Barbara.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Volume/Height relationship in wells with square cross-section"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The width of the well at the bottom is 2.67 mm. and at the top (height, $H$, of 11.43 mm.) is\n",
    "3.63 mm.\n",
    "\n",
    "At a height, $H$, the cross section is a square of size $2.67 + (3.63 - 2.67)H/11.43$ mm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Loading DataFrames support into Gadfly.jl\n",
      "└ @ Gadfly /home/bates/.julia/packages/Gadfly/09PWZ/src/mapping.jl:228\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "2.67 &#43; 0.08398950131233596&#8729;x"
      ],
      "text/latex": [
       "$2.67 + 0.08398950131233596\\cdot x$"
      ],
      "text/plain": [
       "Poly(2.67 + 0.08398950131233596*x)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Polynomials, DataFrames, Gadfly\n",
    "plen = Poly([2.67, 0.96 / 11.43])  # polynomial representing size of square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "7.1289 &#43; 0.448503937007874&#8729;x &#43; 0.007054236330694883&#8729;x^2"
      ],
      "text/latex": [
       "$7.1289 + 0.448503937007874\\cdot x + 0.007054236330694883\\cdot x^{2}$"
      ],
      "text/plain": [
       "Poly(7.1289 + 0.448503937007874*x + 0.007054236330694883*x^2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parea = plen * plen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The volume will be the integral from $0$ to $H$ of `parea`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "7.1289&#8729;x &#43; 0.224251968503937&#8729;x^2 &#43; 0.002351412110231628&#8729;x^3"
      ],
      "text/latex": [
       "$7.1289\\cdot x + 0.224251968503937\\cdot x^{2} + 0.002351412110231628\\cdot x^{3}$"
      ],
      "text/plain": [
       "Poly(7.1289*x + 0.224251968503937*x^2 + 0.002351412110231628*x^3)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pvol = polyint(parea)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A plot of this function is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: `head(df::AbstractDataFrame)` is deprecated, use `first(df, 6)` instead.\n",
      "│   caller = top-level scope at In[4]:4\n",
      "└ @ Core In[4]:4\n"
     ]
    },
    {
     "data": {
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       "<table class=\"data-frame\"><thead><tr><th></th><th>H</th><th>V</th></tr><tr><th></th><th>Float64</th><th>Float64</th></tr></thead><tbody><p>6 rows × 2 columns</p><tr><th>1</th><td>0.0</td><td>0.0</td></tr><tr><th>2</th><td>0.01</td><td>0.0713114</td></tr><tr><th>3</th><td>0.02</td><td>0.142668</td></tr><tr><th>4</th><td>0.03</td><td>0.214069</td></tr><tr><th>5</th><td>0.04</td><td>0.285515</td></tr><tr><th>6</th><td>0.05</td><td>0.357006</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& H & V\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0.0 & 0.0 \\\\\n",
       "\t2 & 0.01 & 0.0713114 \\\\\n",
       "\t3 & 0.02 & 0.142668 \\\\\n",
       "\t4 & 0.03 & 0.214069 \\\\\n",
       "\t5 & 0.04 & 0.285515 \\\\\n",
       "\t6 & 0.05 & 0.357006 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "6×2 DataFrame\n",
       "│ Row │ H       │ V         │\n",
       "│     │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m   │\n",
       "├─────┼─────────┼───────────┤\n",
       "│ 1   │ 0.0     │ 0.0       │\n",
       "│ 2   │ 0.01    │ 0.0713114 │\n",
       "│ 3   │ 0.02    │ 0.142668  │\n",
       "│ 4   │ 0.03    │ 0.214069  │\n",
       "│ 5   │ 0.04    │ 0.285515  │\n",
       "│ 6   │ 0.05    │ 0.357006  │"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = 0.:0.01:11.43;\n",
    "d = DataFrame(H=H);\n",
    "d[:V] = polyval(pvol,d[:H]);\n",
    "first(d, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>H</th><th>V</th></tr><tr><th></th><th>Float64</th><th>Float64</th></tr></thead><tbody><p>6 rows × 2 columns</p><tr><th>1</th><td>11.38</td><td>113.634</td></tr><tr><th>2</th><td>11.39</td><td>113.765</td></tr><tr><th>3</th><td>11.4</td><td>113.897</td></tr><tr><th>4</th><td>11.41</td><td>114.029</td></tr><tr><th>5</th><td>11.42</td><td>114.16</td></tr><tr><th>6</th><td>11.43</td><td>114.292</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& H & V\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 11.38 & 113.634 \\\\\n",
       "\t2 & 11.39 & 113.765 \\\\\n",
       "\t3 & 11.4 & 113.897 \\\\\n",
       "\t4 & 11.41 & 114.029 \\\\\n",
       "\t5 & 11.42 & 114.16 \\\\\n",
       "\t6 & 11.43 & 114.292 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "6×2 DataFrame\n",
       "│ Row │ H       │ V       │\n",
       "│     │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼─────────┼─────────┤\n",
       "│ 1   │ 11.38   │ 113.634 │\n",
       "│ 2   │ 11.39   │ 113.765 │\n",
       "│ 3   │ 11.4    │ 113.897 │\n",
       "│ 4   │ 11.41   │ 114.029 │\n",
       "│ 5   │ 11.42   │ 114.16  │\n",
       "│ 6   │ 11.43   │ 114.292 │"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "last(d, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "f:e,unbind:b(this.node||document,d,e,f||this)}));return this};a[\"un\"+d]=A[\"un\"+d]=function(a){for(var b=this.events||[],e=b.length;e--;)if(b[e].name==d&&(b[e].f==a||!a)){b[e].unbind();b.splice(e,1);!b.length&&delete this.events;break}return this}})(v[y]);A.hover=function(a,b,d,e){return this.mouseover(a,d).mouseout(b,e||d)};A.unhover=function(a,b){return this.unmouseover(a).unmouseout(b)};var r=[];A.drag=function(b,d,f,h,n,p){function u(r,v,w){(r.originalEvent||r).preventDefault();this._drag.x=v;\n",
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       "A.undrag=function(){for(var b=r.length;b--;)r[b].el==this&&(this.unmousedown(r[b].start),r.splice(b,1),k.unbind(\"snap.drag.*.\"+this.id));!r.length&&a.unmousemove(e).unmouseup(l);return this}});C.plugin(function(a,v,y,C){y=y.prototype;var A=/^\\s*url\\((.+)\\)/,w=String,z=a._.$;a.filter={};y.filter=function(d){var f=this;\"svg\"!=f.type&&(f=f.paper);d=a.parse(w(d));var k=a._.id(),u=z(\"filter\");z(u,{id:k,filterUnits:\"userSpaceOnUse\"});u.appendChild(d.node);f.defs.appendChild(u);return new v(u)};k.on(\"snap.util.getattr.filter\",\n",
       "function(){k.stop();var d=z(this.node,\"filter\");if(d)return(d=w(d).match(A))&&a.select(d[1])});k.on(\"snap.util.attr.filter\",function(d){if(d instanceof v&&\"filter\"==d.type){k.stop();var f=d.node.id;f||(z(d.node,{id:d.id}),f=d.id);z(this.node,{filter:a.url(f)})}d&&\"none\"!=d||(k.stop(),this.node.removeAttribute(\"filter\"))});a.filter.blur=function(d,f){null==d&&(d=2);return a.format('<feGaussianBlur stdDeviation=\"{def}\"/>',{def:null==f?d:[d,f]})};a.filter.blur.toString=function(){return this()};a.filter.shadow=\n",
       "function(d,f,k,u,p){\"string\"==typeof k&&(p=u=k,k=4);\"string\"!=typeof u&&(p=u,u=\"#000\");null==k&&(k=4);null==p&&(p=1);null==d&&(d=0,f=2);null==f&&(f=d);u=a.color(u||\"#000\");return a.format('<feGaussianBlur in=\"SourceAlpha\" stdDeviation=\"{blur}\"/><feOffset dx=\"{dx}\" dy=\"{dy}\" result=\"offsetblur\"/><feFlood flood-color=\"{color}\"/><feComposite in2=\"offsetblur\" operator=\"in\"/><feComponentTransfer><feFuncA type=\"linear\" slope=\"{opacity}\"/></feComponentTransfer><feMerge><feMergeNode/><feMergeNode in=\"SourceGraphic\"/></feMerge>',\n",
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       "amount2:1-d})};a.filter.invert.toString=function(){return this()};a.filter.brightness=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\"/><feFuncG type=\"linear\" slope=\"{amount}\"/><feFuncB type=\"linear\" slope=\"{amount}\"/></feComponentTransfer>',{amount:d})};a.filter.brightness.toString=function(){return this()};a.filter.contrast=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncG type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncB type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/></feComponentTransfer>',\n",
       "{amount:d,amount2:0.5-d/2})};a.filter.contrast.toString=function(){return this()}});return C});\n",
       "\n",
       "]]> </script>\n",
       "<script> <![CDATA[\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "    if (typeof define === \"function\" && define.amd) {\n",
       "        // Define as an anonymous module\n",
       "        define(\"Gadfly\", [\"Snap.svg\"], function (Snap) {\n",
       "            return factory(Snap);\n",
       "        });\n",
       "    } else {\n",
       "        // Browser globals (glob is window)\n",
       "        // Snap adds itself to window\n",
       "        glob.Gadfly = factory(glob.Snap);\n",
       "    }\n",
       "}(this, function (Snap) {\n",
       "\n",
       "var Gadfly = {};\n",
       "\n",
       "// Get an x/y coordinate value in pixels\n",
       "var xPX = function(fig, x) {\n",
       "    var client_box = fig.node.getBoundingClientRect();\n",
       "    return x * fig.node.viewBox.baseVal.width / client_box.width;\n",
       "};\n",
       "\n",
       "var yPX = function(fig, y) {\n",
       "    var client_box = fig.node.getBoundingClientRect();\n",
       "    return y * fig.node.viewBox.baseVal.height / client_box.height;\n",
       "};\n",
       "\n",
       "\n",
       "Snap.plugin(function (Snap, Element, Paper, global) {\n",
       "    // Traverse upwards from a snap element to find and return the first\n",
       "    // note with the \"plotroot\" class.\n",
       "    Element.prototype.plotroot = function () {\n",
       "        var element = this;\n",
       "        while (!element.hasClass(\"plotroot\") && element.parent() != null) {\n",
       "            element = element.parent();\n",
       "        }\n",
       "        return element;\n",
       "    };\n",
       "\n",
       "    Element.prototype.svgroot = function () {\n",
       "        var element = this;\n",
       "        while (element.node.nodeName != \"svg\" && element.parent() != null) {\n",
       "            element = element.parent();\n",
       "        }\n",
       "        return element;\n",
       "    };\n",
       "\n",
       "    Element.prototype.plotbounds = function () {\n",
       "        var root = this.plotroot()\n",
       "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
       "        return {\n",
       "            x0: bbox.x,\n",
       "            x1: bbox.x + bbox.width,\n",
       "            y0: bbox.y,\n",
       "            y1: bbox.y + bbox.height\n",
       "        };\n",
       "    };\n",
       "\n",
       "    Element.prototype.plotcenter = function () {\n",
       "        var root = this.plotroot()\n",
       "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
       "        return {\n",
       "            x: bbox.x + bbox.width / 2,\n",
       "            y: bbox.y + bbox.height / 2\n",
       "        };\n",
       "    };\n",
       "\n",
       "    // Emulate IE style mouseenter/mouseleave events, since Microsoft always\n",
       "    // does everything right.\n",
       "    // See: http://www.dynamic-tools.net/toolbox/isMouseLeaveOrEnter/\n",
       "    var events = [\"mouseenter\", \"mouseleave\"];\n",
       "\n",
       "    for (i in events) {\n",
       "        (function (event_name) {\n",
       "            var event_name = events[i];\n",
       "            Element.prototype[event_name] = function (fn, scope) {\n",
       "                if (Snap.is(fn, \"function\")) {\n",
       "                    var fn2 = function (event) {\n",
