [ls/add/rm]：设置命令别名 tmux-setup：tmux 侧边栏 registers：寄存器 elf：ELF 信息 got：全局偏移表 hexdump：二进制工具 vmmap：内存映射 dereferece：解引用 更多的命令可以在 GEF - Commands 内查看。","s":"GEF 命令","u":"/docs/modern-cpp/gdb-lldb/gef","h":"#gef-命令","p":1394},{"i":1402,"t":"gdb lldb (gdb) maintenance info sections (lldb) image dump sections","s":"dump 可执行文件和所有共享库的 section 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和所有共享库的-section-信息","p":1400},{"i":1404,"t":"gdb lldb (lldb) image dump sections a.out","s":"dump 可执行文件的 section 信息","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件的-section-信息","p":1400},{"i":1406,"t":"gdb lldb (lldb) image dump symtab","s":"dump 可执行文件和所有共享库的 symtab 符号","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和所有共享库的-symtab-符号","p":1400},{"i":1408,"t":"gdb lldb (lldb) image dump symtab a.out liba.so","s":"dump 可执行文件和指定共享库的 symtab 符号","u":"/docs/modern-cpp/gdb-lldb/image-dump","h":"#dump-可执行文件和指定共享库的-symtab-符号","p":1400},{"i":1411,"t":"gdb lldb % gdb a.out (gdb) br main (gdb) run % lldb a.out (lldb) br main (lldb) run","s":"设置断点和启动进程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#设置断点和启动进程","p":1409},{"i":1414,"t":"gdb lldb (gdb) step (gdb) s (lldb) thread step-in (lldb) step (lldb) s","s":"step-in 单步调试 (源码级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-in-单步调试-源码级别","p":1409},{"i":1416,"t":"gdb lldb (gdb) next (gdb) n (lldb) thread step-over (lldb) next (lldb) n","s":"step-over 单步调试 (源码级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-单步调试-源码级别","p":1409},{"i":1418,"t":"gdb lldb (gdb) stepi (gdb) si (lldb) thread step-inst (lldb) si","s":"step-in 单步调试 (汇编指令级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-in-单步调试-汇编指令级别","p":1409},{"i":1420,"t":"gdb lldb (gdb) nexti (gdb) ni (lldb) thread step-inst-over (lldb) ni","s":"step-over 单步调试 (汇编指令级别)","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-单步调试-汇编指令级别","p":1409},{"i":1422,"t":"gdb lldb (gdb) finish (lldb) thread step-out (lldb) finish","s":"step-over 跳出栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#step-over-跳出栈帧","p":1409},{"i":1425,"t":"gdb lldb (gdb) continue (gdb) c (lldb) continue (lldb) c","s":"跳转到下一个断点","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#跳转到下一个断点","p":1409},{"i":1427,"t":"gdb lldb (gdb) until 12 (lldb) thread until 12","s":"运行到指定行数","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#运行到指定行数","p":1409},{"i":1430,"t":"gdb lldb (gdb) info threads (lldb) thread list","s":"列出程序中的线程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#列出程序中的线程","p":1409},{"i":1432,"t":"gdb lldb (gdb) thread 1 (lldb) thread select 1 (lldb) t 1","s":"设置后续命令的默认线程","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#设置后续命令的默认线程","p":1409},{"i":1435,"t":"gdb lldb (gdb) info frame (gdb) i f (lldb) frame info (lldb) fr i","s":"显示当前栈帧简略信息","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#显示当前栈帧简略信息","p":1409},{"i":1437,"t":"gdb lldb # check frame source code (gdb) frame (lldb) frame select (lldb) f (lldb) process status","s":"显示当前栈帧源代码行","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#显示当前栈帧源代码行","p":1409},{"i":1439,"t":"gdb lldb (gdb) frame 12 (lldb) frame select 12 (lldb) fr s 12 (lldb) f 12","s":"通过栈帧号选择栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#通过栈帧号选择栈帧","p":1409},{"i":1441,"t":"gdb lldb (gdb) up (lldb) up (lldb) frame select --relative=1 (lldb) fr s -r 1","s":"选择调用当前栈帧的栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#选择调用当前栈帧的栈帧","p":1409},{"i":1443,"t":"gdb lldb (gdb) down (lldb) down (lldb) frame select --relative=-1 (lldb) fr s -r -1","s":"选择被当前栈帧调用的栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#选择被当前栈帧调用的栈帧","p":1409},{"i":1445,"t":"gdb lldb (gdb) up 2 (gdb) down 3 (lldb) frame select --relative 2 (lldb) fr s -r 2 (lldb) frame select --relative -3 (lldb) fr s -r -3","s":"使用栈帧相对偏移选择栈帧","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#使用栈帧相对偏移选择栈帧","p":1409},{"i":1447,"t":"gdb lldb (gdb) return <RETURN EXPRESSION> (lldb) thread return <RETURN EXPRESSION>","s":"从栈帧返回，可以带有返回值","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#从栈帧返回可以带有返回值","p":1409},{"i":1449,"t":"gdb lldb (gdb) set unwindonsignal 0 (gdb) p function_with_a_breakpoint() (lldb) expr -i 0 -- function_with_a_breakpoint()","s":"调用带有断点的函数并在断点处停止","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#调用带有断点的函数并在断点处停止","p":1409},{"i":1451,"t":"gdb lldb (gdb) set unwindonsignal 0 (gdb) p function_which_crashes() (lldb) expr -u 0 -- function_which_crashes()","s":"调用 crash 的函数并在 crash 时停止","u":"/docs/modern-cpp/gdb-lldb/jump-in-debuggers","h":"#调用-crash-的函数并在-crash-时停止","p":1409},{"i":1454,"t":"如果您的源文件不再位于与程序构建时相同的位置 (例如，如果程序是在另外一台计算机上构建的)，您需要告诉调试器如何在本地文件路径中查找源文件，而不是构建系统的文件路径。 gdb lldb (gdb) set pathname-substitutions /buildbot/path /my/path (lldb) settings set target.source-map /buildbot/path /my/path 在 gdb 中，可以提供文件目录来搜索源文件。 gdb lldb (gdb) directory /my/path","s":"重新映射调试对话的源文件路径","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#重新映射调试对话的源文件路径","p":1452},{"i":1457,"t":"gdb lldb (gdb) target remote eorgadd:8000 (lldb) gdb-remote eorgadd:8000","s":"连接到远程调试服务器","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#连接到远程调试服务器","p":1452},{"i":1459,"t":"gdb lldb (gdb) target remote localhost:8000 (lldb) gdb-remote 8000","s":"连接到本地调试服务器","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#连接到本地调试服务器","p":1452},{"i":1462,"t":"gdb lldb (gdb) set $foo = 5 (gdb) set variable $foo = 5 # or using the print command (gdb) print $foo = 5 # or using the call command (gdb) call $foo = 5 # and if you want to specify the type of the variable: (gdb) set $foo = (unsigned int) 5 # In lldb you evaluate a variable declaration expression as you would write it in C: (lldb) expr unsigned int $foo = 5","s":"创建临时变量并赋值","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#创建临时变量并赋值","p":1452},{"i":1464,"t":"gdb lldb (gdb) print (int) printf (\"Print nine: %d.\", 4 + 5) # or if you don’t want to see void returns: (gdb) call (int) printf (\"Print nine: %d.\", 4 + 5) (lldb) expr (int) printf (\"Print nine: %d.\", 4 + 5) # or using the print alias: (lldb) print (int) printf (\"Print nine: %d.\", 4 + 5)","s":"在当前帧中的计算表达式","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#在当前帧中的计算表达式","p":1452},{"i":1466,"t":"gdb lldb (gdb) echo Here is some text\\n (lldb) script print(\"Here is some text\")","s":"打印信息到屏幕","u":"/docs/modern-cpp/gdb-lldb/misc","h":"#打印信息��到屏幕","p":1452},{"i":1469,"t":"gdb lldb % gdb a.out (gdb) run (gdb) r % lldb a.out (lldb) process launch (lldb) run (lldb) r","s":"启动新的进程","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#启动新的进程","p":1467},{"i":1471,"t":"在调试器启动之前设置参数 gdb lldb % gdb --args a.out <args...> (gdb) run % lldb -- a.out <args...> (lldb) run 在调试器启动之后、运行之前设置参数 gdb lldb (gdb) set args <args...> (gdb) run (lldb) settings set target.run-args <args...> (lldb) run 在运行的时候设置参数 gdb lldb (gdb) run <args...> (gdb) r <args...> (lldb) process launch -- <args...> (lldb) run <args...> (lldb) r <args...>","s":"设置进程的运行参数","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#设置进程的运行参数","p":1467},{"i":1473,"t":"在运行前设置环境变量 gdb lldb (gdb) set env DEBUG 1 (lldb) settings set target.env-vars DEBUG=1 (lldb) set se target.env-vars DEBUG=1 (lldb) env DEBUG=1 单条命令设置环境变量并启动进程 gdb lldb (lldb) process launch -E DEBUG=1 在运行前取消环境变量 gdb lldb (gdb) unset env DEBUG (lldb) settings remove target.env-vars DEBUG (lldb) set rem target.env-vars DEBUG","s":"环境变量设置","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#环境变量设置","p":1467},{"i":1475,"t":"根据进程号 pid 进行 attach gdb lldb (gdb) attach 123 (lldb) process attach --pid 123 (lldb) attach -p 123 根据进程名称进行 attach gdb lldb (gdb) attach a.out (lldb) process attach --name a.out (lldb) pro at -n a.out 等待进程名称并 attach gdb lldb (gdb) attach -waitfor a.out (lldb) process attach --name a.out --waitfor (lldb) pro at -n a.out -w","s":"attach 到已有进程","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#attach-到已有进程","p":1467},{"i":1477,"t":"gdb lldb (gdb) show args Argument list to give program being debugged when it is started is \"1 2 3\". (lldb) settings show target.run-args target.run-args (array of strings) = [0]: \"1\" [1]: \"2\" [2]: \"3\"","s":"显示参数","u":"/docs/modern-cpp/gdb-lldb/start-and-attach","h":"#显示参数","p":1467},{"i":1480,"t":"本教程介绍 Linux 命令行 Bash 的基本用法和脚本编程。","s":"Bash 教程","u":"/docs/modern-linux/bash-tutorial/","h":"","p":1479},{"i":1504,"t":"((...))语法可以进行整数的算术运算。 $ ((foo = 5 + 5)) $ echo $foo 10 ((...))会自动忽略内部的空格，所以下面的写法都正确，得到同样的结果。 $ ((2+2)) $ (( 2+2 )) $ (( 2 + 2 )) 这个语法不返回值，命令执行的结果根据算术运算的结果而定。只要算术结果不是0，命令就算执行成功。 $ (( 3 + 2 )) $ echo $? 0 上面例子中，3 + 2的结果是 5，命令就算执行成功，环境变量$?为0。 如果算术结果为0，命令就算执行失败。 $ (( 3 - 3 )) $ echo $? 1 上面例子中，3 - 3的结果是0，环境变量$?为1，表示命令执行失败。 如果要读取算术运算的结果，需要在((...))前面加上美元符号$((...))，使其变成算术表达式，返回算术运算的值。 $ echo $((2 + 2)) 4 ((...))语法支持的算术运算符如下。 +：加法 -：减法 *：乘法 /：除法（整除） %：余数 **：指数 ++：自增运算（前缀或后缀） --：自减运算（前缀或后缀） 注意，除法运算符的返回结果总是整数，比如5除以2，得到的结果是2，而不是2.5。 $ echo $((5 / 2)) 2 ++和--这两个运算符有前缀和后缀的区别。作为前缀是先运算后返回值，作为后缀是先返回值后运算。 $ i=0 $ echo $i 0 $ echo $((i++)) 0 $ echo $i 1 $ echo $((++i)) 2 $ echo $i 2 上面例子中，++作为后缀是先返回值，执行echo命令，再进行自增运算；作为前缀则是先进行自增运算，再返回值执行echo命令。 $((...))内部可以用圆括号改变运算顺序。 $ echo $(( (2 + 3) * 4 )) 20 上面例子中，内部的圆括号让加法先于乘法执行。 $((...))结构可以嵌套。 $ echo $(((5**2) * 3)) 75 # 等同于 $ echo $(($((5**2)) * 3)) 75 这个语法只能计算整数，否则会报错。 # 报错 $ echo $((1.5 + 1)) bash: 语法错误 $((...))的圆括号之中，不需要在变量名之前加上$，不过加上也不报错。 $ number=2 $ echo $(($number + 1)) 3 上面例子中，变量number前面有没有美元符号，结果都是一样的。 如果在$((...))里面使用字符串，Bash 会认为那是一个变量名。如果不存在同名变量，Bash 就会将其作为空值，因此不会报错。 $ echo $(( \"hello\" + 2)) 2 $ echo $(( \"hello\" * 2)) 0 上面例子中，\"hello\"会被当作变量名，返回空值，而$((...))会将空值当作0，所以乘法的运算结果就是0。同理，如果$((...))里面使用不存在的变量，也会当作0处理。 如果一个变量的值为字符串，跟上面的处理逻辑是一样的。即该字符串如果不对应已存在的变量，在$((...))里面会被当作空值。 $ foo=hello $ echo $(( foo + 2)) 2 上面例子中，变量foo的值是hello，而hello也会被看作变量名。这使得有可能写出动态替换的代码。 $ foo=hello $ hello=3 $ echo $(( foo + 2 )) 5 上面代码中，foo + 2取决于变量hello的值。 最后，$[...]是以前的语法，也可以做整数运算，不建议使用。 $ echo $[2+2] 4","s":"算术表达式","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#算术表达式","p":1502},{"i":1506,"t":"Bash 的数值默认都是十进制，但是在算术表达式中，也可以使用其他进制。 number：没有任何特殊表示法的数字是十进制数（以 10 为底）。 0number：八进制数。 0xnumber：十六进制数。 base#number：base进制的数。 下面是一些例子。 $ echo $((0xff)) 255 $ echo $((2#11111111)) 255 上面例子中，0xff是十六进制数，2#11111111是二进制数。","s":"数值的进制","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#数值的进制","p":1502},{"i":1508,"t":"$((...))支持以下的二进制位运算符。 <<：位左移运算，把一个数字的所有位向左移动指定的位。 >>：位右移运算，把一个数字的所有位向右移动指定的位。 &：位的“与”运算，对两个数字的所有位执行一个AND操作。 |：位的“或”运算，对两个数字的所有位执行一个OR操作。 ~：位的“否”运算，对一个数字的所有位取反。 ^：位的异或运算（exclusive or），对两个数字的所有位执行一个异或操作。 下面是右移运算符>>的例子。 $ echo $((16>>2)) 4 下面是左移运算符<<的例子。 $ echo $((16<<2)) 64 下面是17（二进制10001）和3（二进制11）的各种二进制运算的结果。 $ echo $((17&3)) 1 $ echo $((17|3)) 19 $ echo $((17^3)) 18","s":"位运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#位运算","p":1502},{"i":1510,"t":"$((...))支持以下的逻辑运算符。 <：小于 >：大于 <=：小于或相等 >=：大于或相等 ==：相等 !=：不相等 &&：逻辑与 ||：逻辑或 !：逻辑否 expr1?expr2:expr3：三元条件运算符。若表达式expr1的计算结果为非零值（算术真），则执行表达式expr2，否则执行表达式expr3。 如果逻辑表达式为真，返回1，否则返回0。 $ echo $((3 > 2)) 1 $ echo $(( (3 > 2) || (4 <= 1) )) 1 三元运算符执行一个单独的逻辑测试。它用起来类似于if/then/else语句。 $ a=0 $ echo $((a<1 ? 1 : 0)) 1 $ echo $((a>1 ? 1 : 0)) 0 上面例子中，第一个表达式为真时，返回第二个表达式的值，否则返回第三个表达式的值。","s":"逻辑运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#逻辑运算","p":1502},{"i":1512,"t":"算术表达式$((...))可以执行赋值运算。 $ echo $((a=1)) 1 $ echo $a 1 上面例子中，a=1对变量a进行赋值。这个式子本身也是一个表达式，返回值就是等号右边的值。 $((...))支持的赋值运算符，有以下这些。 parameter = value：简单赋值。 parameter += value：等价于parameter = parameter + value。 parameter -= value：等价于parameter = parameter – value。 parameter *= value：等价于parameter = parameter * value。 parameter /= value：等价于parameter = parameter / value。 parameter %= value：等价于parameter = parameter % value。 parameter <<= value：等价于parameter = parameter << value。 parameter >>= value：等价于parameter = parameter >> value。 parameter &= value：等价于parameter = parameter & value。 parameter |= value：等价于parameter = parameter | value。 parameter ^= value：等价于parameter = parameter ^ value。 下面是一个例子。 $ foo=5 $ echo $((foo*=2)) 10 如果在表达式内部赋值，可以放在圆括号中，否则会报错。 $ echo $(( a<1 ? (a+=1) : (a-=1) ))","s":"赋值运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#赋值运算","p":1502},{"i":1514,"t":"逗号,在$((...))内部是求值运算符，执行前后两个表达式，并返回后一个表达式的值。 $ echo $((foo = 1 + 2, 3 * 4)) 12 $ echo $foo 3 上面例子中，逗号前后两个表达式都会执行，然后返回后一个表达式的值12。","s":"求值运算","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#求值运算","p":1502},{"i":1516,"t":"expr命令支持算术运算，可以不使用((...))语法。 $ expr 3 + 2 5 expr命令支持变量替换。 $ foo=3 $ expr $foo + 2 5 expr命令也不支持非整数参数。 $ expr 3.5 + 2 expr: 非整数参数 上面例子中，如果有非整数的运算，expr命令就报错了。","s":"expr 命令","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#expr-命令","p":1502},{"i":1518,"t":"let命令用于将算术运算的结果，赋予一个变量。 $ let x=2+3 $ echo $x 5 上面例子中，变量x等于2+3的运算结果。 注意，x=2+3这个式子里面不能有空格，否则会报错。let命令的详细用法参见《变量》一章。","s":"let 命令","u":"/docs/modern-linux/bash-tutorial/arithmetic","h":"#let-命令","p":1502},{"i":1520,"t":"数组（array）是一个包含多个值的变量。成员的编号从 0 开始，数量没有上限，也没有要求成员被连续索引。","s":"数组","u":"/docs/modern-linux/bash-tutorial/array","h":"","p":1519},{"i":1522,"t":"数组可以采用逐个赋值的方法创建。 ARRAY[INDEX]=value 上面语法中，ARRAY是数组的名字，可以是任意合法的变量名。INDEX是一个大于或等于零的整数，也可以是算术表达式。注意数组第一个元素的下标是 0，而不是 1。 下面创建一个三个成员的数组。 $ array[0]=val $ array[1]=val $ array[2]=val 数组也可以采用一次性赋值的方式创建。 ARRAY=(value1 value2 ... valueN) # 等同于 ARRAY=( value1 value2 value3 ) 采用上面方式创建数组时，可以按照默认顺序赋值，也可以在每个值前面指定位置。 $ array=(a b c) $ array=([2]=c [0]=a [1]=b) $ days=(Sun Mon Tue Wed Thu Fri Sat) $ days=([0]=Sun [1]=Mon [2]=Tue [3]=Wed [4]=Thu [5]=Fri [6]=Sat) 只为某些值指定位置，也是可以的。 names=(hatter [5]=duchess alice) 上面例子中，hatter是数组的 0 号位置，duchess是 5 号位置，alice是 6 号位置。 没有赋值的数组元素的默认值是空字符串。 定义数组的时候，可以使用通配符。 $ mp3s=( *.mp3 ) 上面例子中，将当前目录的所有 MP3 文件，放进一个数组。 先用declare -a命令声明一个数组，也是可以的。 $ declare -a ARRAYNAME read -a命令则是将用户的命令行输入，存入一个数组。 $ read -a dice 上面命令将用户的命令行输入，存入数组dice。","s":"创建数组","u":"/docs/modern-linux/bash-tutorial/array","h":"#创建数组","p":1519},{"i":1525,"t":"读取数组指定位置的成员，要使用下面的语法。 $ echo ${array[i]} # i 是索引 上面语法里面的大括号是必不可少的，否则 Bash 会把索引部分[i]按照原样输出。 $ array[0]=a $ echo ${array[0]} a $ echo $array[0] a[0] 上面例子中，数组的第一个元素是a。如果不加大括号，Bash 会直接读取$array首成员的值，然后将[0]按照原样输出。","s":"读取单个元素","u":"/docs/modern-linux/bash-tutorial/array","h":"#读取单个元素","p":1519},{"i":1527,"t":"@和*是数组的特殊索引，表示返回数组的所有成员。 $ foo=(a b c d e f) $ echo ${foo[@]} a b c d e f 这两个特殊索引配合for循环，就可以用来遍历数组。 for i in \"${names[@]}\"; do echo $i done @和*放不放在双引号之中，是有差别的。 $ activities=( swimming \"water skiing\" canoeing \"white-water rafting\" surfing ) $ for act in ${activities[@]}; \\ do \\ echo \"Activity: $act\"; \\ done Activity: swimming Activity: water Activity: skiing Activity: canoeing Activity: white-water Activity: rafting Activity: surfing 上面的例子中，数组activities实际包含 5 个成员，但是for...in循环直接遍历${activities[@]}，导致返回 7 个结果。为了避免这种情况，一般把${activities[@]}放在双引号之中。 $ for act in \"${activities[@]}\"; \\ do \\ echo \"Activity: $act\"; \\ done Activity: swimming Activity: water skiing Activity: canoeing Activity: white-water rafting Activity: surfing 上面例子中，${activities[@]}放在双引号之中，遍历就会返回正确的结果。 ${activities[*]}不放在双引号之中，跟${activities[@]}不放在双引号之中是一样的。 $ for act in ${activities[*]}; \\ do \\ echo \"Activity: $act\"; \\ done Activity: swimming Activity: water Activity: skiing Activity: canoeing Activity: white-water Activity: rafting Activity: surfing ${activities[*]}放在双引号之中，所有成员就会变成单个字符串返回。 $ for act in \"${activities[*]}\"; \\ do \\ echo \"Activity: $act\"; \\ done Activity: swimming water skiing canoeing white-water rafting surfing 所以，拷贝一个数组的最方便方法，就是写成下面这样。 $ hobbies=( \"${activities[@]}\" ) 上面例子中，数组activities被拷贝给了另一个数组hobbies。 这种写法也可以用来为新数组添加成员。 $ hobbies=( \"${activities[@]}\" diving ) 上面例子中，新数组hobbies在数组activities的所有成员之后，又添加了一个成员。","s":"读取所有成员","u":"/docs/modern-linux/bash-tutorial/array","h":"#读取所有成员","p":1519},{"i":1529,"t":"如果读取数组成员时，没有读取指定哪一个位置的成员，默认使用0号位置。 $ declare -a foo $ foo=A $ echo ${foo[0]} A 上面例子中，foo是一个数组，赋值的时候不指定位置，实际上是给foo[0]赋值。 引用一个不带下标的数组变量，则引用的是0号位置的数组元素。 $ foo=(a b c d e f) $ echo ${foo} a $ echo $foo a 上面例子中，引用数组元素的时候，没有指定位置，结果返回的是0号位置。","s":"默认位置","u":"/docs/modern-linux/bash-tutorial/array","h":"#默认位置","p":1519},{"i":1531,"t":"要想知道数组的长度（即一共包含多少成员），可以使用下面两种语法。 ${#array[*]} ${#array[@]} 下面是一个例子。 $ a[100]=foo $ echo ${#a[*]} 1 $ echo ${#a[@]} 1 上面例子中，把字符串赋值给100位置的数组元素，这时的数组只有一个元素。 注意，如果用这种语法去读取具体的数组成员，就会返回该成员的字符串长度。这一点必须小心。 $ a[100]=foo $ echo ${#a[100]} 3 上面例子中，${#a[100]}实际上是返回数组第 100 号成员a[100]的值（foo）的字符串长度。","s":"数组的长度","u":"/docs/modern-linux/bash-tutorial/array","h":"#数组的长度","p":1519},{"i":1533,"t":"${!array[@]}或${!array[*]}，可以返回数组的成员序号，即哪些位置是有值的。 $ arr=([5]=a [9]=b [23]=c) $ echo ${!arr[@]} 5 9 23 $ echo ${!arr[*]} 5 9 23 上面例子中，数组的 5、9、23 号位置有值。 利用这个语法，也可以通过for循环遍历数组。 arr=(a b c d) for i in ${!arr[@]};do echo ${arr[i]} done","s":"提取数组序号","u":"/docs/modern-linux/bash-tutorial/array","h":"#提取数组序号","p":1519},{"i":1535,"t":"${array[@]:position:length}的语法可以提取数组成员。 $ food=( apples bananas cucumbers dates eggs fajitas grapes ) $ echo ${food[@]:1:1} bananas $ echo ${food[@]:1:3} bananas cucumbers dates 上面例子中，${food[@]:1:1}返回从数组 1 号位置开始的 1 个成员，${food[@]:1:3}返回从 1 号位置开始的 3 个成员。 如果省略长度参数length，则返回从指定位置开始的所有成员。 $ echo ${food[@]:4} eggs fajitas grapes 上面例子返回从 4 号位置开始到结束的所有成员。","s":"提取数组成员","u":"/docs/modern-linux/bash-tutorial/array","h":"#提取数组成员","p":1519},{"i":1537,"t":"数组末尾追加成员，可以使用+=赋值运算符。它能够自动地把值追加到数组末尾。否则，就需要知道数组的最大序号，比较麻烦。 $ foo=(a b c) $ echo ${foo[@]} a b c $ foo+=(d e f) $ echo ${foo[@]} a b c d e f","s":"追加数组成员","u":"/docs/modern-linux/bash-tutorial/array","h":"#追加数组成员","p":1519},{"i":1539,"t":"删除一个数组成员，使用unset命令。 $ foo=(a b c d e f) $ echo ${foo[@]} a b c d e f $ unset foo[2] $ echo ${foo[@]} a b d e f 上面例子中，删除了数组中的第三个元素，下标为 2。 将某个成员设为空值，可以从返回值中“隐藏”这个成员。 $ foo=(a b c d e f) $ foo[1]='' $ echo ${foo[@]} a c d e f 上面例子中，将数组的第二个成员设为空字符串，数组的返回值中，这个成员就“隐藏”了。 注意，这里是“隐藏”，而不是删除，因为这个成员仍然存在，只是值变成了空值。 $ foo=(a b c d e f) $ foo[1]='' $ echo ${#foo[@]} 6 $ echo ${!foo[@]} 0 1 2 3 4 5 上面代码中，第二个成员设为空值后，数组仍然包含 6 个成员。 由于空值就是空字符串，所以下面这样写也有隐藏效果，但是不建议这种写法。 $ foo[1]= 上面的写法也相当于“隐藏”了数组的第二个成员。 直接将数组变量赋值为空字符串，相当于“隐藏”数组的第一个成员。 $ foo=(a b c d e f) $ foo='' $ echo ${foo[@]} b c d e f 上面的写法相当于“隐藏”了数组的第一个成员。 unset ArrayName可以清空整个数组。 $ unset ARRAY $ echo ${ARRAY[*]} <--no output-->","s":"删除数组","u":"/docs/modern-linux/bash-tutorial/array","h":"#删除数组","p":1519},{"i":1541,"t":"Bash 的新版本支持关联数组。关联数组使用字符串而不是整数作为数组索引。 declare -A可以声明关联数组。 declare -A colors colors[\"red\"]=\"#ff0000\" colors[\"green\"]=\"#00ff00\" colors[\"blue\"]=\"#0000ff\" 关联数组必须用带有-A选项的declare命令声明创建。相比之下，整数索引的数组，可以直接使用变量名创建数组，关联数组就不行。 访问关联数组成员的方式，几乎与整数索引数组相同。 echo ${colors[\"blue\"]}","s":"关联数组","u":"/docs/modern-linux/bash-tutorial/array","h":"#关联数组","p":1519},{"i":1543,"t":"本章介绍 Bash 脚本的条件判断语法。","s":"条件判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"","p":1542},{"i":1545,"t":"if是最常用的条件判断结构，只有符合给定条件时，才会执行指定的命令。它的语法如下。 if commands; then commands [elif commands; then commands...] [else commands] fi 这个命令分成三个部分：if、elif和else。其中，后两个部分是可选的。 if关键字后面是主要的判断条件，elif用来添加在主条件不成立时的其他判断条件，else则是所有条件都不成立时要执行的部分。 if test $USER = \"foo\"; then echo \"Hello foo.\" else echo \"You are not foo.\" fi 上面的例子中，判断条件是环境变量$USER是否等于foo，如果等于就输出Hello foo.，否则输出其他内容。 if和then写在同一行时，需要分号分隔。分号是 Bash 的命令分隔符。它们也可以写成两行，这时不需要分号。 if true; then echo 'hello world' fi if false; then echo 'it is false' # 本行不会执行 fi 上面的例子中，true和false是两个特殊命令，前者代表操作成功，后者代表操作失败。if true意味着命令部分总是会执行，if false意味着命令部分永远不会执行。 除了多行的写法，if结构也可以写成单行。 $ if true; then echo 'hello world'; fi hello world $ if false; then echo \"It's true.\"; fi 注意，if关键字后面也可以是一条命令，该条命令执行成功（返回值0），就意味着判断条件成立。 $ if echo 'hi'; then echo 'hello world'; fi hi hello world 上面命令中，if后面是一条命令echo 'hi'。该命令会执行，如果返回值是0，则执行then的部分。 if后面可以跟任意数量的命令。这时，所有命令都会执行，但是判断真伪只看最后一个命令，即使前面所有命令都失败，只要最后一个命令返回0，就会执行then的部分。 $ if false; true; then echo 'hello world'; fi hello world 上面例子中，if后面有两条命令（false;true;），第二条命令（true）决定了then的部分是否会执行。 elif部分可以有多个。 #!/bin/bash echo -n \"输入一个1到3之间的数字（包含两端）> \" read character if [ \"$character\" = \"1\" ]; then echo 1 elif [ \"$character\" = \"2\" ]; then echo 2 elif [ \"$character\" = \"3\" ]; then echo 3 else echo 输入不符合要求 fi 上面例子中，如果用户输入3，就会连续判断 3 次。","s":"if 结构","u":"/docs/modern-linux/bash-tutorial/condition","h":"#if-结构","p":1542},{"i":1547,"t":"if结构的判断条件，一般使用test命令，有三种形式。 # 写法一 test expression # 写法二 [ expression ] # 写法三 [[ expression ]] 上面三种形式是等价的，但是第三种形式还支持正则判断，前两种不支持。 上面的expression是一个表达式。这个表达式为真，test命令执行成功（返回值为0）；表达式为伪，test命令执行失败（返回值为1）。注意，第二种和第三种写法，[和]与内部的表达式之间必须有空格。 $ test -f /etc/hosts $ echo $? 0 $ [ -f /etc/hosts ] $ echo $? 0 上面的例子中，test命令采用两种写法，判断/etc/hosts文件是否存在，这两种写法是等价的。命令执行后，返回值为0，表示该文件确实存在。 实际上，[这个字符是test命令的一种简写形式，可以看作是一个独立的命令，这解释了为什么它后面必须有空格。 下面把test命令的三种形式，用在if结构中，判断一个文件是否存在。 # 写法一 if test -e /tmp/foo.txt; then echo \"Found foo.txt\" fi # 写法二 if [ -e /tmp/foo.txt ]; then echo \"Found foo.txt\" fi # 写法三 if [[ -e /tmp/foo.txt ]]; then echo \"Found foo.txt\" fi","s":"test 命令","u":"/docs/modern-linux/bash-tutorial/condition","h":"#test-命令","p":1542},{"i":1549,"t":"if关键字后面，跟的是一个命令。这个命令可以是test命令，也可以是其他命令。命令的返回值为0表示判断成立，否则表示不成立。因为这些命令主要是为了得到返回值，所以可以视为表达式。 常用的判断表达式有下面这些。","s":"判断表达式","u":"/docs/modern-linux/bash-tutorial/condition","h":"#判断表达式","p":1542},{"i":1551,"t":"以下表达式用来判断文件状态。 [ -a file ]：如果 file 存在，则为true。 [ -b file ]：如果 file 存在并且是一个块（设备）文件，则为true。 [ -c file ]：如果 file 存在并且是一个字符（设备）文件，则为true。 [ -d file ]：如果 file 存在并且是一个目录，则为true。 [ -e file ]：如果 file 存在，则为true。 [ -f file ]：如果 file 存在并且是一个普通文件，则为true。 [ -g file ]：如果 file 存在并且设置了组 ID，则为true。 [ -G file ]：如果 file 存在并且属于有效的组 ID，则为true。 [ -h file ]：如果 file 存在并且是符号链接，则为true。 [ -k file ]：如果 file 存在并且设置了它的“sticky bit”，则为true。 [ -L file ]：如果 file 存在并且是一个符号链接，则为true。 [ -N file ]：如果 file 存在并且自上次读取后已被修改，则为true。 [ -O file ]：如果 file 存在并且属于有效的用户 ID，则为true。 [ -p file ]：如果 file 存在并且是一个命名管道，则为true。 [ -r file ]：如果 file 存在并且可读（当前用户有可读权限），则为true。 [ -s file ]：如果 file 存在且其长度大于零，则为true。 [ -S file ]：如果 file 存在且是一个网络 socket，则为true。 [ -t fd ]：如果 fd 是一个文件描述符，并且重定向到终端，则为true。这可以用来判断是否重定向了标准输入／输出／错误。 [ -u file ]：如果 file 存在并且设置了 setuid 位，则为true。 [ -w file ]：如果 file 存在并且可写（当前用户拥有可写权限），则为true。 [ -x file ]：如果 file 存在并且可执行（有效用户有执行／搜索权限），则为true。 [ FILE1 -nt FILE2 ]：如果 FILE1 比 FILE2 的更新时间更近，或者 FILE1 存在而 FILE2 不存在，则为true。 [ FILE1 -ot FILE2 ]：如果 FILE1 比 FILE2 的更新时间更旧，或者 FILE2 存在而 FILE1 不存在，则为true。 [ FILE1 -ef FILE2 ]：如果 FILE1 和 FILE2 引用相同的设备和 inode 编号，则为true。 下面是一个示例。 #!/bin/bash FILE=~/.bashrc if [ -e \"$FILE\" ]; then if [ -f \"$FILE\" ]; then echo \"$FILE is a regular file.\" fi if [ -d \"$FILE\" ]; then echo \"$FILE is a directory.\" fi if [ -r \"$FILE\" ]; then echo \"$FILE is readable.\" fi if [ -w \"$FILE\" ]; then echo \"$FILE is writable.\" fi if [ -x \"$FILE\" ]; then echo \"$FILE is executable/searchable.\" fi else echo \"$FILE does not exist\" exit 1 fi 上面代码中，$FILE要放在双引号之中，这样可以防止变量$FILE为空，从而出错。因为$FILE如果为空，这时[ -e $FILE ]就变成[ -e ]，这会被判断为真。而$FILE放在双引号之中，[ -e \"$FILE\" ]就变成[ -e \"\" ]，这会被判断为伪。","s":"文件判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#文件判断","p":1542},{"i":1553,"t":"以下表达式用来判断字符串。 [ string ]：如果string不为空（长度大于 0），则判断为真。 [ -n string ]：如果字符串string的长度大于零，则判断为真。 [ -z string ]：如果字符串string的长度为零，则判断为真。 [ string1 = string2 ]：如果string1和string2相同，则判断为真。 [ string1 == string2 ] 等同于[ string1 = string2 ]。 [ string1 != string2 ]：如果string1和string2不相同，则判断为真。 [ string1 '>' string2 ]：如果按照字典顺序string1排列在string2之后，则判断为真。 [ string1 '<' string2 ]：如果按照字典顺序string1排列在string2之前，则判断为真。 注意，test命令内部的>和<，必须用引号引起来（或者是用反斜杠转义）。否则，它们会被 shell 解释为重定向操作符。 下面是一个示例。 #!/bin/bash ANSWER=maybe if [ -z \"$ANSWER\" ]; then echo \"There is no answer.\" >&2 exit 1 fi if [ \"$ANSWER\" = \"yes\" ]; then echo \"The answer is YES.\" elif [ \"$ANSWER\" = \"no\" ]; then echo \"The answer is NO.\" elif [ \"$ANSWER\" = \"maybe\" ]; then echo \"The answer is MAYBE.\" else echo \"The answer is UNKNOWN.\" fi 上面代码中，首先确定$ANSWER字符串是否为空。如果为空，就终止脚本，并把退出状态设为1。注意，这里的echo命令把错误信息There is no answer.重定向到标准错误，这是处理错误信息的常用方法。如果$ANSWER字符串不为空，就判断它的值是否等于yes、no或者maybe。 注意，字符串判断时，变量要放在双引号之中，比如[ -n \"$COUNT\" ]，否则变量替换成字符串以后，test命令可能会报错，提示参数过多。另外，如果不放在双引号之中，变量为空时，命令会变成[ -n ]，这时会判断为真。如果放在双引号之中，[ -n \"\" ]就判断为伪。","s":"字符串判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#字符串判断","p":1542},{"i":1555,"t":"下面的表达式用于判断整数。 [ integer1 -eq integer2 ]：如果integer1等于integer2，则为true。 [ integer1 -ne integer2 ]：如果integer1不等于integer2，则为true。 [ integer1 -le integer2 ]：如果integer1小于或等于integer2，则为true。 [ integer1 -lt integer2 ]：如果integer1小于integer2，则为true。 [ integer1 -ge integer2 ]：如果integer1大于或等于integer2，则为true。 [ integer1 -gt integer2 ]：如果integer1大于integer2，则为true。 下面是一个用法的例子。 #!/bin/bash INT=-5 if [ -z \"$INT\" ]; then echo \"INT is empty.\" >&2 exit 1 fi if [ $INT -eq 0 ]; then echo \"INT is zero.\" else if [ $INT -lt 0 ]; then echo \"INT is negative.\" else echo \"INT is positive.\" fi if [ $((INT % 2)) -eq 0 ]; then echo \"INT is even.\" else echo \"INT is odd.\" fi fi 上面例子中，先判断变量$INT是否为空，然后判断是否为0，接着判断正负，最后通过求余数判断奇偶。","s":"整数判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#整数判断","p":1542},{"i":1557,"t":"[[ expression ]]这种判断形式，支持正则表达式。 [[ string1 =~ regex ]] 上面的语法中，regex是一个正则表示式，=~是正则比较运算符。 下面是一个例子。 #!/bin/bash INT=-5 if [[ \"$INT\" =~ ^-?[0-9]+$ ]]; then echo \"INT is an integer.\" exit 0 else echo \"INT is not an integer.\" >&2 exit 1 fi 上面代码中，先判断变量INT的字符串形式，是否满足^-?[0-9]+$的正则模式，如果满足就表明它是一个整数。","s":"正则判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#正则判断","p":1542},{"i":1559,"t":"通过逻辑运算，可以把多个test判断表达式结合起来，创造更复杂的判断。三种逻辑运算AND，OR，和NOT，都有自己的专用符号。 AND运算：符号&&，也可使用参数-a。 OR运算：符号||，也可使用参数-o。 NOT运算：符号!。 下面是一个AND的例子，判断整数是否在某个范围之内。 #!/bin/bash MIN_VAL=1 MAX_VAL=100 INT=50 if [[ \"$INT\" =~ ^-?[0-9]+$ ]]; then if [[ $INT -ge $MIN_VAL && $INT -le $MAX_VAL ]]; then echo \"$INT is within $MIN_VAL to $MAX_VAL.\" else echo \"$INT is out of range.\" fi else echo \"INT is not an integer.\" >&2 exit 1 fi 上面例子中，&&用来连接两个判断条件：大于等于$MIN_VAL，并且小于等于$MAX_VAL。 使用否定操作符!时，最好用圆括号确定转义的范围。 if [ ! \\( $INT -ge $MIN_VAL -a $INT -le $MAX_VAL \\) ]; then echo \"$INT is outside $MIN_VAL to $MAX_VAL.\" else echo \"$INT is in range.\" fi 上面例子中，test命令内部使用的圆括号，必须使用引号或者转义，否则会被 Bash 解释。 使用-a连接两个判断条件不太直观，一般推荐使用&&代替，上面的脚本可以改写成下面这样。 if !([ $INT -ge $MIN_VAL ] && [ $INT -le $MAX_VAL ]); then echo \"$INT is outside $MIN_VAL to $MAX_VAL.\" else echo \"$INT is in range.\" fi","s":"test 判断的逻辑运算","u":"/docs/modern-linux/bash-tutorial/condition","h":"#test-判断的逻辑运算","p":1542},{"i":1561,"t":"Bash 还提供了((...))作为算术条件，进行算术运算的判断。 if ((3 > 2)); then echo \"true\" fi 上面代码执行后，会打印出true。 注意，算术判断不需要使用test命令，而是直接使用((...))结构。这个结构的返回值，决定了判断的真伪。 如果算术计算的结果是非零值，则表示判断成立。这一点跟命令的返回值正好相反，需要小心。 $ if ((1)); then echo \"It is true.\"; fi It is true. $ if ((0)); then echo \"It is true.\"; else echo \"it is false.\"; fi It is false. 上面例子中，((1))表示判断成立，((0))表示判断不成立。 算术条件((...))也可以用于变量赋值。 $ if (( foo = 5 ));then echo \"foo is $foo\"; fi foo is 5 上面例子中，(( foo = 5 ))完成了两件事情。首先把5赋值给变量foo，然后根据返回值5，判断条件为真。 注意，赋值语句返回等号右边的值，如果返回的是0，则判断为假。 $ if (( foo = 0 ));then echo \"It is true.\";else echo \"It is false.\"; fi It is false. 下面是用算术条件改写的数值判断脚本。 #!/bin/bash INT=-5 if [[ \"$INT\" =~ ^-?[0-9]+$ ]]; then if ((INT == 0)); then echo \"INT is zero.\" else if ((INT < 0)); then echo \"INT is negative.\" else echo \"INT is positive.\" fi if ((((INT % 2)) == 0)); then echo \"INT is even.\" else echo \"INT is odd.\" fi fi else echo \"INT is not an integer.\" >&2 exit 1 fi 只要是算术表达式，都能用于((...))语法，详见《Bash 的算术运算》一章。","s":"算术判断","u":"/docs/modern-linux/bash-tutorial/condition","h":"#算术判断","p":1542},{"i":1563,"t":"如果if结构使用的不是test命令，而是普通命令，比如上一节的((...))算术运算，或者test命令与普通命令混用，那么可以使用 Bash 的命令控制操作符&&（AND）和||（OR），进行多个命令的逻辑运算。 $ command1 && command2 $ command1 || command2 对于&&操作符，先执行command1，只有command1执行成功后，才会执行command2。对于||操作符，先执行command1，只有command1执行失败后，才会执行command2。 $ mkdir temp && cd temp 上面的命令会创建一个名为temp的目录，执行成功后，才会执行第二个命令，进入这个目录。 $ [ -d temp ] || mkdir temp 上面的命令会测试目录temp是否存在，如果不存在，就会执行第二个命令，创建这个目录。这种写法非常有助于在脚本中处理错误。 [ ! -d temp ] && exit 1 上面的命令中，如果temp子目录不存在，脚本会终止，并且返回值为1。 下面就是if与&&结合使用的写法。 if [ condition ] && [ condition ]; then command fi 下面是一个示例。 #! /bin/bash filename=$1 word1=$2 word2=$3 if grep $word1 $filename && grep $word2 $filename; then echo \"$word1 and $word2 are both in $filename.\" fi 上面的例子只有在指定文件里面，同时存在搜索词word1和word2，就会执行if的命令部分。 下面的示例演示如何将一个&&判断表达式，改写成对应的if结构。 [[ -d \"$dir_name\" ]] && cd \"$dir_name\" && rm * # 等同于 if [[ ! -d \"$dir_name\" ]]; then echo \"No such directory: '$dir_name'\" >&2 exit 1 fi if ! cd \"$dir_name\"; then echo \"Cannot cd to '$dir_name'\" >&2 exit 1 fi if ! rm *; then echo \"File deletion failed. Check results\" >&2 exit 1 fi","s":"普通命令的逻辑运算","u":"/docs/modern-linux/bash-tutorial/condition","h":"#普通命令的逻辑运算","p":1542},{"i":1565,"t":"case结构用于多值判断，可以为每个值指定对应的命令，跟包含多个elif的if结构等价，但是语义更好。它的语法如下。 case expression in pattern ) commands ;; pattern ) commands ;; ... esac 上面代码中，expression是一个表达式，pattern是表达式的值或者一个模式，可以有多条，用来匹配多个值，每条以两个分号（;）结尾。 #!/bin/bash echo -n \"输入一个1到3之间的数字（包含两端）> \" read character case $character in 1) echo 1 ;; 2) echo 2 ;; 3) echo 3 ;; *) echo 输入不符合要求 ;; esac 上面例子中，最后一条匹配语句的模式是*，这个通配符可以匹配其他字符和没有输入字符的情况，类似if的else部分。 下面是另一个例子。 #!/bin/bash OS=$(uname -s) case \"$OS\" in FreeBSD) echo \"This is FreeBSD\" ;; Darwin) echo \"This is Mac OSX\" ;; AIX) echo \"This is AIX\" ;; Minix) echo \"This is Minix\" ;; Linux) echo \"This is Linux\" ;; *) echo \"Failed to identify this OS\" ;; esac 上面的例子判断当前是什么操作系统。 case的匹配模式可以使用各种通配符，下面是一些例子。 a)：匹配a。 a|b)：匹配a或b。 [[:alpha:]])：匹配单个字母。 ???)：匹配 3 个字符的单词。 *.txt)：匹配.txt结尾。 *)：匹配任意输入，通常作为case结构的最后一个模式。 #!/bin/bash echo -n \"输入一个字母或数字 > \" read character case $character in [[:lower:]] | [[:upper:]]) echo \"输入了字母 $character\" ;; [0-9]) echo \"输入了数字 $character\" ;; *) echo \"输入不符合要求\" ;; esac 上面例子中，使用通配符[[:lower:]] | [[:upper:]]匹配字母，[0-9]匹配数字。 Bash 4.0 之前，case结构只能匹配一个条件，然后就会退出case结构。Bash 4.0 之后，允许匹配多个条件，这时可以用;;&终止每个条件块。 #!/bin/bash # test.sh read -n 1 -p \"Type a character > \" echo case $REPLY in [[:upper:]]) echo \"'$REPLY' is upper case.\" ;;& [[:lower:]]) echo \"'$REPLY' is lower case.\" ;;& [[:alpha:]]) echo \"'$REPLY' is alphabetic.\" ;;& [[:digit:]]) echo \"'$REPLY' is a digit.\" ;;& [[:graph:]]) echo \"'$REPLY' is a visible character.\" ;;& [[:punct:]]) echo \"'$REPLY' is a punctuation symbol.\" ;;& [[:space:]]) echo \"'$REPLY' is a whitespace character.\" ;;& [[:xdigit:]]) echo \"'$REPLY' is a hexadecimal digit.\" ;;& esac 执行上面的脚本，会得到下面的结果。 $ test.sh Type a character > a 'a' is lower case. 'a' is alphabetic. 'a' is a visible character. 'a' is a hexadecimal digit. 可以看到条件语句结尾添加了;;&以后，在匹配一个条件之后，并没有退出case结构，而是继续判断下一个条件。","s":"case 结构","u":"/docs/modern-linux/bash-tutorial/condition","h":"#case-结构","p":1542},{"i":1567,"t":"The Linux Command Line, William Shotts","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/condition","h":"#参考链接","p":1542},{"i":1569,"t":"本章介绍如何对 Shell 脚本除错。","s":"脚本除错","u":"/docs/modern-linux/bash-tutorial/debug","h":"","p":1568},{"i":1571,"t":"编写 Shell 脚本的时候，一定要考虑到命令失败的情况，否则很容易出错。 #! /bin/bash dir_name=/path/not/exist cd $dir_name rm * 上面脚本中，如果目录$dir_name不存在，cd $dir_name命令就会执行失败。这时，就不会改变当前目录，脚本会继续执行下去，导致rm *命令删光当前目录的文件。 如果改成下面的样子，也会有问题。 cd $dir_name && rm * 上面脚本中，只有cd $dir_name执行成功，才会执行rm *。但是，如果变量$dir_name为空，cd就会进入用户主目录，从而删光用户主目录的文件。 下面的写法才是正确的。 [[ -d $dir_name ]] && cd $dir_name && rm * 上面代码中，先判断目录$dir_name是否存在，然后才执行其他操作。 如果不放心删除什么文件，可以先打印出来看一下。 [[ -d $dir_name ]] && cd $dir_name && echo rm * 上面命令中，echo rm *不会删除文件，只会打印出来要删除的文件。","s":"常见错误","u":"/docs/modern-linux/bash-tutorial/debug","h":"#常见错误","p":1568},{"i":1573,"t":"bash的-x参数可以在执行每一行命令之前，打印该命令。一旦出错，这样就比较容易追查。 下面是一个脚本script.sh。 # script.sh echo hello world 加上-x参数，执行每条命令之前，都会显示该命令。 $ bash -x script.sh + echo hello world hello world 上面例子中，行首为+的行，显示该行是所要执行的命令，下一行才是该命令的执行结果。 下面再看一个-x写在脚本内部的例子。 #! /bin/bash -x # trouble: script to demonstrate common errors number=1 if [ $number = 1 ]; then echo \"Number is equal to 1.\" else echo \"Number is not equal to 1.\" fi 上面的脚本执行之后，会输出每一行命令。 $ trouble + number=1 + '[' 1 = 1 ']' + echo 'Number is equal to 1.' Number is equal to 1. 输出的命令之前的+号，是由系统变量PS4决定，可以修改这个变量。 $ export PS4='$LINENO + ' $ trouble 5 + number=1 7 + '[' 1 = 1 ']' 8 + echo 'Number is equal to 1.' Number is equal to 1. 另外，set命令也可以设置 Shell 的行为参数，有利于脚本除错，详见《set 命令》一章。","s":"bash的-x参数","u":"/docs/modern-linux/bash-tutorial/debug","h":"#bash的-x参数","p":1568},{"i":1575,"t":"有一些环境变量常用于除错。","s":"环境变量","u":"/docs/modern-linux/bash-tutorial/debug","h":"#环境变量","p":1568},{"i":1577,"t":"变量LINENO返回它在脚本里面的行号。 #!/bin/bash echo \"This is line $LINENO\" 执行上面的脚本test.sh，$LINENO会返回3。 $ ./test.sh This is line 3","s":"LINENO","u":"/docs/modern-linux/bash-tutorial/debug","h":"#lineno","p":1568},{"i":1579,"t":"变量FUNCNAME返回一个数组，内容是当前的函数调用堆栈。该数组的 0 号成员是当前调用的函数，1 号成员是调用当前函数的函数，以此类推。 #!/bin/bash function func1() { echo \"func1: FUNCNAME0 is ${FUNCNAME[0]}\" echo \"func1: FUNCNAME1 is ${FUNCNAME[1]}\" echo \"func1: FUNCNAME2 is ${FUNCNAME[2]}\" func2 } function func2() { echo \"func2: FUNCNAME0 is ${FUNCNAME[0]}\" echo \"func2: FUNCNAME1 is ${FUNCNAME[1]}\" echo \"func2: FUNCNAME2 is ${FUNCNAME[2]}\" } func1 执行上面的脚本test.sh，结果如下。 $ ./test.sh func1: FUNCNAME0 is func1 func1: FUNCNAME1 is main func1: FUNCNAME2 is func2: FUNCNAME0 is func2 func2: FUNCNAME1 is func1 func2: FUNCNAME2 is main 上面例子中，执行func1时，变量FUNCNAME的 0 号成员是func1，1 号成员是调用func1的主脚本main。执行func2时，变量FUNCNAME的 0 号成员是func2，1 号成员是调用func2的func1。","s":"FUNCNAME","u":"/docs/modern-linux/bash-tutorial/debug","h":"#funcname","p":1568},{"i":1581,"t":"变量BASH_SOURCE返回一个数组，内容是当前的脚本调用堆栈。该数组的 0 号成员是当前执行的脚本，1 号成员是调用当前脚本的脚本，以此类推，跟变量FUNCNAME是一一对应关系。 下面有两个子脚本lib1.sh和lib2.sh。 # lib1.sh function func1() { echo \"func1: BASH_SOURCE0 is ${BASH_SOURCE[0]}\" echo \"func1: BASH_SOURCE1 is ${BASH_SOURCE[1]}\" echo \"func1: BASH_SOURCE2 is ${BASH_SOURCE[2]}\" func2 } # lib2.sh function func2() { echo \"func2: BASH_SOURCE0 is ${BASH_SOURCE[0]}\" echo \"func2: BASH_SOURCE1 is ${BASH_SOURCE[1]}\" echo \"func2: BASH_SOURCE2 is ${BASH_SOURCE[2]}\" } 然后，主脚本main.sh调用上面两个子脚本。 #!/bin/bash # main.sh source lib1.sh source lib2.sh func1 执行主脚本main.sh，会得到下面的结果。 $ ./main.sh func1: BASH_SOURCE0 is lib1.sh func1: BASH_SOURCE1 is ./main.sh func1: BASH_SOURCE2 is func2: BASH_SOURCE0 is lib2.sh func2: BASH_SOURCE1 is lib1.sh func2: BASH_SOURCE2 is ./main.sh 上面例子中，执行函数func1时，变量BASH_SOURCE的 0 号成员是func1所在的脚本lib1.sh，1 号成员是主脚本main.sh；执行函数func2时，变量BASH_SOURCE的 0 号成员是func2所在的脚本lib2.sh，1 号成员是调用func2的脚本lib1.sh。","s":"BASH_SOURCE","u":"/docs/modern-linux/bash-tutorial/debug","h":"#bash_source","p":1568},{"i":1583,"t":"变量BASH_LINENO返回一个数组，内容是每一轮调用对应的行号。${BASH_LINENO[$i]}跟${FUNCNAME[$i]}是一一对应关系，表示${FUNCNAME[$i]}在调用它的脚本文件${BASH_SOURCE[$i+1]}里面的行号。 下面有两个子脚本lib1.sh和lib2.sh。 # lib1.sh function func1() { echo \"func1: BASH_LINENO is ${BASH_LINENO[0]}\" echo \"func1: FUNCNAME is ${FUNCNAME[0]}\" echo \"func1: BASH_SOURCE is ${BASH_SOURCE[1]}\" func2 } # lib2.sh function func2() { echo \"func2: BASH_LINENO is ${BASH_LINENO[0]}\" echo \"func2: FUNCNAME is ${FUNCNAME[0]}\" echo \"func2: BASH_SOURCE is ${BASH_SOURCE[1]}\" } 然后，主脚本main.sh调用上面两个子脚本。 #!/bin/bash # main.sh source lib1.sh source lib2.sh func1 执行主脚本main.sh，会得到下面的结果。 $ ./main.sh func1: BASH_LINENO is 7 func1: FUNCNAME is func1 func1: BASH_SOURCE is main.sh func2: BASH_LINENO is 8 func2: FUNCNAME is func2 func2: BASH_SOURCE is lib1.sh 上面例子中，函数func1是在main.sh的第 7 行调用，函数func2是在lib1.sh的第 8 行调用的。","s":"BASH_LINENO","u":"/docs/modern-linux/bash-tutorial/debug","h":"#bash_lineno","p":1568},{"i":1586,"t":"Shell 接收到用户输入的命令以后，会根据空格将用户的输入，拆分成一个个词元（token）。然后，Shell 会扩展词元里面的特殊字符，扩展完成后才会调用相应的命令。 这种特殊字符的扩展，称为模式扩展（globbing）。其中有些用到通配符，又称为通配符扩展（wildcard expansion）。Bash 一共提供八种扩展。 波浪线扩展 ? 字符扩展 * 字符扩展 方括号扩展 大括号扩展 变量扩展 子命令扩展 算术扩展 本章介绍这八种扩展。 Bash 是先进行扩展，再执行命令。因此，扩展的结果是由 Bash 负责的，与所要执行的命令无关。命令本身并不存在参数扩展，收到什么参数就原样执行。这一点务必需要记住。 模块扩展的英文单词是globbing，这个词来自于早期的 Unix 系统有一个/etc/glob文件，保存扩展的模板。后来 Bash 内置了这个功能，但是这个名字就保留了下来。 模式扩展与正则表达式的关系是，模式扩展早于正则表达式出现，可以看作是原始的正则表达式。它的功能没有正则那么强大灵活，但是优点是简单和方便。 Bash 允许用户关闭扩展。 $ set -o noglob # 或者 $ set -f 下面的命令可以重新打开扩展。 $ set +o noglob # 或者 $ set +f","s":"简介","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#简介","p":1584},{"i":1588,"t":"波浪线~会自动扩展成当前用户的主目录。 $ echo ~ /home/me ~/dir表示扩展成主目录的某个子目录，dir是主目录里面的一个子目录名。 # 进入 /home/me/foo 目录 $ cd ~/foo ~user表示扩展成用户user的主目录。 $ echo ~foo /home/foo $ echo ~root /root 上面例子中，Bash 会根据波浪号后面的用户名，返回该用户的主目录。 如果~user的user是不存在的用户名，则波浪号扩展不起作用。 $ echo ~nonExistedUser ~nonExistedUser ~+会扩展成当前所在的目录，等同于pwd命令。 $ cd ~/foo $ echo ~+ /home/me/foo","s":"波浪线扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#波浪线扩展","p":1584},{"i":1590,"t":"?字符代表文件路径里面的任意单个字符，不包括空字符。比如，Data???匹配所有Data后面跟着三个字符的文件名。 # 存在文件 a.txt 和 b.txt $ ls ?.txt a.txt b.txt 上面命令中，?表示单个字符，所以会同时匹配a.txt和b.txt。 如果匹配多个字符，就需要多个?连用。 # 存在文件 a.txt、b.txt 和 ab.txt $ ls ??.txt ab.txt 上面命令中，??匹配了两个字符。 ? 字符扩展属于文件名扩展，只有文件确实存在的前提下，才会发生扩展。如果文件不存在，扩展就不会发生。 # 当前目录有 a.txt 文件 $ echo ?.txt a.txt # 当前目录为空目录 $ echo ?.txt ?.txt 上面例子中，如果?.txt可以扩展成文件名，echo命令会输出扩展后的结果；如果不能扩展成文件名，echo就会原样输出?.txt。","s":"? 字符扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#-字符扩展","p":1584},{"i":1592,"t":"*字符代表文件路径里面的任意数量的任意字符，包括零个字符。 # 存在文件 a.txt、b.txt 和 ab.txt $ ls *.txt a.txt b.txt ab.txt 上面例子中，*.txt代表后缀名为.txt的所有文件。 如果想输出当前目录的所有文件，直接用*即可。 $ ls * *可以匹配空字符，下面是一个例子。 # 存在文件 a.txt、b.txt 和 ab.txt $ ls a*.txt a.txt ab.txt $ ls *b* b.txt ab.txt 注意，*不会匹配隐藏文件（以.开头的文件），即ls *不会输出隐藏文件。 如果要匹配隐藏文件，需要写成.*。 # 显示所有隐藏文件 $ echo .* 如果要匹配隐藏文件，同时要排除.和..这两个特殊的隐藏文件，可以与方括号扩展结合使用，写成.[!.]*。 $ echo .[!.]* 注意，*字符扩展属于文件名扩展，只有文件确实存在的前提下才会扩展。如果文件不存在，就会原样输出。 # 当前目录不存在 c 开头的文件 $ echo c*.txt c*.txt 上面例子中，当前目录里面没有c开头的文件，导致c*.txt会原样输出。 *只匹配当前目录，不会匹配子目录。 # 子目录有一个 a.txt # 无效的写法 $ ls *.txt # 有效的写法 $ ls */*.txt 上面的例子，文本文件在子目录，*.txt不会产生匹配，必须写成*/*.txt。有几层子目录，就必须写几层星号。 Bash 4.0 引入了一个参数globstar，当该参数打开时，允许**匹配零个或多个子目录。因此，**/*.txt可以匹配顶层的文本文件和任意深度子目录的文本文件。详细介绍请看后面shopt命令的介绍。","s":"* 字符扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#-字符扩展-1","p":1584},{"i":1594,"t":"方括号扩展的形式是[...]，只有文件确实存在的前提下才会扩展。如果文件不存在，就会原样输出。括号之中的任意一个字符。比如，[aeiou]可以匹配五个元音字母中的任意一个。 # 存在文件 a.txt 和 b.txt $ ls [ab].txt a.txt b.txt # 只存在文件 a.txt $ ls [ab].txt a.txt 上面例子中，[ab]可以匹配a或b，前提是确实存在相应的文件。 方括号扩展属于文件名匹配，即扩展后的结果必须符合现有的文件路径。如果不存在匹配，就会保持原样，不进行扩展。 # 不存在文件 a.txt 和 b.txt $ ls [ab].txt ls: 无法访问'[ab].txt': 没有那个文件或目录 上面例子中，由于扩展后的文件不存在，[ab].txt就原样输出了，导致ls命名报错。 方括号扩展还有两种变体：[^...]和[!...]。它们表示匹配不在方括号里面的字符，这两种写法是等价的。比如，[^abc]或[!abc]表示匹配除了a、b、c以外的字符。 # 存在 aaa、bbb、aba 三个文件 $ ls ?[!a]? aba bbb 上面命令中，[!a]表示文件名第二个字符不是a的文件名，所以返回了aba和bbb两个文件。 注意，如果需要匹配[字符，可以放在方括号内，比如[[aeiou]。如果需要匹配连字号-，只能放在方括号内部的开头或结尾，比如[-aeiou]或[aeiou-]。","s":"方括号扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#方括号扩展","p":1584},{"i":1596,"t":"方括号扩展有一个简写形式[start-end]，表示匹配一个连续的范围。比如，[a-c]等同于[abc]，[0-9]匹配[0123456789]。 # 存在文件 a.txt、b.txt 和 c.txt $ ls [a-c].txt a.txt b.txt c.txt # 存在文件 report1.txt、report2.txt 和 report3.txt $ ls report[0-9].txt report1.txt report2.txt report3.txt ... 下面是一些常用简写的例子。 [a-z]：所有小写字母。 [a-zA-Z]：所有小写字母与大写字母。 [a-zA-Z0-9]：所有小写字母、大写字母与数字。 [abc]*：所有以a、b、c字符之一开头的文件名。 program.[co]：文件program.c与文件program.o。 BACKUP.[0-9][0-9][0-9]：所有以BACKUP.开头，后面是三个数字的文件名。 这种简写形式有一个否定形式[!start-end]，表示匹配不属于这个范围的字符。比如，[!a-zA-Z]表示匹配非英文字母的字符。 $ ls report[!1–3].txt report4.txt report5.txt 上面代码中，[!1-3]表示排除 1、2 和 3。","s":"[start-end] 扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#start-end-扩展","p":1584},{"i":1598,"t":"大括号扩展{...}表示分别扩展成大括号里面的所有值，各个值之间使用逗号分隔。比如，{1,2,3}扩展成1 2 3。 $ echo {1,2,3} 1 2 3 $ echo d{a,e,i,u,o}g dag deg dig dug dog $ echo Front-{A,B,C}-Back Front-A-Back Front-B-Back Front-C-Back 注意，大括号扩展不是文件名扩展。它会扩展成所有给定的值，而不管是否有对应的文件存在。 $ ls {a,b,c}.txt ls: 无法访问'a.txt': 没有那个文件或目录 ls: 无法访问'b.txt': 没有那个文件或目录 ls: 无法访问'c.txt': 没有那个文件或目录 上面例子中，即使不存在对应的文件，{a,b,c}依然扩展成三个文件名，导致ls命令报了三个错误。 另一个需要注意的地方是，大括号内部的逗号前后不能有空格。否则，大括号扩展会失效。 $ echo {1 , 2} {1 , 2} 上面例子中，逗号前后有空格，Bash 就会认为这不是大括号扩展，而是三个独立的参数。 逗号前面可以没有值，表示扩展的第一项为空。 $ cp a.log{,.bak} # 等同于 # cp a.log a.log.bak 大括号可以嵌套。 $ echo {j{p,pe}g,png} jpg jpeg png $ echo a{A{1,2},B{3,4}}b aA1b aA2b aB3b aB4b 大括号也可以与其他模式联用，并且总是先于其他模式进行扩展。 $ echo /bin/{cat,b*} /bin/cat /bin/b2sum /bin/base32 /bin/base64 ... ... # 基本等同于 $ echo /bin/cat;echo /bin/b* 上面例子中，会先进行大括号扩展，然后进行*扩展，等同于执行两条echo命令。 大括号可以用于多字符的模式，方括号不行（只能匹配单字符）。 $ echo {cat,dog} cat dog 由于大括号扩展{...}不是文件名扩展，所以它总是会扩展的。这与方括号扩展[...]完全不同，如果匹配的文件不存在，方括号就不会扩展。这一点要注意区分。 # 不存在 a.txt 和 b.txt $ echo [ab].txt [ab].txt $ echo {a,b}.txt a.txt b.txt 上面例子中，如果不存在a.txt和b.txt，那么[ab].txt就会变成一个普通的文件名，而{a,b}.txt可以照样扩展。","s":"大括号扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#大括号扩展","p":1584},{"i":1600,"t":"大括号扩展有一个简写形式{start..end}，表示扩展成一个连续序列。比如，{a..z}可以扩展成 26 个小写英文字母。 $ echo {a..c} a b c $ echo d{a..d}g dag dbg dcg ddg $ echo {1..4} 1 2 3 4 $ echo Number_{1..5} Number_1 Number_2 Number_3 Number_4 Number_5 这种简写形式支持逆序。 $ echo {c..a} c b a $ echo {5..1} 5 4 3 2 1 注意，如果遇到无法理解的简写，大括号模式就会原样输出，不会扩展。 $ echo {a1..3c} {a1..3c} 这种简写形式可以嵌套使用，形成复杂的扩展。 $ echo .{mp{3..4},m4{a,b,p,v}} .mp3 .mp4 .m4a .m4b .m4p .m4v 大括号扩展的常见用途为新建一系列目录。 $ mkdir {2007..2009}-{01..12} 上面命令会新建 36 个子目录，每个子目录的名字都是”年份 - 月份“。 这个写法的另一个常见用途，是直接用于for循环。 for i in {1..4} do echo $i done 上面例子会循环 4 次。 如果整数前面有前导0，扩展输出的每一项都有前导0。 $ echo {01..5} 01 02 03 04 05 $ echo {001..5} 001 002 003 004 005 这种简写形式还可以使用第二个双点号（start..end..step），用来指定扩展的步长。 $ echo {0..8..2} 0 2 4 6 8 上面代码将0扩展到8，每次递增的长度为2，所以一共输出 5 个数字。 多个简写形式连用，会有循环处理的效果。 $ echo {a..c}{1..3} a1 a2 a3 b1 b2 b3 c1 c2 c3","s":"{start..end} 扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#startend-扩展","p":1584},{"i":1602,"t":"Bash 将美元符号$开头的词元视为变量，将其扩展成变量值，详见《Bash 变量》一章。 $ echo $SHELL /bin/bash 变量名除了放在美元符号后面，也可以放在${}里面。 $ echo ${SHELL} /bin/bash ${!string*}或${!string@}返回所有匹配给定字符串string的变量名。 $ echo ${!S*} SECONDS SHELL SHELLOPTS SHLVL SSH_AGENT_PID SSH_AUTH_SOCK 上面例子中，${!S*}扩展成所有以S开头的变量名。","s":"变量扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#变量扩展","p":1584},{"i":1604,"t":"$(...)可以扩展成另一个命令的运行结果，该命令的所有输出都会作为返回值。 $ echo $(date) Tue Jan 28 00:01:13 CST 2020 上面例子中，$(date)返回date命令的运行结果。 还有另一种较老的语法，子命令放在反引号之中，也可以扩展成命令的运行结果。 $ echo `date` Tue Jan 28 00:01:13 CST 2020 $(...)可以嵌套，比如$(ls $(pwd))。","s":"子命令扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#子命令扩展","p":1584},{"i":1606,"t":"$((...))可以扩展成整数运算的结果，详见《Bash 的算术运算》一章。 $ echo $((2 + 2)) 4","s":"算术扩展","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#算术扩展","p":1584},{"i":1608,"t":"[[:class:]]表示一个字符类，扩展成某一类特定字符之中的一个。常用的字符类如下。 [[:alnum:]]：匹配任意英文字母与数字 [[:alpha:]]：匹配任意英文字母 [[:blank:]]：空格和 Tab 键。 [[:cntrl:]]：ASCII 码 0-31 的不可打印字符。 [[:digit:]]：匹配任意数字 0-9。 [[:graph:]]：A-Z、a-z、0-9 和标点符号。 [[:lower:]]：匹配任意小写字母 a-z。 [[:print:]]：ASCII 码 32-127 的可打印字符。 [[:punct:]]：标点符号（除了 A-Z、a-z、0-9 的可打印字符）。 [[:space:]]：空格、Tab、LF（10）、VT（11）、FF（12）、CR（13）。 [[:upper:]]：匹配任意大写字母 A-Z。 [[:xdigit:]]：16 进制字符（A-F、a-f、0-9）。 请看下面的例子。 $ echo [[:upper:]]* 上面命令输出所有大写字母开头的文件名。 字符类的第一个方括号后面，可以加上感叹号!（或^），表示否定。比如，[![:digit:]](或[^[:digit:]]) 匹配所有非数字。 $ echo [![:digit:]]* 上面命令输出所有不以数字开头的文件名。 字符类也属于文件名扩展，如果没有匹配的文件名，字符类就会原样输出。 # 不存在以大写字母开头的文件 $ echo [[:upper:]]* [[:upper:]]* 上面例子中，由于没有可匹配的文件，字符类就原样输出了。","s":"字符类","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#字符类","p":1584},{"i":1610,"t":"通配符有一些使用注意点，不可不知。 （1）通配符是先解释，再执行。 Bash 接收到命令以后，发现里面有通配符，会进行通配符扩展，然后再执行命令。 $ ls a*.txt ab.txt 上面命令的执行过程是，Bash 先将a*.txt扩展成ab.txt，然后再执行ls ab.txt。 （2）文件名扩展在不匹配时，会原样输出。 文件名扩展在没有可匹配的文件时，会原样输出。 # 不存在 r 开头的文件名 $ echo r* r* 上面代码中，由于不存在r开头的文件名，r*会原样输出。 下面是另一个例子。 $ ls *.csv ls: *.csv: No such file or directory 另外，前面已经说过，大括号扩展{...}不是文件名扩展。 （3）只适用于单层路径。 所有文件名扩展只匹配单层路径，不能跨目录匹配，即无法匹配子目录里面的文件。或者说，?或*这样的通配符，不能匹配路径分隔符（/）。 如果要匹配子目录里面的文件，可以写成下面这样。 $ ls */*.txt Bash 4.0 新增了一个globstar参数，允许**匹配零个或多个子目录，详见后面shopt命令的介绍。 （4）文件名可以使用通配符。 Bash 允许文件名使用通配符，即文件名包括特殊字符。这时引用文件名，需要把文件名放在单引号或双引号里面。 $ touch 'fo*' $ ls fo* 上面代码创建了一个fo*文件，这时*就是文件名的一部分。","s":"使用注意点","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#使用注意点","p":1584},{"i":1612,"t":"量词语法用来控制模式匹配的次数。