diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/README.md b/lib/node_modules/@stdlib/math/base/special/cinv/README.md index 4ebd86f606e..5f3c95f18e6 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/README.md +++ b/lib/node_modules/@stdlib/math/base/special/cinv/README.md @@ -18,9 +18,9 @@ limitations under the License. --> -# inv +# cinv -> Compute the inverse of a complex number. +> Compute the inverse of a double-precision complex floating-point number.
@@ -47,27 +47,23 @@ The inverse (or reciprocal) of a non-zero complex number `z = a + bi` is defined var cinv = require( '@stdlib/math/base/special/cinv' ); ``` -#### cinv( \[out,] re1, im1 ) +#### cinv( z ) -Computes the inverse of a `complex` number comprised of a **real** component `re` and an **imaginary** component `im`. +Computes the inverse of a double-precision complex floating-point number. ```javascript -var v = cinv( 2.0, 4.0 ); -// returns [ 0.1, -0.2 ] -``` - -By default, the function returns real and imaginary components as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object. - -```javascript -var Float64Array = require( '@stdlib/array/float64' ); +var Complex128 = require( '@stdlib/complex/float64' ); +var real = require( '@stdlib/complex/real' ); +var imag = require( '@stdlib/complex/imag' ); -var out = new Float64Array( 2 ); +var v = cinv( new Complex128( 2.0, 4.0 ) ); +// returns -var v = cinv( out, 2.0, 4.0 ); -// returns [ 0.1, -0.2 ] +var re = real( v ); +// returns 0.1 -var bool = ( v === out ); -// returns true +var im = imag( v ); +// returns -0.2 ```
@@ -82,26 +78,16 @@ var bool = ( v === out ); ```javascript var Complex128 = require( '@stdlib/complex/float64' ); -var randu = require( '@stdlib/random/base/randu' ); -var round = require( '@stdlib/math/base/special/round' ); -var real = require( '@stdlib/complex/real' ); -var imag = require( '@stdlib/complex/imag' ); +var uniform = require( '@stdlib/random/base/uniform' ); var cinv = require( '@stdlib/math/base/special/cinv' ); -var re; -var im; var z1; var z2; -var o; var i; for ( i = 0; i < 100; i++ ) { - re = round( randu()*100.0 ) - 50.0; - im = round( randu()*100.0 ) - 50.0; - z1 = new Complex128( re, im ); - - o = cinv( real(z1), imag(z1) ); - z2 = new Complex128( o[ 0 ], o[ 1 ] ); + z1 = new Complex128( uniform( -50.0, 50.0 ), uniform( -50.0, 50.0 ) ); + z2 = cinv( z1 ); console.log( '1.0 / (%s) = %s', z1.toString(), z2.toString() ); } @@ -111,6 +97,117 @@ for ( i = 0; i < 100; i++ ) { + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/math/base/special/cinv.h" +``` + +#### stdlib_base_cinv( z ) + +Computes the inverse of a double-precision complex floating-point number. + +```c +#include "stdlib/complex/float64.h" +#include "stdlib/complex/real.h" +#include "stdlib/complex/imag.h" + +stdlib_complex128_t z = stdlib_complex128( 2.0, 4.0 ); + +stdlib_complex128_t out = stdlib_base_cinv( z ); + +double re = stdlib_real( out ); +// returns 0.1 + +double im = stdlib_imag( out ); +// returns -0.2 +``` + +The function accepts the following arguments: + +- **z**: `[in] stdlib_complex128_t` input value. + +```c +stdlib_complex128_t stdlib_base_cinv( const stdlib_complex128_t z ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/math/base/special/cinv.h" +#include "stdlib/complex/float64.h" +#include "stdlib/complex/reim.h" +#include + +int main() { + const stdlib_complex128_t x[] = { + stdlib_complex128( 3.14, 1.5 ), + stdlib_complex128( -3.14, -1.5 ), + stdlib_complex128( 0.0, 0.0 ), + stdlib_complex128( 0.0/0.0, 0.0/0.0 ) + }; + + stdlib_complex128_t v; + stdlib_complex128_t y; + double re1; + double im1; + double re2; + double im2; + int i; + for ( i = 0; i < 4; i++ ) { + v = x[ i ]; + y = stdlib_base_cinv( v ); + stdlib_reim( v, &re1, &im1 ); + stdlib_reim( y, &re2, &im2 ); + printf( "cinv(%lf + %lfi) = %lf + %lfi\n", re1, im1, re2, im2 ); + } +} +``` + +
+ + + +
+ + + * * *
diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/benchmark.js index 00051efe87e..b1ae301a3dc 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/benchmark.js +++ b/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/benchmark.js @@ -21,8 +21,11 @@ // MODULES // var bench = require( '@stdlib/bench' ); -var randu = require( '@stdlib/random/base/randu' ); -var isArray = require( '@stdlib/assert/is-array' ); +var uniform = require( '@stdlib/random/base/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var Complex128 = require( '@stdlib/complex/float64' ); +var real = require( '@stdlib/complex/real' ); +var imag = require( '@stdlib/complex/imag' ); var pkg = require( './../package.json' ).name; var cinv = require( './../lib' ); @@ -30,49 +33,25 @@ var cinv = require( './../lib' ); // MAIN // bench( pkg, function benchmark( b ) { - var re; - var im; + var values; var y; var i; - b.tic(); - for ( i = 0; i < b.iterations; i++ ) { - re = ( randu()*1000.0 ) - 500.0; - im = ( randu()*1000.0 ) - 500.0; - y = cinv( re, im ); - if ( y.length === 0 ) { - b.fail( 'should not be empty' ); - } - } - b.toc(); - if ( !isArray( y ) ) { - b.fail( 'should return an array' ); - } - b.pass( 'benchmark finished' ); - b.end(); -}); - -bench( pkg+'::memory_reuse', function benchmark( b ) { - var out; - var re; - var im; - var y; - var i; - - out = new Array( 2 ); + values = [ + new Complex128( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ), + new Complex128( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ) + ]; b.tic(); for ( i = 0; i < b.iterations; i++ ) { - re = ( randu()*1000.0 ) - 500.0; - im = ( randu()*1000.0 ) - 500.0; - y = cinv( out, re, im ); - if ( y.length === 0 ) { - b.fail( 'should not be empty' ); + y = cinv( values[ i%values.length ] ); + if ( isnan( real( y ) ) ) { + b.fail( 'should not return NaN' ); } } b.toc(); - if ( !isArray( y ) ) { - b.fail( 'should return an array' ); + if ( isnan( imag( y ) ) ) { + b.fail( 'should not return not NaN' ); } b.pass( 'benchmark finished' ); b.end(); diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/benchmark.native.js new file mode 100644 index 00000000000..4d5d94df1bc --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/benchmark.native.js @@ -0,0 +1,67 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2023 