diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/README.md b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/README.md new file mode 100644 index 000000000000..d3daf45bdca2 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/README.md @@ -0,0 +1,252 @@ + + +# Probability Density Function + +> [Anglit][anglit-distribution] distribution [probability density function][pdf]. + +
+ +The [probability density function][pdf] for an [anglit][anglit-distribution] random variable is + + + +```math +f(x) = \frac{1}{\sigma} \cos\left( \frac{2(x-\mu)}{\sigma} \right) +``` + + + +for `-\pi/4 \le (x-\mu)/\sigma \le \pi/4`, where `μ` is the location parameter and `σ > 0` is the scale parameter. Outside of this interval, the density is zero. + +
+ + + +
+ +## Usage + +```javascript +var pdf = require( '@stdlib/stats/base/dists/anglit/pdf' ); +``` + +#### pdf( x, mu, sigma ) + +Evaluates the [probability density function][pdf] for an [anglit][anglit-distribution] distribution with location parameter `mu` and scale parameter `sigma`. + +```javascript +var y = pdf( 0.0, 0.0, 1.0 ); +// returns 1.0 + +y = pdf( 0.5, 0.0, 1.0 ); +// returns ~0.540 + +y = pdf( 2.0, 0.0, 1.0 ); +// returns 0.0 + +y = pdf( -2.0, 0.0, 1.0 ); +// returns 0.0 +``` + +If provided `NaN` as any argument, the function returns `NaN`. + +```javascript +var y = pdf( NaN, 0.0, 1.0 ); +// returns NaN + +y = pdf( 0.0, NaN, 1.0 ); +// returns NaN + +y = pdf( 0.0, 0.0, NaN ); +// returns NaN +``` + +If provided `σ <= 0`, the function returns `NaN`. + +```javascript +var y = pdf( 0.0, 0.0, -1.0 ); +// returns NaN + +y = pdf( 0.0, 0.0, 0.0 ); +// returns NaN +``` + +#### pdf.factory( mu, sigma ) + +Returns a `function` for evaluating the [PDF][pdf] of an [anglit][anglit-distribution] distribution with location parameter `mu` and scale parameter `sigma`. + +```javascript +var myPDF = pdf.factory( 0.0, 1.0 ); + +var y = myPDF( 0.0 ); +// returns 1.0 + +y = myPDF( 10.0 ); +// returns 0.0 +``` + +
+ + + +
+ +## Examples + + + +```javascript +var uniform = require( '@stdlib/random/array/uniform' ); +var logEachMap = require( '@stdlib/console/log-each-map' ); +var pdf = require( '@stdlib/stats/base/dists/anglit/pdf' ); + +var opts = { + 'dtype': 'float64' +}; + +var x = uniform( 10, -5.0, 5.0, opts ); +var mu = uniform( 10, -5.0, 5.0, opts ); +var sigma = uniform( 10, 0.5, 5.0, opts ); + +logEachMap( 'x: %0.4f, μ: %0.4f, σ: %0.4f, f(x;μ,σ): %0.4f', x, mu, sigma, pdf ); +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +#include "stdlib/stats/base/dists/anglit/pdf.h" +``` + +#### stdlib_base_dists_anglit_pdf( x, mu, sigma ) + +Evaluates the [probability density function][pdf] for an [anglit][anglit-distribution] distribution with location parameter `mu` and scale parameter `sigma` at a value `x`. + +```c +double out = stdlib_base_dists_anglit_pdf( 0.0, 0.0, 1.0 ); +// returns 1.0 +``` + +The function accepts the following arguments: + +- **x**: `[in] double` input value. +- **mu**: `[in] double` location parameter. +- **sigma**: `[in] double` scale parameter. + +```c +double stdlib_base_dists_anglit_pdf( const double x, const double mu, const double sigma ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +#include "stdlib/stats/base/dists/anglit/pdf.h" +#include +#include + +static double random_uniform( const double min, const double max ) { + double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); + return min + ( v*(max-min) ); +} + +int main( void ) { + double sigma; + double mu; + double x; + double y; + int i; + + for ( i = 0; i < 25; i++ ) { + x = random_uniform( -10.0, 10.0 ); + mu = random_uniform( -5.0, 5.0 ); + sigma = random_uniform( 0.1, 5.0 ); + y = stdlib_base_dists_anglit_pdf( x, mu, sigma ); + printf( "x: %lf, μ: %lf, σ: %lf, f(x;μ,σ): %lf\n", x, mu, sigma, y ); + } +} +``` + +
+ + + +
+ + + + + +