它只有在 Bash 的extglob参数打开的情况下才能使用，不过一般是默认打开的。下面的命令可以查询。 $ shopt extglob extglob on 如果extglob参数是关闭的，可以用下面的命令打开。 $ shopt -s extglob 量词语法有下面几个。 ?(pattern-list)：模式匹配零次或一次。 *(pattern-list)：模式匹配零次或多次。 +(pattern-list)：模式匹配一次或多次。 @(pattern-list)：只匹配一次模式。 !(pattern-list)：匹配给定模式以外的任何内容。 $ ls abc?(.)txt abctxt abc.txt 上面例子中，?(.)匹配零个或一个点。 $ ls abc?(def) abc abcdef 上面例子中，?(def)匹配零个或一个def。 $ ls abc@(.txt|.php) abc.php abc.txt 上面例子中，@(.txt|.php)匹配文件有且只有一个.txt或.php后缀名。 $ ls abc+(.txt) abc.txt abc.txt.txt 上面例子中，+(.txt)匹配文件有一个或多个.txt后缀名。 $ ls a!(b).txt a.txt abb.txt ac.txt 上面例子中，!(b)表示匹配单个字母b以外的任意内容，所以除了ab.txt以外，其他文件名都能匹配。 量词语法也属于文件名扩展，如果不存在可匹配的文件，就会原样输出。 # 没有 abc 开头的文件名 $ ls abc?(def) ls: 无法访问'abc?(def)': 没有那个文件或目录 上面例子中，由于没有可匹配的文件，abc?(def)就原样输出，导致ls命令报错。","s":"量词语法","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#量词语法","p":1584},{"i":1614,"t":"shopt命令可以调整 Bash 的行为。它有好几个参数跟通配符扩展有关。 shopt命令的使用方法如下。 # 打开某个参数 $ shopt -s [optionname] # 关闭某个参数 $ shopt -u [optionname] # 查询某个参数关闭还是打开 $ shopt [optionname] （1）dotglob 参数 dotglob参数可以让扩展结果包括隐藏文件（即点开头的文件）。 正常情况下，扩展结果不包括隐藏文件。 $ ls * abc.txt 打开dotglob，就会包括隐藏文件。 $ shopt -s dotglob $ ls * abc.txt .config （2）nullglob 参数 nullglob参数可以让通配符不匹配任何文件名时，返回空字符。 默认情况下，通配符不匹配任何文件名时，会保持不变。 $ rm b* rm: 无法删除'b*': 没有那个文件或目录 上面例子中，由于当前目录不包括b开头的文件名，导致b*不会发生文件名扩展，保持原样不变，所以rm命令报错没有b*这个文件。 打开nullglob参数，就可以让不匹配的通配符返回空字符串。 $ shopt -s nullglob $ rm b* rm: 缺少操作数 上面例子中，由于没有b*匹配的文件名，所以rm b*扩展成了rm，导致报错变成了”缺少操作数“。 （3）failglob 参数 failglob参数使得通配符不匹配任何文件名时，Bash 会直接报错，而不是让各个命令去处理。 $ shopt -s failglob $ rm b* bash: 无匹配: b* 上面例子中，打开failglob以后，由于b*不匹配任何文件名，Bash 直接报错了，不再让rm命令去处理。 （4）extglob 参数 extglob参数使得 Bash 支持 ksh 的一些扩展语法。它默认应该是打开的。 $ shopt extglob extglob on 它的主要应用是支持量词语法。如果不希望支持量词语法，可以用下面的命令关闭。 $ shopt -u extglob （5）nocaseglob 参数 nocaseglob参数可以让通配符扩展不区分大小写。 $ shopt -s nocaseglob $ ls /windows/program* /windows/ProgramData /windows/Program Files /windows/Program Files (x86) 上面例子中，打开nocaseglob以后，program*就不区分大小写了，可以匹配ProgramData等。 （6）globstar 参数 globstar参数可以使得**匹配零个或多个子目录。该参数默认是关闭的。 假设有下面的文件结构。 a.txt sub1/b.txt sub1/sub2/c.txt 上面的文件结构中，顶层目录、第一级子目录sub1、第二级子目录sub1\\sub2里面各有一个文本文件。请问怎样才能使用通配符，将它们显示出来？ 默认情况下，只能写成下面这样。 $ ls *.txt */*.txt */*/*.txt a.txt sub1/b.txt sub1/sub2/c.txt 这是因为*只匹配当前目录，如果要匹配子目录，只能一层层写出来。 打开globstar参数以后，**匹配零个或多个子目录。因此，**/*.txt就可以得到想要的结果。 $ shopt -s globstar $ ls **/*.txt a.txt sub1/b.txt sub1/sub2/c.txt","s":"shopt 命令","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#shopt-命令","p":1584},{"i":1616,"t":"Think You Understand Wildcards? Think Again Advanced Wildcard Patterns Most People Don’t Know","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/expansion","h":"#参考链接","p":1584},{"i":1618,"t":"本章介绍 Bash 函数的用法。","s":"Bash 函数","u":"/docs/modern-linux/bash-tutorial/function","h":"","p":1617},{"i":1620,"t":"函数（function）是可以重复使用的代码片段，有利于代码的复用。它与别名（alias）的区别是，别名只适合封装简单的单个命令，函数则可以封装复杂的多行命令。 函数总是在当前 Shell 执行，这是跟脚本的一个重大区别，Bash 会新建一个子 Shell 执行脚本。如果函数与脚本同名，函数会优先执行。但是，函数的优先级不如别名，即如果函数与别名同名，那么别名优先执行。 Bash 函数定义的语法有两种。 # 第一种 fn() { # codes } # 第二种 function fn() { # codes } 上面代码中，fn是自定义的函数名，函数代码就写在大括号之中。这两种写法是等价的。 下面是一个简单函数的例子。 hello() { echo \"Hello $1\" } 上面代码中，函数体里面的$1表示函数调用时的第一个参数。 调用时，就直接写函数名，参数跟在函数名后面。 $ hello world Hello world 下面是一个多行函数的例子，显示当前日期时间。 today() { echo -n \"Today's date is: \" date +\"%A, %B %-d, %Y\" } 删除一个函数，可以使用unset命令。 unset -f functionName 查看当前 Shell 已经定义的所有函数，可以使用declare命令。 $ declare -f 上面的declare命令不仅会输出函数名，还会输出所有定义。输出顺序是按照函数名的字母表顺序。由于会输出很多内容，最好通过管道命令配合more或less使用。 declare命令还支持查看单个函数的定义。 $ declare -f functionName declare -F可以输出所有已经定义的函数名，不含函数体。 $ declare -F","s":"简介","u":"/docs/modern-linux/bash-tutorial/function","h":"#简介","p":1617},{"i":1622,"t":"函数体内可以使用参数变量，获取函数参数。函数的参数变量，与脚本参数变量是一致的。 $1~$9：函数的第一个到第 9 个的参数。 $0：函数所在的脚本名。 $#：函数的参数总数。 $@：函数的全部参数，参数之间使用空格分隔。 $*：函数的全部参数，参数之间使用变量$IFS值的第一个字符分隔，默认为空格，但是可以自定义。 如果函数的参数多于 9 个，那么第 10 个参数可以用${10}的形式引用，以此类推。 下面是一个示例脚本test.sh。 #!/bin/bash # test.sh function alice { echo \"alice: $@\" echo \"$0: $1 $2 $3 $4\" echo \"$# arguments\" } alice in wonderland 运行该脚本，结果如下。 $ bash test.sh alice: in wonderland test.sh: in wonderland 2 arguments 上面例子中，由于函数alice只有第一个和第二个参数，所以第三个和第四个参数为空。 下面是一个日志函数的例子。 function log_msg { echo \"[$(date '+ %F %T') ]: $@\" } 使用方法如下。 $ log_msg \"This is sample log message\" [ 2018-08-16 19:56:34 ]: This is sample log message","s":"参数变量","u":"/docs/modern-linux/bash-tutorial/function","h":"#参数变量","p":1617},{"i":1624,"t":"return命令用于从函数返回一个值。函数执行到这条命令，就不再往下执行了，直接返回了。 function func_return_value { return 10 } 函数将返回值返回给调用者。如果命令行直接执行函数，下一个命令可以用$?拿到返回值。 $ func_return_value $ echo \"Value returned by function is: $?\" Value returned by function is: 10 return后面不跟参数，只用于返回也是可以的。 function name { commands return }","s":"return 命令","u":"/docs/modern-linux/bash-tutorial/function","h":"#return-命令","p":1617},{"i":1626,"t":"Bash 函数体内直接声明的变量，属于全局变量，整个脚本都可以读取。这一点需要特别小心。 # 脚本 test.sh fn() { foo=1 echo \"fn: foo = $foo\" } fn echo \"global: foo = $foo\" 上面脚本的运行结果如下。 $ bash test.sh fn: foo = 1 global: foo = 1 上面例子中，变量$foo是在函数fn内部声明的，函数体外也可以读取。 函数体内不仅可以声明全局变量，还可以修改全局变量。 #! /bin/bash foo=1 fn() { foo=2 } fn echo $foo 上面代码执行后，输出的变量$foo值为 2。 函数里面可以用local命令声明局部变量。 #! /bin/bash # 脚本 test.sh fn() { local foo foo=1 echo \"fn: foo = $foo\" } fn echo \"global: foo = $foo\" 上面脚本的运行结果如下。 $ bash test.sh fn: foo = 1 global: foo = 上面例子中，local命令声明的$foo变量，只在函数体内有效，函数体外没有定义。","s":"全局变量和局部变量，local 命令","u":"/docs/modern-linux/bash-tutorial/function","h":"#全局变量和局部变量local-命令","p":1617},{"i":1628,"t":"How to define and use functions in Linux Shell Script, by Pradeep Kumar","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/function","h":"#参考链接","p":1617},{"i":1630,"t":"本章介绍 Bash 的最基本语法。","s":"Bash 的基本语法","u":"/docs/modern-linux/bash-tutorial/grammar","h":"","p":1629},{"i":1632,"t":"由于后面的例子会大量用到echo命令，这里先介绍这个命令。 echo命令的作用是在屏幕输出一行文本，可以将该命令的参数原样输出。 $ echo hello world hello world 上面例子中，echo的参数是hello world，可以原样输出。 如果想要输出的是多行文本，即包括换行符。这时就需要把多行文本放在引号里面。 $ echo \"<HTML> <HEAD> <TITLE>Page Title</TITLE> </HEAD> <BODY> Page body. </BODY> </HTML>\" 上面例子中，echo可以原样输出多行文本。","s":"echo 命令","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#echo-命令","p":1629},{"i":1634,"t":"默认情况下，echo输出的文本末尾会有一个回车符。-n参数可以取消末尾的回车符，使得下一个提示符紧跟在输出内容的后面。 $ echo -n hello world hello world$ 上面例子中，world后面直接就是下一行的提示符$。 $ echo a echo b a b $ echo -n a echo b ab 上面例子中，-n参数可以让两个echo命令的输出连在一起，出现在同一行。","s":"-n参数","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#-n参数","p":1629},{"i":1636,"t":"-e参数会解释引号（双引号和单引号）里面的特殊字符（比如换行符\\n）。如果不使用-e参数，即默认情况下，引号会让特殊字符变成普通字符，echo不解释它们，原样输出。 $ echo \"Hello\\nWorld\" Hello\\nWorld # 双引号的情况 $ echo -e \"Hello\\nWorld\" Hello World # 单引号的情况 $ echo -e 'Hello\\nWorld' Hello World 上面代码中，-e参数使得\\n解释为换行符，导致输出内容里面出现换行。","s":"-e参数","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#-e参数","p":1629},{"i":1638,"t":"命令行环境中，主要通过使用 Shell 命令，进行各种操作。Shell 命令基本都是下面的格式。 $ command [ arg1 ... [ argN ]] 上面代码中，command是具体的命令或者一个可执行文件，arg1 ... argN是传递给命令的参数，它们是可选的。 $ ls -l 上面这个命令中，ls是命令，-l是参数。 有些参数是命令的配置项，这些配置项一般都以一个连词线开头，比如上面的-l。同一个配置项往往有长和短两种形式，比如-l是短形式，--list是长形式，它们的作用完全相同。短形式便于手动输入，长形式一般用在脚本之中，可读性更好，利于解释自身的含义。 # 短形式 $ ls -r # 长形式 $ ls --reverse 上面命令中，-r是短形式，--reverse是长形式，作用完全一样。前者便于输入，后者便于理解。 Bash 单个命令一般都是一行，用户按下回车键，就开始执行。有些命令比较长，写成多行会有利于阅读和编辑，这时可以在每一行的结尾加上反斜杠，Bash 就会将下一行跟当前行放在一起解释。 $ echo foo bar # 等同于 $ echo foo \\ bar","s":"命令格式","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#命令格式","p":1629},{"i":1640,"t":"Bash 使用空格（或 Tab 键）区分不同的参数。 $ command foo bar 上面命令中，foo和bar之间有一个空格，所以 Bash 认为它们是两个参数。 如果参数之间有多个空格，Bash 会自动忽略多余的空格。 $ echo this is a test this is a test 上面命令中，a和test之间有多个空格，Bash 会忽略多余的空格。","s":"空格","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#空格","p":1629},{"i":1642,"t":"分号（;）是命令的结束符，使得一行可以放置多个命令，上一个命令执行结束后，再执行第二个命令。 $ clear ls 上面例子中，Bash 先执行clear命令，执行完成后，再执行ls命令。 注意，使用分号时，第二个命令总是接着第一个命令执行，不管第一个命令执行成功或失败。","s":"分号","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#分号","p":1629},{"i":1644,"t":"除了分号，Bash 还提供两个命令组合符&&和||，允许更好地控制多个命令之间的继发关系。 Command1 && Command2 上面命令的意思是，如果Command1命令运行成功，则继续运行Command2命令。 Command1 || Command2 上面命令的意思是，如果Command1命令运行失败，则继续运行Command2命令。 下面是一些例子。 $ cat filelist.txt ls -l filelist.txt 上面例子中，只要cat命令执行结束，不管成功或失败，都会继续执行ls命令。 $ cat filelist.txt && ls -l filelist.txt 上面例子中，只有cat命令执行成功，才会继续执行ls命令。如果cat执行失败（比如不存在文件flielist.txt），那么ls命令就不会执行。 $ mkdir foo || mkdir bar 上面例子中，只有mkdir foo命令执行失败（比如foo目录已经存在），才会继续执行mkdir bar命令。如果mkdir foo命令执行成功，就不会创建bar目录了。","s":"命令的组合符&&和||","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#命令的组合符和","p":1629},{"i":1646,"t":"Bash 本身内置了很多命令，同时也可以执行外部程序。怎么知道一个命令是内置命令，还是外部程序呢？ type命令用来判断命令的来源。 $ type echo echo is a shell builtin $ type ls ls is hashed (/bin/ls) 上面代码中，type命令告诉我们，echo是内部命令，ls是外部程序（/bin/ls）。 type命令本身也是内置命令。 $ type type type is a shell builtin 如果要查看一个命令的所有定义，可以使用type命令的-a参数。 $ type -a echo echo is shell builtin echo is /usr/bin/echo echo is /bin/echo 上面代码表示，echo命令既是内置命令，也有对应的外部程序。 type命令的-t参数，可以返回一个命令的类型：别名（alias），关键词（keyword），函数（function），内置命令（builtin）和文件（file）。 $ type -t bash file $ type -t if keyword 上面例子中，bash是文件，if是关键词。","s":"type 命令","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#type-命令","p":1629},{"i":1648,"t":"Bash 提供很多快捷键，可以大大方便操作。下面是一些最常用的快捷键，完整的介绍参见《行操作》一章。 Ctrl + L：清除屏幕并将当前行移到页面顶部。 Ctrl + C：中止当前正在执行的命令。 Shift + PageUp：向上滚动。 Shift + PageDown：向下滚动。 Ctrl + U：从光标位置删除到行首。 Ctrl + K：从光标位置删除到行尾。 Ctrl + W：删除光标位置前一个单词。 Ctrl + D：关闭 Shell 会话。 ↑，↓：浏览已执行命令的历史记录。 除了上面的快捷键，Bash 还具有自动补全功能。命令输入到一半的时候，可以按下 Tab 键，Bash 会自动完成剩下的部分。比如，输入tou，然后按一下 Tab 键，Bash 会自动补上ch。 除了命令的自动补全，Bash 还支持路径的自动补全。有时，需要输入很长的路径，这时只需要输入前面的部分，然后按下 Tab 键，就会自动补全后面的部分。如果有多个可能的选择，按两次 Tab 键，Bash 会显示所有选项，让你选择。","s":"快捷键","u":"/docs/modern-linux/bash-tutorial/grammar","h":"#快捷键","p":1629},{"i":1651,"t":"Bash 会保留用户的操作历史，即用户输入的每一条命令都会记录，默认是保存最近的 500 条命令。有了操作历史以后，就可以使用方向键的↑和↓，快速浏览上一条和下一条命令。 退出当前 Shell 的时候，Bash 会将用户在当前 Shell 的操作历史写入~/.bash_history文件，该文件默认储存 500 个操作。 环境变量HISTFILE总是指向这个文件。 $ echo $HISTFILE /home/me/.bash_history","s":"简介","u":"/docs/modern-linux/bash-tutorial/history","h":"#简介","p":1649},{"i":1653,"t":"history命令会输出.bash_history文件的全部内容，即输出操作历史。 $ history ... 498 echo Goodbye 499 ls ~ 500 cd 用户可以使用这个命令，查看最近的操作。相比直接读取.bash_history文件，它的优势在于所有命令之前加上了行号。最近的操作在最后面，行号最大。 如果想搜索某个以前执行的命令，可以配合grep命令搜索操作历史。 $ history | grep /usr/bin 上面命令返回.bash_history文件里面，那些包含/usr/bin的命令。 history命令的-c参数可以清除操作历史，即清空.bash_history文件。 $ history -c","s":"history 命令","u":"/docs/modern-linux/bash-tutorial/history","h":"#history-命令","p":1649},{"i":1656,"t":"通过定制环境变量HISTTIMEFORMAT，history的输出结果还可以显示每个操作的时间。 $ export HISTTIMEFORMAT='%F %T ' $ history 1 2013-06-09 10:40:12 cat /etc/issue 2 2013-06-09 10:40:12 clear 上面代码中，%F相当于%Y - %m - %d（年 - 月 - 日），%T相当于 %H : %M : %S（时：分：秒）。 只要设置HISTTIMEFORMAT这个环境变量，就会在.bash_history文件保存命令的执行时间戳。如果不设置，就不会保存时间戳。","s":"HISTTIMEFORMAT","u":"/docs/modern-linux/bash-tutorial/history","h":"#histtimeformat","p":1649},{"i":1658,"t":"环境变量HISTSIZE设置保存历史操作的数量。 $ export HISTSIZE=10000 上面命令设置保存过去 10000 条操作历史。 如果不希望保存本次操作的历史，可以设置HISTSIZE等于 0。 export HISTSIZE=0 如果HISTSIZE=0写入用户主目录的~/.bashrc文件，那么就不会保留该用户的操作历史。如果写入/etc/profile，整个系统都不会保留操作历史。","s":"HISTSIZE","u":"/docs/modern-linux/bash-tutorial/history","h":"#histsize","p":1649},{"i":1660,"t":"环境变量HISTIGNORE可以设置哪些命令不写入操作历史。 export HISTIGNORE='pwd:ls:exit' 上面示例设置，pwd、ls、exit这三个命令不写入操作历史。","s":"HISTIGNORE","u":"/docs/modern-linux/bash-tutorial/history","h":"#histignore","p":1649},{"i":1662,"t":"输入命令时，按下Ctrl + r快捷键，就可以搜索操作历史，选择以前执行过的命令。 Ctrl + r相当于打开一个.bash_history文件的搜索接口，直接键入命令的开头部分，Shell 就会自动在该文件中反向查询（即先查询最近的命令），显示最近一条匹配的结果，这时按下回车键，就会执行那条命令。","s":"Ctrl + r","u":"/docs/modern-linux/bash-tutorial/history","h":"#ctrl--r","p":1649},{"i":1665,"t":"操作历史的每一条记录都有行号。知道了命令的行号以后，可以用感叹号 + 行号执行该命令。如果想要执行.bash_history里面的第 8 条命令，可以像下面这样操作。 $ !8","s":"! + 行号","u":"/docs/modern-linux/bash-tutorial/history","h":"#--行号","p":1649},{"i":1667,"t":"如果想执行本次 Shell 对话中倒数的命令，比如执行倒数第 3 条命令，就可以输入!-3。 $ touch a.txt $ touch b.txt $ touch c.txt $ !-3 touch a.txt 上面示例中，!-3返回倒数第 3 条命令，即touch a.txt。 它跟! + 行号的主要区别是，后者是在.bash_history文件中从头开始计算行数，而!- 数字是从底部开始向上计算行数。","s":"!- 数字","u":"/docs/modern-linux/bash-tutorial/history","h":"#--数字","p":1649},{"i":1669,"t":"!!命令返回上一条命令。如果需要重复执行某一条命令，就可以不断键入!!，这样非常方便。它等同于!-1。 $ echo hello hello $ !! echo hello hello 上面示例中，!!会返回并执行上一条命令echo hello。 有时候，我们使用某条命令，系统报错没有权限，这时就可以使用sudo !!。 # 报错，没有执行权限 $ yum update $ sudo !! sudo yum update 上面示例中，sudo !!返回sudo yum update，从而就可以正确执行了。","s":"!!","u":"/docs/modern-linux/bash-tutorial/history","h":"","p":1649},{"i":1671,"t":"感叹号 + 搜索词可以快速执行匹配的命令。 $ echo Hello World Hello World $ echo Goodbye Goodbye $ !e echo Goodbye Goodbye 上面例子中，!e表示找出操作历史之中，最近的那一条以e开头的命令并执行。Bash 会先输出那一条命令echo Goodbye，然后直接执行。 同理，!echo也会执行最近一条以echo开头的命令。 $ !echo echo Goodbye Goodbye $ !echo H echo Goodbye H Goodbye H $ !echo H G echo Goodbye H G Goodbye H G 注意，感叹号 + 搜索词语法只会匹配命令，不会匹配参数。所以!echo H不会执行echo Hello World，而是会执行echo Goodbye，并把参数H附加在这条命令之后。同理，!echo H G也是等同于echo Goodbye命令之后附加H G。 由于感叹号 + 搜索词会扩展成以前执行过的命令，所以含有!的字符串放在双引号里面，必须非常小心，如果它后面有非空格的字符，就很有可能报错。 $ echo \"I say:\\\"hello!\\\"\" bash: !\\: event not found 上面的命令会报错，原因是感叹号后面是一个反斜杠，Bash 会尝试寻找，以前是否执行过反斜杠开头的命令，一旦找不到就会报错。解决方法就是在感叹号前面，也加上反斜杠。 $ echo \"I say:\\\"hello\\!\\\"\" I say:\"hello\\!\"","s":"! + 搜索词","u":"/docs/modern-linux/bash-tutorial/history","h":"#--搜索词","p":1649},{"i":1673,"t":"!? + 搜索词可以搜索命令的任意部分，包括参数部分。它跟! + 搜索词的主要区别是，后者是从行首开始匹配。 $ cat hello.txt Hello world ..! $ !?hello.txt cat hello.txt Hello world ..! 上面示例中，!?hello.txt会返回最近一条包括hello.txt的命令。","s":"!? + 搜索词","u":"/docs/modern-linux/bash-tutorial/history","h":"#--搜索词-1","p":1649},{"i":1675,"t":"!$代表上一个命令的最后一个参数，它的另一种写法是$_。 !*代表上一个命令的所有参数，即除了命令以外的所有部分。 $ cp a.txt b.txt $ echo !$ b.txt $ cp a.txt b.txt $ echo !* a.txt b.txt 上面示例中，!$代表上一个命令的最后一个参数（b.txt），!*代表上一个命令的所有参数（a.txt b.txt）。 如果想匹配上一个命令的某个指定位置的参数，使用!:n。 $ ls a.txt b.txt c.txt $ echo !:2 b.txt 上面示例中，!:2返回上一条命令的第二个参数（b.txt）。 这种写法的!:$，代表上一个命令的最后一个参数。事实上，!$就是!:$的简写形式。 $ ls a.txt b.txt c.txt $ echo !:$ echo c.txt c.txt 上面示例中，!:$代表上一条命令的最后一个参数（c.txt）。 如果想匹配更久以前的命令的参数，可以使用!<命令>:n（指定位置的参数）和!<命令>:$（最后一个参数）。 $ ls !mkdir:$ 上面示例中，!mkdir:$会返回前面最后一条mkdir命令的最后一个参数。 $ ls !mk:2 上面示例中，!mk:2会返回前面最后一条以mk开头的命令的第二个参数。","s":"!$，!*","u":"/docs/modern-linux/bash-tutorial/history","h":"#-1","p":1649},{"i":1677,"t":"如果只是想输出上一条命令，而不是执行它，可以使用!:p。 $ echo hello $ !:p echo hello 上面示例中，!:p只会输出echo hello，而不会执行这条命令。 如果想输出最近一条匹配的命令，而不执行它，可以使用!<命令>:p。 $ !su:p 上面示例中，!su:p会输出前面最近一条以su开头的命令，而不执行它。","s":"!:p","u":"/docs/modern-linux/bash-tutorial/history","h":"#-2","p":1649},{"i":1679,"t":"^string1^string2用来执行最近一条包含string1的命令，将其替换成string2。 $ rm /var/log/httpd/error.log $ ^error^access rm /var/log/httpd/access.log 上面示例中，^error^access将最近一条含有error的命令里面的error，替换成access。","s":"^string1^string2","u":"/docs/modern-linux/bash-tutorial/history","h":"#string1string2","p":1649},{"i":1681,"t":"上面的那些快捷命令（比如!!命令），都是找到匹配的命令后，直接执行。如果希望增加一个确认步骤，先输出是什么命令，让用户确认后再执行，可以打开 Shell 的histverify选项。 $ shopt -s histverify 打开histverify这个选项后，使用!快捷键所返回的命令，就会先输出，等到用户按下回车键后再执行。","s":"histverify 参数","u":"/docs/modern-linux/bash-tutorial/history","h":"#histverify-参数","p":1649},{"i":1683,"t":"下面是其他一些与操作历史相关的快捷键。 Ctrl + p：显示上一个命令，与向上箭头效果相同（previous）。 Ctrl + n：显示下一个命令，与向下箭头效果相同（next）。 Alt + <：显示第一个命令。 Alt + >：显示最后一个命令，即当前的命令。 Ctrl + o：执行历史文件里面的当前条目，并自动显示下一条命令。这对重复执行某个序列的命令很有帮助。","s":"快捷键","u":"/docs/modern-linux/bash-tutorial/history","h":"#快捷键","p":1649},{"i":1685,"t":"Bash bang commands: A must-know trick for the Linux command line","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/history","h":"#参考链接","p":1649},{"i":1687,"t":"Bash 是 Unix 系统和 Linux 系统的一种 Shell（命令行环境），是目前绝大多数 Linux 发行版的默认 Shell。","s":"Bash 简介","u":"/docs/modern-linux/bash-tutorial/intro","h":"","p":1686},{"i":1689,"t":"学习 Bash，首先需要理解 Shell 是什么。Shell 这个单词的原意是“外壳”，跟 kernel（内核）相对应，比喻内核外面的一层，即用户跟内核交互的对话界面。 具体来说，Shell 这个词有多种含义。 首先，Shell 是一个程序，提供一个与用户对话的环境。这个环境只有一个命令提示符，让用户从键盘输入命令，所以又称为命令行环境（command line interface，简写为 CLI）。Shell 接收到用户输入的命令，将命令送入操作系统执行，并将结果返回给用户。本书中，除非特别指明，Shell 指的就是命令行环境。 其次，Shell 是一个命令解释器，解释用户输入的命令。它支持变量、条件判断、循环操作等语法，所以用户可以用 Shell 命令写出各种小程序，又称为脚本（script）。这些脚本都通过 Shell 的解释执行，而不通过编译。 最后，Shell 是一个工具箱，提供了各种小工具，供用户方便地使用操作系统的功能。","s":"Shell 的含义","u":"/docs/modern-linux/bash-tutorial/intro","h":"#shell-的含义","p":1686},{"i":1691,"t":"Shell 有很多种，只要能给用户提供命令行环境的程序，都可以看作是 Shell。 历史上，主要的 Shell 有下面这些。 Bourne Shell (sh) Bourne Again shell (bash) C Shell (csh) TENEX C Shell (tcsh) Korn shell (ksh) Z Shell (zsh) Friendly Interactive Shell (fish) Bash 是目前最常用的 Shell，除非特别指明，下文的 Shell 和 Bash 当作同义词使用，可以互换。 下面的命令可以查看当前设备的默认 Shell。 $ echo $SHELL /bin/bash 当前正在使用的 Shell 不一定是默认 Shell，一般来说，ps命令结果的倒数第二行是当前 Shell。 $ ps PID TTY TIME CMD 4467 pts/0 00:00:00 bash 5379 pts/0 00:00:00 ps 上面示例中，ps命令结果的倒数第二行显示，运行的命令（cmd）是bash，表明当前正在使用的 Shell 是 Bash。 下面的命令可以查看当前的 Linux 系统安装的所有 Shell。 $ cat /etc/shells 上面三个命令中，$是命令行环境的提示符，用户只需要输入提示符后面的内容。 Linux 允许每个用户使用不同的 Shell，用户的默认 Shell 一般都是 Bash，或者与 Bash 兼容。 使用chsh命令，可以改变系统的默认 Shell。举例来说，要将默认 Shell 从 Bash 改成 Fish，首先要找出 Fish 可执行文件的位置。 $ which fish 上面命令找出 Fish 可执行文件的位置，一般是/usr/bin/fish。 然后，使用chsh命令切换默认 Shell。 $ chsh -s /usr/bin/fish 上面命令会将当前的默认 Shell 改成 Fish。","s":"Shell 的种类","u":"/docs/modern-linux/bash-tutorial/intro","h":"#shell-的种类","p":1686},{"i":1694,"t":"如果是不带有图形环境的 Linux 系统（比如专用于服务器的系统），启动后就直接是命令行环境。 不过，现在大部分的 Linux 发行版，尤其是针对普通用户的发行版，都是图形环境。用户登录系统后，自动进入图形环境，需要自己启动终端模拟器，才能进入命令行环境。 所谓“终端模拟器”（terminal emulator）就是一个模拟命令行窗口的程序，让用户在一个窗口中使用命令行环境，并且提供各种附加功能，比如调整颜色、字体大小、行距等等。 不同 Linux 发行版（准确地说是不同的桌面环境）带有的终端程序是不一样的，比如 KDE 桌面环境的终端程序是 konsole，Gnome 桌面环境的终端程序是 gnome-terminal，用户也可以安装第三方的终端程序。所有终端程序，尽管名字不同，基本功能都是一样的，就是让用户可以进入命令行环境，使用 Shell。","s":"终端模拟器","u":"/docs/modern-linux/bash-tutorial/intro","h":"#终端模拟器","p":1686},{"i":1696,"t":"进入命令行环境以后，用户会看到 Shell 的提示符。提示符往往是一串前缀，最后以一个美元符号$结尾，用户可以在这个符号后面输入各种命令。 [user@hostname] $ 上面例子中，完整的提示符是[user@hostname] $，其中前缀是用户名（user）加上@，再加主机名（hostname）。比如，用户名是bill，主机名是home-machine，前缀就是bill@home-machine。 注意，根用户（root）的提示符，不以美元符号（$）结尾，而以井号（#）结尾，用来提醒用户，现在具有根权限，可以执行各种操作，务必小心，不要出现误操作。这个符号是可以自己定义的，详见《命令提示符》一章。 为了简洁，后文的命令行提示符都只使用$表示。","s":"命令行提示符","u":"/docs/modern-linux/bash-tutorial/intro","h":"#命令行提示符","p":1686},{"i":1698,"t":"进入命令行环境以后，一般就已经打开 Bash 了。如果你的 Shell 不是 Bash，可以输入bash命令启动 Bash。 $ bash 退出 Bash 环境，可以使用exit命令，也可以同时按下Ctrl + d。 $ exit Bash 的基本用法就是在命令行输入各种命令，非常直观。作为练习，可以试着输入pwd命令。按下回车键，就会显示当前所在的目录。 $ pwd /home/me 如果不小心输入了pwe，会返回一个提示，表示输入出错，没有对应的可执行程序。 $ pwe bash: pwe：未找到命令","s":"进入和退出方法","u":"/docs/modern-linux/bash-tutorial/intro","h":"#进入和退出方法","p":1686},{"i":1700,"t":"Shell 伴随着 Unix 系统的诞生而诞生。 1969 年，Ken Thompson 和 Dennis Ritchie 开发了第一版的 Unix。 1971 年，Ken Thompson 编写了最初的 Shell，称为 Thompson shell，程序名是sh，方便用户使用 Unix。 1973 年至 1975 年间，John R. Mashey 扩展了最初的 Thompson shell，添加了编程功能，使得 Shell 成为一种编程语言。这个版本的 Shell 称为 Mashey shell。 1976 年，Stephen Bourne 结合 Mashey shell 的功能，重写一个新的 Shell，称为 Bourne shell。 1978 年，加州大学伯克利分校的 Bill Joy 开发了 C shell，为 Shell 提供 C 语言的语法，程序名是csh。它是第一个真正替代sh的 UNIX shell，被合并到 Berkeley UNIX 的 2BSD 版本中。 1979 年，UNIX 第七版发布，内置了 Bourne Shell，导致它成为 Unix 的默认 Shell。注意，Thompson shell、Mashey shell 和 Bourne shell 都是贝尔实验室的产品，程序名都是sh。对于用户来说，它们是同一个东西，只是底层代码不同而已。 1983 年，David Korn 开发了 Korn shell，程序名是ksh。 1985 年，Richard Stallman 成立了自由软件基金会（FSF），由于 Shell 的版权属于贝尔公司，所以他决定写一个自由版权的、使用 GNU 许可证的 Shell 程序，避免 Unix 的版权争议。 1988 年，自由软件基金会的第一个付薪程序员 Brian Fox 写了一个 Shell，功能基本上是 Bourne shell 的克隆，叫做 Bourne-Again SHell，简称 Bash，程序名为bash，任何人都可以免费使用。后来，它逐渐成为 Linux 系统的标准 Shell。 1989 年，Bash 发布 1.0 版。 1996 年，Bash 发布 2.0 版。 2004 年，Bash 发布 3.0 版。 2009 年，Bash 发布 4.0 版。 2019 年，Bash 发布 5.0 版。 用户可以通过bash命令的--version参数或者环境变量$BASH_VERSION，查看本机的 Bash 版本。 $ bash --version GNU bash，版本 5.0.3(1)-release (x86_64-pc-linux-gnu) # 或者 $ echo $BASH_VERSION 5.0.3(1)-release","s":"Shell 和 Bash 的历史","u":"/docs/modern-linux/bash-tutorial/intro","h":"#shell-和-bash-的历史","p":1686},{"i":1702,"t":"Bash 提供三种循环语法for、while和until。","s":"循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"","p":1701},{"i":1704,"t":"while循环有一个判断条件，只要符合条件，就不断循环执行指定的语句。 while condition; do commands done 上面代码中，只要满足条件condition，就会执行命令commands。然后，再次判断是否满足条件condition，只要满足，就会一直执行下去。只有不满足条件，才会退出循环。 循环条件condition可以使用test命令，跟if结构的判断条件写法一致。 #!/bin/bash number=0 while [ \"$number\" -lt 10 ]; do echo \"Number = $number\" number=$((number + 1)) done 上面例子中，只要变量$number小于 10，就会不断加 1，直到$number等于 10，然后退出循环。 关键字do可以跟while不在同一行，这时两者之间不需要使用分号分隔。 while true; do echo 'Hi, while looping ...' done 上面的例子会无限循环，可以按下 Ctrl + c 停止。 while循环写成一行，也是可以的。 $ while true; do echo 'Hi, while looping ...'; done while的条件部分也可以是执行一个命令。 $ while echo 'ECHO'; do echo 'Hi, while looping ...'; done 上面例子中，判断条件是echo 'ECHO'。由于这个命令总是执行成功，所以上面命令会产生无限循环。 while的条件部分可以执行任意数量的命令，但是执行结果的真伪只看最后一个命令的执行结果。 $ while true; false; do echo 'Hi, looping ...'; done 上面代码运行后，不会有任何输出，因为while的最后一个命令是false。","s":"while 循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"#while-循环","p":1701},{"i":1706,"t":"until循环与while循环恰好相反，只要不符合判断条件（判断条件失败），就不断循环执行指定的语句。一旦符合判断条件，就退出循环。 until condition; do commands done 关键字do可以与until不写在同一行，这时两者之间不需要分号分隔。 until condition; do commands done 下面是一个例子。 $ until false; do echo 'Hi, until looping ...'; done Hi, until looping ... Hi, until looping ... Hi, until looping ... ^C 上面代码中，until的部分一直为false，导致命令无限运行，必须按下 Ctrl + c 终止。 #!/bin/bash number=0 until [ \"$number\" -ge 10 ]; do echo \"Number = $number\" number=$((number + 1)) done 上面例子中，只要变量number小于 10，就会不断加 1，直到number大于等于 10，就退出循环。 until的条件部分也可以是一个命令，表示在这个命令执行成功之前，不断重复尝试。 until cp $1 $2; do echo 'Attempt to copy failed. waiting...' sleep 5 done 上面例子表示，只要cp $1 $2这个命令执行不成功，就 5 秒钟后再尝试一次，直到成功为止。 until循环都可以转为while循环，只要把条件设为否定即可。上面这个例子可以改写如下。 while ! cp $1 $2; do echo 'Attempt to copy failed. waiting...' sleep 5 done 一般来说，until用得比较少，完全可以统一都使用while。","s":"until 循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"#until-循环","p":1701},{"i":1708,"t":"for...in循环用于遍历列表的每一项。 