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/base/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var real = require( '@stdlib/complex/real' ); +var imag = require( '@stdlib/complex/imag' ); +var Complex128 = require( '@stdlib/complex/float64' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var cinv = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( cinv instanceof Error ) +}; + + +// MAIN // + +bench( pkg+'::native', opts, function benchmark( b ) { + var values; + var y; + var i; + + values = [ + new Complex128( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ), + new Complex128( uniform( -500.0, 500.0 ), uniform( -500.0, 500.0 ) ) + ]; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = cinv( values[ i%values.length ] ); + if ( isnan( real( y ) ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( imag( y ) ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/c/native/Makefile b/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/c/native/Makefile new file mode 100644 index 00000000000..7f6bbc4c205 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/c/native/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2021 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := benchmark.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled benchmarks. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/c/native/benchmark.c b/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/c/native/benchmark.c new file mode 100644 index 00000000000..1617c2c0faf --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/benchmark/c/native/benchmark.c @@ -0,0 +1,144 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2023 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/** +* Benchmark `cinv`. +*/ +#include "stdlib/math/base/special/cinv.h" +#include "stdlib/complex/float64.h" +#include "stdlib/complex/reim.h" +#include +#include +#include +#include +#include + +#define NAME "cinv" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +void print_version() { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +void print_summary( int total, int passing ) { + printf( "#\n" ); + printf( "1..%d\n", total ); // TAP plan + printf( "# total %d\n", total ); + printf( "# pass %d\n", passing ); + printf( "#\n" ); + printf( "# ok\n" ); +} + +/** +* Prints benchmarks results. +* +* @param elapsed elapsed time in seconds +*/ +void print_results( double elapsed ) { + double rate = (double)ITERATIONS / elapsed; + printf( " ---\n" ); + printf( " iterations: %d\n", ITERATIONS ); + printf( " elapsed: %0.9f\n", elapsed ); + printf( " rate: %0.9f\n", rate ); + printf( " ...\n" ); +} + +/** +* Returns a clock time. +* +* @return clock time +*/ +double tic() { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +double rand_double() { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +double benchmark() { + double elapsed; + double re; + double im; + double t; + double v; + int i; + + stdlib_complex128_t x; + stdlib_complex128_t y; + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + v = ( 1000.0*rand_double() ) - 500.0; + x = stdlib_complex128( v, v ); + y = stdlib_base_cinv( x ); + stdlib_reim( y, &re, &im ); + if ( re != re ) { + printf( "unexpected result\n" ); + break; + } + } + elapsed = tic() - t; + if ( im != im ) { + printf( "unexpected result\n" ); + } + return elapsed; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + double elapsed; + int i; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + print_version(); + for ( i = 0; i < REPEATS; i++ ) { + printf( "# c::native::%s\n", NAME ); + elapsed = benchmark(); + print_results( elapsed ); + printf( "ok %d benchmark finished\n", i+1 ); + } + print_summary( REPEATS, REPEATS ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/binding.gyp b/lib/node_modules/@stdlib/math/base/special/cinv/binding.gyp new file mode 100644 index 00000000000..f2b466aef5c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2023 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A `.gyp` file for building a Node.js native add-on. +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # List of files to include in this file: + 'includes': [ + './include.gypi', + ], + + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Target name should match the add-on export name: + 'addon_target_name%': 'addon', + + # Set variables based on the host OS: + 'conditions': [ + [ + 'OS=="win"', + { + # Define the object file suffix: + 'obj': 'obj', + }, + { + # Define the object file suffix: + 'obj': 'o', + } + ], # end condition (OS=="win") + ], # end conditions + }, # end variables + + # Define compile targets: + 'targets': [ + + # Target to generate an add-on: + { + # The target name should match the add-on export name: + 'target_name': '<(addon_target_name)', + + # Define dependencies: + 'dependencies': [], + + # Define directories which contain relevant include headers: + 'include_dirs': [ + # Local include directory: + '<@(include_dirs)', + ], + + # List of source files: + 'sources': [ + '<@(src_files)', + ], + + # Settings which should be applied when a target's object files are used as linker input: + 'link_settings': { + # Define libraries: + 'libraries': [ + '<@(libraries)', + ], + + # Define library directories: + 'library_dirs': [ + '<@(library_dirs)', + ], + }, + + # C/C++ compiler flags: + 'cflags': [ + # Enable commonly used warning options: + '-Wall', + + # Aggressive optimization: + '-O3', + ], + + # C specific compiler flags: + 'cflags_c': [ + # Specify the C standard to which a program is expected to conform: + '-std=c99', + ], + + # C++ specific compiler flags: + 'cflags_cpp': [ + # Specify the C++ standard to which a program is expected to conform: + '-std=c++11', + ], + + # Linker flags: + 'ldflags': [], + + # Apply conditions based on the host OS: + 'conditions': [ + [ + 'OS=="mac"', + { + # Linker flags: + 'ldflags': [ + '-undefined dynamic_lookup', + '-Wl,-no-pie', + '-Wl,-search_paths_first', + ], + }, + ], # end condition (OS=="mac") + [ + 'OS!="win"', + { + # C/C++ flags: + 'cflags': [ + # Generate platform-independent code: + '-fPIC', + ], + }, + ], # end condition (OS!