+ +
+ + + + + +
+ +[pdf]: https://en.wikipedia.org/wiki/Probability_density_function + +[anglit-distribution]: https://en.wikipedia.org/wiki/Anglit_distribution + +
+ + diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/benchmark.js new file mode 100644 index 000000000000..bb32fb3d0504 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/benchmark.js @@ -0,0 +1,93 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var format = require( '@stdlib/string/format' ); +var pkg = require( './../package.json' ).name; +var pdf = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var arrayOpts; + var sigma; + var mu; + var x; + var y; + var i; + + arrayOpts = { + 'dtype': 'float64' + }; + x = uniform( 100, -10.0, 10.0, arrayOpts ); + mu = uniform( 100, -5.0, 5.0, arrayOpts ); + sigma = uniform( 100, 0.1, 10.0, arrayOpts ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = pdf( x[ i % x.length ], mu[ i % mu.length ], sigma[ i % sigma.length ] ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); + +bench( format( '%s::factory', pkg ), function benchmark( b ) { + var arrayOpts; + var mypdf; + var sigma; + var mu; + var x; + var y; + var i; + + arrayOpts = { + 'dtype': 'float64' + }; + mu = 0.0; + sigma = 2.0; + mypdf = pdf.factory( mu, sigma ); + x = uniform( 100, -5.0, 5.0, arrayOpts ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = mypdf( x[ i % x.length ] ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/benchmark.native.js new file mode 100644 index 000000000000..401d9f066e66 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/benchmark.native.js @@ -0,0 +1,72 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/array/uniform' ); +var format = require( '@stdlib/string/format' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var pkg = require( './../package.json' ).name; + + +// VARIABLES // + +var pdf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( pdf instanceof Error ) +}; + + +// MAIN // + +bench( format( '%s::native', pkg ), opts, function benchmark( b ) { + var arrayOpts; + var sigma; + var mu; + var x; + var y; + var i; + + arrayOpts = { + 'dtype': 'float64' + }; + + x = uniform( 100, -10.0, 10.0, arrayOpts ); + mu = uniform( 100, -5.0, 5.0, arrayOpts ); + sigma = uniform( 100, 0.1, 10.0, arrayOpts ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = pdf( x[ i % x.length ], mu[ i % mu.length ], sigma[ i % sigma.length ] ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/c/Makefile b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/c/Makefile new file mode 100644 index 000000000000..979768abbcec --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/stats/base/dists/anglit/pdf/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/c/benchmark.c new file mode 100644 index 000000000000..e2872875595f --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/benchmark/c/benchmark.c @@ -0,0 +1,142 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/stats/base/dists/anglit/pdf.h" +#include +#include +#include +#include +#include + +#define NAME "anglit-pdf" +#define ITERATIONS 1000000 +#define REPEATS 3 + +/** +* Prints the TAP version. +*/ +static void print_version( void ) { + printf( "TAP version 13\n" ); +} + +/** +* Prints the TAP summary. +* +* @param total total number of tests +* @param passing total number of passing tests +*/ +static 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 +*/ +static 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 +*/ +static double tic( void ) { + struct timeval now; + gettimeofday( &now, NULL ); + return (double)now.tv_sec + (double)now.tv_usec/1.0e6; +} + +/** +* Generates a random number on the interval [min,max). +* +* @param min minimum value (inclusive) +* @param max maximum value (exclusive) +* @return random number +*/ +static double random_uniform( const double min, const double