for variable in list; do commands done 上面语法中，for循环会依次从list列表中取出一项，作为变量variable，然后在循环体中进行处理。 关键词do可以跟for写在同一行，两者使用分号分隔。 for variable in list; do commands done 下面是一个例子。 #!/bin/bash for i in word1 word2 word3; do echo $i done 上面例子中，word1 word2 word3是一个包含三个单词的列表，变量i依次等于word1、word2、word3，命令echo $i则会相应地执行三次。 列表可以由通配符产生。 for i in *.png; do ls -l $i done 上面例子中，*.png会替换成当前目录中所有 PNG 图片文件，变量i会依次等于每一个文件。 列表也可以通过子命令产生。 #!/bin/bash count=0 for i in $(cat ~/.bash_profile); do count=$((count + 1)) echo \"Word $count ($i) contains $(echo -n $i | wc -c) characters\" done 上面例子中，cat ~/.bash_profile命令会输出~/.bash_profile文件的内容，然后通过遍历每一个词，计算该文件一共包含多少个词，以及每个词有多少个字符。 in list的部分可以省略，这时list默认等于脚本的所有参数$@。但是，为了可读性，最好还是不要省略，参考下面的例子。 for filename; do echo \"$filename\" done # 等同于 for filename in \"$@\"; do echo \"$filename\" done 在函数体中也是一样的，for...in循环省略in list的部分，则list默认等于函数的所有参数。","s":"for...in 循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"#forin-循环","p":1701},{"i":1710,"t":"for循环还支持 C 语言的循环语法。 for ((expression1; expression2; expression3)); do commands done 上面代码中，expression1用来初始化循环条件，expression2用来决定循环结束的条件，expression3在每次循环迭代的末尾执行，用于更新值。 注意，循环条件放在双重圆括号之中。另外，圆括号之中使用变量，不必加上美元符号$。 它等同于下面的while循环。 ((expression1)) while ((expression2)); do commands ((expression3)) done 下面是一个例子。 for ((i = 0; i < 5; i = i + 1)); do echo $i done 上面代码中，初始化变量i的值为 0，循环执行的条件是i小于 5。每次循环迭代结束时，i的值加 1。 for条件部分的三个语句，都可以省略。 for (( ; ; )); do read var if [ \"$var\" = \".\" ]; then break fi done 上面脚本会反复读取命令行输入，直到用户输入了一个点（.）为止，才会跳出循环。","s":"for 循环","u":"/docs/modern-linux/bash-tutorial/loop","h":"#for-循环","p":1701},{"i":1712,"t":"Bash 提供了两个内部命令break和continue，用来在循环内部跳出循环。 break命令立即终止循环，程序继续执行循环块之后的语句，即不再执行剩下的循环。 #!/bin/bash for number in 1 2 3 4 5 6; do echo \"number is $number\" if [ \"$number\" = \"3\" ]; then break fi done 上面例子只会打印 3 行结果。一旦变量$number等于 3，就会跳出循环，不再继续执行。 continue命令立即终止本轮循环，开始执行下一轮循环。 #!/bin/bash while read -p \"What file do you want to test?\" filename; do if [ ! -e \"$filename\" ]; then echo \"The file does not exist.\" continue fi echo \"You entered a valid file..\" done 上面例子中，只要用户输入的文件不存在，continue命令就会生效，直接进入下一轮循环（让用户重新输入文件名），不再执行后面的打印语句。","s":"break，continue","u":"/docs/modern-linux/bash-tutorial/loop","h":"#breakcontinue","p":1701},{"i":1714,"t":"select结构主要用来生成简单的菜单。它的语法与for...in循环基本一致。 select name [in list] do commands done Bash 会对select依次进行下面的处理。 select生成一个菜单，内容是列表list的每一项，并且每一项前面还有一个数字编号。 Bash 提示用户选择一项，输入它的编号。 用户输入以后，Bash 会将该项的内容存在变量name，该项的编号存入环境变量REPLY。如果用户没有输入，就按回车键，Bash 会重新输出菜单，让用户选择。 执行命令体commands。 执行结束后，回到第一步，重复这个过程。 下面是一个例子。 #!/bin/bash # select.sh select brand in Samsung Sony iphone symphony Walton; do echo \"You have chosen $brand\" done 执行上面的脚本，Bash 会输出一个品牌的列表，让用户选择。 $ ./select.sh 1) Samsung 2) Sony 3) iphone 4) symphony 5) Walton #? 如果用户没有输入编号，直接按回车键。Bash 就会重新输出一遍这个菜单，直到用户按下Ctrl + c，退出执行。 select可以与case结合，针对不同项，执行不同的命令。 #!/bin/bash echo \"Which Operating System do you like?\" select os in Ubuntu LinuxMint Windows8 Windows10 WindowsXP; do case $os in \"Ubuntu\" | \"LinuxMint\") echo \"I also use $os.\" ;; \"Windows8\" | \"Windows10\" | \"WindowsXP\") echo \"Why don't you try Linux?\" ;; *) echo \"Invalid entry.\" break ;; esac done 上面例子中，case针对用户选择的不同项，执行不同的命令。","s":"select 结构","u":"/docs/modern-linux/bash-tutorial/loop","h":"#select-结构","p":1701},{"i":1716,"t":"Bash Select Command, Fahmida Yesmin","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/loop","h":"#参考链接","p":1701},{"i":1718,"t":"Bash 脚本有时需要创建临时文件或临时目录。常见的做法是，在/tmp目录里面创建文件或目录，这样做有很多弊端，使用mktemp命令是最安全的做法。","s":"mktemp 命令，trap 命令","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"","p":1717},{"i":1720,"t":"直接创建临时文件，尤其在/tmp目录里面，往往会导致安全问题。 首先，/tmp目录是所有人可读写的，任何用户都可以往该目录里面写文件。创建的临时文件也是所有人可读的。 $ touch /tmp/info.txt $ ls -l /tmp/info.txt -rw-r--r-- 1 ruanyf ruanyf 0 12月 28 17:12 /tmp/info.txt 上面命令在/tmp目录直接创建文件，该文件默认是所有人可读的。 其次，如果攻击者知道临时文件的文件名，他可以创建符号链接，链接到临时文件，可能导致系统运行异常。攻击者也可能向脚本提供一些恶意数据。因此，临时文件最好使用不可预测、每次都不一样的文件名，防止被利用。 最后，临时文件使用完毕，应该删除。但是，脚本意外退出时，往往会忽略清理临时文件。 生成临时文件应该遵循下面的规则。 创建前检查文件是否已经存在。 确保临时文件已成功创建。 临时文件必须有权限的限制。 临时文件要使用不可预测的文件名。 脚本退出时，要删除临时文件（使用trap命令）。","s":"临时文件的安全问题","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#临时文件的安全问题","p":1717},{"i":1722,"t":"mktemp命令就是为安全创建临时文件而设计的。虽然在创建临时文件之前，它不会检查临时文件是否存在，但是它支持唯一文件名和清除机制，因此可以减轻安全攻击的风险。 直接运行mktemp命令，就能生成一个临时文件。 $ mktemp /tmp/tmp.4GcsWSG4vj $ ls -l /tmp/tmp.4GcsWSG4vj -rw------- 1 ruanyf ruanyf 0 12月 28 12:49 /tmp/tmp.4GcsWSG4vj 上面命令中，mktemp命令生成的临时文件名是随机的，而且权限是只有用户本人可读写。 Bash 脚本使用mktemp命令的用法如下。 #!/bin/bash TMPFILE=$(mktemp) echo \"Our temp file is $TMPFILE\" 为了确保临时文件创建成功，mktemp命令后面最好使用 OR 运算符（||），保证创建失败时退出脚本。 #!/bin/bash TMPFILE=$(mktemp) || exit 1 echo \"Our temp file is $TMPFILE\" 为了保证脚本退出时临时文件被删除，可以使用trap命令指定退出时的清除操作。 #!/bin/bash trap 'rm -f \"$TMPFILE\"' EXIT TMPFILE=$(mktemp) || exit 1 echo \"Our temp file is $TMPFILE\"","s":"mktemp 命令的用法","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#mktemp-命令的用法","p":1717},{"i":1724,"t":"-d参数可以创建一个临时目录。 $ mktemp -d /tmp/tmp.Wcau5UjmN6 -p参数可以指定临时文件所在的目录。默认是使用$TMPDIR环境变量指定的目录，如果这个变量没设置，那么使用/tmp目录。 $ mktemp -p /home/ruanyf/ /home/ruanyf/tmp.FOKEtvs2H3 -t参数可以指定临时文件的文件名模板，模板的末尾必须至少包含三个连续的X字符，表示随机字符，建议至少使用六个X。默认的文件名模板是tmp.后接十个随机字符。 $ mktemp -t mytemp.XXXXXXX /tmp/mytemp.yZ1HgZV","s":"mktemp 命令的参数","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#mktemp-��命令的参数","p":1717},{"i":1726,"t":"trap命令用来在 Bash 脚本中响应系统信号。 最常见的系统信号就是 SIGINT（中断），即按 Ctrl + C 所产生的信号。trap命令的-l参数，可以列出所有的系统信号。 $ trap -l 1) SIGHUP 2) SIGINT 3) SIGQUIT 4) SIGILL 5) SIGTRAP 6) SIGABRT 7) SIGBUS 8) SIGFPE 9) SIGKILL 10) SIGUSR1 11) SIGSEGV 12) SIGUSR2 13) SIGPIPE 14) SIGALRM 15) SIGTERM 16) SIGSTKFLT 17) SIGCHLD 18) SIGCONT 19) SIGSTOP 20) SIGTSTP 21) SIGTTIN 22) SIGTTOU 23) SIGURG 24) SIGXCPU 25) SIGXFSZ 26) SIGVTALRM 27) SIGPROF 28) SIGWINCH 29) SIGIO 30) SIGPWR 31) SIGSYS 34) SIGRTMIN 35) SIGRTMIN+1 36) SIGRTMIN+2 37) SIGRTMIN+3 38) SIGRTMIN+4 39) SIGRTMIN+5 40) SIGRTMIN+6 41) SIGRTMIN+7 42) SIGRTMIN+8 43) SIGRTMIN+9 44) SIGRTMIN+10 45) SIGRTMIN+11 46) SIGRTMIN+12 47) SIGRTMIN+13 48) SIGRTMIN+14 49) SIGRTMIN+15 50) SIGRTMAX-14 51) SIGRTMAX-13 52) SIGRTMAX-12 53) SIGRTMAX-11 54) SIGRTMAX-10 55) SIGRTMAX-9 56) SIGRTMAX-8 57) SIGRTMAX-7 58) SIGRTMAX-6 59) SIGRTMAX-5 60) SIGRTMAX-4 61) SIGRTMAX-3 62) SIGRTMAX-2 63) SIGRTMAX-1 64) SIGRTMAX trap的命令格式如下。 $ trap [动作] [信号1] [信号2] ... 上面代码中，“动作”是一个 Bash 命令，“信号”常用的有以下几个。 HUP：编号 1，脚本与所在的终端脱离联系。 INT：编号 2，用户按下 Ctrl + C，意图让脚本终止运行。 QUIT：编号 3，用户按下 Ctrl + 斜杠，意图退出脚本。 KILL：编号 9，该信号用于杀死进程。 TERM：编号 15，这是kill命令发出的默认信号。 EXIT：编号 0，这不是系统信号，而是 Bash 脚本特有的信号，不管什么情况，只要退出脚本就会产生。 trap命令响应EXIT信号的写法如下。 $ trap 'rm -f \"$TMPFILE\"' EXIT 上面命令中，脚本遇到EXIT信号时，就会执行rm -f \"$TMPFILE\"。 trap 命令的常见使用场景，就是在 Bash 脚本中指定退出时执行的清理命令。 #!/bin/bash trap 'rm -f \"$TMPFILE\"' EXIT TMPFILE=$(mktemp) || exit 1 ls /etc > $TMPFILE if grep -qi \"kernel\" $TMPFILE; then echo 'find' fi 上面代码中，不管是脚本正常执行结束，还是用户按 Ctrl + C 终止，都会产生EXIT信号，从而触发删除临时文件。 注意，trap命令必须放在脚本的开头。否则，它上方的任何命令导致脚本退出，都不会被它捕获。 如果trap需要触发多条命令，可以封装一个 Bash 函数。 function egress { command1 command2 command3 } trap egress EXIT","s":"trap 命令","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#trap-命令","p":1717},{"i":1728,"t":"Working with Temporary Files and Directories in Shell Scripts, Steven Vona Using Trap to Exit Bash Scripts Cleanly Sending and Trapping Signals","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/mktemp","h":"#参考链接","p":1717},{"i":1730,"t":"用户进入 Bash 以后，Bash 会显示一个命令提示符，用来提示用户在该位置后面输入命令。","s":"命令提示符","u":"/docs/modern-linux/bash-tutorial/prompt","h":"","p":1729},{"i":1732,"t":"命令提示符通常是美元符号$，对于根用户则是井号#。这个符号是环境变量PS1决定的，执行下面的命令，可以看到当前命令提示符的定义。 $ echo $PS1 Bash 允许用户自定义命令提示符，只要改写这个变量即可。改写后的PS1，可以放在用户的 Bash 配置文件.bashrc里面，以后新建 Bash 对话时，新的提示符就会生效。要在当前窗口看到修改后的提示符，可以执行下面的命令。 $ source ~/.bashrc 命令提示符的定义，可以包含特殊的转义字符，表示特定内容。 \\a：响铃，计算机发出一记声音。 \\d：以星期、月、日格式表示当前日期，例如“Mon May 26”。 \\h：本机的主机名。 \\H：完整的主机名。 \\j：运行在当前 Shell 会话的工作数。 \\l：当前终端设备名。 \\n：一个换行符。 \\r：一个回车符。 \\s：Shell 的名称。 \\t：24 小时制的hours:minutes:seconds格式表示当前时间。 \\T：12 小时制的当前时间。 \\@：12 小时制的AM/PM格式表示当前时间。 \\A：24 小时制的hours:minutes表示当前时间。 \\u：当前用户名。 \\v：Shell 的版本号。 \\V：Shell 的版本号和发布号。 \\w：当前的工作路径。 \\W：当前目录名。 \\!：当前命令在命令历史中的编号。 \\#：当前 shell 会话中的命令数。 \\$：普通用户显示为$字符，根用户显示为#字符。 \\[：非打印字符序列的开始标志。 \\]：非打印字符序列的结束标志。 举例来说，[\\u@\\h \\W]\\$这个提示符定义，显示出来就是[user@host ~]$（具体的显示内容取决于你的系统）。 [user@host ~]$ echo $PS1 [\\u@\\h \\W]\\$ 改写PS1变量，就可以改变这个命令提示符。 $ PS1=\"\\A \\h \\$ \" 17:33 host $ 注意，$后面最好跟一个空格，这样的话，用户的输入与提示符就不会连在一起。","s":"环境变量 PS1","u":"/docs/modern-linux/bash-tutorial/prompt","h":"#环境变量-ps1","p":1729},{"i":1734,"t":"默认情况下，命令提示符是显示终端预定义的颜色。Bash 允许自定义提示符颜色。 使用下面的代码，可以设定其后文本的颜色。 \\033[0;30m：黑色 \\033[1;30m：深灰色 \\033[0;31m：红色 \\033[1;31m：浅红色 \\033[0;32m：绿色 \\033[1;32m：浅绿色 \\033[0;33m：棕色 \\033[1;33m：黄色 \\033[0;34m：蓝色 \\033[1;34m：浅蓝色 \\033[0;35m：粉红 \\033[1;35m：浅粉色 \\033[0;36m：青色 \\033[1;36m：浅青色 \\033[0;37m：浅灰色 \\033[1;37m：白色 举例来说，如果要将提示符设为红色，可以将PS1设成下面的代码。 PS1='\\[\\033[0;31m\\]<\\u@\\h \\W>\\$' 但是，上面这样设置以后，用户在提示符后面输入的文本也是红色的。为了解决这个问题，可以在结尾添加另一个特殊代码\\[\\033[00m\\]，表示将其后的文本恢复到默认颜色。 PS1='\\[\\033[0;31m\\]<\\u@\\h \\W>\\$\\[\\033[00m\\]' 除了设置前景颜色，Bash 还允许设置背景颜色。 \\033[0;40m：蓝色 \\033[1;44m：黑色 \\033[0;41m：红色 \\033[1;45m：粉红 \\033[0;42m：绿色 \\033[1;46m：青色 \\033[0;43m：棕色 \\033[1;47m：浅灰色 下面是一个带有红色背景的提示符。 PS1='\\[\\033[0;41m\\]<\\u@\\h \\W>\\$\\[\\033[0m\\] '","s":"颜色","u":"/docs/modern-linux/bash-tutorial/prompt","h":"#颜色","p":1729},{"i":1736,"t":"除了PS1，Bash 还提供了提示符相关的另外三个环境变量。 环境变量PS2是命令行折行输入时系统的提示符，默认为> 。 $ echo \"hello > world\" 上面命令中，输入hello以后按下回车键，系统会提示继续输入。这时，第二行显示的提示符就是PS2定义的> 。 环境变量PS3是使用select命令时，系统输入菜单的提示符。 环境变量PS4默认为+ 。它是使用 Bash 的-x参数执行脚本时，每一行命令在执行前都会先打印出来，并且在行首出现的那个提示符。 比如下面是脚本test.sh。 #!/bin/bash echo \"hello world\" 使用-x参数执行这个脚本。 $ bash -x test.sh + echo 'hello world' hello world 上面例子中，输出的第一行前面有一个+ ，这就是变量PS4定义的。","s":"环境变量 PS2，PS3，PS4","u":"/docs/modern-linux/bash-tutorial/prompt","h":"#环境变量-ps2ps3ps4","p":1729},{"i":1738,"t":"Bash 只有一种数据类型，就是字符串。不管用户输入什么数据，Bash 都视为字符串。因此，字符串相关的引号和转义，对 Bash 来说就非常重要。","s":"引号和转义","u":"/docs/modern-linux/bash-tutorial/quotation","h":"","p":1737},{"i":1740,"t":"某些字符在 Bash 里面有特殊含义（比如$、&、*）。 $ echo $date $ 上面例子中，输出$date不会有任何结果，因为$是一个特殊字符。 如果想要原样输出这些特殊字符，就必须在它们前面加上反斜杠，使其变成普通字符。这就叫做“转义”（escape）。 $ echo \\$date $date 上面命令中，只有在特殊字符$前面加反斜杠，才能原样输出。 反斜杠本身也是特殊字符，如果想要原样输出反斜杠，就需要对它自身转义，连续使用两个反斜线（\\\\）。 $ echo \\\\ 上面例子输出了反斜杠本身。 反斜杠除了用于转义，还可以表示一些不可打印的字符。 \\a：响铃 \\b：退格 \\n：换行 \\r：回车 \\t：制表符 如果想要在命令行使用这些不可打印的字符，可以把它们放在引号里面，然后使用echo命令的-e参数。 $ echo a\\tb atb $ echo -e \"a\\tb\" a b 上面例子中，命令行直接输出不可打印字符\\t，Bash 不能正确解释。必须把它们放在引号之中，然后使用echo命令的-e参数。 换行符是一个特殊字符，表示命令的结束，Bash 收到这个字符以后，就会对输入的命令进行解释执行。换行符前面加上反斜杠转义，就使得换行符变成一个普通字符，Bash 会将其当作长度为0的空字符处理，从而可以将一行命令写成多行。 $ mv \\ /path/to/foo \\ /path/to/bar # 等同于 $ mv /path/to/foo /path/to/bar 上面例子中，如果一条命令过长，就可以在行尾使用反斜杠，将其改写成多行。这是常见的多行命令的写法。","s":"转义","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#转义","p":1737},{"i":1742,"t":"Bash 允许字符串放在单引号或双引号之中，加以引用。 单引号用于保留字符的字面含义，各种特殊字符在单引号里面，都会变为普通字符，比如星号（*）、美元符号（$）、反斜杠（\\）等。 $ echo '*' * $ echo '$USER' $USER $ echo '$((2+2))' $((2 + 2)) $ echo '$(echo foo)' $(echo foo) 上面命令中，单引号使得 Bash 扩展、变量引用、算术运算和子命令，都失效了。如果不使用单引号，它们都会被 Bash 自动扩展。 由于反斜杠在单引号里面变成了普通字符，所以如果单引号之中，还要使用单引号，不能使用转义，需要在外层的单引号前面加上一个美元符号（$），然后再对里层的单引号转义。 # 不正确 $ echo it's # 不正确 $ echo 'it\\'s' # 正确 $ echo $'it\\'s' 不过，更合理的方法是改在双引号之中使用单引号。 $ echo \"it's\" it's","s":"单引号","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#单引号","p":1737},{"i":1744,"t":"双引号比单引号宽松，大部分特殊字符在双引号里面，都会失去特殊含义，变成普通字符。 $ echo \"*\" * 上面例子中，通配符*是一个特殊字符，放在双引号之中，就变成了普通字符，会原样输出。这一点需要特别留意，这意味着，双引号里面不会进行文件名扩展。 但是，三个特殊字符除外：美元符号（$）、反引号（`）和反斜杠（\\）。这三个字符在双引号之中，依然有特殊含义，会被 Bash 自动扩展。 $ echo \"$SHELL\" /bin/bash $ echo \"$(date)\" Mon Jan 27 13:33:18 CST 2020 上面例子中，美元符号（$）和反引号（`）在双引号中，都保持特殊含义。美元符号用来引用变量，反引号则是执行子命令。 $ echo \"I'd say: \\\"hello.\\\"\" I'd say: \"hello.\" $ echo \"\\\\\" \\ 上面例子中，反斜杠在双引号之中保持特殊含义，用来转义。所以，可以使用反斜杠，在双引号之中插入双引号，或者插入反斜杠本身。 换行符在双引号之中，会失去特殊含义，Bash 不再将其解释为命令的结束，只是作为普通的换行符。所以可以利用双引号，在命令行输入多行文本。 $ echo \"hello world\" hello world 上面命令中，Bash 正常情况下会将换行符解释为命令结束，但是换行符在双引号之中就失去了这种特殊作用，只用来换行，所以可以输入多行。echo命令会将换行符原样输出，显示的时候正常解释为换行。 双引号的另一个常见的使用场合是，文件名包含空格。这时就必须使用双引号（或单引号），将文件名放在里面。 $ ls \"two words.txt\" 上面命令中，two words.txt是一个包含空格的文件名，如果不放在双引号里面，就会被 Bash 当作两个文件。 双引号会原样保存多余的空格。 $ echo \"this is a test\" this is a test 双引号还有一个作用，就是保存原始命令的输出格式。 # 单行输出 $ echo $(cal) 一月 2020 日 一 二 三 四 五 六 1 2 3 ... 31 # 原始格式输出 $ echo \"$(cal)\" 一月 2020 日 一 二 三 四 五 六 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 上面例子中，如果$(cal)不放在双引号之中，echo就会将所有结果以单行输出，丢弃了所有原始的格式。","s":"双引号","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#双引号","p":1737},{"i":1746,"t":"Here 文档（here document）是一种输入多行字符串的方法，格式如下。 << token text token 它的格式分成开始标记（<< token）和结束标记（token）。开始标记是两个小于号 + Here 文档的名称，名称可以随意取，后面必须是一个换行符；结束标记是单独一行顶格写的 Here 文档名称，如果不是顶格，结束标记不起作用。两者之间就是多行字符串的内容。 下面是一个通过 Here 文档输出 HTML 代码的例子。 $ cat << _EOF_ <html> <head> <title> The title of your page </title> </head> <body> Your page content goes here. </body> </html> _EOF_ Here 文档内部会发生变量替换，同时支持反斜杠转义，但是不支持通配符扩展，双引号和单引号也失去语法作用，变成了普通字符。 $ foo='hello world' $ cat << _example_ $foo \"$foo\" '$foo' _example_ hello world \"hello world\" 'hello world' 上面例子中，变量$foo发生了替换，但是双引号和单引号都原样输出了，表明它们已经失去了引用的功能。 如果不希望发生变量替换，可以把 Here 文档的开始标记放在单引号之中。 $ foo='hello world' $ cat << '_example_' $foo \"$foo\" '$foo' _example_ $foo \"$foo\" '$foo' 上面例子中，Here 文档的开始标记（_example_）放在单引号之中，导致变量替换失效了。 Here 文档的本质是重定向，它将字符串重定向输出给某个命令，相当于包含了echo命令。 $ command << token string token # 等同于 $ echo string | command 上面代码中，Here 文档相当于echo命令的重定向。 所以，Here 字符串只适合那些可以接受标准输入作为参数的命令，对于其他命令无效，比如echo命令就不能用 Here 文档作为参数。 $ echo << _example_ hello _example_ 上面例子不会有任何输出，因为 Here 文档对于echo命令无效。 此外，Here 文档也不能作为变量的值，只能用于命令的参数。","s":"Here 文档","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#here-文档","p":1737},{"i":1748,"t":"Here 文档还有一个变体，叫做 Here 字符串（Here string），使用三个小于号（<<<）表示。 <<< string 它的作用是将字符串通过标准输入，传递给命令。 有些命令直接接受给定的参数，与通过标准输入接受参数，结果是不一样的。所以才有了这个语法，使得将字符串通过标准输入传递给命令更方便，比如cat命令只接受标准输入传入的字符串。 $ cat <<< 'hi there' # 等同于 $ echo 'hi there' | cat 上面的第一种语法使用了 Here 字符串，要比第二种语法看上去语义更好，也更简洁。 $ md5sum <<< 'ddd' # 等同于 $ echo 'ddd' | md5sum 上面例子中，md5sum命令只能接受标准输入作为参数，不能直接将字符串放在命令后面，会被当作文件名，即md5sum ddd里面的ddd会被解释成文件名。这时就可以用 Here 字符串，将字符串传给md5sum命令。","s":"Here 字符串","u":"/docs/modern-linux/bash-tutorial/quotation","h":"#here-字符串","p":1737},{"i":1751,"t":"有时，脚本需要在执行过程中，由用户提供一部分数据，这时可以使用read命令。它将用户的输入存入一个变量，方便后面的代码使用。用户按下回车键，就表示输入结束。 read命令的格式如下。 read [-options] [variable...] 上面语法中，options是参数选项，variable是用来保存输入数值的一个或多个变量名。如果没有提供变量名，环境变量REPLY会包含用户输入的一整行数据。 下面是一个例子demo.sh。 #!/bin/bash echo -n \"输入一些文本 > \" read text echo \"你的输入：$text\" 上面例子中，先显示一行提示文本，然后会等待用户输入文本。用户输入的文本，存入变量text，在下一行显示出来。 $ bash demo.sh 输入一些文本 > 你好，世界 你的输入：你好，世界 read可以接受用户输入的多个值。 #!/bin/bash echo Please, enter your firstname and lastname read FN LN echo \"Hi! $LN, $FN !\" 上面例子中，read根据用户的输入，同时为两个变量赋值。 如果用户的输入项少于read命令给出的变量数目，那么额外的变量值为空。如果用户的输入项多于定义的变量，那么多余的输入项会包含到最后一个变量中。 如果read命令之后没有定义变量名，那么环境变量REPLY会包含所有的输入。 #!/bin/bash # read-single: read multiple values into default variable echo -n \"Enter one or more values > \" read echo \"REPLY = '$REPLY'\" 上面脚本的运行结果如下。 $ read-single Enter one or more values > a b c d REPLY = 'a b c d' read命令除了读取键盘输入，可以用来读取文件。 #!/bin/bash filename='/etc/hosts' while read myline do echo \"$myline\" done < $filename 上面的例子通过read命令，读取一个文件的内容。done命令后面的定向符<，将文件内容导向read命令，每次读取一行，存入变量myline，直到文件读取完毕。","s":"用法","u":"/docs/modern-linux/bash-tutorial/read","h":"#用法","p":1749},{"i":1753,"t":"read命令的参数如下。 （1）-t 参数 read命令的-t参数，设置了超时的秒数。如果超过了指定时间，用户仍然没有输入，脚本将放弃等待，继续向下执行。 #!/bin/bash echo -n \"输入一些文本 > \" if read -t 3 response; then echo \"用户已经输入了\" else echo \"用户没有输入\" fi 上面例子中，输入命令会等待 3 秒，如果用户超过这个时间没有输入，这个命令就会执行失败。if根据命令的返回值，转入else代码块，继续往下执行。 环境变量TMOUT也可以起到同样作用，指定read命令等待用户输入的时间（单位为秒）。 $ TMOUT=3 $ read response 上面例子也是等待 3 秒，如果用户还没有输入，就会超时。 （2）-p 参数 -p参数指定用户输入的提示信息。 read -p \"Enter one or more values > \" echo \"REPLY = '$REPLY'\" 上面例子中，先显示Enter one or more values >，再接受用户的输入。 （3）-a 参数 -a参数把用户的输入赋值给一个数组，从零号位置开始。 $ read -a people alice duchess dodo $ echo ${people[2]} dodo 上面例子中，用户输入被赋值给一个数组people，这个数组的 2 号成员就是dodo。 （4）-n 参数 -n参数指定只读取若干个字符作为变量值，而不是整行读取。 $ read -n 3 letter abcdefghij $ echo $letter abc 上面例子中，变量letter只包含 3 个字母。 （5）-e 参数 -e参数允许用户输入的时候，使用readline库提供的快捷键，比如自动补全。具体的快捷键可以参阅《行操作》一章。 #!/bin/bash echo Please input the path to the file: read -e fileName echo $fileName 上面例子中，read命令接受用户输入的文件名。这时，用户可能想使用 Tab 键的文件名“自动补全”功能，但是read命令的输入默认不支持readline库的功能。-e参数就可以允许用户使用自动补全。 （6）其他参数 -d delimiter：定义字符串delimiter的第一个字符作为用户输入的结束，而不是一个换行符。 -r：raw 模式，表示不把用户输入的反斜杠字符解释为转义字符。 -s：使得用户的输入不显示在屏幕上，这常常用于输入密码或保密信息。 -u fd：使用文件描述符fd作为输入。","s":"参数","u":"/docs/modern-linux/bash-tutorial/read","h":"#参数","p":1749},{"i":1755,"t":"read命令读取的值，默认是以空格分隔。可以通过自定义环境变量IFS（内部字段分隔符，Internal Field Separator 的缩写），修改分隔标志。 IFS的默认值是空格、Tab 符号、换行符号，通常取第一个（即空格）。 如果把IFS定义成冒号（:）或分号（;），就可以分隔以这两个符号分隔的值，这对读取文件很有用。 #!/bin/bash # read-ifs: read fields from a file FILE=/etc/passwd read -p \"Enter a username > \" user_name file_info=\"$(grep \"^$user_name:\" $FILE)\" if [ -n \"$file_info\" ]; then IFS=\":\" read user pw uid gid name home shell <<< \"$file_info\" echo \"User = '$user'\" echo \"UID = '$uid'\" echo \"GID = '$gid'\" echo \"Full Name = '$name'\" echo \"Home Dir. = '$home'\" echo \"Shell = '$shell'\" else echo \"No such user '$user_name'\" >&2 exit 1 fi 上面例子中，IFS设为冒号，然后用来分解/etc/passwd文件的一行。IFS的赋值命令和read命令写在一行，这样的话，IFS的改变仅对后面的命令生效，该命令执行后IFS会自动恢复原来的值。如果不写在一行，就要采用下面的写法。 OLD_IFS=\"$IFS\" IFS=\":\" read user pw uid gid name home shell <<< \"$file_info\" IFS=\"$OLD_IFS\" 另外，上面例子中，<<<是 Here 字符串，用于将变量值转为标准输入，因为read命令只能解析标准输入。 如果IFS设为空字符串，就等同于将整行读入一个变量。 #!/bin/bash input=\"/path/to/txt/file\" while IFS= read -r line do echo \"$line\" done < \"$input\" 上面的命令可以逐行读取文件，每一行存入变量line，打印出来以后再读取下一行。","s":"IFS 变量","u":"/docs/modern-linux/bash-tutorial/read","h":"#ifs-变量","p":1749},{"i":1758,"t":"Bash 内置了 Readline 库，具有这个库提供的很多“行操作”功能，比如命令的自动补全，可以大大加快操作速度。 这个库默认采用 Emacs 快捷键，也可以改成 Vi 快捷键。 $ set -o vi 下面的命令可以改回 Emacs 快捷键。 $ set -o emacs 如果想永久性更改编辑模式（Emacs / Vi），可以将命令写在~/.inputrc文件，这个文件是 Readline 的配置文件。 set editing-mode vi 本章介绍的快捷键都属于 Emacs 模式。Vi 模式的快捷键，读者可以参考 Vi 编辑器的教程。 Bash 默认开启这个库，但是允许关闭。 $ bash --noediting 上面命令中，--noediting参数关闭了 Readline 库，启动的 Bash 就不带有行操作功能。","s":"简介","u":"/docs/modern-linux/bash-tutorial/readline","h":"#简介","p":1756},{"i":1760,"t":"Readline 提供快速移动光标的快捷键。 Ctrl + a：移到行首。 Ctrl + b：向行首移动一个字符，与左箭头作用相同。 Ctrl + e：移到行尾。 Ctrl + f：向行尾移动一个字符，与右箭头作用相同。 Alt + f：移动到当前单词的词尾。 Alt + b：移动到当前单词的词首。 上面快捷键的 Alt 键，也可以用 ESC 键代替。","s":"光标移动","u":"/docs/modern-linux/bash-tutorial/readline","h":"#光标移动","p":1756},{"i":1762,"t":"Ctrl + l快捷键可以清除屏幕，即将当前行移到屏幕的第一行，与clear命令作用相同。","s":"清除屏幕","u":"/docs/modern-linux/bash-tutorial/readline","h":"#清除屏幕","p":1756},{"i":1764,"t":"下面的快捷键可以编辑命令行内容。 Ctrl + d：删除光标位置的字符（delete）。 Ctrl + w：删除光标前面的单词。 Ctrl + t：光标位置的字符与它前面一位的字符交换位置（transpose）。 Alt + t：光标位置的词与它前面一位的词交换位置（transpose）。 Alt + l：将光标位置至词尾转为小写（lowercase）。 Alt + u：将光标位置至词尾转为大写（uppercase）。 使用Ctrl + d的时候，如果当前行没有任何字符，会导致退出当前 Shell，所以要小心。 剪切和粘贴快捷键如下。 Ctrl + k：剪切光标位置到行尾的文本。 Ctrl + u：剪切光标位置到行首的文本。 Alt + d：剪切光标位置到词尾的文本。 Alt + Backspace：剪切光标位置到词首的文本。 Ctrl + y：在光标位置粘贴文本。 同样地，Alt 键可以用 Esc 键代替。","s":"编辑操作","u":"/docs/modern-linux/bash-tutorial/readline","h":"#编辑操作","p":1756},{"i":1766,"t":"命令输入到一半的时候，可以按一下 Tab 键，Readline 会自动补全命令或路径。比如，输入cle，再按下 Tab 键，Bash 会自动将这个命令补全为clear。 如果符合条件的命令或路径有多个，就需要连续按两次 Tab 键，Bash 会提示所有符合条件的命令或路径。 除了命令或路径，Tab 还可以补全其他值。如果一个值以$开头，则按下 Tab 键会补全变量；如果以~开头，则补全用户名；如果以@开头，则补全主机名（hostname），主机名以列在/etc/hosts文件里面的主机为准。 自动补全相关的快捷键如下。 Tab：完成自动补全。 Alt + ?：列出可能的补全，与连按两次 Tab 键作用相同。 Alt + /：尝试文件路径补全。 Ctrl + x /：先按Ctrl + x，再按/，等同于Alt + ?，列出可能的文件路径补全。 Alt + !：命令补全。 Ctrl + x !：先按Ctrl + x，再按!，等同于Alt + !，命令补全。 Alt + ~：用户名补全。 Ctrl + x ~：先按Ctrl + x，再按~，等同于Alt + ~，用户名补全。 Alt + $：变量名补全。 Ctrl + x $：先按Ctrl + x，再按$，等同于Alt + $，变量名补全。 Alt + @：主机名补全。 Ctrl + x @：先按Ctrl + x，再按@，等同于Alt + @，主机名补全。 Alt + *：在命令行一次性插入所有可能的补全。 Alt + Tab：尝试用.bash_history里面以前执行命令，进行补全。 上面的Alt键也可以用 ESC 键代替。","s":"自动补全","u":"/docs/modern-linux/bash-tutorial/readline","h":"#自动补全","p":1756},{"i":1768,"t":"Ctrl + j：等同于回车键（LINEFEED）。 Ctrl + m：等同于回车键（CARRIAGE RETURN）。 Ctrl + o：等同于回车键，并展示操作历史的下一个命令。 Ctrl + v：将下一个输入的特殊字符变成字面量，比如回车变成^M。 Ctrl + [：等同于 ESC。 Alt + .：插入上一个命令的最后一个词。 Alt + _：等同于Alt + .。 上面的Alt + .快捷键，对于很长的文件路径，有时会非常方便。因为 Unix 命令的最后一个参数通常是文件路径。 $ mkdir foo_bar $ cd #按下 Alt + . 上面例子中，在cd命令后按下Alt + .，就会自动插入foo_bar。","s":"其他快捷键","u":"/docs/modern-linux/bash-tutorial/readline","h":"#其他快捷键","p":1756},{"i":1770,"t":"脚本（script）就是包含一系列命令的一个文本文件。Shell 读取这个文件，依次执行里面的所有命令，就好像这些命令直接输入到命令行一样。所有能够在命令行完成的任务，都能够用脚本完成。 脚本的好处是可以重复使用，也可以指定在特定场合自动调用，比如系统启动或关闭时自动执行脚本。","s":"Bash 脚本入门","u":"/docs/modern-linux/bash-tutorial/script","h":"","p":1769},{"i":1772,"t":"脚本的第一行通常是指定解释器，即这个脚本必须通过什么解释器执行。这一行以#!字符开头，这个字符称为 Shebang，所以这一行就叫做 Shebang 行。 #!后面就是脚本解释器的位置，Bash 脚本的解释器一般是/bin/sh或/bin/bash。 #!/bin/sh # 或者 #!/bin/bash #!与脚本解释器之间有没有空格，都是可以的。 如果 Bash 解释器不放在目录/bin，脚本就无法执行了。为了保险，可以写成下面这样。 #!/usr/bin/env bash 上面命令使用env命令（这个命令总是在/usr/bin目录），返回 Bash 可执行文件的位置。env命令的详细介绍，请看后文。 Shebang 行不是必需的，但是建议加上这行。如果缺少该行，就需要手动将脚本传给解释器。举例来说，脚本是script.sh，有 Shebang 行的时候，可以直接调用执行。 $ ./script.sh 上面例子中，script.sh是脚本文件名。脚本通常使用.sh后缀名，不过这不是必需的。 如果没有 Shebang 行，就只能手动将脚本传给解释器来执行。 $ /bin/sh ./script.sh # 或者 $ bash ./script.sh","s":"Shebang 行","u":"/docs/modern-linux/bash-tutorial/script","h":"#shebang-行","p":1769},{"i":1774,"t":"前面说过，只要指定了 Shebang 行的脚本，可以直接执行。这有一个前提条件，就是脚本需要有执行权限。可以使用下面的命令，赋予脚本执行权限。 # 给所有用户执行权限 $ chmod +x script.sh # 给所有用户读权限和执行权限 $ chmod +rx script.sh # 或者 $ chmod 755 script.sh # 只给脚本拥有者读权限和执行权限 $ chmod u+rx script.sh 脚本的权限通常设为755（拥有者有所有权限，其他人有读和执行权限）或者700（只有拥有者可以执行）。 除了执行权限，脚本调用时，一般需要指定脚本的路径（比如path/script.sh）。如果将脚本放在环境变量$PATH指定的目录中，就不需要指定路径了。因为 Bash 会自动到这些目录中，寻找是否存在同名的可执行文件。 建议在主目录新建一个~/bin子目录，专门存放可执行脚本，然后把~/bin加入$PATH。 