       "                        if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
       "                            return;\n",
       "                        }\n",
       "\n",
       "                        var reltg = event.relatedTarget ? event.relatedTarget :\n",
       "                            event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
       "                        while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
       "\n",
       "                        if (reltg != this.node) {\n",
       "                            return fn.apply(this, event);\n",
       "                        }\n",
       "                    };\n",
       "\n",
       "                    if (event_name == \"mouseenter\") {\n",
       "                        this.mouseover(fn2, scope);\n",
       "                    } else {\n",
       "                        this.mouseout(fn2, scope);\n",
       "                    }\n",
       "                }\n",
       "                return this;\n",
       "            };\n",
       "        })(events[i]);\n",
       "    }\n",
       "\n",
       "\n",
       "    Element.prototype.mousewheel = function (fn, scope) {\n",
       "        if (Snap.is(fn, \"function\")) {\n",
       "            var el = this;\n",
       "            var fn2 = function (event) {\n",
       "                fn.apply(el, [event]);\n",
       "            };\n",
       "        }\n",
       "\n",
       "        this.node.addEventListener(\n",
       "            /Firefox/i.test(navigator.userAgent) ? \"DOMMouseScroll\" : \"mousewheel\",\n",
       "            fn2);\n",
       "\n",
       "        return this;\n",
       "    };\n",
       "\n",
       "\n",
       "    // Snap's attr function can be too slow for things like panning/zooming.\n",
       "    // This is a function to directly update element attributes without going\n",
       "    // through eve.\n",
       "    Element.prototype.attribute = function(key, val) {\n",
       "        if (val === undefined) {\n",
       "            return this.node.getAttribute(key);\n",
       "        } else {\n",
       "            this.node.setAttribute(key, val);\n",
       "            return this;\n",
       "        }\n",
       "    };\n",
       "\n",
       "    Element.prototype.init_gadfly = function() {\n",
       "        this.mouseenter(Gadfly.plot_mouseover)\n",
       "            .mousemove(Gadfly.plot_mousemove)\n",
       "            .mouseleave(Gadfly.plot_mouseout)\n",
       "            .dblclick(Gadfly.plot_dblclick)\n",
       "            .mousewheel(Gadfly.guide_background_scroll)\n",
       "            .drag(Gadfly.guide_background_drag_onmove,\n",
       "                  Gadfly.guide_background_drag_onstart,\n",
       "                  Gadfly.guide_background_drag_onend);\n",
       "        this.mouseenter(function (event) {\n",
       "            init_pan_zoom(this.plotroot());\n",
       "        });\n",
       "        return this;\n",
       "    };\n",
       "});\n",
       "\n",
       "\n",
       "Gadfly.plot_mousemove = function(event, x_px, y_px) {\n",
       "    var root = this.plotroot();\n",
       "    if (root.data(\"crosshair\")) {\n",
       "        px_per_mm = root.data(\"px_per_mm\");\n",
       "        bB = root.select('boundingbox').node.getAttribute('value').split(' ');\n",
       "        uB = root.select('unitbox').node.getAttribute('value').split(' ');\n",
       "        xscale = root.data(\"xscale\");\n",
       "        yscale = root.data(\"yscale\");\n",
       "        xtranslate = root.data(\"tx\");\n",
       "        ytranslate = root.data(\"ty\");\n",
       "\n",
       "        xoff_mm = bB[0].substr(0,bB[0].length-2)/1;\n",
       "        yoff_mm = bB[1].substr(0,bB[1].length-2)/1;\n",
       "        xoff_unit = uB[0]/1;\n",
       "        yoff_unit = uB[1]/1;\n",
       "        mm_per_xunit = bB[2].substr(0,bB[2].length-2) / uB[2];\n",
       "        mm_per_yunit = bB[3].substr(0,bB[3].length-2) / uB[3];\n",
       "         \n",
       "        x_unit = ((x_px / px_per_mm - xtranslate) / xscale - xoff_mm) / mm_per_xunit + xoff_unit;\n",
       "        y_unit = ((y_px / px_per_mm - ytranslate) / yscale - yoff_mm) / mm_per_yunit + yoff_unit;\n",
       "\n",
       "        root.select('.crosshair').select('.primitive').select('text')\n",
       "                .node.innerHTML = x_unit.toPrecision(3)+\",\"+y_unit.toPrecision(3);\n",
       "    };\n",
       "};\n",
       "\n",
       "Gadfly.helpscreen_visible = function(event) {\n",
       "    helpscreen_visible(this.plotroot());\n",
       "};\n",
       "var helpscreen_visible = function(root) {\n",
       "    root.select(\".helpscreen\").animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "Gadfly.helpscreen_hidden = function(event) {\n",
       "    helpscreen_hidden(this.plotroot());\n",
       "};\n",
       "var helpscreen_hidden = function(root) {\n",
       "    root.select(\".helpscreen\").animate({opacity: 0.0}, 250);\n",
       "};\n",
       "\n",
       "// When the plot is moused over, emphasize the grid lines.\n",
       "Gadfly.plot_mouseover = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    var keyboard_help = function(event) {\n",
       "        if (event.which == 191) { // ?\n",
       "            helpscreen_visible(root);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_help\", keyboard_help);\n",
       "    window.addEventListener(\"keydown\", keyboard_help);\n",
       "\n",
       "    var keyboard_pan_zoom = function(event) {\n",
       "        var bounds = root.plotbounds(),\n",
       "            width = bounds.x1 - bounds.x0;\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        if (event.which == 187 || event.which == 73) { // plus or i\n",
       "            increase_zoom_by_position(root, 0.1, true);\n",
       "        } else if (event.which == 189 || event.which == 79) { // minus or o\n",
       "            increase_zoom_by_position(root, -0.1, true);\n",
       "        } else if (event.which == 39 || event.which == 76) { // right-arrow or l\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\")-width/10, root.data(\"ty\"),\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 40 || event.which == 74) { // down-arrow or j\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\"), root.data(\"ty\")-height/10,\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 37 || event.which == 72) { // left-arrow or h\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\")+width/10, root.data(\"ty\"),\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 38 || event.which == 75) { // up-arrow or k\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\"), root.data(\"ty\")+height/10,\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 82) { // r\n",
       "            set_plot_pan_zoom(root, 0.0, 0.0, 1.0, 1.0);\n",
       "        } else if (event.which == 191) { // ?\n",
       "            helpscreen_hidden(root);\n",
       "        } else if (event.which == 67) { // c\n",
       "            root.data(\"crosshair\",!root.data(\"crosshair\"));\n",
       "            root.select(\".crosshair\")\n",
       "                .animate({opacity: root.data(\"crosshair\") ? 1.0 : 0.0}, 250);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_pan_zoom\", keyboard_pan_zoom);\n",
       "    window.addEventListener(\"keyup\", keyboard_pan_zoom);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    if (xgridlines) {\n",
       "        xgridlines.data(\"unfocused_strokedash\",\n",
       "                        xgridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "        var destcolor = root.data(\"focused_xgrid_color\");\n",
       "        xgridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines.data(\"unfocused_strokedash\",\n",
       "                        ygridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "        var destcolor = root.data(\"focused_ygrid_color\");\n",
       "        ygridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    root.select(\".crosshair\")\n",
       "        .animate({opacity: root.data(\"crosshair\") ? 1.0 : 0.0}, 250);\n",
       "    root.select(\".questionmark\").animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "// Reset pan and zoom on double click\n",
       "Gadfly.plot_dblclick = function(event) {\n",
       "  set_plot_pan_zoom(this.plotroot(), 0.0, 0.0, 1.0, 1.0);\n",
       "};\n",
       "\n",
       "// Unemphasize grid lines on mouse out.\n",
       "Gadfly.plot_mouseout = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    window.removeEventListener(\"keyup\", root.data(\"keyboard_pan_zoom\"));\n",
       "    root.data(\"keyboard_pan_zoom\", undefined);\n",
       "    window.removeEventListener(\"keydown\", root.data(\"keyboard_help\"));\n",
       "    root.data(\"keyboard_help\", undefined);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    if (xgridlines) {\n",
       "        var destcolor = root.data(\"unfocused_xgrid_color\");\n",
       "        xgridlines.attribute(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        var destcolor = root.data(\"unfocused_ygrid_color\");\n",
       "        ygridlines.attribute(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    root.select(\".crosshair\").animate({opacity: 0.0}, 250);\n",
       "    root.select(\".questionmark\").animate({opacity: 0.0}, 250);\n",
       "    helpscreen_hidden(root);\n",
       "};\n",
       "\n",
       "\n",
       "var set_geometry_transform = function(root, tx, ty, xscale, yscale) {\n",
       "    var xscalable = root.hasClass(\"xscalable\"),\n",
       "        yscalable = root.hasClass(\"yscalable\");\n",
       "\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\");\n",
       "\n",
       "    var xscale = xscalable ? xscale : 1.0,\n",
       "        yscale = yscalable ? yscale : 1.0;\n",
       "\n",
       "    tx = xscalable ? tx : 0.0;\n",
       "    ty = yscalable ? ty : 0.0;\n",
       "\n",
       "    var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
       "    root.selectAll(\".geometry, image\").forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        });\n",
       "\n",
       "    var t = new Snap.Matrix().scale(1.0/xscale, 1.0/yscale);\n",
       "    root.selectAll('.marker').forEach(function (element, i) {\n",
       "        element.selectAll('.primitive').forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        }) });\n",
       "\n",
       "    bounds = root.plotbounds();\n",
       "    px_per_mm = root.data(\"px_per_mm\");\n",
       "\n",
       "    if (yscalable) {\n",
       "        var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
       "        root.selectAll(\".xfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(xfixed_t);\n",
       "            });\n",
       "\n",
       "        ylabels = root.select(\".ylabels\");\n",
       "        if (ylabels) {\n",
       "            ylabels.transform(xfixed_t)\n",
       "                   .selectAll(\"g\")\n",
       "                   .forEach(function (element, i) {\n",
       "                       if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                           unscale_t = new Snap.Matrix();\n",
       "                           unscale_t.scale(1, 1/yscale);\n",
       "                           element.select(\"text\").transform(unscale_t);\n",