="win") + ], # end conditions + }, # end target <(addon_target_name) + + # Target to copy a generated add-on to a standard location: + { + 'target_name': 'copy_addon', + + # Declare that the output of this target is not linked: + 'type': 'none', + + # Define dependencies: + 'dependencies': [ + # Require that the add-on be generated before building this target: + '<(addon_target_name)', + ], + + # Define a list of actions: + 'actions': [ + { + 'action_name': 'copy_addon', + 'message': 'Copying addon...', + + # Explicitly list the inputs in the command-line invocation below: + 'inputs': [], + + # Declare the expected outputs: + 'outputs': [ + '<(addon_output_dir)/<(addon_target_name).node', + ], + + # Define the command-line invocation: + 'action': [ + 'cp', + '<(PRODUCT_DIR)/<(addon_target_name).node', + '<(addon_output_dir)/<(addon_target_name).node', + ], + }, + ], # end actions + }, # end target copy_addon + ], # end targets +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/cinv/docs/repl.txt index 47416943e6d..1d74a24e85c 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/docs/repl.txt +++ b/lib/node_modules/@stdlib/math/base/special/cinv/docs/repl.txt @@ -1,33 +1,25 @@ -{{alias}}( [out,] re, im ) - Computes the inverse of a complex number. +{{alias}}( z ) + Computes the inverse of a double-precision complex floating-point number. Parameters ---------- - out: Array|TypedArray|Object (optional) - Output array. - - re: number - Real component. - - im: number - Imaginary component. + z: Complex128 + Complex number. Returns ------- - out: Array|TypedArray|Object - Real and imaginary components. + out: Complex128 + Result. Examples -------- - > var y = {{alias}}( 2.0, 4.0 ) - [ 0.1, -0.2 ] - - > var out = new {{alias:@stdlib/array/float64}}( 2 ); - > var v = {{alias}}( out, 2.0, 4.0 ) - [ 0.1, -0.2 ] - > var bool = ( v === out ) - true + > var v = {{alias}}( new {{alias:@stdlib/complex/float64}}( 2.0, 4.0 ) ) + + > var re = {{alias:@stdlib/complex/real}}( v ) + 0.1 + > var im = {{alias:@stdlib/complex/imag}}( v ) + -0.2 See Also -------- diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/cinv/docs/types/index.d.ts index fabad5fa2dc..ddc8ab864f2 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/docs/types/index.d.ts +++ b/lib/node_modules/@stdlib/math/base/special/cinv/docs/types/index.d.ts @@ -20,41 +20,29 @@ /// -import { ArrayLike } from '@stdlib/types/array'; +import { Complex128 } from '@stdlib/types/object'; /** -* Computes the inverse of a complex number. +* Computes the inverse of a double-precision complex floating-point number. * -* @param out - output array -* @param re - real component -* @param im - imaginary component -* @returns real and imaginary components +* @param z - input value +* @returns result * * @example -* var Float32Array = require( `@stdlib/array/float32` ); +* var Complex128 = require( `@stdlib/complex/float64` ); +* var real = require( `@stdlib/complex/real` ); +* var imag = require( `@stdlib/complex/imag` ); * -* var out = new Float32Array( 2 ); +* var v = cinv( new Complex128( 2.0, 4.0 ) ); +* // returns * -* var v = cinv( out, 2.0, 4.0 ); -* // returns [ 0.1, -0.2 ] +* var re = real( v ); +* // returns 0.1 * -* var bool = ( v === out ); -* // returns true +* var im = imag( v ); +* // returns -0.2 */ -declare function cinv( out: ArrayLike, re: number, im: number ): ArrayLike; // tslint-disable-line max-line-length - -/** -* Computes the inverse of a complex number. -* -* @param re - real component -* @param im - imaginary component -* @returns real and imaginary components -* -* @example -* var v = cinv( 2.0, 4.0 ); -* // returns [ 0.1, -0.2 ] -*/ -declare function cinv( re: number, im: number ): ArrayLike; +declare function cinv( z: Complex128 ): Complex128; // EXPORTS // diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/cinv/docs/types/test.ts index d9c02e933a1..b4b234e29e9 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/docs/types/test.ts +++ b/lib/node_modules/@stdlib/math/base/special/cinv/docs/types/test.ts @@ -16,53 +16,30 @@ * limitations under the License. */ +import Complex128 = require( '@stdlib/complex/float64' ); import cinv = require( './index' ); // TESTS // -// The function returns an array of numbers... +// The function returns a double-precision complex floating-point number... { - cinv( 5, 3 ); // $ExpectType ArrayLike - cinv( [], 5, 3 ); // $ExpectType ArrayLike + cinv( new Complex128( 1.0, 2.0 ) ); // $ExpectType Complex128 } -// The compiler throws an error if the function is provided a real component which is not a number... +// The compiler throws an error if the function is provided a value other than a complex number... { - cinv( true, 3 ); // $ExpectError - cinv( false, 3 ); // $ExpectError - cinv( null, 3 ); // $ExpectError - cinv( undefined, 3 ); // $ExpectError - cinv( '5', 3 ); // $ExpectError - cinv( [], 3 ); // $ExpectError - cinv( {}, 3 ); // $ExpectError - cinv( ( x: number ): number => x, 3 ); // $ExpectError + cinv( true ); // $ExpectError + cinv( false ); // $ExpectError + cinv( null ); // $ExpectError + cinv( undefined ); // $ExpectError + cinv( '5' ); // $ExpectError + cinv( [] ); // $ExpectError + cinv( {} ); // $ExpectError + cinv( ( x: number ): number => x ); // $ExpectError } -// The compiler throws an error if the function is provided an imaginary component which is not a number... -{ - cinv( 5, true ); // $ExpectError - cinv( 5, false ); // $ExpectError - cinv( 5, null ); // $ExpectError - cinv( 5, undefined ); // $ExpectError - cinv( 5, '5' ); // $ExpectError - cinv( 5, [] ); // $ExpectError - cinv( 5, {} ); // $ExpectError - cinv( 5, ( x: number ): number => x ); // $ExpectError -} - -// The compiler throws an error if the function is provided an output array which is not array-like... -{ - cinv( true, 5, 3 ); // $ExpectError - cinv( false, 5, 3 ); // $ExpectError - cinv( 'abc', 5, 3 ); // $ExpectError - cinv( {}, 5, 3 ); // $ExpectError - cinv( ( x: number ): number => x, 5, 3 ); // $ExpectError - cinv( 123, 5, 3 ); // $ExpectError -} - -// The compiler throws an error if the function is provided insufficient arguments... +// The compiler throws an error if the function is provided an unsupported number of arguments... { cinv(); // $ExpectError - cinv( 2 ); // $ExpectError } diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/examples/c/Makefile b/lib/node_modules/@stdlib/math/base/special/cinv/examples/c/Makefile new file mode 100644 index 00000000000..f0ae66fecf0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2023 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate position independent code ([1][1], [2][2]). +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`): +INCLUDE ?