max ) { + double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); + return min + ( v*(max-min) ); +} + +/** +* Runs a benchmark. +* +* @return elapsed time in seconds +*/ +static double benchmark( void ) { + double sigma[ 100 ]; + double mu[ 100 ]; + double x[ 100 ]; + double elapsed; + double y; + double t; + int i; + + for ( i = 0; i < 100; i++ ) { + x[ i ] = random_uniform( -10.0, 10.0 ); + mu[ i ] = random_uniform( -5.0, 5.0 ); + sigma[ i ] = random_uniform( 0.1, 10.0 ); + } + + t = tic(); + for ( i = 0; i < ITERATIONS; i++ ) { + y = stdlib_base_dists_anglit_pdf( x[ i%100 ], mu[ i%100 ], sigma[ i%100 ] ); + if ( y != y ) { + printf( "should not return NaN\n" ); + break; + } + } + elapsed = tic() - t; + if ( y != y ) { + printf( "should not return NaN\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::%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/stats/base/dists/anglit/pdf/binding.gyp b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/binding.gyp new file mode 100644 index 000000000000..0d6508a12e99 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/binding.gyp @@ -0,0 +1,170 @@ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/stats/base/dists/anglit/pdf/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/docs/repl.txt new file mode 100644 index 000000000000..dbd97c5469d1 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/docs/repl.txt @@ -0,0 +1,75 @@ + +{{alias}}( x, μ, σ ) + Evaluates the probability density function (PDF) for an anglit + distribution with location parameter `μ` and scale parameter + `σ` at a value `x`. + + If provided `NaN` as any argument, the function returns `NaN`. + + If provided `σ <= 0`, the function returns `NaN`. + + Parameters + ---------- + x: number + Input value. + + μ: number + Location parameter. + + σ: number + Scale parameter. + + Returns + ------- + out: number + Evaluated PDF. + + Examples + -------- + > var y = {{alias}}( -10.0, 0.0, 1.0 ) + 0.0 + > y = {{alias}}( 0.0, 0.0, 1.0 ) + 1.0 + > y = {{alias}}( 10.0, 0.0, 1.0 ) + 0.0 + > y = {{alias}}( NaN, 0.0, 1.0 ) + NaN + > y = {{alias}}( 0.0, NaN, 1.0 ) + NaN + > y = {{alias}}( 0.0, 0.0, NaN ) + NaN + > y = {{alias}}( 0.0, 0.0, -1.0 ) + NaN + + +{{alias}}.factory( μ, σ ) + Returns a function for evaluating the probability density + function (PDF) of an anglit distribution with location parameter + `μ` and scale parameter `σ`. + + Parameters + ---------- + μ: number + Location parameter. + + σ: number + Scale parameter. + + Returns + ------- + pdf: Function + Probability density function (PDF). + + Examples + -------- + > var myPDF = {{alias}}.factory( 0.0, 1.0 ); + > var y = myPDF( -10.0 ) + 0.0 + > y = myPDF( 0.0 ) + 1.0 + > y = myPDF( 10.0 ) + 0.0 + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/docs/types/index.d.ts new file mode 100644 index 000000000000..fdfd318b5f9b --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/docs/types/index.d.ts @@ -0,0 +1,118 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +// TypeScript Version: 4.1 + +/** +* Evaluates the probability density function (PDF) for an anglit distribution. +* +* @param x - input value +* @returns evaluated PDF +*/ +type Unary = ( x: number ) => number; + +/** +* Interface for the probability density function (PDF) of an anglit distribution. +*/ +interface PDF { + /** + * Evaluates the probability density function (PDF) for an anglit distribution with location parameter `mu` and scale parameter `sigma` at a value `x`. + * + * ## Notes + * + * - If provided `sigma <= 0`, the function returns `NaN`. + * - If provided a value outside the support of the distribution, the function returns `0`. + * + * @param x - input value + * @param mu - location parameter + * @param sigma - scale parameter + * @returns evaluated PDF + * + * @example + * var y = pdf( -10.0, 0.0, 1.0 ); + * // returns 0.0 + * + * @example + * var y = pdf( 0.0, 0.0, 1.0 ); + * // returns 1.0 + * + * @example + * var y = pdf( 10.0, 0.0, 1.0 ); + * // returns 0.0 + * + * @example + * var y = pdf( NaN, 0.0, 1.0 ); + * // returns NaN + * + * @example + * var y = pdf( 0.0, NaN, 1.0 ); + * // returns NaN + * + * @example + * var y = pdf( 0.0, 0.0, NaN ); + * // returns NaN + * + * @example + * var y = pdf( 0.0, 0.0, -1.0 ); + * // returns NaN + */ + ( x: number, mu: number, sigma: number ): number; + + /** + * Returns a function for evaluating the probability density function (PDF) for an anglit distribution with location parameter `mu` and scale parameter `sigma` at a value `x`. + * + * @param mu - location parameter + * @param sigma - scale parameter + * @returns PDF + * + * @example + * var myPdf = pdf.factory( 0.0, 1.0 ); + * var y = myPdf( -10.0 ); + * // returns 0.0 + * + * y = myPdf( 0.0 ); + * // returns 1.0 + */ + factory( mu: number, sigma: number ): Unary; +} + +/** +* Anglit distribution probability density function (PDF). +* +* @param x - input value +* @param mu - location parameter +* @param sigma - scale parameter +* @returns evaluated PDF +* +* @example +* var y = pdf( 0.0, 0.0, 1.0 ); +* // returns 1.0 +* +* var myPdf = pdf.factory( 0.0, 1.0 ); +* y = myPdf( -10.0 ); +* // returns 0.0 +* +* y = myPdf( 0.0 ); +* // returns 1.0 +*/ +declare var pdf: PDF; + + +// EXPORTS // + +export = pdf; diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/docs/types/test.ts new file mode 100644 index 000000000000..51bb96e2d2f3 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/docs/types/test.ts @@ -0,0 +1,119 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +import pdf = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + pdf( 2, 0, 4 ); // $ExpectType number + pdf( 1, 2, 8 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided values other than three numbers... +{ + pdf( true, 3, 6 ); // $ExpectError + pdf( false, 2, 4 ); // $ExpectError + pdf( '5', 1, 2 ); // $ExpectError + pdf( [], 1, 2 ); // $ExpectError + pdf( {}, 2, 4 ); // $ExpectError + pdf( ( x: number ): number => x, 2, 4 ); // $ExpectError + + pdf( 9, true, 12 ); // $ExpectError + pdf( 9, false, 12 ); // $ExpectError + pdf( 5, '5', 10 ); // $ExpectError + pdf( 8, [], 16 ); // $ExpectError + pdf( 9, {}, 18 ); // $ExpectError + pdf( 8, ( x: number ): number => x, 16 ); // $ExpectError + + pdf( 9, 5, true ); // $ExpectError + pdf( 9, 5, false ); // $ExpectError + pdf( 5, 2, '5' ); // $ExpectError + pdf( 8, 4, [] ); // $ExpectError + pdf( 9, 4, {} ); // $ExpectError + pdf( 8, 5, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an unsupported number of arguments... +{ + pdf(); // $ExpectError + pdf( 2 ); // $ExpectError + pdf( 2, 0 ); // $ExpectError + pdf( 2, 0, 4, 1 ); // $ExpectError +} + +// Attached to main export is a `factory` method which returns a function... +{ + pdf.factory( 0, 4 ); // $ExpectType Unary +} + +// The `factory` method returns a function which returns a number... +{ + const fcn = pdf.factory( 0, 4 ); + fcn( 2 ); // $ExpectType number +} + +// The compiler throws an error if the function returned by the `factory` method is provided invalid arguments... +{ + const fcn = pdf.factory( 0, 4 ); + fcn( true ); // $ExpectError + fcn( false ); // $ExpectError + fcn( '5' ); // $ExpectError + fcn( [] ); // $ExpectError + fcn( {} ); // $ExpectError + fcn( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function returned by the `factory` method is provided an unsupported number of arguments... +{ + const fcn = pdf.factory( 0, 4 ); + fcn(); // $ExpectError + fcn( 2, 0 ); // $ExpectError + fcn( 2, 0, 1 ); // $ExpectError +} + +// The compiler throws an error if the `factory` method is provided values other than two numbers... +{ + pdf.factory( true, 3 ); // $ExpectError + pdf.factory( false, 