export PATH=$PATH:~/bin 上面命令改变环境变量$PATH，将~/bin添加到$PATH的末尾。可以将这一行加到~/.bashrc文件里面，然后重新加载一次.bashrc，这个配置就可以生效了。 $ source ~/.bashrc 以后不管在什么目录，直接输入脚本文件名，脚本就会执行。 $ script.sh 上面命令没有指定脚本路径，因为script.sh在$PATH指定的目录中。","s":"执行权限和路径","u":"/docs/modern-linux/bash-tutorial/script","h":"#执行权限和路径","p":1769},{"i":1776,"t":"env命令总是指向/usr/bin/env文件，或者说，这个二进制文件总是在目录/usr/bin。 #!/usr/bin/env NAME这个语法的意思是，让 Shell 查找$PATH环境变量里面第一个匹配的NAME。如果你不知道某个命令的具体路径，或者希望兼容其他用户的机器，这样的写法就很有用。 /usr/bin/env bash的意思就是，返回bash可执行文件的位置，前提是bash的路径是在$PATH里面。其他脚本文件也可以使用这个命令。比如 Node.js 脚本的 Shebang 行，可以写成下面这样。 #!/usr/bin/env node env命令的参数如下。 -i, --ignore-environment：不带环境变量启动。 -u, --unset=NAME：从环境变量中删除一个变量。 --help：显示帮助。 --version：输出版本信息。 下面是一个例子，新建一个不带任何环境变量的 Shell。 $ env -i /bin/sh","s":"env 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#env-命令","p":1769},{"i":1778,"t":"Bash 脚本中，#表示注释，可以放在行首，也可以放在行尾。 # 本行是注释 echo 'Hello World!' echo 'Hello World!' # 井号后面的部分也是注释 建议在脚本开头，使用注释说明当前脚本的作用，这样有利于日后的维护。","s":"注释","u":"/docs/modern-linux/bash-tutorial/script","h":"#注释","p":1769},{"i":1780,"t":"调用脚本的时候，脚本文件名后面可以带有参数。 $ script.sh word1 word2 word3 上面例子中，script.sh是一个脚本文件，word1、word2和word3是三个参数。 脚本文件内部，可以使用特殊变量，引用这些参数。 $0：脚本文件名，即script.sh。 $1~$9：对应脚本的第一个参数到第九个参数。 $#：参数的总数。 $@：全部的参数，参数之间使用空格分隔。 $*：全部的参数，参数之间使用变量$IFS值的第一个字符分隔，默认为空格，但是可以自定义。 如果脚本的参数多于 9 个，那么第 10 个参数可以用${10}的形式引用，以此类推。 注意，如果命令是command -o foo bar，那么-o是$1，foo是$2，bar是$3。 下面是一个脚本内部读取命令行参数的例子。 #!/bin/bash # script.sh echo \"全部参数：\" $@ echo \"命令行参数数量：\" $# echo '$0 = ' $0 echo '$1 = ' $1 echo '$2 = ' $2 echo '$3 = ' $3 执行结果如下。 $ ./script.sh a b c 全部参数：a b c 命令行参数数量：3 $0 = script.sh $1 = a $2 = b $3 = c 用户可以输入任意数量的参数，利用for循环，可以读取每一个参数。 #!/bin/bash for i in \"$@\"; do echo $i done 上面例子中，$@返回一个全部参数的列表，然后使用for循环遍历。 如果多个参数放在双引号里面，视为一个参数。 $ ./script.sh \"a b\" 上面例子中，Bash 会认为\"a b\"是一个参数，$1会返回a b。注意，返回时不包括双引号。","s":"脚本参数","u":"/docs/modern-linux/bash-tutorial/script","h":"#脚本参数","p":1769},{"i":1782,"t":"shift命令可以改变脚本参数，每次执行都会移除脚本当前的第一个参数（$1），使得后面的参数向前一位，即$2变成$1、$3变成$2、$4变成$3，以此类推。 while循环结合shift命令，也可以读取每一个参数。 #!/bin/bash echo \"一共输入了 $# 个参数\" while [ \"$1\" != \"\" ]; do echo \"剩下 $# 个参数\" echo \"参数：$1\" shift done 上面例子中，shift命令每次移除当前第一个参数，从而通过while循环遍历所有参数。 shift命令可以接受一个整数作为参数，指定所要移除的参数个数，默认为1。 shift 3 上面的命令移除前三个参数，原来的$4变成$1。","s":"shift 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#shift-命令","p":1769},{"i":1784,"t":"getopts命令用在脚本内部，可以解析复杂的脚本命令行参数，通常与while循环一起使用，取出脚本所有的带有前置连词线（-）的参数。 getopts optstring name 它带有两个参数。第一个参数optstring是字符串，给出脚本所有的连词线参数。比如，某个脚本可以有三个配置项参数-l、-h、-a，其中只有-a可以带有参数值，而-l和-h是开关参数，那么getopts的第一个参数写成lha:，顺序不重要。注意，a后面有一个冒号，表示该参数带有参数值，getopts规定带有参数值的配置项参数，后面必须带有一个冒号（:）。getopts的第二个参数name是一个变量名，用来保存当前取到的配置项参数，即l、h或a。 下面是一个例子。 while getopts 'lha:' OPTION; do case \"$OPTION\" in l) echo \"linuxconfig\" ;; h) echo \"h stands for h\" ;; a) avalue=\"$OPTARG\" echo \"The value provided is $OPTARG\" ;; ?) echo \"script usage: $(basename $0) [-l] [-h] [-a somevalue]\" >&2 exit 1 ;; esac done shift \"$(($OPTIND - 1))\" 上面例子中，while循环不断执行getopts 'lha:' OPTION命令，每次执行就会读取一个连词线参数（以及对应的参数值），然后进入循环体。变量OPTION保存的是，当前处理的那一个连词线参数（即l、h或a）。如果用户输入了没有指定的参数（比如-x），那么OPTION等于?。循环体内使用case判断，处理这四种不同的情况。 如果某个连词线参数带有参数值，比如-a foo，那么处理a参数的时候，环境变量$OPTARG保存的就是参数值。 注意，只要遇到不带连词线的参数，getopts就会执行失败，从而退出while循环。比如，getopts可以解析command -l foo，但不可以解析command foo -l。另外，多个连词线参数写在一起的形式，比如command -lh，getopts也可以正确处理。 变量$OPTIND在getopts开始执行前是1，然后每次执行就会加1。等到退出while循环，就意味着连词线参数全部处理完毕。这时，$OPTIND - 1就是已经处理的连词线参数个数，使用shift命令将这些参数移除，保证后面的代码可以用$1、$2等处理命令的主参数。","s":"getopts 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#getopts-命令","p":1769},{"i":1786,"t":"-和--开头的参数，会被 Bash 当作配置项解释。但是，有时它们不是配置项，而是实体参数的一部分，比如文件名叫做-f或--file。 $ cat -f $ cat --file 上面命令的原意是输出文件-f和--file的内容，但是会被 Bash 当作配置项解释。 这时就可以使用配置项参数终止符--，它的作用是告诉 Bash，在它后面的参数开头的-和--不是配置项，只能当作实体参数解释。 $ cat -- -f $ cat -- --file 上面命令可以正确展示文件-f和--file的内容，因为它们放在--的后面，开头的-和--就不再当作配置项解释了。 如果要确保某个变量不会被当作配置项解释，就要在它前面放上参数终止符--。 $ ls -- $myPath 上面示例中，--强制变量$myPath只能当作实体参数（即路径名）解释。如果变量不是路径名，就会报错。 $ myPath=\"-l\" $ ls -- $myPath ls: 无法访问'-l': 没有那个文件或目录 上面例子中，变量myPath的值为-l，不是路径。但是，--强制$myPath只能作为路径解释，导致报错“不存在该路径”。 下面是另一个实际的例子，如果想在文件里面搜索--hello，这时也要使用参数终止符--。 $ grep -- \"--hello\" example.txt 上面命令在example.txt文件里面，搜索字符串--hello。这个字符串是--开头，如果不用参数终止符，grep命令就会把--hello当作配置项参数，从而报错。","s":"配置项参数终止符 --","u":"/docs/modern-linux/bash-tutorial/script","h":"#配置项参数终止符---","p":1769},{"i":1788,"t":"exit命令用于终止当前脚本的执行，并向 Shell 返回一个退出值。 $ exit 上面命令中止当前脚本，将最后一条命令的退出状态，作为整个脚本的退出状态。 exit命令后面可以跟参数，该参数就是退出状态。 # 退出值为0（成功） $ exit 0 # 退出值为1（失败） $ exit 1 退出时，脚本会返回一个退出值。脚本的退出值，0表示正常，1表示发生错误，2表示用法不对，126表示不是可执行脚本，127表示命令没有发现。如果脚本被信号N终止，则退出值为128 + N。简单来说，只要退出值非 0，就认为执行出错。 下面是一个例子。 if [ $(id -u) != \"0\" ]; then echo \"根用户才能执行当前脚本\" exit 1 fi 上面的例子中，id -u命令返回用户的 ID，一旦用户的 ID 不等于0（根用户的 ID），脚本就会退出，并且退出码为1，表示运行失败。 exit与return命令的差别是，return命令是函数的退出，并返回一个值给调用者，脚本依然执行。exit是整个脚本的退出，如果在函数之中调用exit，则退出函数，并终止脚本执行。","s":"exit 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#exit-命令","p":1769},{"i":1790,"t":"命令执行结束后，会有一个返回值。0表示执行成功，非0（通常是1）表示执行失败。环境变量$?可以读取前一个命令的返回值。 利用这一点，可以在脚本中对命令执行结果进行判断。 cd /path/to/somewhere if [ \"$?\" = \"0\" ]; then rm * else echo \"无法切换目录！\" 1>&2 exit 1 fi 上面例子中，cd /path/to/somewhere这个命令如果执行成功（返回值等于0），就删除该目录里面的文件，否则退出脚本，整个脚本的返回值变为1，表示执行失败。 由于if可以直接判断命令的执行结果，执行相应的操作，上面的脚本可以改写成下面的样子。 if cd /path/to/somewhere; then rm * else echo \"Could not change directory! Aborting.\" 1>&2 exit 1 fi 更简洁的写法是利用两个逻辑运算符&&（且）和||（或）。 # 第一步执行成功，才会执行第二步 cd /path/to/somewhere && rm * # 第一步执行失败，才会执行第二步 cd /path/to/somewhere || exit 1","s":"命令执行结果","u":"/docs/modern-linux/bash-tutorial/script","h":"#命令执行结果","p":1769},{"i":1792,"t":"source命令用于执行一个脚本，通常用于重新加载一个配置文件。 $ source .bashrc source命令最大的特点是在当前 Shell 执行脚本，不像直接执行脚本时，会新建一个子 Shell。所以，source命令执行脚本时，不需要export变量。 #!/bin/bash # test.sh echo $foo 上面脚本输出$foo变量的值。 # 当前 Shell 新建一个变量 foo $ foo=1 # 打印输出 1 $ source test.sh 1 # 打印输出空字符串 $ bash test.sh 上面例子中，当前 Shell 的变量foo并没有export，所以直接执行无法读取，但是source执行可以读取。 source命令的另一个用途，是在脚本内部加载外部库。 #!/bin/bash source ./lib.sh function_from_lib 上面脚本在内部使用source命令加载了一个外部库，然后就可以在脚本里面，使用这个外部库定义的函数。 source有一个简写形式，可以使用一个点（.）来表示。 $ . .bashrc","s":"source 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#source-命令","p":1769},{"i":1794,"t":"alias命令用来为一个命令指定别名，这样更便于记忆。下面是alias的格式。 alias NAME=DEFINITION 上面命令中，NAME是别名的名称，DEFINITION是别名对应的原始命令。注意，等号两侧不能有空格，否则会报错。 一个常见的例子是为grep命令起一个search的别名。 alias search=grep alias也可以用来为长命令指定一个更短的别名。下面是通过别名定义一个today的命令。 $ alias today='date +\"%A, %B %-d, %Y\"' $ today 星期一, 一月 6, 2020 有时为了防止误删除文件，可以指定rm命令的别名。 $ alias rm='rm -i' 上面命令指定rm命令是rm -i，每次删除文件之前，都会让用户确认。 alias定义的别名也可以接受参数，参数会直接传入原始命令。 $ alias echo='echo It says: ' $ echo hello world It says: hello world 上面例子中，别名定义了echo命令的前两个参数，等同于修改了echo命令的默认行为。 指定别名以后，就可以像使用其他命令一样使用别名。一般来说，都会把常用的别名写在~/.bashrc的末尾。另外，只能为命令定义别名，为其他部分（比如很长的路径）定义别名是无效的。 直接调用alias命令，可以显示所有别名。 $ alias unalias命令可以解除别名。 $ unalias lt","s":"别名，alias 命令","u":"/docs/modern-linux/bash-tutorial/script","h":"#别名alias-命令","p":1769},{"i":1796,"t":"How to use getopts to parse a script options, Egidio Docile","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/script","h":"#参考链接","p":1769},{"i":1798,"t":"set命令是 Bash 脚本的重要环节，却常常被忽视，导致脚本的安全性和可维护性出问题。本章介绍set的基本用法，帮助你写出更安全的 Bash 脚本。","s":"set 命令，shopt 命令","u":"/docs/modern-linux/bash-tutorial/set","h":"","p":1797},{"i":1800,"t":"我们知道，Bash 执行脚本时，会创建一个子 Shell。 $ bash script.sh 上面代码中，script.sh是在一个子 Shell 里面执行。这个子 Shell 就是脚本的执行环境，Bash 默认给定了这个环境的各种参数。 set命令用来修改子 Shell 环境的运行参数，即定制环境。一共有十几个参数可以定制，官方手册有完整清单，本章介绍其中最常用的几个。 顺便提一下，如果命令行下不带任何参数，直接运行set，会显示所有的环境变量和 Shell 函数。 $ set","s":"简介","u":"/docs/modern-linux/bash-tutorial/set","h":"#简介","p":1797},{"i":1802,"t":"执行脚本时，如果遇到不存在的变量，Bash 默认忽略它。 #!/usr/bin/env bash echo $a echo bar 上面代码中，$a是一个不存在的变量。执行结果如下。 $ bash script.sh bar 可以看到，echo $a输出了一个空行，Bash 忽略了不存在的$a，然后继续执行echo bar。大多数情况下，这不是开发者想要的行为，遇到变量不存在，脚本应该报错，而不是一声不响地往下执行。 set -u就用来改变这种行为。脚本在头部加上它，遇到不存在的变量就会报错，并停止执行。 #!/usr/bin/env bash set -u echo $a echo bar 运行结果如下。 $ bash script.sh bash: script.sh:行4: a: 未绑定的变量 可以看到，脚本报错了，并且不再执行后面的语句。 -u还有另一种写法-o nounset，两者是等价的。 set -o nounset","s":"set -u","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--u","p":1797},{"i":1804,"t":"默认情况下，脚本执行后，只输出运行结果，没有其他内容。如果多个命令连续执行，它们的运行结果就会连续输出。有时会分不清，某一段内容是什么命令产生的。 set -x用来在运行结果之前，先输出执行的那一行命令。 #!/usr/bin/env bash set -x echo bar 执行上面的脚本，结果如下。 $ bash script.sh + echo bar bar 可以看到，执行echo bar之前，该命令会先打印出来，行首以+表示。这对于调试复杂的脚本是很有用的。 -x还有另一种写法-o xtrace。 set -o xtrace 脚本当中如果要关闭命令输出，可以使用set +x。 #!/bin/bash number=1 set -x if [ $number = \"1\" ]; then echo \"Number equals 1\" else echo \"Number does not equal 1\" fi set +x 上面的例子中，只对特定的代码段打开命令输出。","s":"set -x","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--x","p":1797},{"i":1806,"t":"如果脚本里面有运行失败的命令（返回值非0），Bash 默认会继续执行后面的命令。 #!/usr/bin/env bash foo echo bar 上面脚本中，foo是一个不存在的命令，执行时会报错。但是，Bash 会忽略这个错误，继续往下执行。 $ bash script.sh script.sh:行3: foo: 未找到命令 bar 可以看到，Bash 只是显示有错误，并没有终止执行。 这种行为很不利于脚本安全和除错。实际开发中，如果某个命令失败，往往需要脚本停止执行，防止错误累积。这时，一般采用下面的写法。 command || exit 1 上面的写法表示只要command有非零返回值，脚本就会停止执行。 如果停止执行之前需要完成多个操作，就要采用下面三种写法。 # 写法一 command || { echo \"command failed\"; exit 1; } # 写法二 if ! command; then echo \"command failed\"; exit 1; fi # 写法三 command if [ \"$?\" -ne 0 ]; then echo \"command failed\"; exit 1; fi 另外，除了停止执行，还有一种情况。如果两个命令有继承关系，只有第一个命令成功了，才能继续执行第二个命令，那么就要采用下面的写法。 command1 && command2","s":"Bash 的错误处理","u":"/docs/modern-linux/bash-tutorial/set","h":"#bash-的错误处理","p":1797},{"i":1808,"t":"上面这些写法多少有些麻烦，容易疏忽。set -e从根本上解决了这个问题，它使得脚本只要发生错误，就终止执行。 #!/usr/bin/env bash set -e foo echo bar 执行结果如下。 $ bash script.sh script.sh:行4: foo: 未找到命令 可以看到，第 4 行执行失败以后，脚本就终止执行了。 set -e根据返回值来判断，一个命令是否运行失败。但是，某些命令的非零返回值可能不表示失败，或者开发者希望在命令失败的情况下，脚本继续执行下去。这时可以暂时关闭set -e，该命令执行结束后，再重新打开set -e。 set +e command1 command2 set -e 上面代码中，set +e表示关闭-e选项，set -e表示重新打开-e选项。 还有一种方法是使用command || true，使得该命令即使执行失败，脚本也不会终止执行。 #!/bin/bash set -e foo || true echo bar 上面代码中，true使得这一行语句总是会执行成功，后面的echo bar会执行。 -e还有另一种写法-o errexit。 set -o errexit","s":"set -e","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--e","p":1797},{"i":1810,"t":"set -e有一个例外情况，就是不适用于管道命令。 所谓管道命令，就是多个子命令通过管道运算符（|）组合成为一个大的命令。Bash 会把最后一个子命令的返回值，作为整个命令的返回值。也就是说，只要最后一个子命令不失败，管道命令总是会执行成功，因此它后面命令依然会执行，set -e就失效了。 请看下面这个例子。 #!/usr/bin/env bash set -e foo | echo a echo bar 执行结果如下。 $ bash script.sh a script.sh:行4: foo: 未找到命令 bar 上面代码中，foo是一个不存在的命令，但是foo | echo a这个管道命令会执行成功，导致后面的echo bar会继续执行。 set -o pipefail用来解决这种情况，只要一个子命令失败，整个管道命令就失败，脚本就会终止执行。 #!/usr/bin/env bash set -eo pipefail foo | echo a echo bar 运行后，结果如下。 $ bash script.sh a script.sh:行4: foo: 未找到命令 可以看到，echo bar没有执行。","s":"set -o pipefail","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--o-pipefail","p":1797},{"i":1812,"t":"一旦设置了-e参数，会导致函数内的错误不会被trap命令捕获（参考《trap 命令》一章）。-E参数可以纠正这个行为，使得函数也能继承trap命令。 #!/bin/bash set -e trap \"echo ERR trap fired!\" ERR myfunc() { # 'foo' 是一个不存在的命令 foo } myfunc 上面示例中，myfunc函数内部调用了一个不存在的命令foo，导致执行这个函数会报错。 $ bash test.sh test.sh:行9: foo：未找到命令 但是，由于设置了set -e，函数内部的报错并没有被trap命令捕获，需要加上-E参数才可以。 #!/bin/bash set -Eeuo pipefail trap \"echo ERR trap fired!\" ERR myfunc() { # 'foo' 是一个不存在的命令 foo } myfunc 执行上面这个脚本，就可以看到trap命令生效了。 $ bash test.sh test.sh:行9: foo：未找到命令 ERR trap fired!","s":"set -E","u":"/docs/modern-linux/bash-tutorial/set","h":"#set--e-1","p":1797},{"i":1814,"t":"set命令还有一些其他参数。 set -n：等同于set -o noexec，不运行命令，只检查语法是否正确。 set -f：等同于set -o noglob，表示不对通配符进行文件名扩展。 set -v：等同于set -o verbose，表示打印 Shell 接收到的每一行输入。 set -o noclobber：防止使用重定向运算符>覆盖已经存在的文件。 上面的-f和-v参数，可以分别使用set +f、set +v关闭。","s":"其他参数","u":"/docs/modern-linux/bash-tutorial/set","h":"#其他参数","p":1797},{"i":1816,"t":"上面重点介绍的set命令的几个参数，一般都放在一起使用。 # 写法一 set -Eeuxo pipefail # 写法二 set -Eeux set -o pipefail 这两种写法建议放在所有 Bash 脚本的头部。 另一种办法是在执行 Bash 脚本的时候，从命令行传入这些参数。 $ bash -euxo pipefail script.sh","s":"set 命令总结","u":"/docs/modern-linux/bash-tutorial/set","h":"#set-命令总结","p":1797},{"i":1818,"t":"shopt命令用来调整 Shell 的参数，跟set命令的作用很类似。之所以会有这两个类似命令的主要原因是，set是从 Ksh 继承的，属于 POSIX 规范的一部分，而shopt是 Bash 特有的。 直接输入shopt可以查看所有参数，以及它们各自打开和关闭的状态。 $ shopt shopt命令后面跟着参数名，可以查询该参数是否打开。 $ shopt globstar globstar off 上面例子表示globstar参数默认是关闭的。 （1）-s -s用来打开某个参数。 $ shopt -s optionNameHere （2）-u -u用来关闭某个参数。 $ shopt -u optionNameHere 举例来说，histappend这个参数表示退出当前 Shell 时，将操作历史追加到历史文件中。这个参数默认是打开的，如果使用下面的命令将其关闭，那么当前 Shell 的操作历史将替换掉整个历史文件。 $ shopt -u histappend （3）-q -q的作用也是查询某个参数是否打开，但不是直接输出查询结果，而是通过命令的执行状态（$?）表示查询结果。如果状态为0，表示该参数打开；如果为1，表示该参数关闭。 $ shopt -q globstar $ echo $? 1 上面命令查询globstar参数是否打开。返回状态为1，表示该参数是关闭的。 这个用法主要用于脚本，供if条件结构使用。下面例子是如果打开了这个参数，就执行if结构内部的语句。 if (shopt -q globstar); then ... fi","s":"shopt 命令","u":"/docs/modern-linux/bash-tutorial/set","h":"#shopt-命令","p":1797},{"i":1820,"t":"The Set Builtin Safer bash scripts with 'set -euxo pipefail' Writing Robust Bash Shell Scripts","s":"参考链接","u":"/docs/modern-linux/bash-tutorial/set","h":"#参考链接","p":1797},{"i":1822,"t":"为了方便用户在不同目录之间切换，Bash 提供了目录堆栈功能。","s":"目录堆栈","u":"/docs/modern-linux/bash-tutorial/stack","h":"","p":1821},{"i":1824,"t":"Bash 可以记忆用户进入过的目录。默认情况下，只记忆前一次所在的目录，cd -命令可以返回前一次的目录。 # 当前目录是 /path/to/foo $ cd bar # 重新回到 /path/to/foo $ cd - 上面例子中，用户原来所在的目录是/path/to/foo，进入子目录bar以后，使用cd -可以回到原来的目录。","s":"cd -","u":"/docs/modern-linux/bash-tutorial/stack","h":"#cd--","p":1821},{"i":1826,"t":"如果希望记忆多重目录，可以使用pushd命令和popd命令。它们用来操作目录堆栈。 pushd命令的用法类似cd命令，可以进入指定的目录。 $ pushd dirname 上面命令会进入目录dirname，并将该目录放入堆栈。 第一次使用pushd命令时，会将当前目录先放入堆栈，然后将所要进入的目录也放入堆栈，位置在前一个记录的上方。以后每次使用pushd命令，都会将所要进入的目录，放在堆栈的顶部。 popd命令不带有参数时，会移除堆栈的顶部记录，并进入新的栈顶目录（即原来的第二条目录）。 下面是一个例子。 # 当前处在主目录，堆栈为空 $ pwd /home/me # 进入 /home/me/foo # 当前堆栈为 /home/me/foo /home/me $ pushd ~/foo # 进入 /etc # 当前堆栈为 /etc /home/me/foo /home/me $ pushd /etc # 进入 /home/me/foo # 当前堆栈为 /home/me/foo /home/me $ popd # 进入 /home/me # 当前堆栈为 /home/me $ popd # 目录不变，当前堆栈为空 $ popd 这两个命令的参数如下。 （1）-n 参数 -n的参数表示仅操作堆栈，不改变目录。 $ popd -n 上面的命令仅删除堆栈顶部的记录，不改变目录，执行完成后还停留在当前目录。 （2）整数参数 这两个命令还可以接受一个整数作为参数，该整数表示堆栈中指定位置的记录（从 0 开始）。pushd命令会把这条记录移动到栈顶，同时切换到该目录；popd则从堆栈中删除这条记录，不会切换目录。 # 将从栈顶算起的3号目录（从0开始）移动到栈顶，同时切换到该目录 $ pushd +3 # 将从栈底算起的3号目录（从0开始）移动到栈顶，同时切换到该目录 $ pushd -3 # 删除从栈顶算起的3号目录（从0开始），不改变当前目录 $ popd +3 # 删除从栈底算起的3号目录（从0开始），不改变当前目录 $ popd -3 上面例子的整数编号都是从 0 开始计算，popd +0是删除第一个目录，popd +1是删除第二个，popd -0是删除最后一个目录，popd -1是删除倒数第二个。 （3）目录参数 pushd可以接受一个目录作为参数，表示将该目录放到堆栈顶部，并进入该目录。 $ pushd dir popd没有这个参数。","s":"pushd，popd","u":"/docs/modern-linux/bash-tutorial/stack","h":"#pushdpopd","p":1821},{"i":1828,"t":"dirs命令可以显示目录堆栈的内容，一般用来查看pushd和popd操作后的结果。 $ dirs ~/foo/bar ~/foo ~ 该命令会输出一行文本，列出目录堆栈，目录之间使用空格分隔。栈顶（最晚入栈的目录）在最左边，栈底（最早入栈的目录）在最右边。 它有以下参数。 -c：清空目录栈。 -l：用户主目录不显示波浪号前缀，而打印完整的目录。 -p：每行一个条目打印目录栈，默认是打印在一行。 -v：每行一个条目，每个条目之前显示位置编号（从 0 开始）。 +N：N为整数，表示显示堆顶算起的第 N 个目录，从零开始。 -N：N为整数，表示显示堆底算起的第 N 个目录，从零开始。","s":"dirs 命令","u":"/docs/modern-linux/bash-tutorial/stack","h":"#dirs-命令","p":1821},{"i":1831,"t":"用户每次使用 Shell，都会开启一个与 Shell 的 Session（对话）。 Session 有两种类型：登录 Session 和非登录 Session，也可以叫做 login shell 和 non-login shell。","s":"Session","u":"/docs/modern-linux/bash-tutorial/startup","h":"#session","p":1829},{"i":1833,"t":"登录 Session 是用户登录系统以后，系统为用户开启的原始 Session，通常需要用户输入用户名和密码进行登录。 登录 Session 一般进行整个系统环境的初始化，启动的初始化脚本依次如下。 /etc/profile：所有用户的全局配置脚本。 /etc/profile.d目录里面所有.sh文件 ~/.bash_profile：用户的个人配置脚本。如果该脚本存在，则执行完就不再往下执行。 ~/.bash_login：如果~/.bash_profile没找到，则尝试执行这个脚本（C shell 的初始化脚本）。如果该脚本存在，则执行完就不再往下执行。 ~/.profile：如果~/.bash_profile和~/.bash_login都没找到，则尝试读取这个脚本（Bourne shell 和 Korn shell 的初始化脚本）。 Linux 发行版更新的时候，会更新/etc里面的文件，比如/etc/profile，因此不要直接修改这个文件。如果想修改所有用户的登陆环境，就在/etc/profile.d目录里面新建.sh脚本。 如果想修改你个人的登录环境，一般是写在~/.bash_profile里面。下面是一个典型的.bash_profile文件。 # .bash_profile PATH=/sbin:/usr/sbin:/bin:/usr/bin:/usr/local/bin PATH=$PATH:$HOME/bin SHELL=/bin/bash MANPATH=/usr/man:/usr/X11/man EDITOR=/usr/bin/vi PS1='\\h:\\w\\$ ' PS2='> ' if [ -f ~/.bashrc ]; then . ~/.bashrc fi export PATH export EDITOR 可以看到，这个脚本定义了一些最基本的环境变量，然后执行了~/.bashrc。 bash命令的--login参数，会强制执行登录 Session 会执行的脚本。 $ bash --login bash命令的--noprofile参数，会跳过上面这些 Profile 脚本。 $ bash --noprofile","s":"登录 Session","u":"/docs/modern-linux/bash-tutorial/startup","h":"#登录-session","p":1829},{"i":1835,"t":"非登录 Session 是用户进入系统以后，手动新建的 Session，这时不会进行环境初始化。比如，在命令行执行bash命令，就会新建一个非登录 Session。 非登录 Session 的初始化脚本依次如下。 /etc/bash.bashrc：对全体用户有效。 ~/.bashrc：仅对当前用户有效。 对用户来说，~/.bashrc通常是最重要的脚本。非登录 Session 默认会执行它，而登录 Session 一般也会通过调用执行它。每次新建一个 Bash 窗口，就相当于新建一个非登录 Session，所以~/.bashrc每次都会执行。注意，执行脚本相当于新建一个非互动的 Bash 环境，但是这种情况不会调用~/.bashrc。 bash命令的--norc参数，可以禁止在非登录 Session 执行~/.bashrc脚本。 $ bash --norc bash命令的--rcfile参数，指定另一个脚本代替.bashrc。 $ bash --rcfile testrc","s":"非登录 Session","u":"/docs/modern-linux/bash-tutorial/startup","h":"#非登录-session","p":1829},{"i":1837,"t":"~/.bash_logout脚本在每次退出 Session 时执行，通常用来做一些清理工作和记录工作，比如删除临时文件，记录用户在本次 Session 花费的时间。 如果没有退出时要执行的命令，这个文件也可以不存在。","s":".bash_logout","u":"/docs/modern-linux/bash-tutorial/startup","h":"#bash_logout","p":1829},{"i":1839,"t":"为了方便 Debug，有时在启动 Bash 的时候，可以加上启动参数。 -n：不运行脚本，只检查是否有语法错误。 -v：输出每一行语句运行结果前，会先输出该行语句。 -x：每一个命令处理之前，先输出该命令，再执行该命令。 $ bash -n scriptname $ bash -v scriptname $ bash -x scriptname","s":"启动选项","u":"/docs/modern-linux/bash-tutorial/startup","h":"#启动选项","p":1829},{"i":1841,"t":"Bash 允许用户定义自己的快捷键。全局的键盘绑定文件默认为/etc/inputrc，你可以在主目录创建自己的键盘绑定文件.inputrc文件。如果定义了这个文件，需要在其中加入下面这行，保证全局绑定不会被遗漏。 $include /etc/inputrc .inputrc文件里面的快捷键，可以像这样定义，\"\\C-t\":\"pwd\\n\"表示将Ctrl + t绑定为运行pwd命令。","s":"键盘绑定","u":"/docs/modern-linux/bash-tutorial/startup","h":"#键盘绑定","p":1829},{"i":1843,"t":"本章介绍 Bash 字符串操作的语法。","s":"字符串操作","u":"/docs/modern-linux/bash-tutorial/string","h":"","p":1842},{"i":1845,"t":"获取字符串长度的语法如下。 ${#varname} 下面是一个例子。 $ myPath=/home/cam/book/long.file.name $ echo ${#myPath} 29 大括号{}是必需的，否则 Bash 会将$#理解成脚本的参数个数，将变量名理解成文本。 $ echo $#myvar 0myvar 上面例子中，Bash 将$#和myvar分开解释了。","s":"字符串的长度","u":"/docs/modern-linux/bash-tutorial/string","h":"#字符串的长度","p":1842},{"i":1847,"t":"字符串提取子串的语法如下。 ${varname:offset:length} 上面语法的含义是返回变量$varname的子字符串，从位置offset开始（从0开始计算），长度为length。 $ count=frogfootman $ echo ${count:4:4} foot 上面例子返回字符串frogfootman从 4 号位置开始的长度为 4 的子字符串foot。 这种语法不能直接操作字符串，只能通过变量来读取字符串，并且不会改变原始字符串。 # 报错 $ echo ${\"hello\":2:3} 上面例子中，\"hello\"不是变量名，导致 Bash 报错。 如果省略length，则从位置offset开始，一直返回到字符串的结尾。 $ count=frogfootman $ echo ${count:4} footman 上面例子是返回变量count从 4 号位置一直到结尾的子字符串。 如果offset为负值，表示从字符串的末尾开始算起。注意，负数前面必须有一个空格，以防止与${variable:-word}的变量的设置默认值语法混淆。这时还可以指定length，length可以是正值，也可以是负值（负值不能超过offset的长度）。 $ foo=\"This string is long.\" $ echo ${foo: -5} long. $ echo ${foo: -5:2} lo $ echo ${foo: -5:-2} lon 上面例子中，offset为-5，表示从倒数第 5 个字符开始截取，所以返回long.。如果指定长度length为2，则返回lo；如果length为-2，表示要排除从字符串末尾开始的 2 个字符，所以返回lon。","s":"子字符串","u":"/docs/modern-linux/bash-tutorial/string","h":"#子字符串","p":1842},{"i":1849,"t":"Bash 提供字符串搜索和替换的多种方法。 （1）字符串头部的模式匹配。 以下两种语法可以检查字符串开头，是否匹配给定的模式。如果匹配成功，就删除匹配的部分，返回剩下的部分。原始变量不会发生变化。 # 如果 pattern 匹配变量 variable 的开头， # 删除最短匹配（非贪婪匹配）的部分，返回剩余部分 ${variable#pattern} # 如果 pattern 匹配变量 variable 的开头， # 删除最长匹配（贪婪匹配）的部分，返回剩余部分 ${variable##pattern} 上面两种语法会删除变量字符串开头的匹配部分（将其替换为空），返回剩下的部分。区别是一个是最短匹配（又称非贪婪匹配），另一个是最长匹配（又称贪婪匹配）。 匹配模式pattern可以使用*、?、[]等通配符。 $ myPath=/home/cam/book/long.file.name $ echo ${myPath#/*/} cam/book/long.file.name $ echo ${myPath##/*/} long.file.name 上面例子中，匹配的模式是/*/，其中*可以匹配任意数量的字符，所以最短匹配是/home/，最长匹配是/home/cam/book/。 下面写法可以删除文件路径的目录部分，只留下文件名。 $ path=/home/cam/book/long.file.name $ echo ${path##*/} long.file.name 上面例子中，模式*/匹配目录部分，所以只返回文件名。 下面再看一个例子。 $ phone=\"555-456-1414\" $ echo ${phone#*-} 456-1414 $ echo ${phone##*-} 1414 如果匹配不成功，则返回原始字符串。 $ phone=\"555-456-1414\" $ echo ${phone#444} 555-456-1414 上面例子中，原始字符串里面无法匹配模式444，所以原样返回。 如果要将头部匹配的部分，替换成其他内容，采用下面的写法。 # 模式必须出现在字符串的开头 ${variable/#pattern/string} # 示例 $ foo=JPG.JPG $ echo ${foo/#JPG/jpg} jpg.JPG 上面例子中，被替换的JPG必须出现在字符串头部，所以返回jpg.JPG。 （2）字符串尾部的模式匹配。 以下两种语法可以检查字符串结尾，是否匹配给定的模式。如果匹配成功，就删除匹配的部分，返回剩下的部分。原始变量不会发生变化。 # 如果 pattern 匹配变量 variable 的结尾， # 删除最短匹配（非贪婪匹配）的部分，返回剩余部分 ${variable%pattern} # 如果 pattern 匹配变量 variable 的结尾， # 删除最长匹配（贪婪匹配）的部分，返回剩余部分 ${variable%%pattern} 上面两种语法会删除变量字符串结尾的匹配部分（将其替换为空），返回剩下的部分。区别是一个是最短匹配（又称非贪婪匹配），另一个是最长匹配（又称贪婪匹配）。 $ path=/home/cam/book/long.file.name $ echo ${path%.*} /home/cam/book/long.file $ echo ${path%%.*} /home/cam/book/long 上面例子中，匹配模式是.*，其中*可以匹配任意数量的字符，所以最短匹配是.name，最长匹配是.file.name。 下面写法可以删除路径的文件名部分，只留下目录部分。 $ path=/home/cam/book/long.file.name $ echo ${path%/*} /home/cam/book 上面例子中，模式/*匹配文件名部分，所以只返回目录部分。 下面的写法可以替换文件的后缀名。 $ file=foo.png $ echo ${file%.png}.jpg foo.jpg 上面的例子将文件的后缀名，从.png改成了.jpg。 下面再看一个例子。 $ phone=\"555-456-1414\" $ echo ${phone%-*} 555-456 $ echo ${phone%%-*} 555 如果匹配不成功，则返回原始字符串。 如果要将尾部匹配的部分，替换成其他内容，采用下面的写法。 # 模式必须出现在字符串的结尾 ${variable/%pattern/string} # 示例 $ foo=JPG.JPG $ echo ${foo/%JPG/jpg} JPG.jpg 上面例子中，被替换的JPG必须出现在字符串尾部，所以返回JPG.jpg。 （3）任意位置的模式匹配。 以下两种语法可以检查字符串内部，是否匹配给定的模式。如果匹配成功，就删除匹配的部分，换成其他的字符串返回。原始变量不会发生变化。 # 如果 pattern 匹配变量 variable 的一部分， # 最长匹配（贪婪匹配）的那部分被 string 替换，但仅替换第一个匹配 ${variable/pattern/string} # 如果 pattern 匹配变量 variable 的一部分， # 最长匹配（贪婪匹配）的那部分被 string 替换，所有匹配都替换 ${variable//pattern/string} 上面两种语法都是最长匹配（贪婪匹配）下的替换，区别是前一个语法仅仅替换第一个匹配，后一个语法替换所有匹配。 $ path=/home/cam/foo/foo.name $ echo ${path/foo/bar} /home/cam/bar/foo.name $ echo ${path//foo/bar} /home/cam/bar/bar.name 上面例子中，前一个命令只替换了第一个foo，后一个命令将两个foo都替换了。 下面的例子将分隔符从:换成换行符。 $ echo -e ${PATH//:/'\\n'} /usr/local/bin /usr/bin /bin ... 上面例子中，echo命令的-e参数，表示将替换后的字符串的\\n字符，解释为换行符。 模式部分可以使用通配符。 $ phone=\"555-456-1414\" $ echo ${phone/5?4/-} 55-56-1414 上面的例子将5-4替换成-。 如果省略了string部分，那么就相当于匹配的部分替换成空字符串，即删除匹配的部分。 $ path=/home/cam/foo/foo.name $ echo ${path/.*/} /home/cam/foo/foo 上面例子中，第二个斜杠后面的string部分省略了，所以模式.*匹配的部分.name被删除后返回。 前面提到过，这个语法还有两种扩展形式。 # 模式必须出现在字符串的开头 ${variable/#pattern/string} # 模式必须出现在字符串的结尾 ${variable/%pattern/string}","s":"搜索和替换","u":"/docs/modern-linux/bash-tutorial/string","h":"#搜索和替换","p":1842},{"i":1851,"t":"下面的语法可以改变变量的大小写。 # 转为大写 ${varname^^} # 转为小写 ${varname,,} 下面是一个例子。 $ foo=heLLo $ echo ${foo^^} HELLO $ echo ${foo,,} hello","s":"改变大小写","u":"/docs/modern-linux/bash-tutorial/string","h":"#改变大小写","p":1842},{"i":1854,"t":"Bash 变量分成环境变量和自定义变量两类。","s":"简介","u":"/docs/modern-linux/bash-tutorial/variable","h":"#简介","p":1852},{"i":1856,"t":"环境变量是 Bash 环境自带的变量，进入 Shell 时已经定义好了，可以直接使用。它们通常是系统定义好的，也可以由用户从父 Shell 传入子 Shell。 env命令或printenv命令，可以显示所有环境变量。 $ env # 或者 $ printenv 下面是一些常见的环境变量。 BASHPID：Bash 进程的进程 ID。 BASHOPTS：当前 Shell 的参数，可以用shopt命令修改。 DISPLAY：图形环境的显示器名字，通常是:0，表示 X Server 的第一个显示器。 EDITOR：默认的文本编辑器。 HOME：用户的主目录。 HOST：当前主机的名称。 IFS：词与词之间的分隔符，默认为空格。 LANG：字符集以及语言编码，比如zh_CN.UTF-8。 PATH：由冒号分开的目录列表，当输入可执行程序名后，会搜索这个目录列表。 PS1：Shell 提示符。 PS2：输入多行命令时，次要的 Shell 提示符。 PWD：当前工作目录。 RANDOM：返回一个 0 到 32767 之间的随机数。 SHELL：Shell 的名字。 SHELLOPTS：启动当前 Shell 的set命令的参数，参见《set 命令》一章。 TERM：终端类型名，即终端仿真器所用的协议。 UID：当前用户的 ID 编号。 USER：当前用户的用户名。 很多环境变量很少发生变化，而且是只读的，可以视为常量。由于它们的变量名全部都是大写，所以传统上，如果用户要自己定义一个常量，也会使用全部大写的变量名。 注意，Bash 变量名区分大小写，HOME和home是两个不同的变量。 查看单个环境变量的值，可以使用printenv命令或echo命令。 $ printenv PATH # 或者 $ echo $PATH 注意，printenv命令后面的变量名，不用加前缀$。","s":"环境变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#环境变量","p":1852},{"i":1858,"t":"自定义变量是用户在当前 Shell 里面自己定义的变量，仅在当前 Shell 可用。一旦退出当前 Shell，该变量就不存在了。 set命令可以显示所有变量（包括环境变量和自定义变量），以及所有的 Bash 函数。 $ set","s":"自定义变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#自定义变量","p":1852},{"i":1860,"t":"用户创建变量的时候，变量名必须遵守下面的规则。 字母、数字和下划线字符组成。 第一个字符必须是一个字母或一个下划线，不能是数字。 不允许出现空格和标点符号。 变量声明的语法如下。 variable=value 上面命令中，等号左边是变量名，右边是变量。注意，等号两边不能有空格。 如果变量的值包含空格，则必须将值放在引号中。 myvar=\"hello world\" Bash 没有数据类型的概念，所有的变量值都是字符串。 下面是一些自定义变量的例子。 a=z # 变量 a 赋值为字符串 z b=\"a string\" # 变量值包含空格，就必须放在引号里面 c=\"a string and $b\" # 变量值可以引用其他变量的值 d=\"\\t\\ta string\\n\" # 变量值可以使用转义字符 e=$(ls -l foo.txt) # 变量值可以是命令的执行结果 f=$((5 * 7)) # 变量值可以是数学运算的结果 变量可以重复赋值，后面的赋值会覆盖前面的赋值。 $ foo=1 $ foo=2 $ echo $foo 2 上面例子中，变量foo的第二次赋值会覆盖第一次赋值。 如果同一行定义多个变量，必须使用分号（;）分隔。 $ foo=1;bar=2 上面例子中，同一行定义了foo和bar两个变量。","s":"创建变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#创建变量","p":1852},{"i":1862,"t":"读取变量的时候，直接在变量名前加上$就可以了。 $ foo=bar $ echo $foo bar 每当 Shell 看到以$开头的单词时，就会尝试读取这个变量名对应的值。 如果变量不存在，Bash 不会报错，而会输出空字符。 由于$在 Bash 中有特殊含义，把它当作美元符号使用时，一定要非常小心， $ echo The total is $100.00 The total is 00.00 上面命令的原意是输入$100，但是 Bash 将$1解释成了变量，该变量为空，因此输入就变成了00.00。所以，如果要使用$的原义，需要在$前面放上反斜杠，进行转义。 $ echo The total is \\$100.00 The total is $100.00 读取变量的时候，变量名也可以使用花括号{}包围，比如$a也可以写成${a}。这种写法可以用于变量名与其他字符连用的情况。 $ a=foo $ echo $a_file $ echo ${a}_file foo_file 上面代码中，变量名a_file不会有任何输出，因为 Bash 将其整个解释为变量，而这个变量是不存在的。只有用花括号区分$a，Bash 才能正确解读。 事实上，读取变量的语法$foo，可以看作是${foo}的简写形式。 如果变量的值本身也是变量，可以使用${!varname}的语法，读取最终的值。 $ myvar=USER $ echo ${!myvar} ruanyf 上面的例子中，变量myvar的值是USER，${!myvar}的写法将其展开成最终的值。 如果变量值包含连续空格（或制表符和换行符），最好放在双引号里面读取。 $ a=\"1 2 3\" $ echo $a 1 2 3 $ echo \"$a\" 1 2 3 上面示例中，变量a的值包含两个连续空格。如果直接读取，Shell 会将连续空格合并成一个。只有放在双引号里面读取，才能保持原来的格式。","s":"读取变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#读取变量","p":1852},{"i":1864,"t":"unset命令用来删除一个变量。 unset NAME 这个命令不是很有用。因为不存在的 Bash 变量一律等于空字符串，所以即使unset命令删除了变量，还是可以读取这个变量，值为空字符串。 所以，删除一个变量，也可以将这个变量设成空字符串。 $ foo='' $ foo= 上面两种写法，都是删除了变量foo。由于不存在的值默认为空字符串，所以后一种写法可以在等号右边不写任何值。","s":"删除变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#删除变量","p":1852},{"i":1866,"t":"用户创建的变量仅可用于当前 Shell，子 Shell 默认读取不到父 Shell 定义的变量。为了把变量传递给子 Shell，需要使用export命令。这样输出的变量，对于子 Shell 来说就是环境变量。 export命令用来向子 Shell 输出变量。 NAME=foo export NAME 上面命令输出了变量NAME。变量的赋值和输出也可以在一个步骤中完成。 export NAME=value 上面命令执行后，当前 Shell 及随后新建的子 Shell，都可以读取变量$NAME。 子 Shell 如果修改继承的变量，不会影响父 Shell。 # 输出变量 $foo $ export foo=bar # 新建子 Shell $ bash # 读取 $foo $ echo $foo bar # 修改继承的变量 $ foo=baz # 退出子 Shell $ exit # 读取 $foo $ echo $foo bar 上面例子中，子 Shell 修改了继承的变量$foo，对父 Shell 没有影响。","s":"输出变量，export 命令","u":"/docs/modern-linux/bash-tutorial/variable","h":"#输出变量export-命令","p":1852},{"i":1868,"t":"Bash 提供一些特殊变量。这些变量的值由 Shell 提供，用户不能进行赋值。 （1）$? $?为上一个命令的退出码，用来判断上一个命令是否执行成功。返回值是0，表示上一个命令执行成功；如果不是零，表示上一个命令执行失败。 $ ls doesnotexist ls: doesnotexist: No such file or directory $ echo $? 1 上面例子中，ls命令查看一个不存在的文件，导致报错。$?为 1，表示上一个命令执行失败。 （2）$$ $$为当前 Shell 的进程 ID。 $ echo $$ 10662 这个特殊变量可以用来命名临时文件。 LOGFILE=/tmp/output_log.$$ （3）$_ $_为上一个命令的最后一个参数。 $ grep dictionary /usr/share/dict/words dictionary $ echo $_ /usr/share/dict/words （4）$! $!为最近一个后台执行的异步命令的进程 ID。 $ firefox & [1] 11064 $ echo $! 11064 上面例子中，firefox是后台运行的命令，$!返回该命令的进程 ID。 （5）$0 $0为当前 Shell 的名称（在命令行直接执行时）或者脚本名（在脚本中执行时）。 $ echo $0 bash 上面例子中，$0返回当前运行的是 Bash。 （6）$- $-为当前 Shell 的启动参数。 $ echo $- himBHs （7）$@和$# $#表示脚本的参数数量，$@表示脚本的参数值，参见脚本一章。","s":"特殊变量","u":"/docs/modern-linux/bash-tutorial/variable","h":"#特殊变量","p":1852},{"i":1870,"t":"Bash 提供四个特殊语法，跟变量的默认值有关，目的是保证变量不为空。 ${varname:-word} 上面语法的含义是，如果变量varname存在且不为空，则返回它的值，否则返回word。它的目的是返回一个默认值，比如${count:-0}表示变量count不存在时返回0。 ${varname:=word} 上面语法的含义是，如果变量varname存在且不为空，则返回它的值，否则将它设为word，并且返回word。它的目的是设置变量的默认值，比如${count:=0}表示变量count不存在时返回0，且将count设为0。 ${varname:+word} 上面语法的含义是，如果变量名存在且不为空，则返回word，否则返回空值。它的目的是测试变量是否存在，比如${count:+1}表示变量count存在时返回1（表示true），否则返回空值。 ${varname:?message} 上面语法的含义是，如果变量varname存在且不为空，则返回它的值，否则打印出varname: message，并中断脚本的执行。如果省略了message，则输出默认的信息“parameter null or not set.”。它的目的是防止变量未定义，比如${count:?\"undefined!\"}表示变量count未定义时就中断执行，抛出错误，返回给定的报错信息undefined!。 上面四种语法如果用在脚本中，变量名的部分可以用数字1到9，表示脚本的参数。 filename=${1:?\"filename missing.\"} 上面代码出现在脚本中，1表示脚本的第一个参数。如果该参数不存在，就退出脚本并报错。","s":"变量的默认值","u":"/docs/modern-linux/bash-tutorial/variable","h":"#变量的默认值","p":1852},{"i":1872,"t":"declare命令可以声明一些特殊类型的变量，为变量设置一些限制，比如声明只读类型的变量和整数类型的变量。 它的语法形式如下。 declare OPTION VARIABLE=value declare命令的主要参数（OPTION）如下。 -a：声明数组变量。 -f：输出所有函数定义。 -F：输出所有函数名。 -i：声明整数变量。 -l：声明变量为小写字母。 -p：查看变量信息。 -r：声明只读变量。 -u：声明变量为大写字母。 -x：该变量输出为环境变量。 declare命令如果用在函数中，声明的变量只在函数内部有效，等同于local命令。 不带任何参数时，declare命令输出当前环境的所有变量，包括函数在内，等同于不带有任何参数的set命令。 $ declare （1）-i参数 -i参数声明整数变量以后，可以直接进行数学运算。 $ declare -i val1=12 val2=5 $ declare -i result $ result=val1*val2 $ echo $result 60 上面例子中，如果变量result不声明为整数，val1*val2会被当作字面量，不会进行整数运算。另外，val1和val2其实不需要声明为整数，因为只要result声明为整数，它的赋值就会自动解释为整数运算。 注意，一个变量声明为整数以后，依然可以被改写为字符串。 $ declare -i var=12 $ var=foo $ echo $var 0 上面例子中，变量var声明为整数，覆盖以后，Bash 不会报错，但会赋以不确定的值，上面的例子中可能输出 0，也可能输出的是 3。 （2）-x参数 -x参数等同于export命令，可以输出一个变量为子 Shell 的环境变量。 $ declare -x foo # 等同于 $ export foo （3）-r参数 -r参数可以声明只读变量，无法改变变量值，也不能unset变量。 $ declare -r bar=1 $ bar=2 bash: bar：只读变量 $ echo $? 1 $ unset bar bash: bar：只读变量 $ echo $? 1 上面例子中，后两个赋值语句都会报错，命令执行失败。 （4）-u参数 -u参数声明变量为大写字母，可以自动把变量值转成大写字母。 $ declare -u foo $ foo=upper $ echo $foo UPPER （5）-l参数 -l参数声明变量为小写字母，可以自动把变量值转成小写字母。 $ declare -l bar $ bar=LOWER $ echo $bar lower （6）-p参数 -p参数输出变量信息。 $ foo=hello $ declare -p foo declare -- foo=\"hello\" $ declare -p bar bar：未找到 上面例子中，declare -p可以输出已定义变量的值，对于未定义的变量，会提示找不到。 如果不提供变量名，declare -p输出所有变量的信息。 $ declare -p （7）-f参数 -f参数输出当前环境的所有函数，包括它的定义。 $ declare -f （8）-F参数 -F参数输出当前环境的所有函数名，不包含函数定义。 $ declare -F","s":"declare 命令","u":"/docs/modern-linux/bash-tutorial/variable","h":"#declare-命令","p":1852},{"i":1874,"t":"readonly命令等同于declare -r，用来声明只读变量，不能改变变量值，也不能unset变量。 $ readonly foo=1 $ foo=2 bash: foo：只读变量 $ echo $? 1 上面例子中，更改只读变量foo会报错，命令执行失败。 readonly命令有三个参数。 -f：声明的变量为函数名。 -p：打印出所有的只读变量。 -a：声明的变量为数组。","s":"readonly 命令","u":"/docs/modern-linux/bash-tutorial/variable","h":"#readonly-命令","p":1852},{"i":1876,"t":"let命令声明变量时，可以直接执行算术表达式。 $ let foo=1+2 $ echo $foo 3 上面例子中，let命令可以直接计算1 + 2。 let命令的参数表达式如果包含空格，就需要使用引号。 $ let \"foo = 1 + 2\" let可以同时对多个变量赋值，赋值表达式之间使用空格分隔。 $ let \"v1 = 1\" \"v2 = v1++\" $ echo $v1,$v2 2,1 上面例子中，let声明了两个变量v1和v2，其中v2等于v1++，表示先返回v1的值，然后v1自增。 这种语法支持的运算符，参考《Bash 的算术运算》一章。","s":"let 命令","u":"/docs/modern-linux/bash-tutorial/variable","h":"#let-命令","p":1852},{"i":1878,"t":"For modern CLI Tools on x86_64 Linux distros, see: CLI Prebuilts. I'll recommend some best plugins I use frequently.","s":"Modern CLI Tools","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"","p":1877},{"i":1880,"t":"mise is a runtime manager to auto install and manager different software versions, like asdf, but much faster as it's built upon Rust. Suppose you need to use node version 21, but your distro do not support now. With mise, you can skip the procedure from downloading the package, build, and add to environment variable PATH; instead, you only need to: mise global node@21 Later in some day, you find some legacy projects and it's build upon node 18, you can simply do: mise local node@18 mise is compatible with asdf. you can see all supported plugins on asdf-plugins.","s":"mise","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#mise","p":1877},{"i":1882,"t":"Fast grep-like, git-aware code-search with colourized output, written in Rust. It’s a tool intended for performing blazing fast searches of your code, but unlike grep, it respects the patterns defined in your .gitignore file, and it doesn’t search your .git directory either. To search with rg, use: -t > rg md README README.md 1:# README black/README.md 974: Use the badge in your project README.md: 980: Using the badge in README.rst:","s":"rg","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#rg","p":1877},{"i":1884,"t":"Fast git-aware file searching with colourized output. fd is for find what Ripgrep is for grep: It searches filenames and respects your .gitignore patterns. But unlike the find command, the options are easy to remember. To search with filename: passwd > fd /etc /etc/default/passwd /etc/pam.d/passwd /etc/passwd To search all markdown files, use -e: -e > fd md CONTRIBUTING.md README.md","s":"fd","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#fd","p":1877},{"i":1886,"t":"fzf is a general-purpose command-line fuzzy finder. 备注 Suggest to install rg and fd before using fzf. It offers key bindings CTRL-T to search for filenames with fuzzy in an interactive way.","s":"fzf","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#fzf","p":1877},{"i":1888,"t":"eza and lsd are git-aware ls replacements with clever utilization of colour. eza is a fork of original project exa which is not under maintained anymore.","s":"eza or lsd.","u":"/docs/modern-linux/command-line-tools/modern-cli-tools","h":"#eza-or-lsd","p":1877},{"i":1890,"t":"信息 I've created a dotfiles for multi softwares including multi configurations, see GitHub - ShangjinTang/dotfiles. You can clone it or take it as a dotfiles sample. Dotfiles are important files that will play an integral role in your career as a software developer. First, they can help make you more productive. But not only that - you'll be able to have that productive setup you created for youself on any machine. This article is an introduction on how to get started with dotfiles.","s":"Manage Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"","p":1889},{"i":1892,"t":"Many computer software programs store their configuration settings in plain, text-based files or directories. Dotfiles are configuration files for various programs, and they help those programs manage their functionality. What sets them apart from regular files and directories is their prefix. Dotfiles are named that way because each file and directory starts with a dot (.) On Unix based systems, dotfiles are hidden by the Operating System by default. Examples of common dotfiles Most programs store their configurations in your home directory by default. Some common dotfiles that you may have heard of or used before are: If you use the Bash shell, you might have a .bash_profile and .bashrc file, both of which contain scripts that load each time you start a new terminal session and configure the shell. If you use the Zsh shell, you would have (or would've created) a .zshrc file which configures and customises the shell. If you use the command line code editor Vim, you would store its configurations in a .vimrc file. After setting up and configuring Git on your local machine, you would have a .gitconfig file, which would contain all your information and settings. Many programs, instead of storing their configurations in your home directory, instead store them in the hidden .config directory (folder) on your system.","s":"What are dotfiles?","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#what-are-dotfiles","p":1889},{"i":1894,"t":"Your dotfiles are personal to you. You spend a sufficient amount of time fine-tuning your setup. You curate configurations and settings that best suit your workflow, aesthetic, and preferences. And you end up with a development environment that helps you, personally, be more productive. What if after all that time you spent, you now have to switch to a new, different machine? Does that mean you have to start all over again from the beginning? How would you remember the exact settings and commands you used? Or what if you have a second machine and you want your set up to be exactly the same on both systems? One of the main goals of developers is to automate repetitive tasks. Creating a dotfile repository that is source-controlled and hosted on GitHub will save you time when you want to set up a new computer and install the exact same settings you created for your previous one. That way all your settings and preferences can be reusable and consistent on other machines.","s":"Why Use Dotfiles?","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#why-use-dotfiles","p":1889},{"i":1896,"t":"It's good practice to have all your dotfiles in their own folder. For simplicity's sake, I'll show an example of how to create a folder at the root of your home directory. But you can add the folder wherever is more convenient for you. Also, I'll be showing examples of how to create a .zshrc and .vimrc file, but similar ideas apply to any other dotfiles you create. cd ~ mkdir .dotfiles cp ~/.zshrc ~/.dotfiles/.zshrc ~/.dotfiles/.vimrc","s":"How to Create Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#how-to-create-dotfiles","p":1889},{"i":1898,"t":"You may have noticed that none of the settings you added to the files in the dotfiles folder have any effect on your system. A program's configuration files, as mentioned previously, are hidden and stored in the home directory by default. This is where the program will look for and read its settings from. It's a good idea to symlink (or create a symbolic link -a pointer) the file in the dotfiles directory where you have stored your preferred settings alongside with other files you created, with the file in its default home directory. It's like the file will be in two places at the same time! The file will be in both the dotfiles directory and there will also be a 'copy' of it in the home directory. To create a link, you use the ln (stands for link) command with the -s argument (which stands for symbolic). Here's how to symlink the .zshrc and .vimrc files: ln -s ~/dotfiles/.vimrc ~/.vimrc ln -s ~/dotfiles/.zshrc ~/.zshrc","s":"How to Symlink your Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#how-to-symlink-your-dotfiles","p":1889},{"i":1900,"t":"Having your files under version control will help you track all the changes you make to them over time, and will also allow you to share them on GitHub. Make sure to change directory into the dotfiles directory (cd ~/.dotfiles). Follow these steps to organise your files in a git repository: Initialise the repository: git init Add all the files you've created so far: git add . Commit the changes and add a commit message: git commit -m \"Added dotfiles\" Once git repository is created, you can upload it to GitHub or GitLab so it won't be lost. 危险 Do you create public repository if you want to store some privacy data, such as GitHub token, ssh keys, etc. 信息 These link procedure are done by hand and hard to maintain across different environments; for automatically installation with config files, I recommend to use GitHub - dotbot.","s":"How to Version Control your Dotfiles","u":"/docs/modern-linux/dotfiles/manage-dotfiles","h":"#how-to-version-control-your-dotfiles","p":1889},{"i":1902,"t":"It is based on Ubuntu Latest LTS (currently 22.04) or ArchLinux. You can use these in WSL2.","s":"Modern Linux","u":"/docs/modern-linux/intro","h":"","p":1901},{"i":1904,"t":"Linux is an operating system, similar to Windows, but with many different versions due to the nature of being open source and fully customizable. To install Linux, you must choose an install method and choose a Linux distribution. To install Linux: Choose an install method: Windows Subsystem for Linux (WSL), bare metal Linux, or create a Virtual Machine (VM) to run Linux locally. Choose a Linux distribution: Ubuntu, Debian, Kali Linux, openSUSE, ArchLinux, etc. Follow the steps for your preferred install method: Use the install Linux command with Windows Subsystem for Linux (WSL) Create a Linux Virtual Machine (VM) on your local machine Create a bootable USB to install bare-metal Linux After installing Linux: Get familiar with your distribution's package manager, update and upgrade the packages available, and get familiar with the other Linux resources at Microsoft, such as training courses, Linux-versions of popular tools, news, and Open Source events.","s":"Linux Installation","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"","p":1903},{"i":1906,"t":"The choice of which method to use for installing Linux depends on your needs and preferences. Only want to run Linux as your primary operating system? If you are good with a slightly more complicated install process and don't need access to Windows tools (like Outlook, Teams, Word, PowerPoint, etc), you can run Linux on bare metal to access the full potential of your hardware without any overhead from virtualization or emulation. New to using Linux? We recommend starting with Windows Subsystem for Linux (WSL) as it's the easiest way to get up and running. Learn more about these options below.","s":"Step 1 - Choose a method to install Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-1---choose-a-method-to-install-linux","p":1903},{"i":1908,"t":"Available to those with a Windows machine, this is the most simple way to install Linux. Just run the Linux install command: wsl --install to install the Ubuntu distribution. This method uses virtualization to integrate the Windows operating system (OS) with the Linux OS (running on an actual Linux kernel). You can add as many different Linux distributions as you please and run your favorite Linux tools, including GUI apps, alongside your favorite Windows tools. You can also mix and match Bash and PowerShell commands in the same command line. A Linux file system hosts your project files, while a separate Windows file systems hosts any developer tools, such as VS Code, that you'd like to work on the files with. This method of running Linux is highly efficient and performant. Once you choose a Linux distribution or opt to use the default Ubuntu distro, follow the instructions to Use the install Linux command with Windows Subsystem for Linux or learn more in the WSL documentation.","s":"Windows Subsystem for Linux (WSL)","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-2---choose-a-linux-distribution-choose-wsl","p":1903},{"i":1910,"t":"Available to everyone regardless if you're using a Windows or MacOS-based machine, but will require a virtualization software, if creating a VM directly on your machine (locally). A VM is a digital version of a physical computer and is a popular option for running Linux in environments that may require you to scale the level of hardware support (Memory and processing power required) and the level of Security (antimalware, encryption, backups, policy management, etc). Like with WSL, you can create VM instances of as many different Linux distributions as you'd like, running them in an isolated environment, free from any conflicts and great for software development testing. While running a Linux distribution on WSL has slightly faster performance, a Linux VM is easier to clone or migrate. Creating a VM on your local machine requires virtualization using a hypervisor. Windows includes a \"type 1\" hypervisor called Hyper-V to run virtualization directly on your device hardware. There are also \"type 2\" hypervisors that run on top of the operating system, like VirtualBox or VMware Workstation Pro. If you are using a Mac, the most commonly recommended hypervisor is Parallels Desktop, though this is a paid service. VirtualBox also supports both Windows and MacOS. You are responsible for managing the virtual machine when using a hypervisor, including allocating resources like memory and disk space, and ensuring that it is secure and up-to-date. This requires more technical expertise than some of the other options and may not be as scalable or fault-tolerant. Once you've chosen a distribution and decided whether you want to run the VM locally, using a hypervisor, follow the instructions to Create a Linux Virtual Machine locally using a Hypervisor.","s":"Create a Virtual Machine (VM)","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-2---choose-a-linux-distribution-create-vm","p":1903},{"i":1912,"t":"Bare metal Linux just means that Linux is running directly on the device hardware. This install method requires you to create a bootable USB drive by downloading an iso install file from the site hosting your chosen Linux distribution. You will need to use a Windows computer (or any desktop device with an existing OS) to create this drive. Many users choose the traditional method of installing bare metal Linux on a device that is also running Windows and using the \"dual boot\" method. To boot Linux and Windows, you need to partition your hard drive to create separate spaces for both the Linux and Windows OS. The performance speed between WSL, virtual machines, and bare metal Linux has become so close that