= + +# List of source files: +SOURCE_FILES ?= + +# List of libraries (e.g., `-lopenblas -lpthread`): +LIBRARIES ?= + +# List of library paths (e.g., `-L /foo/bar -L /beep/boop`): +LIBPATH ?= + +# List of C targets: +c_targets := example.out + + +# RULES # + +#/ +# Compiles source files. +# +# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`) +# @param {string} [CFLAGS] - C compiler options +# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`) +# @param {string} [SOURCE_FILES] - list of source files +# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`) +# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`) +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler (e.g., `gcc`) +# @param {string} CFLAGS - C compiler options +# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`) +# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`) +# @param {string} SOURCE_FILES - list of source files +# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`) +# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`) +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES) + +#/ +# Runs compiled examples. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/examples/c/example.c b/lib/node_modules/@stdlib/math/base/special/cinv/examples/c/example.c new file mode 100644 index 00000000000..39a04a9a6bb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/examples/c/example.c @@ -0,0 +1,46 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2023 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/cinv.h" +#include "stdlib/complex/float64.h" +#include "stdlib/complex/reim.h" +#include + +int main() { + const stdlib_complex128_t x[] = { + stdlib_complex128( 3.14, 1.5 ), + stdlib_complex128( -3.14, -1.5 ), + stdlib_complex128( 0.0, 0.0 ), + stdlib_complex128( 0.0/0.0, 0.0/0.0 ) + }; + + stdlib_complex128_t v; + stdlib_complex128_t y; + double re1; + double im1; + double re2; + double im2; + int i; + for ( i = 0; i < 4; i++ ) { + v = x[ i ]; + y = stdlib_base_cinv( v ); + stdlib_reim( v, &re1, &im1 ); + stdlib_reim( y, &re2, &im2 ); + printf( "cinv(%lf + %lfi) = %lf + %lfi\n", re1, im1, re2, im2 ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/examples/index.js b/lib/node_modules/@stdlib/math/base/special/cinv/examples/index.js index 6e56472efc7..aa9803874e6 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/examples/index.js +++ b/lib/node_modules/@stdlib/math/base/special/cinv/examples/index.js @@ -19,26 +19,16 @@ 'use strict'; var Complex128 = require( '@stdlib/complex/float64' ); -var randu = require( '@stdlib/random/base/randu' ); -var round = require( '@stdlib/math/base/special/round' ); -var real = require( '@stdlib/complex/real' ); -var imag = require( '@stdlib/complex/imag' ); +var uniform = require( '@stdlib/random/base/uniform' ); var cinv = require( './../lib' ); -var re; -var im; var z1; var z2; -var o; var i; for ( i = 0; i < 100; i++ ) { - re = round( randu()*100.0 ) - 50.0; - im = round( randu()*100.0 ) - 50.0; - z1 = new Complex128( re, im ); - - o = cinv( [], real(z1), imag(z1) ); - z2 = new Complex128( o[ 0 ], o[ 1 ] ); + z1 = new Complex128( uniform( -50.0, 50.0 ), uniform( -50.0, 50.0 ) ); + z2 = cinv( z1 ); console.log( '1.0 / (%s) = %s', z1.toString(), z2.toString() ); } diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/include.gypi b/lib/node_modules/@stdlib/math/base/special/cinv/include.gypi new file mode 100644 index 00000000000..78db9faf8c7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2023 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# A GYP include file for building a Node.js native add-on. +# +# Main documentation: +# +# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md +# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md +{ + # Define variables to be used throughout the configuration for all targets: + 'variables': { + # Source directory: + 'src_dir': './src', + + # Include directories: + 'include_dirs': [ + '= LARGE_THRESHOLD ) { - re *= 0.5; - im *= 0.5; - s *= 0.5; - } else if ( ab <= SMALL_THRESHOLD ) { - re *= RECIP_EPS_SQR; - im *= RECIP_EPS_SQR; - s *= RECIP_EPS_SQR; - } - if ( abs( im ) <= abs( re ) ) { - r = im / re; - t = 1.0 / ( re + (im*r) ); - out[ 0 ] = t; - out[ 1 ] = -r * t; - } else { - r = re / im; - t = 1.0 / ( im + (re*r) ); - out[ 0 ] = r * t; - out[ 1 ] = -t; - } - out[ 0 ] *= s; - out[ 1 ] *= s; - return out; -} - - -// EXPORTS // - -module.exports = cinv; diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/lib/index.js b/lib/node_modules/@stdlib/math/base/special/cinv/lib/index.js index e5b472fd1be..3769a9635ba 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/lib/index.js +++ b/lib/node_modules/@stdlib/math/base/special/cinv/lib/index.js @@ -19,26 +19,24 @@ 'use strict'; /** -* Compute the inverse of a complex number. +* Compute the inverse of a double-precision complex floating-point number. * * @module @stdlib/math/base/special/cinv * * @example +* var Complex128 = require( '@stdlib/complex/float64' ); +* var real = require( '@stdlib/complex/real' ); +* var imag = require( '@stdlib/complex/imag' ); * var cinv = require( '@stdlib/math/base/special/cinv' ); * -* var v = cinv( 2.0, 4.0 ); -* // returns [ 0.1, -0.2 ] +* var v = cinv( new Complex128( 2.0, 4.0 ) ); +* // returns * -* @example -* var cinv = require( '@stdlib/math/base/special/cinv' ); -* -* var out = new Array( 2 ); -* -* var v = cinv( out, 2.0, 4.0 ); -* // returns [ 0.1, -0.2 ] +* var re = real( v ); +* // returns 0.1 * -* var bool = ( v === out ); -* // returns true +* var im = imag( v ); +* // returns -0.2 */ // MODULES // diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/lib/main.js b/lib/node_modules/@stdlib/math/base/special/cinv/lib/main.js index aac4e1fd68c..93dc44327d6 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/cinv/lib/main.js @@ -20,42 +20,85 @@ // MODULES // -var inverse = require( './cinv.js' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var