       " \n",
       "                           var y = element.attr(\"transform\").globalMatrix.f / px_per_mm;\n",
       "                           element.attr(\"visibility\",\n",
       "                               bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
       "                       }\n",
       "                   });\n",
       "        }\n",
       "    }\n",
       "\n",
       "    if (xscalable) {\n",
       "        var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
       "        var xtrans = new Snap.Matrix().translate(tx, 0);\n",
       "        root.selectAll(\".yfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(yfixed_t);\n",
       "            });\n",
       "\n",
       "        xlabels = root.select(\".xlabels\");\n",
       "        if (xlabels) {\n",
       "            xlabels.transform(yfixed_t)\n",
       "                   .selectAll(\"g\")\n",
       "                   .forEach(function (element, i) {\n",
       "                       if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                           unscale_t = new Snap.Matrix();\n",
       "                           unscale_t.scale(1/xscale, 1);\n",
       "                           element.select(\"text\").transform(unscale_t);\n",
       "\n",
       "                           var x = element.attr(\"transform\").globalMatrix.e / px_per_mm;\n",
       "                           element.attr(\"visibility\",\n",
       "                               bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
       "                           }\n",
       "                   });\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "// Find the most appropriate tick scale and update label visibility.\n",
       "var update_tickscale = function(root, scale, axis) {\n",
       "    if (!root.hasClass(axis + \"scalable\")) return;\n",
       "\n",
       "    var tickscales = root.data(axis + \"tickscales\");\n",
       "    var best_tickscale = 1.0;\n",
       "    var best_tickscale_dist = Infinity;\n",
       "    for (tickscale in tickscales) {\n",
       "        var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
       "        if (dist < best_tickscale_dist) {\n",
       "            best_tickscale_dist = dist;\n",
       "            best_tickscale = tickscale;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
       "        root.data(axis + \"tickscale\", best_tickscale);\n",
       "        var mark_inscale_gridlines = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:inscale\") == null) { return; }\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        var mark_inscale_labels = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:inscale\") == null) { return; }\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        root.select(\".\" + axis + \"gridlines\").selectAll(\"g\").forEach(mark_inscale_gridlines);\n",
       "        root.select(\".\" + axis + \"labels\").selectAll(\"g\").forEach(mark_inscale_labels);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "var set_plot_pan_zoom = function(root, tx, ty, xscale, yscale) {\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\");\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    // compute the viewport derived from tx, ty, xscale, and yscale\n",
       "    var x_min = -width * xscale - (xscale * width - width),\n",
       "        x_max = width * xscale,\n",
       "        y_min = -height * yscale - (yscale * height - height),\n",
       "        y_max = height * yscale;\n",
       "\n",
       "    var x0 = bounds.x0 - xscale * bounds.x0,\n",
       "        y0 = bounds.y0 - yscale * bounds.y0;\n",
       "\n",
       "    var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
       "        ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
       "\n",
       "    tx += x0;\n",
       "    ty += y0;\n",
       "\n",
       "    // when the scale changes, we may need to alter which set of\n",
       "    // ticks are being displayed\n",
       "    if (xscale != old_xscale) {\n",
       "        update_tickscale(root, xscale, \"x\");\n",
       "    }\n",
       "    if (yscale != old_yscale) {\n",
       "        update_tickscale(root, yscale, \"y\");\n",
       "    }\n",
       "\n",
       "    set_geometry_transform(root, tx, ty, xscale, yscale);\n",
       "\n",
       "    root.data(\"xscale\", xscale);\n",
       "    root.data(\"yscale\", yscale);\n",
       "    root.data(\"tx\", tx);\n",
       "    root.data(\"ty\", ty);\n",
       "};\n",
       "\n",
       "\n",
       "var scale_centered_translation = function(root, xscale, yscale) {\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    var tx0 = root.data(\"tx\"),\n",
       "        ty0 = root.data(\"ty\");\n",
       "\n",
       "    var xscale0 = root.data(\"xscale\"),\n",
       "        yscale0 = root.data(\"yscale\");\n",
       "\n",
       "    // how off from center the current view is\n",
       "    var xoff = tx0 - (bounds.x0 * (1 - xscale0) + (width * (1 - xscale0)) / 2),\n",
       "        yoff = ty0 - (bounds.y0 * (1 - yscale0) + (height * (1 - yscale0)) / 2);\n",
       "\n",
       "    // rescale offsets\n",
       "    xoff = xoff * xscale / xscale0;\n",
       "    yoff = yoff * yscale / yscale0;\n",
       "\n",
       "    // adjust for the panel position being scaled\n",
       "    var x_edge_adjust = bounds.x0 * (1 - xscale),\n",
       "        y_edge_adjust = bounds.y0 * (1 - yscale);\n",
       "\n",
       "    return {\n",
       "        x: xoff + x_edge_adjust + (width - width * xscale) / 2,\n",
       "        y: yoff + y_edge_adjust + (height - height * yscale) / 2\n",
       "    };\n",
       "};\n",
       "\n",
       "\n",
       "// Initialize data for panning zooming if it isn't already.\n",
       "var init_pan_zoom = function(root) {\n",
       "    if (root.data(\"zoompan-ready\")) {\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    root.data(\"crosshair\",false);\n",
       "\n",
       "    // The non-scaling-stroke trick. Rather than try to correct for the\n",
       "    // stroke-width when zooming, we force it to a fixed value.\n",
       "    var px_per_mm = root.node.getCTM().a;\n",
       "\n",
       "    // Drag events report deltas in pixels, which we'd like to convert to\n",
       "    // millimeters.\n",
       "    root.data(\"px_per_mm\", px_per_mm);\n",
       "\n",
       "    root.selectAll(\"path\")\n",
       "        .forEach(function (element, i) {\n",
       "        sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
       "        if (sw > 0) {\n",
       "            element.attribute(\"stroke-width\", sw);\n",
       "            element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
       "        }\n",
       "    });\n",
       "\n",
       "    // Store ticks labels original tranformation\n",
       "    root.selectAll(\".xlabels > g, .ylabels > g\")\n",
       "        .forEach(function (element, i) {\n",
       "            var lm = element.transform().localMatrix;\n",
       "            element.data(\"static_transform\",\n",
       "                new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
       "        });\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\");\n",
       "    var ygridlines = root.select(\".ygridlines\");\n",
       "    var xlabels = root.select(\".xlabels\");\n",
       "    var ylabels = root.select(\".ylabels\");\n",
       "\n",
       "    if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
       "    if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
       "    if (root.data(\"xscale\") === undefined) root.data(\"xscale\", 1.0);\n",
       "    if (root.data(\"yscale\") === undefined) root.data(\"yscale\", 1.0);\n",
       "    if (root.data(\"xtickscales\") === undefined) {\n",
       "\n",
       "        // index all the tick scales that are listed\n",
       "        var xtickscales = {};\n",
       "        var ytickscales = {};\n",
       "        var add_x_tick_scales = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:scale\")==null) { return; }\n",
       "            xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "        var add_y_tick_scales = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:scale\")==null) { return; }\n",
       "            ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "\n",
       "        if (xgridlines) xgridlines.selectAll(\"g\").forEach(add_x_tick_scales);\n",
       "        if (ygridlines) ygridlines.selectAll(\"g\").forEach(add_y_tick_scales);\n",
       "        if (xlabels) xlabels.selectAll(\"g\").forEach(add_x_tick_scales);\n",
       "        if (ylabels) ylabels.selectAll(\"g\").forEach(add_y_tick_scales);\n",
       "\n",
       "        root.data(\"xtickscales\", xtickscales);\n",
       "        root.data(\"ytickscales\", ytickscales);\n",
       "        root.data(\"xtickscale\", 1.0);\n",
       "        root.data(\"ytickscale\", 1.0);  // ???\n",
       "    }\n",
       "\n",
       "    var min_scale = 1.0, max_scale = 1.0;\n",
       "    for (scale in xtickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    for (scale in ytickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    root.data(\"min_scale\", min_scale);\n",
       "    root.data(\"max_scale\", max_scale);\n",
       "\n",
       "    // store the original positions of labels\n",
       "    if (xlabels) {\n",
       "        xlabels.selectAll(\"g\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"x\", element.asPX(\"x\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    if (ylabels) {\n",
       "        ylabels.selectAll(\"g\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"y\", element.asPX(\"y\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    // mark grid lines and ticks as in or out of scale.\n",
       "    var mark_inscale = function (element, i) {\n",
       "        if (element.attribute(\"gadfly:scale\") == null) { return; }\n",
       "        element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
       "    };\n",
       "\n",
       "    if (xgridlines) xgridlines.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (ygridlines) ygridlines.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (xlabels) xlabels.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (ylabels) ylabels.selectAll(\"g\").forEach(mark_inscale);\n",
       "\n",
       "    // figure out the upper ond lower bounds on panning using the maximum\n",
       "    // and minum grid lines\n",
       "    var bounds = root.plotbounds();\n",
       "    var pan_bounds = {\n",
       "        x0: 0.0,\n",
       "        y0: 0.0,\n",
       "        x1: 0.0,\n",
       "        y1: 0.0\n",
       "    };\n",
       "\n",
       "    if (xgridlines) {\n",
       "        xgridlines\n",
       "            .selectAll(\"g\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
       "                        pan_bounds.x0 = bounds.x1 - bbox.x;\n",
       "                    }\n",
       "                    if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
       "                        pan_bounds.x1 = bounds.x0 - bbox.x;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines\n",
       "            .selectAll(\"g\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