few developers choose this method due to the overhead of needing to restart (reboot) your device any time you want to switch between the operating systems. If you choose the bare metal Linux install route, you may also need to deal with potential driver issues or hardware compatibility problems that may arise with Linux on some devices. You can find a list of Popular Linux Distributions available for download on Linux.org. Once you've chosen a distro, follow the instructions to Create a bootable USB to install bare-metal Linux.","s":"Bare metal Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-2---choose-a-linux-distribution-bare-metal-linux","p":1903},{"i":1914,"t":"The different versions of Linux are called \"distributions\" (sometimes shortened to “distros”). So there isn’t actually a way to just “install Linux”, you first need to choose which distribution that uses the Linux kernel you want to download and install. There are over 600 active Linux distributions, such as Ubuntu, Debian, Kali Linux, openSUSE, and more. There are a number of factors to consider in choosing a distribution, such as:","s":"Step 2 - Choose a Linux distribution","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-2---choose-a-linux-distribution","p":1903},{"i":1916,"t":"If you’re new to Linux, you may want to start with Ubuntu. This is one of the most common starting places for Linux users due to the level of support and ease of use. Ubuntu offers a desktop-version and a server-version depending on how you plan to use it. The specific tasks that the operating system will be responsible for may help you determine which distribution to use. Arch Linux is a popular choice for those who want a highly customizable, do-it-yourself approach that is still stable and well-supported by a large user base. It is a much more complicated place to start, but can help you to get a better understanding of how Linux works due to the amount of custom configuration.","s":"Required Linux experience","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#required-linux-experience","p":1903},{"i":1918,"t":"A minimal, or \"lightweight\", distribution means a small footprint, with lower memory and processing speed requirements. Alpine Linux is a popular option where users will find most features disabled or not installed by default, but still has everything you need for a containerized app. Security needs: Some Linux users may have specific security concerns to consider. Kali Linux is an example of a distro designed for security tasks, such as Penetration Testing, Security Research, Computer Forensics and Reverse Engineering.","s":"System requirements","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#system-requirements","p":1903},{"i":1920,"t":"A large user community that consistently contributes to the distribution, fixing bugs, adding features, helping with questions, etc. is another good consideration. Ubuntu is one of the most popular distos. Many other distros rapidly grow popular as the needs and preferences of the user community change. The Linux.org site has resources to help you assess what's available, well-supported, or growing in popularity.","s":"Community support","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#community-support","p":1903},{"i":1923,"t":"To install Linux on a Windows PC, use the install Linux command. Open PowerShell or Windows Command Prompt in administrator mode by right-clicking and selecting \"Run as administrator\". Enter the Linux install command: wsl --install. Restart your machine.","s":"Install Linux with Windows Subsystem for Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#install-linux-with-windows-subsystem-for-linux","p":1903},{"i":1925,"t":"By default, the install command will use the Ubuntu distribution of Linux. You can see the other distributions that are available in the Microsoft Store by entering the command: wsl -l -o. If you'd like to install a distribution other than Ubuntu, just add -d to the command with the name of the distribution you'd like to install: wsl --install -d <Distro Name> Some distributions are not official supported, but you can find them in open source projects. For example, ArchLinux is a great distribution and can be installed using GitHub - yuk7/ArchWSL.","s":"Install Linux command options","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#install-linux-command-options","p":1903},{"i":1927,"t":"To create a Linux VM that is hosted on your local machine using a hypervisor, you can choose a virtual machine software: VMware Workstation Pro VirtualBox The most obvious distinction between the two is that VirtualBox is a free and open-source software programme.","s":"Create a Linux Virtual Machine locally using a hypervisor","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#create-a-linux-virtual-machine-locally-using-a-hypervisor","p":1903},{"i":1929,"t":"If you want bare-metal Linux, whether to run a distribution alone on a device or to dual-boot between the distribution and Windows, here are the steps: Download an image file for your chosen Linux distribution. This is usually an ISO file. As an example, you can find an image file for the most recent version of Ubuntu at Download Ubuntu Desktop. Some Linux distributions may require you to verify the image signature before downloading. Some Linux distributions also cannot be installed unless Windows Secure Boot is disabled (which is not recommended). Create a bootable USB drive. You will typically need a USB drive with at least 16gb of space. You will also need software to create the bootable drive. There are many options (such as balenaEtcher, Rufus, UNetbootin, etc.). Often the download site for your chosen Linux distribution will recommend which startup disk creater software to use. Boot your device from the USB drive. When restarting the device, you will need to enter the boot menu. This is typically done by holding down the F12 key during startup. You can then select the USB drive containing your Linux distribution ISO to install from. Select install options. Typically the installer for your Linux distribution will include a set of installation steps that will involve choosing options about whether you want to include certain features, third-party software packages, etc. You may also need to specify whether to erase the disk in the case that this Linux distro will be the only operating system, or to use a partition, if you plan to run multiple operating systems. You may also be asked about whether you'd like to enable encryption. Finally, as with any Linux installation, you will be asked to create a user name and password.","s":"Create a bootable USB drive to install bare-metal Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#create-a-bootable-usb-drive-to-install-bare-metal-linux","p":1903},{"i":1931,"t":"Once you have successfully installed a Linux distribution, there are a few more important steps: Get familiar with the preferred package manager used by your chosen Linux distribution. Linux uses package manager's to download and update any software that you plan to use. For example, Ubuntu uses the Advanced Packaging Tool (apt), ArchLinux uses the Package Manager (pacman). Use your distribution's package manager to update and upgrade your distribution. Software packages in a stable release of a Linux distribution are often outdated. It is recommended to regularly run an update. You may also want to run an upgrade, which installs newer versions of any packages that you've already installed. For example, if you're using Ubuntu, run: sudo apt update && sudo apt upgrade; if you're using ArchLinux, run: sudo pacman -Syu. Learn more about the Linux tools, such as Visual Studio Code, vim, git to speed up your development and usage.","s":"Step 4 - After installing Linux","u":"/docs/modern-linux/linux-user-guide/linux-installation","h":"#step-4---after-installing-linux","p":1903},{"i":1934,"t":"The Vim editor is a successor to the vi editor found on the original UNIX. As a fork of Vim, Neovim is an editor that aims to improve the quality of life for all developers, better than Vim.","s":"What is NVIM?","u":"/docs/modern-linux/nvim/use-nvim","h":"#what-is-nvim","p":1932},{"i":1936,"t":"Project maintenance and feature improvements: Vim codebase is less maintainable compared to Neovim; and compared to Vim Language, NeoVim uses Lua which is easier to read and write. Code auto-completion (LSP): Neovim ships with out-of-box support for LSP and uses Lua for further configuration. Support for better plugins: With an actual programming language, this configuration is comparatively easier than Vim.","s":"Why use NVIM?","u":"/docs/modern-linux/nvim/use-nvim","h":"#why-use-nvim","p":1932},{"i":1938,"t":"If you are using ArchLinux, just run sudo pacman -Syu neovim. If you are using Ubuntu, follow the steps: Download NVIM appimage with latest version. Install fuse by sudo apt install -y fuse. Run chmod u+x nvim.appimage && mkdir ~/bin && mv nvim.appimage ./bin/nvim","s":"How to install NVIM","u":"/docs/modern-linux/nvim/use-nvim","h":"#how-to-install-nvim","p":1932},{"i":1940,"t":"Pick up one of the top NVIM framework. LazyVim NvChad LunarVim AstroNvim I use LunarVim and the configurations are as below, managed by dotfiles for syncing. See: NVIM Plugins and Configurations LunarVim Customization Diff Files","s":"NVIM-based configurations","u":"/docs/modern-linux/nvim/use-nvim","h":"#nvim-based-configurations","p":1932},{"i":1942,"t":"Bash, or the Bourne Again Shell, is a hallmark of Linux systems. However, there are other shells out there that may offer extra functionality. Here's how to install one popular alternative, ZSH.","s":"Use ZSH","u":"/docs/modern-linux/zsh/use-zsh","h":"","p":1941},{"i":1944,"t":"ZSH, also called the Z shell, is an extended version of the Bourne Shell (sh), with new features and support for plugins and themes. Since it's based on the same shell as Bash, ZSH has many of the same features, and switching over is a breeze. ZSH vs. Bash: The Important Differences ZSH has too many features to list here, some just minor improvements to Bash, but here are some of the major ones: Automatic cd: Just type the name of the directory Recursive path expansion: For example /u/lo/b expands to /usr/local/bin Automatic Syntax Highlighting: Words, file extensions, and other things visible in the Terminal are color-coded Spelling correction and approximate completion: If you make a minor mistake typing a directory name, ZSH will fix it for you Plugin and theme support: ZSH includes many different plugin frameworks Plugin and theme support is probably the coolest feature of ZSH and is what we'll focus on here. If you're on Linux, the command to install ZSH varies by the distro, but it should be a default package in your package manager.","s":"What is ZSH?","u":"/docs/modern-linux/zsh/use-zsh","h":"#what-is-zsh","p":1941},{"i":1946,"t":"To install ZSH on Ubuntu, or any other Debian-based distro, open up the Terminal, then run: sudo apt install zsh To install ZSH on ArchLinux, run: sudo pacman -Syu zsh Confirm that zsh has been installed correctly by running zsh --version in the console. Now that ZSH has been downloaded and installed correctly, we need to change the default shell from Bash to ZSH. Run: chsh -s $(which zsh) If you are using a command line SSH (including WSL), logout and re-login. If you are using a graphics distribution, you should restart your PC to make it work. When you reopen the Terminal, you'll be given some configuration options for ZSH. Once you've installed ZSH you can start adding themes and using plugins. We've covered how to do that in the last two sections of the article.","s":"How to install ZSH?","u":"/docs/modern-linux/zsh/use-zsh","h":"#how-to-install-zsh","p":1941},{"i":1948,"t":"Generally speaking, you'll want to use your distros default package manager to install ZSH, as it is included by default in most repositories (repos). If it is not present for some reason, you can always download the source code and install that. Additionally, the ZSH GitHub has instructions for installing it on the most popular Linux distros. Oh-My-Zsh is the most popular plugin manager for ZSH, and it comes with many built-in plugins and themes as well. There are also a couple of other plugin frameworks, including Antigen, which is a full package manager for ZSH, but Oh-My-Zsh has loads of plugins built right in and does its job well. Oh-My-Zsh has a simple install script you can run: sh -c \"$(curl -fsSL https://raw.githubusercontent.com/robbyrussell/oh-my-zsh/master/tools/install.sh)\"","s":"Install ZSH on Other Linux Systems","u":"/docs/modern-linux/zsh/use-zsh","h":"#install-zsh-on-other-linux-systems","p":1941},{"i":1950,"t":"There are plenty of themes to go around, but powerlevel10k is by far the coolest. It adds a right-aligned info box, integration with git and command history, incredible customization, and wraps it all up in a slick interface based on the powerline plugin for vim. You'll want to use iTerm on macOS, or any terminal with 24-bit color, to get the most out of powerlevel10k (or any ZSH theme, really). See Powerlevel10k for details. You can also use Starship. Install Nerd Font You need to install the Nerd Fonts to use modern icons and themes in zsh. You can either download and manual install in Nerd Fonts Releases, or use a script getnf.","s":"How to Use ZSH Themes","u":"/docs/modern-linux/zsh/use-zsh","h":"#how-to-use-zsh-themes","p":1941},{"i":1952,"t":"zsh-autosuggestions zsh-syntax-highlighting The plugins required are not included in Oh My Zsh plugins. We will add them manually: git clone https://github.com/zsh-users/zsh-autosuggestions.git $ZSH/plugins/zsh-autosuggestions git clone https://github.com/zsh-users/zsh-syntax-highlighting.git $ZSH/plugins/zsh-syntax-highlighting Open the .zshrc file, replace the line plugins=(git z) by plugins=(git z zsh-autosuggestions zsh-syntax-highlighting). Reload ZSH to make it work: exec zsh","s":"Recommend Plugins","u":"/docs/modern-linux/zsh/use-zsh","h":"#recommend-plugins","p":1941},{"i":1954,"t":"备注 npm package create-react-app is not under maintained, but it's very helpful for starters.","s":"Create React App with TypeScript","u":"/docs/typescript-react/create-react-app-with-typescript","h":"","p":1953},{"i":1956,"t":"yarn npx yarn create react-app react-typescript-app --template typescript && cd react-typescript-app npx create-react-app react-typescript-app --template typescript && cd react-typescript-app do not use globally If you've previously installed create-react-app globally via npm install -g create-react-app, we recommend you uninstall the package using npm uninstall -g create-react-app or yarn global remove create-react-app to ensure that npx always uses the latest version. Global installs of create-react-app are no longer supported.","s":"Installation","u":"/docs/typescript-react/create-react-app-with-typescript","h":"#installation","p":1953},{"i":1958,"t":". ├── node_modules │ ├── ... │ ├── ... │ └── ... ├── public │ ├── favicon.ico │ ├── index.html │ ├── logo192.png │ ├── logo512.png │ ├── manifest.json │ └── robots.txt ├── src │ ├── App.css │ ├── App.test.tsx │ ├── App.tsx │ ├── index.css │ ├── index.tsx │ ├── logo.svg │ ├── react-app-env.d.ts │ ├── reportWebVitals.ts │ └── setupTests.ts ├── package-lock.json ├── package.json ├── README.md └── tsconfig.json","s":"File Structure","u":"/docs/typescript-react/create-react-app-with-typescript","h":"#file-structure","p":1953},{"i":1960,"t":"React 是著名的开源 JavaScript 库，它已成为寻求构建响应式且功能强大的用户界面的开发人员青睐的工具。 同时，TypeScript 是一个静态类型的 JavaScript 超集，拥有许多优点，例如类定义、接口和类型注释、为代码库提供结构和可靠性以及简化错误检测。","s":"TypeScript 和 React","u":"/docs/typescript-react/intro","h":"","p":1959},{"i":1963,"t":"TypeScript 将静态类型引入 JavaScript，使开发人员能够在开发过程中捕获与类型相关的错误。这可以提高代码质量、提高可维护性并减少运行时错误。","s":"静态类型和类型安全","u":"/docs/typescript-react/intro","h":"#static-safety","p":1959},{"i":1965,"t":"TypeScript 提供出色的工具和 IDE 支持，包括自动完成、类型检查和重构工具等功能。这提高了开发人员的工作效率，并有助于快速识别和修复错误。","s":"增强的工具和 IDE 支持","u":"/docs/typescript-react/intro","h":"#ide-support","p":1959},{"i":1967,"t":"TypeScript 的静态类型和清晰的界面使代码更加自文档化并且更易于理解。这提高了代码的可维护性并促进开发团队内部更好的协作。","s":"改进代码可维护性和协作","u":"/docs/typescript-react/intro","h":"#maintainability-collaboration","p":1959},{"i":1969,"t":"TypeScript 是 JavaScript 的超集，允许开发者在现有 JavaScript 项目中逐步采用 TypeScript。这种兼容性使得迁移代码库和利用现有 JavaScript 库变得更加容易。","s":"与 JavaScript 和现有代码库的兼容性","u":"/docs/typescript-react/intro","h":"#compatible-with-js","p":1959},{"i":1971,"t":"TypeScript 允许开发人员定义和强制执行 API 类型，使它们更加明确和不言自明。这可以带来更好的文档、改进的代码可发现性以及更轻松地与外部库集成。","s":"强类型 API 和更好的文档","u":"/docs/typescript-react/intro","h":"#strongly-typed-apis","p":1959},{"i":1974,"t":"React 遵循基于组件的架构，允许开发人员构建可重用和模块化的 UI 组件。这提高了代码的可重用性、可维护性和可扩展性。","s":"基于组件的架构","u":"/docs/typescript-react/intro","h":"#component-architecture","p":1959},{"i":1976,"t":"React 使用虚拟 DOM 来优化渲染过程。它仅更新必要的组件，最大限度地减少 DOM 操作并提高性能。","s":"虚拟 DOM 和高效渲染","u":"/docs/typescript-react/intro","h":"#virtual-dom","p":1959},{"i":1978,"t":"React 提倡单向数据流的概念，即数据从父组件向子组件单向流动。这有助于维护可预测的数据流并简化状态管理。它还使得调试和优化 React 应用程序变得更加容易。","s":"单向数据流和状态管理","u":"/docs/typescript-react/intro","h":"#unidirection-data-and-state-management","p":1959},{"i":1980,"t":"React 可以与 React Native 结合使用来开发适用于 iOS 和 Android 平台的移动应用程序。通过共享单一代码库，开发人员可以节省构建跨平台应用程序的时间和精力。","s":"用于跨平台开发的 React Native","u":"/docs/typescript-react/intro","h":"#cross-platform","p":1959},{"i":1982,"t":"React 拥有庞大的生态系统，其中包含社区开发的众多库、工具和资源。这使开发人员能够利用现有解决方案并加速开发。","s":"丰富的生态系统和社区支持","u":"/docs/typescript-react/intro","h":"#rich-ecosystem","p":1959},{"i":1984,"t":"通过将 React 基于组件的方法与 TypeScript 的静态类型相结合，开发人员可以从 Web 开发项目中改进的代码质量、可维护性、生产力和协作中受益。","s":"结合","u":"/docs/typescript-react/intro","h":"#combination","p":1959},{"i":1986,"t":"信息 Pandas 是用于数据分析 Python 的软件库，提供了大量快速便捷地处理数据的函数和方法。 本文翻译自官方文档 10 Minutes to pandas，对应的 pandas 版本为 2.1.3。 导入所需的软件包： In [1]: import numpy as np In [2]: import pandas as pd","s":"Pandas 快速入门","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"","p":1985},{"i":1988,"t":"Pandas 提供了两类处理数据的类别： Series：任何类型的一维标签阵列数据 例如整数、字符串、Python 对象等。 DataFrame：二维数据结构，它储存着像一个二维数组或带行列的表的数据。","s":"Pandas 基础数据结构","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#basic-data-structures","p":1985},{"i":1990,"t":"通过传递列表创建 Series，其中 pandas 会创建默认的整数索引： In [3]: s = pd.Series([1, 3, 5, np.nan, 6, 8]) In [4]: s Out[4]: 0 1.0 1 3.0 2 5.0 3 NaN 4 6.0 5 8.0 dtype: float64 通过传递具有日期时间索引和标签列的 NumPy 数组来创建 DataFrame： In [5]: dates = pd.date_range(\"20130101\", periods=6) In [6]: dates Out[6]: DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04', '2013-01-05', '2013-01-06'], dtype='datetime64[ns]', freq='D') In [7]: df = pd.DataFrame(np.random.randn(6, 4), index=dates, columns=list(\"ABCD\")) In [8]: df Out[8]: A B C D 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 2013-01-06 -0.673690 0.113648 -1.478427 0.524988 通过传递对象字典来创建 DataFrame： In [9]: df2 = pd.DataFrame( ...: { ...: \"A\": 1.0, ...: \"B\": pd.Timestamp(\"20130102\"), ...: \"C\": pd.Series(1, index=list(range(4)), dtype=\"float32\"), ...: \"D\": np.array([3] * 4, dtype=\"int32\"), ...: \"E\": pd.Categorical([\"test\", \"train\", \"test\", \"train\"]), ...: \"F\": \"foo\", ...: } ...: ) ...: In [10]: df2 Out[10]: A B C D E F 0 1.0 2013-01-02 1.0 3 test foo 1 1.0 2013-01-02 1.0 3 train foo 2 1.0 2013-01-02 1.0 3 test foo 3 1.0 2013-01-02 1.0 3 train foo 生成的 DataFrame 列有不同的数据类型 dtypes： In [11]: df2.dtypes Out[11]: A float64 B datetime64[s] C float32 D int32 E category F object dtype: object 使用 IPython 时，按 TAB 可以自动补全： In [12]: df2.<TAB> # noqa: E225, E999 df2.A df2.bool df2.abs df2.boxplot df2.add df2.C df2.add_prefix df2.clip df2.add_suffix df2.columns df2.align df2.copy df2.all df2.count df2.any df2.combine df2.append df2.D df2.apply df2.describe df2.applymap df2.diff df2.B df2.duplicated 正如你可以看到的那样，A、B、C 和 D 等列在自动补全中。后续列已简略。","s":"对象创建","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#object-creation","p":1985},{"i":1992,"t":"使用 DataFrame.head 和 DataFrame.tail 分别查看 df 的顶部和底部的行： In [13]: df.head() Out[13]: A B C D 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 In [14]: df.tail(3) Out[14]: A B C D 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 2013-01-06 -0.673690 0.113648 -1.478427 0.524988 显示索引 DataFrame.index，列 DataFrame.columns 和 numpy 数据： In [15]: df.index Out[15]: DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04', '2013-01-05', '2013-01-06'], dtype='datetime64[ns]', freq='D') In [16]: df.columns Out[16]: Index(['A', 'B', 'C', 'D'], dtype='object') 以 DataFrame.to_numpy 返回底层数据的数字表示，而不带索引或列标签： In [17]: df.to_numpy() Out[17]: array([[ 0.4691, -0.2829, -1.5091, -1.1356], [ 1.2121, -0.1732, 0.1192, -1.0442], [-0.8618, -2.1046, -0.4949, 1.0718], [ 0.7216, -0.7068, -1.0396, 0.2719], [-0.425 , 0.567 , 0.2762, -1.0874], [-0.6737, 0.1136, -1.4784, 0.525 ]]) 信息 NumPy 整个数组是同一种类型，而 pandas DataFrames 每列有一种类型。当你调用 DataFrame.to_numpy 时，pandas 将找到可以容纳 DataFrame 中所有数据类型的 NumPy 数据类型。如果通用数据类型是 object，DataFrame.to_numpy 将复制数据。 