max = require( '@stdlib/math/base/special/max' ); +var FLOAT64_BIGGEST = require( '@stdlib/constants/float64/max' ); +var FLOAT64_SMALLEST = require( '@stdlib/constants/float64/smallest-normal' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var Complex128 = require( '@stdlib/complex/float64' ); +var real = require( '@stdlib/complex/real' ); +var imag = require( '@stdlib/complex/imag' ); + + +// VARIABLES // + +var LARGE_THRESHOLD = FLOAT64_BIGGEST * 0.5; +var SMALL_THRESHOLD = FLOAT64_SMALLEST * ( 2.0 / EPS ); +var RECIP_EPS_SQR = 2.0 / ( EPS * EPS ); // MAIN // /** -* Computes the inverse of a complex number. +* Computes the inverse of a double-precision complex floating-point number. * * ## References * * - Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS\] (October): 1–25. . * * -* @param {(Array|TypedArray|Object)} [out] - output array -* @param {number} re - real component -* @param {number} im - imaginary component -* @returns {(Array|TypedArray|Object)} output array +* @param {Complex128} z - complex number +* @returns {Complex128} result * * @example -* var v = cinv( 2.0, 4.0 ); -* // returns [ 0.1, -0.2 ] +* var Complex128 = require( '@stdlib/complex/float64' ); +* var real = require( '@stdlib/complex/real' ); +* var imag = require( '@stdlib/complex/imag' ); * -* @example -* var out = new Array( 2 ); +* var v = cinv( new Complex128( 2.0, 4.0 ) ); +* // returns * -* var v = cinv( out, 2.0, 4.0 ); -* // returns [ 0.1, -0.2 ] +* var re = real( v ); +* // returns 0.1 * -* var bool = ( v === out ); -* // returns true +* var im = imag( v ); +* // returns -0.2 */ -function cinv( out, re, im ) { - if ( arguments.length === 2 ) { - return inverse( [ 0.0, 0.0 ], out, re ); +function cinv( z ) { + var ab; + var re; + var im; + var s; + var r; + var t; + + re = real( z ); + im = imag( z ); + ab = max( abs(re), abs(im) ); + s = 1.0; + if ( ab >= LARGE_THRESHOLD ) { + re *= 0.5; + im *= 0.5; + s *= 0.5; + } else if ( ab <= SMALL_THRESHOLD ) { + re *= RECIP_EPS_SQR; + im *= RECIP_EPS_SQR; + s *= RECIP_EPS_SQR; + } + if ( abs( im ) <= abs( re ) ) { + r = im / re; + t = 1.0 / ( re + (im*r) ); + re = t; + im = -r * t; + } else { + r = re / im; + t = 1.0 / ( im + (re*r) ); + re = r * t; + im = -t; } - return inverse( out, re, im ); + re *= s; + im *= s; + return new Complex128( re, im); } diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/lib/native.js b/lib/node_modules/@stdlib/math/base/special/cinv/lib/native.js new file mode 100644 index 00000000000..10b9acb231b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/lib/native.js @@ -0,0 +1,58 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2023 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var Complex128 = require( '@stdlib/complex/float64' ); +var addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Computes the inverse of a double-precision complex floating-point number. +* +* @private +* @param {Complex128} z - complex number +* @returns {Complex128} result +* +* @example +* var Complex128 = require( '@stdlib/complex/float64' ); +* var real = require( '@stdlib/complex/real' ); +* var imag = require( '@stdlib/complex/imag' ); +* +* var v = cinv( new Complex128( 2.0, 4.0 ) ); +* // returns +* +* var re = real( v ); +* // returns 0.1 +* +* var im = imag( v ); +* // returns -0.2 +*/ +function cinv( z ) { + var v = addon( z ); + return new Complex128( v.re, v.im ); +} + + +// EXPORTS // + +module.exports = cinv; diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/manifest.json b/lib/node_modules/@stdlib/math/base/special/cinv/manifest.json new file mode 100644 index 00000000000..d0f5faffa60 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/manifest.json @@ -0,0 +1,88 @@ +{ + "options": { + "task": "build" + }, + "fields": [ + { + "field": "src", + "resolve": true, + "relative": true + }, + { + "field": "include", + "resolve": true, + "relative": true + }, + { + "field": "libraries", + "resolve": false, + "relative": false + }, + { + "field": "libpath", + "resolve": true, + "relative": false + } + ], + "confs": [ + { + "task": "build", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/napi/unary", + "@stdlib/complex/float64", + "@stdlib/complex/reim", + "@stdlib/math/base/special/abs", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/smallest-normal" + ] + }, + { + "task": "benchmark", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/complex/float64", + "@stdlib/complex/reim", + "@stdlib/math/base/special/abs", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/smallest-normal" + ] + }, + { + "task": "examples", + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/complex/float64", + "@stdlib/complex/reim", + "@stdlib/math/base/special/abs", + "@stdlib/constants/float64/max", + "@stdlib/constants/float64/eps", + "@stdlib/constants/float64/smallest-normal" + ] + } + ] +} + diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/package.json b/lib/node_modules/@stdlib/math/base/special/cinv/package.json index 084ac84cfe0..42c4ab584c5 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/package.json +++ b/lib/node_modules/@stdlib/math/base/special/cinv/package.json @@ -1,7 +1,7 @@ { "name": "@stdlib/math/base/special/cinv", "version": "0.0.0", - "description": "Compute the inverse of a complex number.", + "description": "Compute the inverse of a double-precision complex floating-point number.", "license": "Apache-2.0", "author": { "name": "The Stdlib Authors", @@ -14,6 +14,7 @@ } ], "main": "./lib", + "gypfile": true, "directories": { "benchmark": "./benchmark", "doc": "./docs", diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/src/Makefile b/lib/node_modules/@stdlib/math/base/special/cinv/src/Makefile new file mode 100644 index 00000000000..904c7dc4bd7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2023 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +else + QUIET := +endif + +# Determine the OS ([1][1], [2][2]). +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +else +ifneq (, $(findstring Windows_NT,$(OS))) + OS := WINNT +endif +endif +endif +endif + + +# RULES # + +#/ +# Removes generated files for building an add-on. +# +# @example +# make clean-addon +#/ +clean-addon: + $(QUIET) -rm -f *.o *.node + +.PHONY: clean-addon + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: clean-addon + +.PHONY: clean diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/src/addon.c b/lib/node_modules/@stdlib/math/base/special/cinv/src/addon.c new file mode 100644 index 00000000000..b3cae9ced65 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/src/addon.c @@ -0,0 +1,23 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2023 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/cinv.h" +#include "stdlib/math/base/napi/unary.h" + +// cppcheck-suppress shadowFunction +STDLIB_MATH_BASE_NAPI_MODULE_Z_Z( stdlib_base_cinv ) diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/src/main.c b/lib/node_modules/@stdlib/math/base/special/cinv/src/main.c new file mode 100644 index 00000000000..45a55cbc9f9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/src/main.c @@ -0,0 +1,100 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2023 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +#include "stdlib/math/base/special/cinv.h" +#include "stdlib/math/base/special/abs.h" +#include "stdlib/constants/float64/max.h" +#include "stdlib/constants/float64/eps.h" +#include "stdlib/constants/float64/smallest_normal.h" +#include "stdlib/complex/float64.h" +#include "stdlib/complex/reim.h" +#include + + +// VARIABLES // + +static const double LARGE_THRESHOLD = STDLIB_CONSTANT_FLOAT64_MAX * 0.5; +static const double SMALL_THRESHOLD = STDLIB_CONSTANT_FLOAT64_SMALLEST_NORMAL * ( 2.0 / STDLIB_CONSTANT_FLOAT64_EPS ); +static const double RECIP_EPS_SQR = 2.0 / ( STDLIB_CONSTANT_FLOAT64_EPS * STDLIB_CONSTANT_FLOAT64_EPS ); + + +// MAIN // + +/** +Computes the inverse of a double-precision complex floating-point number. +* +* ## References +* +* - Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS\] (October): 1–25. . +* +* @param z input value +* @return result +* +* @example +* #include "stdlib/complex/float64.h" +* #include "stdlib/complex/real.h" +* #include "stdlib/complex/imag.h" +* +* stdlib_complex128_t z = stdlib_complex128( 2.0, 4.0 ); +* +* stdlib_complex128_t out = stdlib_base_cinv( z ); +* +* double re = stdlib_real( out ); +* // returns 0.1 +* +* double im = stdlib_imag( out ); +* // returns -0.2 +*/ +stdlib_complex128_t stdlib_base_cinv( const stdlib_complex128_t z ) { + double re; + double im; + double ab; + double s; + double r; + double t; + + stdlib_reim( z, &re, &im ); + + // TODO: replace `fmax` with stdlib max implementation once available + ab = fmax( stdlib_base_abs( re ), stdlib_base_abs( im ) ); + s = 1.0; + if ( ab >= LARGE_THRESHOLD ) { + re *= 0.5; + im *= 0.5; + s *= 0.5; + } + else if ( ab <= SMALL_THRESHOLD ) { + re *= RECIP_EPS_SQR; + im *= RECIP_EPS_SQR; + s *= RECIP_EPS_SQR; + } + if ( stdlib_base_abs( im ) <= stdlib_base_abs( re ) ) { + r = im / re; + t = 1.0 / ( re + (im * r) ); + re = t; + im = -r * t; + } else { + r = re / im; + t = 1.0 / ( im + (re * r) ); + re = r * t; + im = -t; + } + re *= s; + im *= s; + return stdlib_complex128( re, im ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/test/test.js b/lib/node_modules/@stdlib/math/base/special/cinv/test/test.js index f2e80b885cd..3683e3f2c00 100644 --- a/lib/node_modules/@stdlib/math/base/special/cinv/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/cinv/test/test.js @@ -28,6 +28,9 @@ var abs = require( '@stdlib/math/base/special/abs' ); var EPS = require( '@stdlib/constants/float64/eps' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); +var Complex128 = require( '@stdlib/complex/float64' ); +var real = require( '@stdlib/complex/real' ); +var imag = require( '@stdlib/complex/imag' ); var cinv = require( './../lib' ); @@ -52,20 +55,12 @@ tape( 'main export is a function', function test( t ) { t.end(); }); -tape( 'the function accepts an optional output array', function test( t ) { - var result; - var out; - - out = new Array( 2 ); - result = cinv( out, 2.0, 4.0 ); - t.deepEqual( out, [ 0.1, -0.2 ], 'values are correct' ); - t.equal( out, result, 'array reference is identical' ); - t.end(); -}); +tape( 'the function computes the inverse of a double-precision complex floating-point number', function test( t ) { + var v; -tape( 'the function works without output array specified', function test( t ) { - var result = cinv( 2.0, 4.0 ); - t.deepEqual( result, [ 0.1, -0.2 ], 'values are correct' ); + v = cinv( new Complex128( 2.0, 4.0 ) ); + t.strictEqual( real( v ), 0.1, 'returns expected value' ); + t.strictEqual( imag( v ), -0.2, 'returns expected value' ); t.end(); }); @@ -85,21 +80,21 @@ tape( 'the function computes a complex inverse', function test( t ) { qim = data.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -121,21 +116,21 @@ tape( 'the function computes a complex inverse (large negative imaginary compone qim = largeNegativeImaginaryComponents.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -157,21 +152,21 @@ tape( 'the function computes a complex inverse (large negative real components)' qim = largeNegativeRealComponents.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -193,21 +188,21 @@ tape( 'the function computes a complex inverse (large positive imaginary compone qim = largePositiveImaginaryComponents.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -229,21 +224,21 @@ tape( 'the function computes a complex inverse (large positive real components)' qim = largePositiveRealComponents.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -265,21 +260,21 @@ tape( 'the function computes a complex inverse (tiny negative imaginary componen qim = tinyNegativeImaginaryComponents.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -301,21 +296,21 @@ tape( 'the function computes a complex inverse (tiny negative real components)', qim = tinyNegativeRealComponents.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -337,21 +332,21 @@ tape( 'the function computes a complex inverse (tiny positive imaginary componen qim = tinyPositiveImaginaryComponents.