       "                        pan_bounds.y0 = bounds.y1 - bbox.y;\n",
       "                    }\n",
       "                    if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
       "                        pan_bounds.y1 = bounds.y0 - bbox.y;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    // nudge these values a little\n",
       "    pan_bounds.x0 -= 5;\n",
       "    pan_bounds.x1 += 5;\n",
       "    pan_bounds.y0 -= 5;\n",
       "    pan_bounds.y1 += 5;\n",
       "    root.data(\"pan_bounds\", pan_bounds);\n",
       "\n",
       "    root.data(\"zoompan-ready\", true)\n",
       "};\n",
       "\n",
       "\n",
       "// drag actions, i.e. zooming and panning\n",
       "var pan_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        root.data(\"dx\", 0);\n",
       "        root.data(\"dy\", 0);\n",
       "        root.data(\"tx0\", root.data(\"tx\"));\n",
       "        root.data(\"ty0\", root.data(\"ty\"));\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        dx /= px_per_mm;\n",
       "        dy /= px_per_mm;\n",
       "\n",
       "        var tx0 = root.data(\"tx\"),\n",
       "            ty0 = root.data(\"ty\");\n",
       "\n",
       "        var dx0 = root.data(\"dx\"),\n",
       "            dy0 = root.data(\"dy\");\n",
       "\n",
       "        root.data(\"dx\", dx);\n",
       "        root.data(\"dy\", dy);\n",
       "\n",
       "        dx = dx - dx0;\n",
       "        dy = dy - dy0;\n",
       "\n",
       "        var tx = tx0 + dx,\n",
       "            ty = ty0 + dy;\n",
       "\n",
       "        set_plot_pan_zoom(root, tx, ty, root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        set_plot_pan_zoom(root, root.data(\"tx0\"), root.data(\"ty0\"),\n",
       "                root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "    }\n",
       "};\n",
       "\n",
       "var zoom_box;\n",
       "var zoom_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        var bounds = root.plotbounds();\n",
       "        var width = bounds.x1 - bounds.x0,\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        x = xscalable ? x / px_per_mm : bounds.x0;\n",
       "        y = yscalable ? y / px_per_mm : bounds.y0;\n",
       "        var w = xscalable ? 0 : width;\n",
       "        var h = yscalable ? 0 : height;\n",
       "        zoom_box = root.rect(x, y, w, h).attr({\n",
       "            \"fill\": \"#000\",\n",
       "            \"opacity\": 0.25\n",
       "        });\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        var bounds = root.plotbounds();\n",
       "        if (yscalable) {\n",
       "            y /= px_per_mm;\n",
       "            y = Math.max(bounds.y0, y);\n",
       "            y = Math.min(bounds.y1, y);\n",
       "        } else {\n",
       "            y = bounds.y1;\n",
       "        }\n",
       "        if (xscalable) {\n",
       "            x /= px_per_mm;\n",
       "            x = Math.max(bounds.x0, x);\n",
       "            x = Math.min(bounds.x1, x);\n",
       "        } else {\n",
       "            x = bounds.x1;\n",
       "        }\n",
       "\n",
       "        dx = x - zoom_box.attr(\"x\");\n",
       "        dy = y - zoom_box.attr(\"y\");\n",
       "        var xoffset = 0,\n",
       "            yoffset = 0;\n",
       "        if (dx < 0) {\n",
       "            xoffset = dx;\n",
       "            dx = -1 * dx;\n",
       "        }\n",
       "        if (dy < 0) {\n",
       "            yoffset = dy;\n",
       "            dy = -1 * dy;\n",
       "        }\n",
       "        if (isNaN(dy)) {\n",
       "            dy = 0.0;\n",
       "        }\n",
       "        if (isNaN(dx)) {\n",
       "            dx = 0.0;\n",
       "        }\n",
       "        zoom_box.transform(\"T\" + xoffset + \",\" + yoffset);\n",
       "        zoom_box.attr(\"width\", dx);\n",
       "        zoom_box.attr(\"height\", dy);\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var zoom_bounds = zoom_box.getBBox();\n",
       "        if (zoom_bounds.width * zoom_bounds.height <= 0) {\n",
       "            return;\n",
       "        }\n",
       "        var plot_bounds = root.plotbounds();\n",
       "        var xzoom_factor = 1.0,\n",
       "            yzoom_factor = 1.0;\n",
       "        if (xscalable) {\n",
       "            xzoom_factor = (plot_bounds.x1 - plot_bounds.x0) / zoom_bounds.width;\n",
       "        }\n",
       "        if (yscalable) {\n",
       "            yzoom_factor = (plot_bounds.y1 - plot_bounds.y0) / zoom_bounds.height;\n",
       "        }\n",
       "        var tx = (root.data(\"tx\") - zoom_bounds.x) * xzoom_factor + plot_bounds.x0,\n",
       "            ty = (root.data(\"ty\") - zoom_bounds.y) * yzoom_factor + plot_bounds.y0;\n",
       "        set_plot_pan_zoom(root, tx, ty,\n",
       "                root.data(\"xscale\") * xzoom_factor, root.data(\"yscale\") * yzoom_factor);\n",
       "        zoom_box.remove();\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        zoom_box.remove();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var scalable = root.hasClass(\"xscalable\") || root.hasClass(\"yscalable\");\n",
       "    var zoomable = !event.altKey && !event.ctrlKey && event.shiftKey && scalable;\n",
       "    var panable = !event.altKey && !event.ctrlKey && !event.shiftKey && scalable;\n",
       "    var drag_action = zoomable ? zoom_action :\n",
       "                      panable  ? pan_action :\n",
       "                                 undefined;\n",
       "    root.data(\"drag_action\", drag_action);\n",
       "    if (drag_action) {\n",
       "        var cancel_drag_action = function(event) {\n",
       "            if (event.which == 27) { // esc key\n",
       "                drag_action.cancel(root);\n",
       "                root.data(\"drag_action\", undefined);\n",
       "            }\n",
       "        };\n",
       "        window.addEventListener(\"keyup\", cancel_drag_action);\n",
       "        root.data(\"cancel_drag_action\", cancel_drag_action);\n",
       "        drag_action.start(root, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.update(root, dx, dy, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onend = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    window.removeEventListener(\"keyup\", root.data(\"cancel_drag_action\"));\n",
       "    root.data(\"cancel_drag_action\", undefined);\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.end(root, event);\n",
       "    }\n",
       "    root.data(\"drag_action\", undefined);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_scroll = function(event) {\n",
       "    if (event.shiftKey) {\n",
       "        increase_zoom_by_position(this.plotroot(), 0.001 * event.wheelDelta);\n",
       "        event.preventDefault();\n",
       "    }\n",
       "};\n",
       "\n",
       "// Map slider position x to scale y using the function y = a*exp(b*x)+c.\n",
       "// The constants a, b, and c are solved using the constraint that the function\n",
       "// should go through the points (0; min_scale), (0.5; 1), and (1; max_scale).\n",
       "var scale_from_slider_position = function(position, min_scale, max_scale) {\n",
       "    if (min_scale==max_scale) { return 1; }\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return a * Math.exp(b * position) + c;\n",
       "}\n",
       "\n",
       "// inverse of scale_from_slider_position\n",
       "var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
       "    if (min_scale==max_scale) { return min_scale; }\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return 1 / b * Math.log((scale - c) / a);\n",
       "}\n",
       "\n",
       "var increase_zoom_by_position = function(root, delta_position, animate) {\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\");\n",
       "    var xposition = slider_position_from_scale(old_xscale, min_scale, max_scale),\n",
       "        yposition = slider_position_from_scale(old_yscale, min_scale, max_scale);\n",
       "    xposition += (root.hasClass(\"xscalable\") ? delta_position : 0.0);\n",
       "    yposition += (root.hasClass(\"yscalable\") ? delta_position : 0.0);\n",
       "    old_xscale = scale_from_slider_position(xposition, min_scale, max_scale);\n",
       "    old_yscale = scale_from_slider_position(yposition, min_scale, max_scale);\n",
       "    var new_xscale = Math.max(min_scale, Math.min(old_xscale, max_scale)),\n",
       "        new_yscale = Math.max(min_scale, Math.min(old_yscale, max_scale));\n",
       "    if (animate) {\n",
       "        Snap.animate(\n",
       "            [old_xscale, old_yscale],\n",
       "            [new_xscale, new_yscale],\n",
       "            function (new_scale) {\n",
       "                update_plot_scale(root, new_scale[0], new_scale[1]);\n",
       "            },\n",
       "            200);\n",
       "    } else {\n",
       "        update_plot_scale(root, new_xscale, new_yscale);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "var update_plot_scale = function(root, new_xscale, new_yscale) {\n",
       "    var trans = scale_centered_translation(root, new_xscale, new_yscale);\n",
       "    set_plot_pan_zoom(root, trans.x, trans.y, new_xscale, new_yscale);\n",
       "};\n",
       "\n",
       "\n",
       "var toggle_color_class = function(root, color_class, ison) {\n",
       "    var escaped_color_class = color_class.replace(/([^0-9a-zA-z])/g,\"\\\\$1\");\n",
       "    var guides = root.selectAll(\".guide.\" + escaped_color_class + \",.guide .\" + escaped_color_class);\n",
       "    var geoms = root.selectAll(\".geometry.\" + escaped_color_class + \",.geometry .\" + escaped_color_class);\n",
       "    if (ison) {\n",
       "        guides.animate({opacity: 0.5}, 250);\n",
       "        geoms.animate({opacity: 0.0}, 250);\n",
       "    } else {\n",
       "        guides.animate({opacity: 1.0}, 250);\n",
       "        geoms.animate({opacity: 1.0}, 250);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.colorkey_swatch_click = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    var color_class = this.data(\"color_class\");\n",
       "\n",
       "    if (event.shiftKey) {\n",
       "        root.selectAll(\".colorkey g\")\n",
       "            .forEach(function (element) {\n",
       "                var other_color_class = element.data(\"color_class\");\n",
       "                if (typeof other_color_class !== 'undefined' && other_color_class != color_class) {\n",
       "                    toggle_color_class(root, other_color_class,\n",
       "                                       element.attr(\"opacity\") == 1.0);\n",
       "                }\n",
       "            });\n",
       "    } else {\n",
       "        toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "return Gadfly;\n",
       "\n",
       "}));\n",
       "\n",
       "\n",
       "//@ sourceURL=gadfly.js\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "      if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
       "        require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
       "            factory(Snap, Gadfly);\n",
       "        });\n",
       "      } else {\n",
       "          factory(glob.Snap, glob.Gadfly);\n",
       "      }\n",
       "})(window, function (Snap, Gadfly) {\n",