In [18]: df2.dtypes Out[18]: A float64 B datetime64[s] C float32 D int32 E category F object dtype: object In [19]: df2.to_numpy() Out[19]: array([[1.0, Timestamp('2013-01-02 00:00:00'), 1.0, 3, 'test', 'foo'], [1.0, Timestamp('2013-01-02 00:00:00'), 1.0, 3, 'train', 'foo'], [1.0, Timestamp('2013-01-02 00:00:00'), 1.0, 3, 'test', 'foo'], [1.0, Timestamp('2013-01-02 00:00:00'), 1.0, 3, 'train', 'foo']], dtype=object) DataFrame.description 显示数据的快速统计摘要： In [20]: df.describe() Out[20]: A B C D count 6.000000 6.000000 6.000000 6.000000 mean 0.073711 -0.431125 -0.687758 -0.233103 std 0.843157 0.922818 0.779887 0.973118 min -0.861849 -2.104569 -1.509059 -1.135632 25% -0.611510 -0.600794 -1.368714 -1.076610 50% 0.022070 -0.228039 -0.767252 -0.386188 75% 0.658444 0.041933 -0.034326 0.461706 max 1.212112 0.567020 0.276232 1.071804 对数据 df 进行转置： In [21]: df.T Out[21]: 2013-01-01 2013-01-02 2013-01-03 2013-01-04 2013-01-05 2013-01-06 A 0.469112 1.212112 -0.861849 0.721555 -0.424972 -0.673690 B -0.282863 -0.173215 -2.104569 -0.706771 0.567020 0.113648 C -1.509059 0.119209 -0.494929 -1.039575 0.276232 -1.478427 D -1.135632 -1.044236 1.071804 0.271860 -1.087401 0.524988 DataFrame.sort_index 按轴排序： In [22]: df.sort_index(axis=1, ascending=False) Out[22]: D C B A 2013-01-01 -1.135632 -1.509059 -0.282863 0.469112 2013-01-02 -1.044236 0.119209 -0.173215 1.212112 2013-01-03 1.071804 -0.494929 -2.104569 -0.861849 2013-01-04 0.271860 -1.039575 -0.706771 0.721555 2013-01-05 -1.087401 0.276232 0.567020 -0.424972 2013-01-06 0.524988 -1.478427 0.113648 -0.673690 DataFrame.sort_values 按值排序： In [23]: df.sort_values(by=\"B\") Out[23]: A B C D 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-06 -0.673690 0.113648 -1.478427 0.524988 2013-01-05 -0.424972 0.567020 0.276232 -1.087401","s":"查看数据","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#viewing_data","p":1985},{"i":1994,"t":"信息 虽然标准 Python / Numpy 表达式非常直观并且可以方便地用于交互式工作，但对于生产代码，我们建议使用优化的 pandas 数据访问方法 DataFrame.at、DataFrame.iat、DataFrame.loc 和 DataFrame.iloc。","s":"选择数据","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#selection","p":1985},{"i":1996,"t":"传递单个标签会选择一个列，将会返回一个 Series，相当于 df.A： In [24]: df[\"A\"] Out[24]: 2013-01-01 0.469112 2013-01-02 1.212112 2013-01-03 -0.861849 2013-01-04 0.721555 2013-01-05 -0.424972 2013-01-06 -0.673690 Freq: D, Name: A, dtype: float64 对于 DataFrame，传递一个分片 : 对行进行切片： In [25]: df[0:3] Out[25]: A B C D 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 In [26]: df[\"20130102\":\"20130104\"] Out[26]: A B C D 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 2013-01-04 0.721555 -0.706771 -1.039575 0.271860","s":"获取数据项 ([])","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#getitem","p":1985},{"i":1998,"t":"选择匹配标签的行： In [27]: df.loc[dates[0]] Out[27]: A 0.469112 B -0.282863 C -1.509059 D -1.135632 Name: 2013-01-01 00:00:00, dtype: float64 选择所有行 (:)，并选择列标签： In [28]: df.loc[:, [\"A\", \"B\"]] Out[28]: A B 2013-01-01 0.469112 -0.282863 2013-01-02 1.212112 -0.173215 2013-01-03 -0.861849 -2.104569 2013-01-04 0.721555 -0.706771 2013-01-05 -0.424972 0.567020 2013-01-06 -0.673690 0.113648 对于标签切片，起止两个端点都包括在内： In [29]: df.loc[\"20130102\":\"20130104\", [\"A\", \"B\"]] Out[29]: A B 2013-01-02 1.212112 -0.173215 2013-01-03 -0.861849 -2.104569 2013-01-04 0.721555 -0.706771 选择单个行和列标签，将返回一个标量： In [30]: df.loc[dates[0], \"A\"] Out[30]: 0.4691122999071863 快速访问标量 (相当于上面的方法)： In [31]: df.at[dates[0], \"A\"] Out[31]: 0.4691122999071863","s":"按标签选择","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#selection-by-label","p":1985},{"i":2000,"t":"通过传递整数位置进行选择： In [32]: df.iloc[3] Out[32]: A 0.721555 B -0.706771 C -1.039575 D 0.271860 Name: 2013-01-04 00:00:00, dtype: float64 使用整数进行切片，类似于 NumPy/Python： In [33]: df.iloc[3:5, 0:2] Out[33]: A B 2013-01-04 0.721555 -0.706771 2013-01-05 -0.424972 0.567020 指定整数位置列表取行列： In [34]: df.iloc[[1, 2, 4], [0, 2]] Out[34]: A C 2013-01-02 1.212112 0.119209 2013-01-03 -0.861849 -0.494929 2013-01-05 -0.424972 0.276232 对行进行切片： In [35]: df.iloc[1:3, :] Out[35]: A B C D 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 对列进行切片： In [36]: df.iloc[:, 1:3] Out[36]: B C 2013-01-01 -0.282863 -1.509059 2013-01-02 -0.173215 0.119209 2013-01-03 -2.104569 -0.494929 2013-01-04 -0.706771 -1.039575 2013-01-05 0.567020 0.276232 2013-01-06 0.113648 -1.478427 按位置取值： In [37]: df.iloc[1, 1] Out[37]: -0.17321464905330858 快速按位置取值 (相当于上面的方法)： In [38]: df.iat[1, 1] Out[38]: -0.17321464905330858","s":"按位置选择","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#selection-by-position","p":1985},{"i":2002,"t":"选择 df.A 大于 0 的行。 In [39]: df[df[\"A\"] > 0] Out[39]: A B C D 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 从符合布尔条件的 DataFrame 中选择值： In [40]: df[df > 0] Out[40]: A B C D 2013-01-01 0.469112 NaN NaN NaN 2013-01-02 1.212112 NaN 0.119209 NaN 2013-01-03 NaN NaN NaN 1.071804 2013-01-04 0.721555 NaN NaN 0.271860 2013-01-05 NaN 0.567020 0.276232 NaN 2013-01-06 NaN 0.113648 NaN 0.524988 使用 Series.isin 方法进行过滤： In [41]: df2 = df.copy() In [42]: df2[\"E\"] = [\"one\", \"one\", \"two\", \"three\", \"four\", \"three\"] In [43]: df2 Out[43]: A B C D E 2013-01-01 0.469112 -0.282863 -1.509059 -1.135632 one 2013-01-02 1.212112 -0.173215 0.119209 -1.044236 one 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 two 2013-01-04 0.721555 -0.706771 -1.039575 0.271860 three 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 four 2013-01-06 -0.673690 0.113648 -1.478427 0.524988 three In [44]: df2[df2[\"E\"].isin([\"two\", \"four\"])] Out[44]: A B C D E 2013-01-03 -0.861849 -2.104569 -0.494929 1.071804 two 2013-01-05 -0.424972 0.567020 0.276232 -1.087401 four","s":"布尔索引","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#boolean-indexing","p":1985},{"i":2004,"t":"设置新列会自动按索引对齐数据： In [45]: s1 = pd.Series([1, 2, 3, 4, 5, 6], index=pd.date_range(\"20130102\", periods=6)) In [46]: s1 Out[46]: 2013-01-02 1 2013-01-03 2 2013-01-04 3 2013-01-05 4 2013-01-06 5 2013-01-07 6 Freq: D, dtype: int64 In [47]: df[\"F\"] = s1 按标签设置新的值： In [48]: df.at[dates[0], \"A\"] = 0 按位置设置新的值： In [49]: df.iat[0, 1] = 0 通过 NumPy 数组来设置新的值： In [50]: df.loc[:, \"D\"] = np.array([5] * len(df)) 上述操作结果如下： In [51]: df Out[51]: A B C D F 2013-01-01 0.000000 0.000000 -1.509059 5.0 NaN 2013-01-02 1.212112 -0.173215 0.119209 5.0 1.0 2013-01-03 -0.861849 -2.104569 -0.494929 5.0 2.0 2013-01-04 0.721555 -0.706771 -1.039575 5.0 3.0 2013-01-05 -0.424972 0.567020 0.276232 5.0 4.0 2013-01-06 -0.673690 0.113648 -1.478427 5.0 5.0 通过 where 设置值： In [52]: df2 = df.copy() In [53]: df2[df2 > 0] = -df2 In [54]: df2 Out[54]: A B C D F 2013-01-01 0.000000 0.000000 -1.509059 -5.0 NaN 2013-01-02 -1.212112 -0.173215 -0.119209 -5.0 -1.0 2013-01-03 -0.861849 -2.104569 -0.494929 -5.0 -2.0 2013-01-04 -0.721555 -0.706771 -1.039575 -5.0 -3.0 2013-01-05 -0.424972 -0.567020 -0.276232 -5.0 -4.0 2013-01-06 -0.673690 -0.113648 -1.478427 -5.0 -5.0","s":"设置值","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#setting","p":1985},{"i":2006,"t":"pandas 使用 np.nan 来表示缺失值，缺失值默认不参与任何计算。 reindex() 允许更改/添加/删除指定轴上的索引，并返回数据的副本： In [55]: df1 = df.reindex(index=dates[0:4], columns=list(df.columns) + [\"E\"]) In [56]: df1.loc[dates[0] : dates[1], \"E\"] = 1 In [57]: df1 Out[57]: A B C D F E 2013-01-01 0.000000 0.000000 -1.509059 5.0 NaN 1.0 2013-01-02 1.212112 -0.173215 0.119209 5.0 1.0 1.0 2013-01-03 -0.861849 -2.104569 -0.494929 5.0 2.0 NaN 2013-01-04 0.721555 -0.706771 -1.039575 5.0 3.0 NaN DataFramework.dropna 将删除任何包含缺失值的行： In [58]: df1.dropna(how=\"any\") Out[58]: A B C D F E 2013-01-02 1.212112 -0.173215 0.119209 5.0 1.0 1.0 DataFramework.fillna 对缺失值进行填充： In [59]: df1.fillna(value=5) Out[59]: A B C D F E 2013-01-01 0.000000 0.000000 -1.509059 5.0 5.0 1.0 2013-01-02 1.212112 -0.173215 0.119209 5.0 1.0 1.0 2013-01-03 -0.861849 -2.104569 -0.494929 5.0 2.0 5.0 2013-01-04 0.721555 -0.706771 -1.039575 5.0 3.0 5.0 isna 获取 nan 值的布尔值掩码： In [60]: pd.isna(df1) Out[60]: A B C D F E 2013-01-01 False False False False True False 2013-01-02 False False False False False False 2013-01-03 False False False False False True 2013-01-04 False False False False False True","s":"缺失值","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#missing-data","p":1985},{"i":2009,"t":"一般情况下，操作会排除缺失值。 计算每列的平均值： In [61]: df.mean() Out[61]: A -0.004474 B -0.383981 C -0.687758 D 5.000000 F 3.000000 dtype: float64 计算每行的平均值： In [62]: df.mean(axis=1) Out[62]: 2013-01-01 0.872735 2013-01-02 1.431621 2013-01-03 0.707731 2013-01-04 1.395042 2013-01-05 1.883656 2013-01-06 1.592306 Freq: D, dtype: float64 使用具有不同索引或列的另一个 Series 或 DataFrame 进行操作会将结果与索引或列标签的并集对齐。此外，pandas 会自动沿指定维度进行广播，并会用 np.nan 填充未对齐的标签。 In [63]: s = pd.Series([1, 3, 5, np.nan, 6, 8], index=dates).shift(2) In [64]: s Out[64]: 2013-01-01 NaN 2013-01-02 NaN 2013-01-03 1.0 2013-01-04 3.0 2013-01-05 5.0 2013-01-06 NaN Freq: D, dtype: float64 In [65]: df.sub(s, axis=\"index\") Out[65]: A B C D F 2013-01-01 NaN NaN NaN NaN NaN 2013-01-02 NaN NaN NaN NaN NaN 2013-01-03 -1.861849 -3.104569 -1.494929 4.0 1.0 2013-01-04 -2.278445 -3.706771 -4.039575 2.0 0.0 2013-01-05 -5.424972 -4.432980 -4.723768 0.0 -1.0 2013-01-06 NaN NaN NaN NaN NaN","s":"状态","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#stats","p":1985},{"i":2011,"t":"DataFrame.agg 和 DataFrame.transform 分别应用一个用户自定义的函数来减少或广播其结果。 In [66]: df.agg(lambda x: np.mean(x) * 5.6) Out[66]: A -0.025054 B -2.150294 C -3.851445 D 28.000000 F 16.800000 dtype: float64 In [67]: df.transform(lambda x: x * 101.2) Out[67]: A B C D F 2013-01-01 0.000000 0.000000 -152.716721 506.0 NaN 2013-01-02 122.665737 -17.529322 12.063922 506.0 101.2 2013-01-03 -87.219115 -212.982405 -50.086843 506.0 202.4 2013-01-04 73.021382 -71.525239 -105.204988 506.0 303.6 2013-01-05 -43.007200 57.382459 27.954680 506.0 404.8 2013-01-06 -68.177398 11.501219 -149.616767 506.0 506.0","s":"用户自定义函数","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#user-defined-functions","p":1985},{"i":2013,"t":"In [68]: s = pd.Series(np.random.randint(0, 7, size=10)) In [69]: s Out[69]: 0 4 1 2 2 1 3 2 4 6 5 4 6 4 7 6 8 4 9 4 dtype: int64 In [70]: s.value_counts() Out[70]: 4 5 2 2 6 2 1 1 Name: count, dtype: int64","s":"值计数","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#value-counts","p":1985},{"i":2015,"t":"Series 在 str 属性中配备了一组字符串处理方法，可以方便地对数组的每个元素进行操作，如下面的代码片段所示。 In [71]: s = pd.Series([\"A\", \"B\", \"C\", \"Aaba\", \"Baca\", np.nan, \"CABA\", \"dog\", \"cat\"]) In [72]: s.str.lower() Out[72]: 0 a 1 b 2 c 3 aaba 4 baca 5 NaN 6 caba 7 dog 8 cat dtype: object","s":"字符串方法","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#string-methods","p":1985},{"i":2018,"t":"pandas 提供了各种工具，可以在连接/合并类型操作的情况下轻松地将 Series 和 DataFrame 与索引和关系代数功能的各种集合逻辑组合在一起。 使用 concat 将 pandas 对象按行连接在一起： In [73]: df = pd.DataFrame(np.random.randn(10, 4)) In [74]: df Out[74]: 0 1 2 3 0 -0.548702 1.467327 -1.015962 -0.483075 1 1.637550 -1.217659 -0.291519 -1.745505 2 -0.263952 0.991460 -0.919069 0.266046 3 -0.709661 1.669052 1.037882 -1.705775 4 -0.919854 -0.042379 1.247642 -0.009920 5 0.290213 0.495767 0.362949 1.548106 6 -1.131345 -0.089329 0.337863 -0.945867 7 -0.932132 1.956030 0.017587 -0.016692 8 -0.575247 0.254161 -1.143704 0.215897 9 1.193555 -0.077118 -0.408530 -0.862495 # break it into pieces In [75]: pieces = [df[:3], df[3:7], df[7:]] In [76]: pd.concat(pieces) Out[76]: 0 1 2 3 0 -0.548702 1.467327 -1.015962 -0.483075 1 1.637550 -1.217659 -0.291519 -1.745505 2 -0.263952 0.991460 -0.919069 0.266046 3 -0.709661 1.669052 1.037882 -1.705775 4 -0.919854 -0.042379 1.247642 -0.009920 5 0.290213 0.495767 0.362949 1.548106 6 -1.131345 -0.089329 0.337863 -0.945867 7 -0.932132 1.956030 0.017587 -0.016692 8 -0.575247 0.254161 -1.143704 0.215897 9 1.193555 -0.077118 -0.408530 -0.862495 信息 向 DataFrame 添加列相对较快。但是，添加行需要副本，并且可能很昂贵。我们建议将预先构建的记录列表传递给 DataFrame 构造函数，而不是通过迭代地向其追加记录来构建 DataFrame。","s":"Concat","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#concat","p":1985},{"i":2020,"t":"merge 启用沿特定列的 SQL 样式联接类型。 In [77]: left = pd.DataFrame({\"key\": [\"foo\", \"foo\"], \"lval\": [1, 2]}) In [78]: right = pd.DataFrame({\"key\": [\"foo\", \"foo\"], \"rval\": [4, 5]}) In [79]: left Out[79]: key lval 0 foo 1 1 foo 2 In [80]: right Out[80]: key rval 0 foo 4 1 foo 5 In [81]: pd.merge(left, right, on=\"key\") Out[81]: key lval rval 0 foo 1 4 1 foo 1 5 2 foo 2 4 3 foo 2 5 按值 merge： In [82]: left = pd.DataFrame({\"key\": [\"foo\", \"bar\"], \"lval\": [1, 2]}) In [83]: right = pd.DataFrame({\"key\": [\"foo\", \"bar\"], \"rval\": [4, 5]}) In [84]: left Out[84]: key lval 0 foo 1 1 bar 2 In [85]: right Out[85]: key rval 0 foo 4 1 bar 5 In [86]: pd.merge(left, right, on=\"key\") Out[86]: key lval rval 0 foo 1 4 1 bar 2 5","s":"Join","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#join","p":1985},{"i":2022,"t":"group by 指的是涉及一个或多个以下步骤的过程： 根据一些规则将数据分组 对于每组数据分别应用函数 将结果组合成一个数据结构 In [87]: df = pd.DataFrame( ....: { ....: \"A\": [\"foo\", \"bar\", \"foo\", \"bar\", \"foo\", \"bar\", \"foo\", \"foo\"], ....: \"B\": [\"one\", \"one\", \"two\", \"three\", \"two\", \"two\", \"one\", \"three\"], ....: \"C\": np.random.randn(8), ....: \"D\": np.random.randn(8), ....: } ....: ) ....: In [88]: df Out[88]: A B C D 0 foo one 1.346061 -1.577585 1 bar one 1.511763 0.396823 2 foo two 1.627081 -0.105381 3 bar three -0.990582 -0.532532 4 foo two -0.441652 1.453749 5 bar two 1.211526 1.208843 6 foo one 0.268520 -0.080952 7 foo three 0.024580 -0.264610 按多列分组会生成分层索引，然后应用函数 sum： In [89]: df.groupby(\"A\")[[\"C\", \"D\"]].sum() Out[89]: C D A bar 1.732707 1.073134 foo 2.824590 -0.574779 按多列标签分组形成 MultiIndex。 In [90]: df.groupby([\"A\", \"B\"]).sum() Out[90]: C D A B bar one 1.511763 0.396823 three -0.990582 -0.532532 two 1.211526 1.208843 foo one 1.614581 -1.658537 three 0.024580 -0.264610 two 1.185429 1.348368","s":"分组","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#grouping","p":1985},{"i":2025,"t":"In [91]: arrays = [ ....: [\"bar\", \"bar\", \"baz\", \"baz\", \"foo\", \"foo\", \"qux\", \"qux\"], ....: [\"one\", \"two\", \"one\", \"two\", \"one\", \"two\", \"one\", \"two\"], ....: ] ....: In [92]: index = pd.MultiIndex.from_arrays(arrays, names=[\"first\", \"second\"]) In [93]: df = pd.DataFrame(np.random.randn(8, 2), index=index, columns=[\"A\", \"B\"]) In [94]: df2 = df[:4] In [95]: df2 Out[95]: A B first second bar one -0.727965 -0.589346 two 0.339969 -0.693205 baz one -0.339355 0.593616 two 0.884345 1.591431 The DataFrame.stack 方法对 DataFrame 的列进行“压缩”。 In [96]: stacked = df2.stack(future_stack=True) In [97]: stacked Out[97]: first second bar one A -0.727965 B -0.589346 two A 0.339969 B -0.693205 baz one A -0.339355 B 0.593616 two A 0.884345 B 1.591431 dtype: float64 对于“堆叠的”DataFrame 或 Series (多索引)，stack() 的逆操作是 unstack()，默认拆下最后一层： In [98]: stacked.unstack() Out[98]: A B first second bar one -0.727965 -0.589346 two 0.339969 -0.693205 baz one -0.339355 0.593616 two 0.884345 1.591431 In [99]: stacked.unstack(1) Out[99]: second one two first bar A -0.727965 0.339969 B -0.589346 -0.693205 baz A -0.339355 0.884345 B 0.593616 1.591431 In [100]: stacked.unstack(0) Out[100]: first bar baz second one A -0.727965 -0.339355 B -0.589346 0.593616 two A 0.339969 0.884345 B -0.693205 1.591431","s":"堆叠","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#stack","p":1985},{"i":2027,"t":"In [101]: df = pd.DataFrame( .....: { .....: \"A\": [\"one\", \"one\", \"two\", \"three\"] * 3, .....: \"B\": [\"A\", \"B\", \"C\"] * 4, .....: \"C\": [\"foo\", \"foo\", \"foo\", \"bar\", \"bar\", \"bar\"] * 2, .....: \"D\": np.random.randn(12), .....: \"E\": np.random.randn(12), .....: } .....: ) .....: In [102]: df Out[102]: A B C D E 0 one A foo -1.202872 0.047609 1 one B foo -1.814470 -0.136473 2 two C foo 1.018601 -0.561757 3 three A bar -0.595447 -1.623033 4 one B bar 1.395433 0.029399 5 one C bar -0.392670 -0.542108 6 two A foo 0.007207 0.282696 7 three B foo 1.928123 -0.087302 8 one C foo -0.055224 -1.575170 9 one A bar 2.395985 1.771208 10 two B bar 1.552825 0.816482 11 three C bar 0.166599 1.100230 从上述数据指定 values，index and columns 生成透视表： In [103]: pd.pivot_table(df, values=\"D\", index=[\"A\", \"B\"], columns=[\"C\"]) Out[103]: C bar foo A B one A 2.395985 -1.202872 B 1.395433 -1.814470 C -0.392670 -0.055224 three A -0.595447 NaN B NaN 1.928123 C 0.166599 NaN two A NaN 0.007207 B 1.552825 NaN C NaN 1.018601","s":"透视表","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#pivot-tables","p":1985},{"i":2029,"t":"pandas 在对频率转换进行重新采样时拥有简单、强大且高效的功能 (如将按秒采样的数据转换为按 5 分钟为单位进行采样的数据)。这种操作常见于 (但并不限于) 金融领域。 In [104]: rng = pd.date_range(\"1/1/2012\", periods=100, freq=\"S\") In [105]: ts = pd.Series(np.random.randint(0, 500, len(rng)), index=rng) In [106]: ts.resample(\"5Min\").sum() Out[106]: 2012-01-01 24182 Freq: 5T, dtype: int64 Series.tz_localize 将时间序列本地化到时区： In [107]: rng = pd.date_range(\"3/6/2012 00:00\", periods=5, freq=\"D\") In [108]: ts = pd.Series(np.random.randn(len(rng)), rng) In [109]: ts Out[109]: 2012-03-06 1.857704 2012-03-07 -1.193545 2012-03-08 0.677510 2012-03-09 -0.153931 2012-03-10 0.520091 Freq: D, dtype: float64 In [110]: ts_utc = ts.tz_localize(\"UTC\") In [111]: ts_utc Out[111]: 2012-03-06 00:00:00+00:00 1.857704 2012-03-07 00:00:00+00:00 -1.193545 2012-03-08 00:00:00+00:00 0.677510 2012-03-09 00:00:00+00:00 -0.153931 2012-03-10 00:00:00+00:00 0.520091 Freq: D, dtype: float64 Series.tz_convert 将时区感知时间序列转换为另一个时区： In [112]: ts_utc.tz_convert(\"US/Eastern\") Out[112]: 2012-03-05 19:00:00-05:00 1.857704 2012-03-06 19:00:00-05:00 -1.193545 2012-03-07 19:00:00-05:00 0.677510 2012-03-08 19:00:00-05:00 -0.153931 2012-03-09 19:00:00-05:00 0.520091 Freq: D, dtype: float64 向时间序列添加非固定持续时间 pandas.tseries.offsets.BusinessDay： In [113]: rng Out[113]: DatetimeIndex(['2012-03-06', '2012-03-07', '2012-03-08', '2012-03-09', '2012-03-10'], dtype='datetime64[ns]', freq='D') In [114]: rng + pd.offsets.BusinessDay(5) Out[114]: DatetimeIndex(['2012-03-13', '2012-03-14', '2012-03-15', '2012-03-16', '2012-03-16'], dtype='datetime64[ns]', freq=None)","s":"时间序列","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#time-series","p":1985},{"i":2031,"t":"pandas 可以在“DataFrame”中包含分类数据。 In [115]: df = pd.DataFrame( .....: {\"id\": [1, 2, 3, 4, 5, 6], \"raw_grade\": [\"a\", \"b\", \"b\", \"a\", \"a\", \"e\"]} .....: ) .....: Converting the raw grades to a categorical data type: In [116]: df[\"grade\"] = df[\"raw_grade\"].astype(\"category\") In [117]: df[\"grade\"] Out[117]: 0 a 1 b 2 b 3 a 4 a 5 e Name: grade, dtype: category Categories (3, object): ['a', 'b', 'e'] 将类别重命名为更有意义的名称： In [118]: new_categories = [\"very good\", \"good\", \"very bad\"] In [119]: df[\"grade\"] = df[\"grade\"].cat.rename_categories(new_categories) 对类别重新排序并同时添加缺少的类别 (Series.cat 方法默认返回一个新的 Series)： In [120]: df[\"grade\"] = df[\"grade\"].cat.set_categories( .....: [\"very bad\", \"bad\", \"medium\", \"good\", \"very good\"] .....: ) .....: In [121]: df[\"grade\"] Out[121]: 0 very good 1 good 2 good 3 very good 4 very good 5 very bad Name: grade, dtype: category Categories (5, object): ['very bad', 'bad', 'medium', 'good', 'very good'] 排序是按照类别中的顺序，而不是词汇顺序： In [122]: df.sort_values(by=\"grade\") Out[122]: id raw_grade grade 5 6 e very bad 1 2 b good 2 3 b good 0 1 a very good 3 4 a very good 4 5 a very good 按带有 observed=False 的分类列分组也会显示空类别： In [123]: df.groupby(\"grade\", observed=False).size() Out[123]: grade very bad 1 bad 0 medium 0 good 2 very good 3 dtype: int64","s":"分类数据","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#categoricals","p":1985},{"i":2033,"t":"我们使用标准约定来引用 matplotlib API： In [124]: import matplotlib.pyplot as plt In [125]: plt.close(\"all\") The plt.close method is used to close a figure window: In [126]: ts = pd.Series(np.random.randn(1000), index=pd.date_range(\"1/1/2000\", periods=1000)) In [127]: ts = ts.cumsum() In [128]: ts.plot(); 信息 使用 Jupyter 时，绘图将使用 Series.plot 显示。或使用 matplotlib.pyplot.show 显示绘图，或使用 matplotlib.pyplot.savefig 将其写入文件。 DataFrame.plot 绘制所有列： In [129]: df = pd.DataFrame( .....: np.random.randn(1000, 4), index=ts.index, columns=[\"A\", \"B\", \"C\", \"D\"] .....: ) .....: In [130]: df = df.cumsum() In [131]: plt.figure(); In [132]: df.plot(); In [133]: plt.legend(loc='best');","s":"绘图","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#plotting","p":1985},{"i":2036,"t":"使用 DataFrame.to_csv 写入 csv 文件： In [134]: df = pd.DataFrame(np.random.randint(0, 5, (10, 5))) In [135]: df.to_csv(\"foo.csv\") 使用 pandas.to_csv 读取 csv 文件： In [136]: pd.read_csv(\"foo.csv\") Out[136]: Unnamed: 0 0 1 2 3 4 0 0 4 3 1 1 2 1 1 1 0 2 3 2 2 2 1 4 2 1 2 3 3 0 4 0 2 2 4 4 4 2 2 3 4 5 5 4 0 4 3 1 6 6 2 1 2 0 3 7 7 4 0 4 4 4 8 8 4 4 1 0 1 9 9 0 4 3 0 3","s":"CSV","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#csv","p":1985},{"i":2038,"t":"使用 DataFrame.read_parquet 写入 Parquet 文件： In [137]: df.to_parquet(\"foo.parquet\") 使用 pandas.read_parquet 读取 Parquet 文件： In [138]: pd.read_parquet(\"foo.parquet\") Out[138]: 0 1 2 3 4 0 4 3 1 1 2 1 1 0 2 3 2 2 1 4 2 1 2 3 0 4 0 2 2 4 4 2 2 3 4 5 4 0 4 3 1 6 2 1 2 0 3 7 4 0 4 4 4 8 4 4 1 0 1 9 0 4 3 0 3","s":"Parquet","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#parquet","p":1985},{"i":2040,"t":"使用 DataFrame.to_excel 写入 Excel 文件： In [139]: df.to_excel(\"foo.xlsx\", sheet_name=\"Sheet1\") 使用 pandas.read_parquet 读取 Excel 文件： In [140]: pd.read_excel(\"foo.xlsx\", \"Sheet1\", index_col=None, na_values=[\"NA\"]) Out[140]: Unnamed: 0 0 1 2 3 4 1 1 1 0 2 3 2 0 0 4 3 1 1 2 2 2 1 4 2 1 2 3 3 0 4 0 2 2 4 4 4 2 2 3 4 5 5 4 0 4 3 1 6 6 2 1 2 0 3 7 7 4 0 4 4 4 8 8 4 4 1 0 1 9 9 0 4 3 0 3","s":"Excel","u":"/docs/machine-learning/numpy-pandas/pandas-quickstart","h":"#excel","p":1985},{"i":2042,"t":"如果您尝试对 Series 或 DataFrame 执行布尔运算，您可能会看到如下异常： In [141]: if pd.Series([False, True, False]): .....: print(\"I was true\") .....: --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-141-b27eb9c1dfc0> in ?() ----> 1 if pd.Series([False, True, False]): 2 print(\"I was true\") ~/work/pandas/pandas/pandas/core/generic.py in ?(self) 1517 @final 1518 def __nonzero__(self) -> NoReturn: -> 1519 raise ValueError( 1520 f\"The truth value of a {type(self).__name__} is ambiguous. \" 1521 \"Use a.empty, a.bool(), a.item(), a.any() or a.all().\" 1522 ) ValueError: The truth value of a Series is ambiguous. Use a.empty, a.bool(), a.item(), a.any() or 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