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -373,21 +368,21 @@ tape( 'the function computes a complex inverse (tiny positive real components)', qim = tinyPositiveRealComponents.qim; for ( i = 0; i < re.length; i++ ) { - q = cinv( re[ i ], im[ i ] ); + q = cinv( new Complex128( re[ i ], im[ i ] ) ); - if ( q[ 0 ] === qre[ i ] ) { - t.strictEqual( q[ 0 ], qre[ i ], 'returns expected real component' ); + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); } else { - delta = abs( q[ 0 ] - qre[ i ] ); + delta = abs( real( q ) - qre[ i ] ); tol = EPS * abs( qre[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+q[0]+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } - if ( q[ 1 ] === qim[ i ] ) { - t.strictEqual( q[ 1 ], qim[ i ], 'returns expected imaginary component' ); + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); } else { - delta = abs( q[ 1 ] - qim[ i ] ); + delta = abs( imag( q ) - qim[ i ] ); tol = EPS * abs( qim[ i ] ); - t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+q[1]+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); } } t.end(); @@ -396,37 +391,37 @@ tape( 'the function computes a complex inverse (tiny positive real components)', tape( 'the function may overflow', function test( t ) { var v; - v = cinv( 5.0e-324, 5.0e-324 ); - t.strictEqual( v[ 0 ], PINF, 'real component is +infinity' ); - t.strictEqual( v[ 1 ], NINF, 'imaginary component is -infinity' ); + v = cinv( new Complex128( 5.0e-324, 5.0e-324 ) ); + t.strictEqual( real( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imag( v ), NINF, 'imaginary component is -infinity' ); - v = cinv( -5.0e-324, 5.0e-324 ); - t.strictEqual( v[ 0 ], NINF, 'real component is -infinity' ); - t.strictEqual( v[ 1 ], NINF, 'imaginary component is -infinity' ); + v = cinv( new Complex128( -5.0e-324, 5.0e-324 ) ); + t.strictEqual( real( v ), NINF, 'real component is -infinity' ); + t.strictEqual( imag( v ), NINF, 'imaginary component is -infinity' ); - v = cinv( -5.0e-324, -5.0e-324 ); - t.strictEqual( v[ 0 ], NINF, 'real component is -infinity' ); - t.strictEqual( v[ 1 ], PINF, 'imaginary component is +infinity' ); + v = cinv( new Complex128( -5.0e-324, -5.0e-324 ) ); + t.strictEqual( real( v ), NINF, 'real component is -infinity' ); + t.strictEqual( imag( v ), PINF, 'imaginary component is +infinity' ); - v = cinv( 5.0e-324, -5.0e-324 ); - t.strictEqual( v[ 0 ], PINF, 'real component is +infinity' ); - t.strictEqual( v[ 1 ], PINF, 'imaginary component is +infinity' ); + v = cinv( new Complex128( 5.0e-324, -5.0e-324 ) ); + t.strictEqual( real( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imag( v ), PINF, 'imaginary component is +infinity' ); - v = cinv( 0.0, 5.0e-324 ); - t.strictEqual( v[ 0 ], 0.0, 'real component is 0' ); - t.strictEqual( v[ 1 ], NINF, 'imaginary component is -infinity' ); + v = cinv( new Complex128( 0.0, 5.0e-324 ) ); + t.strictEqual( real( v ), 0.0, 'real component is 0' ); + t.strictEqual( imag( v ), NINF, 'imaginary component is -infinity' ); - v = cinv( 0.0, -5.0e-324 ); - t.strictEqual( v[ 0 ], 0.0, 'real component is 0' ); - t.strictEqual( v[ 1 ], PINF, 'imaginary component is +infinity' ); + v = cinv( new Complex128( 0.0, -5.0e-324 ) ); + t.strictEqual( real( v ), 0.0, 'real component is 0' ); + t.strictEqual( imag( v ), PINF, 'imaginary component is +infinity' ); - v = cinv( 5.0e-324, 0.0 ); - t.strictEqual( v[ 0 ], PINF, 'real component is +infinity' ); - t.strictEqual( v[ 1 ], 0.0, 'imaginary component is 0' ); + v = cinv( new Complex128( 5.0e-324, 0.0 ) ); + t.strictEqual( real( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imag( v ), 0.0, 'imaginary component is 0' ); - v = cinv( -5.0e-324, 0.0 ); - t.strictEqual( v[ 0 ], NINF, 'real component is -infinity' ); - t.strictEqual( v[ 1 ], 0.0, 'imaginary component is 0' ); + v = cinv( new Complex128( -5.0e-324, 0.0 ) ); + t.strictEqual( real( v ), NINF, 'real component is -infinity' ); + t.strictEqual( imag( v ), 0.0, 'imaginary component is 0' ); t.end(); }); @@ -434,17 +429,17 @@ tape( 'the function may overflow', function test( t ) { tape( 'if a real or imaginary component is `NaN`, all components are `NaN`', function test( t ) { var v; - v = cinv( NaN, 3.0 ); - t.strictEqual( isnan( v[ 0 ] ), true, 'returns NaN' ); - t.strictEqual( isnan( v[ 1 ] ), true, 'returns NaN' ); + v = cinv( new Complex128( NaN, 3.0 ) ); + t.strictEqual( isnan( real( v ) ), true, 'returns NaN' ); + t.strictEqual( isnan( imag( v ) ), true, 'returns NaN' ); - v = cinv( 5.0, NaN ); - t.strictEqual( isnan( v[ 0 ] ), true, 'returns NaN' ); - t.strictEqual( isnan( v[ 1 ] ), true, 'returns NaN' ); + v = cinv( new Complex128( 5.0, NaN ) ); + t.strictEqual( isnan( real( v ) ), true, 'returns NaN' ); + t.strictEqual( isnan( imag( v ) ), true, 'returns NaN' ); - v = cinv( NaN, NaN ); - t.strictEqual( isnan( v[ 0 ] ), true, 'returns NaN' ); - t.strictEqual( isnan( v[ 1 ] ), true, 'returns NaN' ); + v = cinv( new Complex128( NaN, NaN ) ); + t.strictEqual( isnan( real( v ) ), true, 'returns NaN' ); + t.strictEqual( isnan( imag( v ) ), true, 'returns NaN' ); t.end(); }); diff --git a/lib/node_modules/@stdlib/math/base/special/cinv/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/cinv/test/test.native.js new file mode 100644 index 00000000000..22dabf1751d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/cinv/test/test.native.js @@ -0,0 +1,454 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2023 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/* eslint-disable id-length */ + +'use strict'; + +// MODULES // + +var resolve = require( 'path' ).resolve; +var tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var Complex128 = require( '@stdlib/complex/float64' ); +var real = require( '@stdlib/complex/real' ); +var imag = require( '@stdlib/complex/imag' ); +var tryRequire = require( '@stdlib/utils/try-require' ); + + +// VARIABLES // + +var cinv = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( cinv instanceof Error ) +}; + + +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); +var largeNegativeImaginaryComponents = require( './fixtures/julia/large_negative_imaginary_components.json' ); +var largeNegativeRealComponents = require( './fixtures/julia/large_negative_real_components.json' ); +var largePositiveImaginaryComponents = require( './fixtures/julia/large_positive_imaginary_components.json' ); +var largePositiveRealComponents = require( './fixtures/julia/large_positive_real_components.json' ); +var tinyNegativeImaginaryComponents = require( './fixtures/julia/tiny_negative_imaginary_components.json' ); +var