       "    var fig = Snap(\"#img-bda6c4ab\");\n",
       "fig.select(\"#img-bda6c4ab-5\")\n",
       "   .init_gadfly();\n",
       "fig.select(\"#img-bda6c4ab-8\")\n",
       "   .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-bda6c4ab-8\")\n",
       "   .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-bda6c4ab-162\")\n",
       "   .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-bda6c4ab-162\")\n",
       "   .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-bda6c4ab-334\")\n",
       "   .mouseenter(Gadfly.helpscreen_visible)\n",
       ".mouseleave(Gadfly.helpscreen_hidden)\n",
       ";\n",
       "    });\n",
       "]]> </script>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot(...)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(d,x=\"H\",y=\"V\",Geom.line)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-48.357046148247086"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real(roots(pvol - 10.)[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-48.48516975908005"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real(roots(pvol -12.)[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-48.97899098468442"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real(roots(pvol - 20.)[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculations for a cylindrical well"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cylindrical wells have a depth of 11.47 mm and a diameter (top/bottom) of 5.0/4.5 mm., corresponding to a radius of 2.5/2.25 mm.\n",
    "\n",
    "The radius $r$ at a height $H$ will be $2.25 + (0.25)*H/11.47$ mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.25 &#43; 0.021795989537925022&#8729;x"
      ],
      "text/latex": [
       "$2.25 + 0.021795989537925022\\cdot x$"
      ],
      "text/plain": [
       "Poly(2.25 + 0.021795989537925022*x)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pradius = Poly([2.25, (0.25)/(11.47)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just to make sure that I got that right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 2.25\n",
       " 2.5 "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polyval(pradius,[0.,11.47])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "15.904312808798327 &#43; 0.3081335427452936&#8729;x &#43; 0.001492461216435598&#8729;x^2"
      ],
      "text/latex": [
       "$15.904312808798327 + 0.3081335427452936\\cdot x + 0.001492461216435598\\cdot x^{2}$"
      ],
      "text/plain": [
       "Poly(15.904312808798327 + 0.3081335427452936*x + 0.001492461216435598*x^2)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parea = π * pradius * pradius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 15.904312808798327\n",
       " 19.634954084936208"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polyval(parea,[0.,11.47])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "15.904312808798327&#8729;x &#43; 0.1540667713726468&#8729;x^2 &#43; 0.0004974870721451993&#8729;x^3"
      ],
      "text/latex": [
       "$15.904312808798327\\cdot x + 0.1540667713726468\\cdot x^{2} + 0.0004974870721451993\\cdot x^{3}$"
      ],
      "text/plain": [
       "Poly(15.904312808798327*x + 0.1540667713726468*x^2 + 0.0004974870721451993*x^3)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pvol = polyint(parea)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H = collect(0.:0.01:12.);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\"\n",
       "     xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     xmlns:gadfly=\"http://www.gadflyjl.org/ns\"\n",
       "     version=\"1.2\"\n",
       "     width=\"141.42mm\" height=\"100mm\" viewBox=\"0 0 141.42 100\"\n",
       "     stroke=\"none\"\n",
       "     fill=\"#000000\"\n",
       "     stroke-width=\"0.3\"\n",
       "     font-size=\"3.88\"\n",
       ">\n",
       "<defs>\n",
       "  <marker id=\"arrow\" markerWidth=\"15\" markerHeight=\"7\" refX=\"5\" refY=\"3.5\" orient=\"auto\" markerUnits=\"strokeWidth\">\n",
       "    <path d=\"M0,0 L15,3.5 L0,7 z\" stroke=\"context-stroke\" fill=\"context-stroke\"/>\n",
       "  </marker>\n",
       "</defs>\n",
       "<g class=\"plotroot xscalable yscalable\" id=\"img-0a4e3fb7-1\">\n",
       "  <g font-size=\"3.88\" font-family=\"'PT Sans','Helvetica Neue','Helvetica',sans-serif\" fill=\"#564A55\" stroke=\"#000000\" stroke-opacity=\"0.000\" id=\"img-0a4e3fb7-2\">\n",
       "    <g transform=\"translate(78.03,88.39)\">\n",
       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.6em\">Height above well bottom (mm)</text>\n",
       "      </g>\n",
       "    </g>\n",
       "  </g>\n",
       "  <g class=\"guide xlabels\" font-size=\"2.82\" font-family=\"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\" fill=\"#6C606B\" id=\"img-0a4e3fb7-3\">\n",
       "    <g transform=\"translate(21.63,81.72)\">\n",
       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.6em\">0</text>\n",
       "      </g>\n",
       "    </g>\n",
       "    <g transform=\"translate(40.43,81.72)\">\n",
       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.6em\">2</text>\n",
       "      </g>\n",
       "    </g>\n",
       "    <g transform=\"translate(59.23,81.72)\">\n",
       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.6em\">4</text>\n",
       "      </g>\n",
       "    </g>\n",
       "    <g transform=\"translate(78.03,81.72)\">\n",
       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.6em\">6</text>\n",
       "      </g>\n",
       "    </g>\n",
       "    <g transform=\"translate(96.82,81.72)\">\n",
       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.6em\">8</text>\n",
       "      </g>\n",
       "    </g>\n",
       "    <g transform=\"translate(115.62,81.72)\">\n",
       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.6em\">10</text>\n",
       "      </g>\n",
       "    </g>\n",
       "    <g transform=\"translate(134.42,81.72)\">\n",
       "      <g class=\"primitive\">\n",
       "        <text text-anchor=\"middle\" dy=\"0.6em\">12</text>\n",
       "      </g>\n",
       "    </g>\n",
       "  </g>\n",
       "  <g clip-path=\"url(#img-0a4e3fb7-4)\">\n",
       "    <g id=\"img-0a4e3fb7-5\">\n",
       "      <g pointer-events=\"visible\" fill=\"#000000\" fill-opacity=\"0.000\" stroke=\"#000000\" stroke-opacity=\"0.000\" class=\"guide background\" id=\"img-0a4e3fb7-6\">\n",
       "        <g transform=\"translate(78.03,42.86)\" id=\"img-0a4e3fb7-7\">\n",
       "          <path d=\"M-58.39,-37.86 L 58.39 -37.86 58.39 37.86 -58.39 37.86 z\" class=\"primitive\"/>\n",
       "        </g>\n",
       "      </g>\n",
       "      <g class=\"guide ygridlines xfixed\" stroke-dasharray=\"0.5,0.5\" stroke-width=\"0.2\" stroke=\"#D0D0E0\" id=\"img-0a4e3fb7-8\">\n",
       "        <g transform=\"translate(78.03,78.72)\" id=\"img-0a4e3fb7-9\">\n",
       "          <path fill=\"none\" d=\"M-58.39,0 L 58.39 0\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(78.03,64.37)\" id=\"img-0a4e3fb7-10\">\n",
       "          <path fill=\"none\" d=\"M-58.39,0 L 58.39 0\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(78.03,50.03)\" id=\"img-0a4e3fb7-11\">\n",
       "          <path fill=\"none\" d=\"M-58.39,0 L 58.39 0\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(78.03,35.69)\" id=\"img-0a4e3fb7-12\">\n",
       "          <path fill=\"none\" d=\"M-58.39,0 L 58.39 0\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(78.03,21.34)\" id=\"img-0a4e3fb7-13\">\n",
       "          <path fill=\"none\" d=\"M-58.39,0 L 58.39 0\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(78.03,7)\" id=\"img-0a4e3fb7-14\">\n",
       "          <path fill=\"none\" d=\"M-58.39,0 L 58.39 0\" class=\"primitive\"/>\n",
       "        </g>\n",
       "      </g>\n",
       "      <g class=\"guide xgridlines yfixed\" stroke-dasharray=\"0.5,0.5\" stroke-width=\"0.2\" stroke=\"#D0D0E0\" id=\"img-0a4e3fb7-15\">\n",
       "        <g transform=\"translate(21.63,42.86)\" id=\"img-0a4e3fb7-16\">\n",
       "          <path fill=\"none\" d=\"M0,-37.86 L 0 37.86\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(40.43,42.86)\" id=\"img-0a4e3fb7-17\">\n",
       "          <path fill=\"none\" d=\"M0,-37.86 L 0 37.86\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(59.23,42.86)\" id=\"img-0a4e3fb7-18\">\n",
       "          <path fill=\"none\" d=\"M0,-37.86 L 0 37.86\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(78.03,42.86)\" id=\"img-0a4e3fb7-19\">\n",
       "          <path fill=\"none\" d=\"M0,-37.86 L 0 37.86\" class=\"primitive\"/>\n",
       "        </g>\n",
       "        <g transform=\"translate(96.82,42.86)\" id=\"img-0a4e3fb7-20\">\n",
       "          <path fill=\"none\" d=\"M0,-37.86 L 0 37.86\" class=\"primitive\"/>\n",
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       "            Element.prototype[event_name] = function (fn, scope) {\n",
       "                if (Snap.is(fn, \"function\")) {\n",
       "                    var fn2 = function (event) {\n",
       "                        if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
       "                            return;\n",
       "                        }\n",
       "\n",
       "                        var reltg = event.relatedTarget ? event.relatedTarget :\n",
       "                            event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
       "                        while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
       "\n",
       "                        if (reltg != this.node) {\n",
       "                            return fn.apply(this, event);\n",
       "                        }\n",
       "                    };\n",
       "\n",
       "                    if (event_name == \"mouseenter\") {\n",
       "                        this.mouseover(fn2, scope);\n",
       "                    } else {\n",
       "                        this.mouseout(fn2, scope);\n",
       "                    }\n",
       "                }\n",
       "                return this;\n",
       "            };\n",
       "        })(events[i]);\n",
       "    }\n",
       "\n",
       "\n",
       "    Element.prototype.mousewheel = function (fn, scope) {\n",
       "        if (Snap.is(fn, \"function\")) {\n",
       "            var el = this;\n",
       "            var fn2 = function (event) {\n",
       "                fn.apply(el, [event]);\n",
       "            };\n",
       "        }\n",
       "\n",
       "        this.node.addEventListener(\n",
       "            /Firefox/i.test(navigator.userAgent) ? \"DOMMouseScroll\" : \"mousewheel\",\n",
       "            fn2);\n",
       "\n",
       "        return this;\n",
       "    };\n",
       "\n",
       "\n",
       "    // Snap's attr function can be too slow for things like panning/zooming.\n",
       "    // This is a function to directly update element attributes without going\n",
       "    // through eve.\n",
       "    Element.prototype.attribute = function(key, val) {\n",
       "        if (val === undefined) {\n",
       "            return this.node.getAttribute(key);\n",
       "        } else {\n",
       "            this.node.setAttribute(key, val);\n",
       "            return this;\n",
       "        }\n",
       "    };\n",
       "\n",
       "    Element.prototype.init_gadfly = function() {\n",