2 ); // $ExpectError + pdf.factory( '5', 1 ); // $ExpectError + pdf.factory( [], 1 ); // $ExpectError + pdf.factory( {}, 2 ); // $ExpectError + pdf.factory( ( x: number ): number => x, 2 ); // $ExpectError + + pdf.factory( 9, true ); // $ExpectError + pdf.factory( 9, false ); // $ExpectError + pdf.factory( 5, '5' ); // $ExpectError + pdf.factory( 8, [] ); // $ExpectError + pdf.factory( 9, {} ); // $ExpectError + pdf.factory( 8, ( x: number ): number => x ); // $ExpectError + + pdf.factory( [], true ); // $ExpectError + pdf.factory( {}, false ); // $ExpectError + pdf.factory( false, '5' ); // $ExpectError + pdf.factory( {}, [] ); // $ExpectError + pdf.factory( '5', ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the `factory` method is provided an unsupported number of arguments... +{ + pdf.factory( 0 ); // $ExpectError + pdf.factory( 0, 4, 8 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/examples/c/Makefile b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/examples/c/Makefile new file mode 100644 index 000000000000..c8f8e9a1517b --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/examples/c/Makefile @@ -0,0 +1,146 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/stats/base/dists/anglit/pdf/examples/c/example.c b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/examples/c/example.c new file mode 100644 index 000000000000..a82f28b34351 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/examples/c/example.c @@ -0,0 +1,42 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/stats/base/dists/anglit/pdf.h" +#include +#include + +static double random_uniform( const double min, const double max ) { + double v = (double)rand() / ( (double)RAND_MAX + 1.0 ); + return min + ( v*(max-min) ); +} + +int main( void ) { + double sigma; + double mu; + double x; + double y; + int i; + + for ( i = 0; i < 25; i++ ) { + x = random_uniform( -5.0, 5.0 ); + mu = random_uniform( -5.0, 5.0 ); + sigma = random_uniform( 0.5, 5.0 ); + y = stdlib_base_dists_anglit_pdf( x, mu, sigma ); + printf( "x: %lf, μ: %lf, σ: %lf, f(x;μ,σ): %lf\n", x, mu, sigma, y ); + } +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/examples/index.js new file mode 100644 index 000000000000..201821337a12 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/examples/index.js @@ -0,0 +1,32 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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'; + +var uniform = require( '@stdlib/random/array/uniform' ); +var logEachMap = require( '@stdlib/console/log-each-map' ); +var pdf = require( './../lib' ); + +var opts = { + 'dtype': 'float64' +}; +var x = uniform( 10, -5.0, 5.0, opts ); +var mu = uniform( 10, -5.0, 5.0, opts ); +var sigma = uniform( 10, 0.5, 5.0, opts ); + +logEachMap( 'x: %0.4f, μ: %0.4f, σ: %0.4f, f(x;μ,σ): %0.4f', x, mu, sigma, pdf ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/include.gypi b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/include.gypi new file mode 100644 index 000000000000..bee8d41a2caf --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/include.gypi @@ -0,0 +1,53 @@ +# @license Apache-2.0 +# +# Copyright (c) 2026 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': [ + ' + */ + function pdf( x ) { + var y; + + if ( isnan( x ) ) { + return NaN; + } + + // Transform x to the standardized form + y = ( x - mu ) / sigma; + if ( y < -PI_OVER_4 || y > PI_OVER_4 ) { + return 0.0; + } + return cos( 2.0 * y ) / sigma; + } +} + + +// EXPORTS // + +module.exports = factory; diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/index.js new file mode 100644 index 000000000000..2494069c1897 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/index.js @@ -0,0 +1,54 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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'; + +/** +* Anglit distribution