tinyNegativeRealComponents = require( './fixtures/julia/tiny_negative_real_components.json' ); +var tinyPositiveImaginaryComponents = require( './fixtures/julia/tiny_positive_imaginary_components.json' ); +var tinyPositiveRealComponents = require( './fixtures/julia/tiny_positive_real_components.json' ); + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof cinv, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function computes the inverse of a double-precision complex floating-point number', opts, function test( t ) { + var v; + + v = cinv( new Complex128( 2.0, 4.0 ) ); + t.strictEqual( real( v ), 0.1, 'returns expected value' ); + t.strictEqual( imag( v ), -0.2, 'returns expected value' ); + t.end(); +}); + +tape( 'the function computes a complex inverse', opts, function test( t ) { + var delta; + var qre; + var qim; + var tol; + var re; + var im; + var i; + var q; + + re = data.re; + im = data.im; + qre = data.qre; + qim = data.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large negative imaginary components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largeNegativeImaginaryComponents.re; + im = largeNegativeImaginaryComponents.im; + qre = largeNegativeImaginaryComponents.qre; + qim = largeNegativeImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large negative real components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largeNegativeRealComponents.re; + im = largeNegativeRealComponents.im; + qre = largeNegativeRealComponents.qre; + qim = largeNegativeRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large positive imaginary components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largePositiveImaginaryComponents.re; + im = largePositiveImaginaryComponents.im; + qre = largePositiveImaginaryComponents.qre; + qim = largePositiveImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (large positive real components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = largePositiveRealComponents.re; + im = largePositiveRealComponents.im; + qre = largePositiveRealComponents.qre; + qim = largePositiveRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny negative imaginary components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyNegativeImaginaryComponents.re; + im = tinyNegativeImaginaryComponents.im; + qre = tinyNegativeImaginaryComponents.qre; + qim = tinyNegativeImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny negative real components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyNegativeRealComponents.re; + im = tinyNegativeRealComponents.im; + qre = tinyNegativeRealComponents.qre; + qim = tinyNegativeRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny positive imaginary components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyPositiveImaginaryComponents.re; + im = tinyPositiveImaginaryComponents.im; + qre = tinyPositiveImaginaryComponents.qre; + qim = tinyPositiveImaginaryComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a complex inverse (tiny positive real components)', opts, function test( t ) { + var delta; + var tol; + var qre; + var qim; + var re; + var im; + var i; + var q; + + re = tinyPositiveRealComponents.re; + im = tinyPositiveRealComponents.im; + qre = tinyPositiveRealComponents.qre; + qim = tinyPositiveRealComponents.qim; + + for ( i = 0; i < re.length; i++ ) { + q = cinv( new Complex128( re[ i ], im[ i ] ) ); + + if ( real( q ) === qre[ i ] ) { + t.strictEqual( real( q ), qre[ i ], 'returns expected real component' ); + } else { + delta = abs( real( q ) - qre[ i ] ); + tol = EPS * abs( qre[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. real: '+real( q )+'. expected: '+qre[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + if ( imag( q ) === qim[ i ] ) { + t.strictEqual( imag( q ), qim[ i ], 'returns expected imaginary component' ); + } else { + delta = abs( imag( q ) - qim[ i ] ); + tol = EPS * abs( qim[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+re[i]+'+ '+im[i]+'i. imag: '+imag( q )+'. expected: '+qim[i]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function may overflow', opts, function test( t ) { + var v; + + v = cinv( new Complex128( 5.0e-324, 5.0e-324 ) ); + t.strictEqual( real( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imag( v ), NINF, 'imaginary component is -infinity' ); + + v = cinv( new Complex128( -5.0e-324, 5.0e-324 ) ); + t.strictEqual( real( v ), NINF, 'real component is -infinity' ); + t.strictEqual( imag( v ), NINF, 'imaginary component is -infinity' ); + + v = cinv( new Complex128( -5.0e-324, -5.0e-324 ) ); + t.strictEqual( real( v ), NINF, 'real component is -infinity' ); + t.strictEqual( imag( v ), PINF, 'imaginary component is +infinity' ); + + v = cinv( new Complex128( 5.0e-324, -5.0e-324 ) ); + t.strictEqual( real( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imag( v ), PINF, 'imaginary component is +infinity' ); + + v = cinv( new Complex128( 0.0, 5.0e-324 ) ); + t.strictEqual( real( v ), 0.0, 'real component is 0' ); + t.strictEqual( imag( v ), NINF, 'imaginary component is -infinity' ); + + v = cinv( new Complex128( 0.0, -5.0e-324 ) ); + t.strictEqual( real( v ), 0.0, 'real component is 0' ); + t.strictEqual( imag( v ), PINF, 'imaginary component is +infinity' ); + + v = cinv( new Complex128( 5.0e-324, 0.0 ) ); + t.strictEqual( real( v ), PINF, 'real component is +infinity' ); + t.strictEqual( imag( v ), 0.0, 'imaginary component is 0' ); + + v = cinv( new Complex128( -5.0e-324, 0.0 ) ); + t.strictEqual( real( v ), NINF, 'real component is -infinity' ); + t.strictEqual( imag( v ), 0.0, 'imaginary component is 0' ); + + t.end(); +}); + +tape( 'if a real or imaginary component is `NaN`, all components are `NaN`', opts, function test( t ) { + var v; + + v = cinv( new Complex128( NaN, 3.0 ) ); + t.strictEqual( isnan( real( v ) ), true, 'returns NaN' ); + t.strictEqual( isnan( imag( v ) ), true, 'returns NaN' ); + + v = cinv( new Complex128( 5.0, NaN ) ); + t.strictEqual( isnan( real( v ) ), true, 'returns NaN' ); + t.strictEqual( isnan( imag( v ) ), true, 'returns NaN' ); + + v = cinv( new Complex128( NaN, NaN ) ); + t.strictEqual( isnan( real( v ) ), true, 'returns NaN' ); + t.strictEqual( isnan( imag( v ) ), true, 'returns NaN' ); + + t.end(); +});