       "        this.mouseenter(Gadfly.plot_mouseover)\n",
       "            .mousemove(Gadfly.plot_mousemove)\n",
       "            .mouseleave(Gadfly.plot_mouseout)\n",
       "            .dblclick(Gadfly.plot_dblclick)\n",
       "            .mousewheel(Gadfly.guide_background_scroll)\n",
       "            .drag(Gadfly.guide_background_drag_onmove,\n",
       "                  Gadfly.guide_background_drag_onstart,\n",
       "                  Gadfly.guide_background_drag_onend);\n",
       "        this.mouseenter(function (event) {\n",
       "            init_pan_zoom(this.plotroot());\n",
       "        });\n",
       "        return this;\n",
       "    };\n",
       "});\n",
       "\n",
       "\n",
       "Gadfly.plot_mousemove = function(event, x_px, y_px) {\n",
       "    var root = this.plotroot();\n",
       "    if (root.data(\"crosshair\")) {\n",
       "        px_per_mm = root.data(\"px_per_mm\");\n",
       "        bB = root.select('boundingbox').node.getAttribute('value').split(' ');\n",
       "        uB = root.select('unitbox').node.getAttribute('value').split(' ');\n",
       "        xscale = root.data(\"xscale\");\n",
       "        yscale = root.data(\"yscale\");\n",
       "        xtranslate = root.data(\"tx\");\n",
       "        ytranslate = root.data(\"ty\");\n",
       "\n",
       "        xoff_mm = bB[0].substr(0,bB[0].length-2)/1;\n",
       "        yoff_mm = bB[1].substr(0,bB[1].length-2)/1;\n",
       "        xoff_unit = uB[0]/1;\n",
       "        yoff_unit = uB[1]/1;\n",
       "        mm_per_xunit = bB[2].substr(0,bB[2].length-2) / uB[2];\n",
       "        mm_per_yunit = bB[3].substr(0,bB[3].length-2) / uB[3];\n",
       "         \n",
       "        x_unit = ((x_px / px_per_mm - xtranslate) / xscale - xoff_mm) / mm_per_xunit + xoff_unit;\n",
       "        y_unit = ((y_px / px_per_mm - ytranslate) / yscale - yoff_mm) / mm_per_yunit + yoff_unit;\n",
       "\n",
       "        root.select('.crosshair').select('.primitive').select('text')\n",
       "                .node.innerHTML = x_unit.toPrecision(3)+\",\"+y_unit.toPrecision(3);\n",
       "    };\n",
       "};\n",
       "\n",
       "Gadfly.helpscreen_visible = function(event) {\n",
       "    helpscreen_visible(this.plotroot());\n",
       "};\n",
       "var helpscreen_visible = function(root) {\n",
       "    root.select(\".helpscreen\").animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "Gadfly.helpscreen_hidden = function(event) {\n",
       "    helpscreen_hidden(this.plotroot());\n",
       "};\n",
       "var helpscreen_hidden = function(root) {\n",
       "    root.select(\".helpscreen\").animate({opacity: 0.0}, 250);\n",
       "};\n",
       "\n",
       "// When the plot is moused over, emphasize the grid lines.\n",
       "Gadfly.plot_mouseover = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    var keyboard_help = function(event) {\n",
       "        if (event.which == 191) { // ?\n",
       "            helpscreen_visible(root);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_help\", keyboard_help);\n",
       "    window.addEventListener(\"keydown\", keyboard_help);\n",
       "\n",
       "    var keyboard_pan_zoom = function(event) {\n",
       "        var bounds = root.plotbounds(),\n",
       "            width = bounds.x1 - bounds.x0;\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        if (event.which == 187 || event.which == 73) { // plus or i\n",
       "            increase_zoom_by_position(root, 0.1, true);\n",
       "        } else if (event.which == 189 || event.which == 79) { // minus or o\n",
       "            increase_zoom_by_position(root, -0.1, true);\n",
       "        } else if (event.which == 39 || event.which == 76) { // right-arrow or l\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\")-width/10, root.data(\"ty\"),\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 40 || event.which == 74) { // down-arrow or j\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\"), root.data(\"ty\")-height/10,\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 37 || event.which == 72) { // left-arrow or h\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\")+width/10, root.data(\"ty\"),\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 38 || event.which == 75) { // up-arrow or k\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\"), root.data(\"ty\")+height/10,\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 82) { // r\n",
       "            set_plot_pan_zoom(root, 0.0, 0.0, 1.0, 1.0);\n",
       "        } else if (event.which == 191) { // ?\n",
       "            helpscreen_hidden(root);\n",
       "        } else if (event.which == 67) { // c\n",
       "            root.data(\"crosshair\",!root.data(\"crosshair\"));\n",
       "            root.select(\".crosshair\")\n",
       "                .animate({opacity: root.data(\"crosshair\") ? 1.0 : 0.0}, 250);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_pan_zoom\", keyboard_pan_zoom);\n",
       "    window.addEventListener(\"keyup\", keyboard_pan_zoom);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    if (xgridlines) {\n",
       "        xgridlines.data(\"unfocused_strokedash\",\n",
       "                        xgridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "        var destcolor = root.data(\"focused_xgrid_color\");\n",
       "        xgridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines.data(\"unfocused_strokedash\",\n",
       "                        ygridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "        var destcolor = root.data(\"focused_ygrid_color\");\n",
       "        ygridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    root.select(\".crosshair\")\n",
       "        .animate({opacity: root.data(\"crosshair\") ? 1.0 : 0.0}, 250);\n",
       "    root.select(\".questionmark\").animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "// Reset pan and zoom on double click\n",
       "Gadfly.plot_dblclick = function(event) {\n",
       "  set_plot_pan_zoom(this.plotroot(), 0.0, 0.0, 1.0, 1.0);\n",
       "};\n",
       "\n",
       "// Unemphasize grid lines on mouse out.\n",
       "Gadfly.plot_mouseout = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    window.removeEventListener(\"keyup\", root.data(\"keyboard_pan_zoom\"));\n",
       "    root.data(\"keyboard_pan_zoom\", undefined);\n",
       "    window.removeEventListener(\"keydown\", root.data(\"keyboard_help\"));\n",
       "    root.data(\"keyboard_help\", undefined);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    if (xgridlines) {\n",
       "        var destcolor = root.data(\"unfocused_xgrid_color\");\n",
       "        xgridlines.attribute(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        var destcolor = root.data(\"unfocused_ygrid_color\");\n",
       "        ygridlines.attribute(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    root.select(\".crosshair\").animate({opacity: 0.0}, 250);\n",
       "    root.select(\".questionmark\").animate({opacity: 0.0}, 250);\n",
       "    helpscreen_hidden(root);\n",
       "};\n",
       "\n",
       "\n",
       "var set_geometry_transform = function(root, tx, ty, xscale, yscale) {\n",
       "    var xscalable = root.hasClass(\"xscalable\"),\n",
       "        yscalable = root.hasClass(\"yscalable\");\n",
       "\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\");\n",
       "\n",
       "    var xscale = xscalable ? xscale : 1.0,\n",
       "        yscale = yscalable ? yscale : 1.0;\n",
       "\n",
       "    tx = xscalable ? tx : 0.0;\n",
       "    ty = yscalable ? ty : 0.0;\n",
       "\n",
       "    var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
       "    root.selectAll(\".geometry, image\").forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        });\n",
       "\n",
       "    var t = new Snap.Matrix().scale(1.0/xscale, 1.0/yscale);\n",
       "    root.selectAll('.marker').forEach(function (element, i) {\n",
       "        element.selectAll('.primitive').forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        }) });\n",
       "\n",
       "    bounds = root.plotbounds();\n",
       "    px_per_mm = root.data(\"px_per_mm\");\n",
       "\n",
       "    if (yscalable) {\n",
       "        var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
       "        root.selectAll(\".xfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(xfixed_t);\n",
       "            });\n",
       "\n",
       "        ylabels = root.select(\".ylabels\");\n",
       "        if (ylabels) {\n",
       "            ylabels.transform(xfixed_t)\n",
       "                   .selectAll(\"g\")\n",
       "                   .forEach(function (element, i) {\n",
       "                       if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                           unscale_t = new Snap.Matrix();\n",
       "                           unscale_t.scale(1, 1/yscale);\n",
       "                           element.select(\"text\").transform(unscale_t);\n",
       " \n",
       "                           var y = element.attr(\"transform\").globalMatrix.f / px_per_mm;\n",
       "                           element.attr(\"visibility\",\n",
       "                               bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
       "                       }\n",
       "                   });\n",
       "        }\n",
       "    }\n",
       "\n",
       "    if (xscalable) {\n",
       "        var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
       "        var xtrans = new Snap.Matrix().translate(tx, 0);\n",
       "        root.selectAll(\".yfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(yfixed_t);\n",
       "            });\n",
       "\n",
       "        xlabels = root.select(\".xlabels\");\n",
       "        if (xlabels) {\n",
       "            xlabels.transform(yfixed_t)\n",
       "                   .selectAll(\"g\")\n",
       "                   .forEach(function (element, i) {\n",
       "                       if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                           unscale_t = new Snap.Matrix();\n",
       "                           unscale_t.scale(1/xscale, 1);\n",
       "                           element.select(\"text\").transform(unscale_t);\n",
       "\n",
       "                           var x = element.attr(\"transform\").globalMatrix.e / px_per_mm;\n",
       "                           element.attr(\"visibility\",\n",
       "                               bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
       "                           }\n",
       "                   });\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "// Find the most appropriate tick scale and update label visibility.\n",
       "var update_tickscale = function(root, scale, axis) {\n",
       "    if (!root.hasClass(axis + \"scalable\")) return;\n",
       "\n",
       "    var tickscales = root.data(axis + \"tickscales\");\n",
       "    var best_tickscale = 1.0;\n",
       "    var best_tickscale_dist = Infinity;\n",
       "    for (tickscale in tickscales) {\n",
       "        var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
       "        if (dist < best_tickscale_dist) {\n",
       "            best_tickscale_dist = dist;\n",
       "            best_tickscale = tickscale;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
       "        root.data(axis + \"tickscale\", best_tickscale);\n",
       "        var mark_inscale_gridlines = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:inscale\") == null) { return; }\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        var mark_inscale_labels = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:inscale\") == null) { return; }\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        root.select(\".\" + axis + \"gridlines\").selectAll(\"g\").forEach(mark_inscale_gridlines);\n",
       "        root.select(\".\" + axis + \"labels\").selectAll(\"g\").forEach(mark_inscale_labels);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "var set_plot_pan_zoom = function(root, tx, ty, xscale, yscale) {\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\");\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    // compute the viewport derived from tx, ty, xscale, and yscale\n",
       "    var x_min = -width * xscale - (xscale * width - width),\n",
       "        x_max = width * xscale,\n",
       "        y_min = -height * yscale - (yscale * height - height),\n",
       "        y_max = height * yscale;\n",
       "\n",
       "    var x0 = bounds.x0 - xscale * bounds.x0,\n",
       "        y0 = bounds.y0 - yscale * bounds.y0;\n",
       "\n",
       "    var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
       "        ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
       "\n",
       "    tx += x0;\n",
       "    ty += y0;\n",
       "\n",
       "    // when the scale changes, we may need to alter which set of\n",
       "    // ticks are being displayed\n",
       "    if (xscale != old_xscale) {\n",
       "        update_tickscale(root, xscale, \"x\");\n",
       "    }\n",
       "    if (yscale != old_yscale) {\n",
       "        update_tickscale(root, yscale, \"y\");\n",
       "    }\n",
       "\n",
       "    set_geometry_transform(root, tx, ty, xscale, yscale);\n",
       "\n",
       "    root.data(\"xscale\", xscale);\n",
       "    root.data(\"yscale\", yscale);\n",
       "    root.data(\"tx\", tx);\n",
       "    root.data(\"ty\", ty);\n",
       "};\n",
       "\n",
       "\n",
       "var scale_centered_translation = function(root, xscale, yscale) {\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    var tx0 = root.data(\"tx\"),\n",
       "        ty0 = root.data(\"ty\");\n",
       "\n",
       "    var xscale0 = root.data(\"xscale\"),\n",
       "        yscale0 = root.data(\"yscale\");\n",
       "\n",
       "    // how off from center the current view is\n",
       "    var xoff = tx0 - (bounds.x0 * (1 - xscale0) + (width * (1 - xscale0)) / 2),\n",
       "        yoff = ty0 - (bounds.y0 * (1 - yscale0) + (height * (1 - yscale0)) / 2);\n",
       "\n",
       "    // rescale offsets\n",
       "    xoff = xoff * xscale / xscale0;\n",
       "    yoff = yoff * yscale / yscale0;\n",
       "\n",
       "    // adjust for the panel position being scaled\n",
       "    var x_edge_adjust = bounds.x0 * (1 - xscale),\n",
       "        y_edge_adjust = bounds.y0 * (1 - yscale);\n",
       "\n",
       "    return {\n",
       "        x: xoff + x_edge_adjust + (width - width * xscale) / 2,\n",
       "        y: yoff + y_edge_adjust + (height - height * yscale) / 2\n",
       "    };\n",
       "};\n",
       "\n",
       "\n",
       "// Initialize data for panning zooming if it isn't already.\n",
       "var init_pan_zoom = function(root) {\n",
       "    if (root.data(\"zoompan-ready\")) {\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    root.data(\"crosshair\",false);\n",
       "\n",
       "    // The non-scaling-stroke trick. Rather than try to correct for the\n",
       "    // stroke-width when zooming, we force it to a fixed value.\n",
       "    var px_per_mm = root.node.getCTM().a;\n",
       "\n",
       "    // Drag events report deltas in pixels, which we'd like to convert to\n",
       "    // millimeters.\n",
       "    root.data(\"px_per_mm\", px_per_mm);\n",
       "\n",
       "    root.selectAll(\"path\")\n",
       "        .forEach(function (element, i) {\n",
       "        sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
       "        if (sw > 0) {\n",
       "            element.attribute(\"stroke-width\", sw);\n",
       "            element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
       "        }\n",
       "    });\n",
       "\n",
       "    // Store ticks labels original tranformation\n",
       "    root.selectAll(\".xlabels > g, .ylabels > g\")\n",
       "        .forEach(function (element, i) {\n",
       "            var lm = element.transform().localMatrix;\n",
       "            element.data(\"static_transform\",\n",
       "                new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
       "        });\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\");\n",
       "    var ygridlines = root.select(\".ygridlines\");\n",
       "    var xlabels = root.select(\".xlabels\");\n",
       "    var ylabels = root.select(\".ylabels\");\n",
       "\n",
       "    if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
       "    if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
       "    if (root.data(\"xscale\") === undefined) root.data(\"xscale\", 1.0);\n",
       "    if (root.data(\"yscale\") === undefined) root.data(\"yscale\", 1.0);\n",
       "    if (root.data(\"xtickscales\") === undefined) {\n",
       "\n",
       "        // index all the tick scales that are listed\n",
       "        var xtickscales = {};\n",
       "        var ytickscales = {};\n",
       "        var add_x_tick_scales = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:scale\")==null) { return; }\n",
       "            xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "        var add_y_tick_scales = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:scale\")==null) { return; }\n",
       "            ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "\n",
       "        if (xgridlines) xgridlines.selectAll(\"g\").forEach(add_x_tick_scales);\n",
       "        if (ygridlines) ygridlines.selectAll(\"g\").forEach(add_y_tick_scales);\n",
       "        if (xlabels) xlabels.selectAll(\"g\").forEach(add_x_tick_scales);\n",
       "        if (ylabels) ylabels.selectAll(\"g\").forEach(add_y_tick_scales);\n",
       "\n",
       "        root.data(\"xtickscales\", xtickscales);\n",
       "        root.data(\"ytickscales\", ytickscales);\n",
       "        root.data(\"xtickscale\", 1.0);\n",
       "        root.data(\"ytickscale\", 1.0);  // ???\n",
       "    }\n",
       "\n",
       "    var min_scale = 1.0, max_scale = 1.0;\n",
       "    for (scale in xtickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    for (scale in ytickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    root.data(\"min_scale\", min_scale);\n",
       "    root.data(\"max_scale\", max_scale);\n",
       "\n",
       "    // store the original positions of labels\n",
       "    if (xlabels) {\n",
       "        xlabels.selectAll(\"g\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"x\", element.asPX(\"x\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    if (ylabels) {\n",
       "        ylabels.selectAll(\"g\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"y\", element.asPX(\"y\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    // mark grid lines and ticks as in or out of scale.\n",
       "    var mark_inscale = function (element, i) {\n",
       "        if (element.attribute(\"gadfly:scale\") == null) { return; }\n",
       "        element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
       "    };\n",
       "\n",
       "    if (xgridlines) xgridlines.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (ygridlines) ygridlines.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (xlabels) xlabels.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (ylabels) ylabels.selectAll(\"g\").forEach(mark_inscale);\n",
       "\n",
       "    // figure out the upper ond lower bounds on panning using the maximum\n",
       "    // and minum grid lines\n",
       "    var bounds = root.plotbounds();\n",
       "    var pan_bounds = {\n",
       "        x0: 0.0,\n",
       "        y0: 0.0,\n",
       "        x1: 0.0,\n",
       "        y1: 0.0\n",
       "    };\n",
       "\n",
       "    if (xgridlines) {\n",
       "        xgridlines\n",
       "            .selectAll(\"g\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
       "                        pan_bounds.x0 = bounds.x1 - bbox.x;\n",
       "                    }\n",
       "                    if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
       "                        pan_bounds.x1 = bounds.x0 - bbox.x;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines\n",
       "            .selectAll(\"g\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
       "                        pan_bounds.y0 = bounds.y1 - bbox.y;\n",
       "                    }\n",
       "                    if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
       "                        pan_bounds.y1 = bounds.y0 - bbox.y;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    // nudge these values a little\n",
       "    pan_bounds.x0 -= 5;\n",
       "    pan_bounds.x1 += 5;\n",
       "    pan_bounds.y0 -= 5;\n",
       "    pan_bounds.y1 += 5;\n",
       "    root.data(\"pan_bounds\", pan_bounds);\n",
       "\n",
       "    root.data(\"zoompan-ready\", true)\n",
       "};\n",
       "\n",
       "\n",
       "// drag actions, i.e. zooming and panning\n",
       "var pan_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        root.data(\"dx\", 0);\n",
       "        root.data(\"dy\", 0);\n",
       "        root.data(\"tx0\", root.data(\"tx\"));\n",
       "        root.data(\"ty0\", root.data(\"ty\"));\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        dx /= px_per_mm;\n",
       "        dy /= px_per_mm;\n",
       "\n",
       "        var tx0 = root.data(\"tx\"),\n",
       "            ty0 = root.data(\"ty\");\n",
       "\n",
       "        var dx0 = root.data(\"dx\"),\n",
       "            dy0 = root.data(\"dy\");\n",
       "\n",
       "        root.data(\"dx\", dx);\n",
       "        root.data(\"dy\", dy);\n",
       "\n",
       "        dx = dx - dx0;\n",
       "        dy = dy - dy0;\n",
       "\n",
       "        var tx = tx0 + dx,\n",
       "            ty = ty0 + dy;\n",
       "\n",
       "        set_plot_pan_zoom(root, tx, ty, root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        set_plot_pan_zoom(root, root.data(\"tx0\"), root.data(\"ty0\"),\n",
       "                root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "    }\n",
       "};\n",
       "\n",
       "var zoom_box;\n",
       "var zoom_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        var bounds = root.plotbounds();\n",
       "        var width = bounds.x1 - bounds.x0,\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        x = xscalable ? x / px_per_mm : bounds.x0;\n",
       "        y = yscalable ? y / px_per_mm : bounds.y0;\n",
       "        var w = xscalable ? 0 : width;\n",
       "        var h = yscalable ? 0 : height;\n",
       "        zoom_box = root.rect(x, y, w, h).attr({\n",
       "            \"fill\": \"#000\",\n",
       "            \"opacity\": 0.25\n",
       "        });\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        var bounds = root.plotbounds();\n",
       "        if (yscalable) {\n",
       "            y /= px_per_mm;\n",
       "            y = Math.max(bounds.y0, y);\n",
       "            y = Math.min(bounds.y1, y);\n",
       "        } else {\n",
       "            y = bounds.y1;\n",
       "        }\n",
       "        if (xscalable) {\n",
       "            x /= px_per_mm;\n",
       "            x = Math.max(bounds.x0, x);\n",
       "            x = Math.min(bounds.x1, x);\n",
       "        } else {\n",
       "            x = bounds.x1;\n",
       "        }\n",
       "\n",
       "        dx = x - zoom_box.attr(\"x\");\n",
       "        dy = y - zoom_box.attr(\"y\");\n",
       "        var xoffset = 0,\n",
       "            yoffset = 0;\n",
       "        if (dx < 0) {\n",
       "            xoffset = dx;\n",
       "            dx = -1 * dx;\n",
       "        }\n",
       "        if (dy < 0) {\n",
       "            yoffset = dy;\n",
       "            dy = -1 * dy;\n",
       "        }\n",
       "        if (isNaN(dy)) {\n",
       "            dy = 0.0;\n",
       "        }\n",
       "        if (isNaN(dx)) {\n",
       "            dx = 0.0;\n",
       "        }\n",
       "        zoom_box.transform(\"T\" + xoffset + \",\" + yoffset);\n",
       "        zoom_box.attr(\"width\", dx);\n",
       "        zoom_box.attr(\"height\", dy);\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var zoom_bounds = zoom_box.getBBox();\n",
       "        if (zoom_bounds.width * zoom_bounds.height <= 0) {\n",
       "            return;\n",
       "        }\n",
       "        var plot_bounds = root.plotbounds();\n",
       "        var xzoom_factor = 1.0,\n",
       "            yzoom_factor = 1.0;\n",
       "        if (xscalable) {\n",
       "            xzoom_factor = (plot_bounds.x1 - plot_bounds.x0) / zoom_bounds.width;\n",
       "        }\n",
       "        if (yscalable) {\n",
       "            yzoom_factor = (plot_bounds.y1 - plot_bounds.y0) / zoom_bounds.height;\n",
       "        }\n",
       "        var tx = (root.data(\"tx\") - zoom_bounds.x) * xzoom_factor + plot_bounds.x0,\n",
       "            ty = (root.data(\"ty\") - zoom_bounds.y) * yzoom_factor + plot_bounds.y0;\n",
       "        set_plot_pan_zoom(root, tx, ty,\n",
       "                root.data(\"xscale\") * xzoom_factor, root.data(\"yscale\") * yzoom_factor);\n",
       "        zoom_box.remove();\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        zoom_box.remove();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var scalable = root.hasClass(\"xscalable\") || root.hasClass(\"yscalable\");\n",
       "    var zoomable = !event.altKey && !event.ctrlKey && event.shiftKey && scalable;\n",
       "    var panable = !event.altKey && !event.ctrlKey && !event.shiftKey && scalable;\n",
       "    var drag_action = zoomable ? zoom_action :\n",
       "                      panable  ? pan_action :\n",
       "                                 undefined;\n",
       "    root.data(\"drag_action\", drag_action);\n",
       "    if (drag_action) {\n",
       "        var cancel_drag_action = function(event) {\n",
       "            if (event.which == 27) { // esc key\n",
       "                drag_action.cancel(root);\n",
       "                root.data(\"drag_action\", undefined);\n",
       "            }\n",
       "        };\n",
       "        window.addEventListener(\"keyup\", cancel_drag_action);\n",
       "        root.data(\"cancel_drag_action\", cancel_drag_action);\n",
       "        drag_action.start(root, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.update(root, dx, dy, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onend = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    window.removeEventListener(\"keyup\", root.data(\"cancel_drag_action\"));\n",
       "    root.data(\"cancel_drag_action\", undefined);\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.end(root, event);\n",
       "    }\n",
       "    root.data(\"drag_action\", undefined);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_scroll = function(event) {\n",
       "    if (event.shiftKey) {\n",
       "        increase_zoom_by_position(this.plotroot(), 0.001 * event.wheelDelta);\n",
       "        event.preventDefault();\n",
       "    }\n",
       "};\n",
       "\n",
       "// Map slider position x to scale y using the function y = a*exp(b*x)+c.\n",
       "// The constants a, b, and c are solved using the constraint that the function\n",
       "// should go through the points (0; min_scale), (0.5; 1), and (1; max_scale).\n",
       "var scale_from_slider_position = function(position, min_scale, max_scale) {\n",
       "    if (min_scale==max_scale) { return 1; }\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return a * Math.exp(b * position) + c;\n",
       "}\n",
       "\n",
       "// inverse of scale_from_slider_position\n",
       "var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
       "    if (min_scale==max_scale) { return min_scale; }\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return 1 / b * Math.log((scale - c) / a);\n",
       "}\n",
       "\n",
       "var increase_zoom_by_position = function(root, delta_position, animate) {\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\");\n",
       "    var xposition = slider_position_from_scale(old_xscale, min_scale, max_scale),\n",
       "        yposition = slider_position_from_scale(old_yscale, min_scale, max_scale);\n",
       "    xposition += (root.hasClass(\"xscalable\") ? delta_position : 0.0);\n",
       "    yposition += (root.hasClass(\"yscalable\") ? delta_position : 0.0);\n",
       "    old_xscale = scale_from_slider_position(xposition, min_scale, max_scale);\n",
       "    old_yscale = scale_from_slider_position(yposition, min_scale, max_scale);\n",
       "    var new_xscale = Math.max(min_scale, Math.min(old_xscale, max_scale)),\n",
       "        new_yscale = Math.max(min_scale, Math.min(old_yscale, max_scale));\n",
       "    if (animate) {\n",
       "        Snap.animate(\n",
       "            [old_xscale, old_yscale],\n",
       "            [new_xscale, new_yscale],\n",
       "            function (new_scale) {\n",
       "                update_plot_scale(root, new_scale[0], new_scale[1]);\n",
       "            },\n",
       "            200);\n",
       "    } else {\n",
       "        update_plot_scale(root, new_xscale, new_yscale);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "var update_plot_scale = function(root, new_xscale, new_yscale) {\n",
       "    var trans = scale_centered_translation(root, new_xscale, new_yscale);\n",
       "    set_plot_pan_zoom(root, trans.x, trans.y, new_xscale, new_yscale);\n",
       "};\n",
       "\n",
       "\n",
       "var toggle_color_class = function(root, color_class, ison) {\n",
       "    var escaped_color_class = color_class.replace(/([^0-9a-zA-z])/g,\"\\\\$1\");\n",
       "    var guides = root.selectAll(\".guide.\" + escaped_color_class + \",.guide .\" + escaped_color_class);\n",
       "    var geoms = root.selectAll(\".geometry.\" + escaped_color_class + \",.geometry .\" + escaped_color_class);\n",
       "    if (ison) {\n",
       "        guides.animate({opacity: 0.5}, 250);\n",
       "        geoms.animate({opacity: 0.0}, 250);\n",
       "    } else {\n",
       "        guides.animate({opacity: 1.0}, 250);\n",
       "        geoms.animate({opacity: 1.0}, 250);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.colorkey_swatch_click = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    var color_class = this.data(\"color_class\");\n",
       "\n",
       "    if (event.shiftKey) {\n",
       "        root.selectAll(\".colorkey g\")\n",
       "            .forEach(function (element) {\n",
       "                var other_color_class = element.data(\"color_class\");\n",
       "                if (typeof other_color_class !== 'undefined' && other_color_class != color_class) {\n",
       "                    toggle_color_class(root, other_color_class,\n",
       "                                       element.attr(\"opacity\") == 1.0);\n",
       "                }\n",
       "            });\n",
       "    } else {\n",
       "        toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "return Gadfly;\n",
       "\n",
       "}));\n",
       "\n",
       "\n",
       "//@ sourceURL=gadfly.js\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "      if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
       "        require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
       "            factory(Snap, Gadfly);\n",
       "        });\n",
       "      } else {\n",
       "          factory(glob.Snap, glob.Gadfly);\n",
       "      }\n",
       "})(window, function (Snap, Gadfly) {\n",
       "    var fig = Snap(\"#img-c91ab265\");\n",
       "fig.select(\"#img-c91ab265-5\")\n",
       "   .init_gadfly();\n",
       "fig.select(\"#img-c91ab265-8\")\n",
       "   .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-c91ab265-8\")\n",
       "   .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-c91ab265-146\")\n",
       "   .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-c91ab265-146\")\n",
       "   .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-c91ab265-300\")\n",
       "   .mouseenter(Gadfly.helpscreen_visible)\n",
       ".mouseleave(Gadfly.helpscreen_hidden)\n",
       ";\n",
       "    });\n",
       "]]> </script>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot(...)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x=H,y=polyval(pvol,H),Geom.line,\n",
    "Guide.XLabel(\"Height above well bottom (mm)\"),\n",
    "Guide.YLabel(\"Volume (cubic mm)\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-156.37132054994754"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real(roots(pvol - 50.)[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-157.81466509468657"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real(roots(pvol - 100.)[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-159.18546710697348"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "real(roots(pvol - 150.)[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "121×2 Array{Float64,2}:\n",
       "  0.0    0.0    \n",
       "  0.1    1.59197\n",
       "  0.2    3.18703\n",
       "  0.3    4.78517\n",
       "  0.4    6.38641\n",
       "  0.5    7.99074\n",
       "  0.6    9.59816\n",
       "  0.7   11.2087 \n",
       "  0.8   12.8223 \n",
       "  0.9   14.439  \n",
       "  1.0   16.0589 \n",
       "  1.1   17.6818 \n",
       "  1.2   19.3079 \n",
       "  ⋮             \n",
       " 10.9  192.306  \n",
       " 11.0  194.252  \n",
       " 11.1  196.201  \n",
       " 11.2  198.153  \n",
       " 11.3  200.109  \n",
       " 11.4  202.069  \n",
       " 11.5  204.032  \n",
       " 11.6  205.998  \n",
       " 11.7  207.967  \n",
       " 11.8  209.941  \n",
       " 11.9  211.917  \n",
       " 12.0  213.897  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = 0.0:0.1:12.0;\n",
    "[H polyval(pvol,H)]"
   ]
  }
 ],
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