probability density function (PDF). +* +* @module @stdlib/stats/base/dists/anglit/pdf +* +* @example +* var pdf = require( '@stdlib/stats/base/dists/anglit/pdf' ); +* +* var y = pdf( 0.0, 0.0, 1.0 ); +* // returns 1.0 +* +* var myPDF = pdf.factory( 0.0, 1.0 ); +* y = myPDF( 0.0 ); +* // returns 1.0 +* +* y = myPDF( 10.0 ); +* // returns 0.0 +*/ + +// MODULES // + +var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' ); +var main = require( './main.js' ); +var factory = require( './factory.js' ); + + +// MAIN // + +setReadOnly( main, 'factory', factory ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/main.js new file mode 100644 index 000000000000..f06ddbab363d --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/main.js @@ -0,0 +1,98 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 isnan = require( '@stdlib/math/base/assert/is-nan' ); +var cos = require( '@stdlib/math/base/special/cos' ); +var PI = require( '@stdlib/constants/float64/pi' ); + + +// VARIABLES // + +var PI_OVER_4 = PI / 4.0; + + +// MAIN // + +/** +* Evaluates the probability density function (PDF) for an anglit distribution with location parameter `mu` and scale parameter `sigma` at a value `x`. +* +* @param {number} x - input value +* @param {number} mu - location parameter +* @param {PositiveNumber} sigma - scale parameter +* @returns {NonNegativeNumber} evaluated PDF +* +* @example +* var y = pdf( 0.0, 0.0, 1.0 ); +* // returns 1.0 +* +* @example +* var y = pdf( 0.5, 0.0, 1.0 ); +* // returns ~0.540 +* +* @example +* var y = pdf( 2.0, 0.0, 1.0 ); +* // returns 0.0 +* +* @example +* var y = pdf( -2.0, 0.0, 1.0 ); +* // returns 0.0 +* +* @example +* var y = pdf( NaN, 0.0, 1.0 ); +* // returns NaN +* +* @example +* var y = pdf( 0.0, NaN, 1.0 ); +* // returns NaN +* +* @example +* var y = pdf( 0.0, 0.0, NaN ); +* // returns NaN +* +* @example +* var y = pdf( 0.0, 0.0, -1.0 ); +* // returns NaN +*/ +function pdf( x, mu, sigma ) { + var y; + + if ( + isnan( x ) || + isnan( mu ) || + isnan( sigma ) || + sigma <= 0.0 + ) { + return NaN; + } + + // Transform x to the standardized form + y = ( x - mu ) / sigma; + if ( y < -PI_OVER_4 || y > PI_OVER_4 ) { + return 0.0; + } + return cos( 2.0 * y ) / sigma; +} + + +// EXPORTS // + +module.exports = pdf; diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/native.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/native.js new file mode 100644 index 000000000000..1d0a45f7f8e4 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/lib/native.js @@ -0,0 +1,76 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 addon = require( './../src/addon.node' ); + + +// MAIN // + +/** +* Evaluates the probability density function (PDF) for an anglit distribution with location parameter `mu` and scale parameter `sigma` at a value `x`. +* +* @private +* @param {number} x - input value +* @param {number} mu - location parameter +* @param {PositiveNumber} sigma - scale parameter +* @returns {NonNegativeNumber} evaluated PDF +* +* @example +* var y = pdf( 0.0, 0.0, 1.0 ); +* // returns 1.0 +* +* @example +* var y = pdf( 0.5, 0.0, 1.0 ); +* // returns ~0.540 +* +* @example +* var y = pdf( 2.0, 0.0, 1.0 ); +* // returns 0.0 +* +* @example +* var y = pdf( -2.0, 0.0, 1.0 ); +* // returns 0.0 +* +* @example +* var y = pdf( NaN, 0.0, 1.0 ); +* // returns NaN +* +* @example +* var y = pdf( 0.0, NaN, 1.0 ); +* // returns NaN +* +* @example +* var y = pdf( 0.0, 0.0, NaN ); +* // returns NaN +* +* @example +* var y = pdf( 0.0, 0.0, -1.0 ); +* // returns NaN +*/ +function pdf( x, mu, sigma ) { + return addon( x, mu, sigma ); +} + + +// EXPORTS // + +module.exports = pdf; diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/manifest.json new file mode 100644 index 000000000000..4bedefbd2042 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/manifest.json @@ -0,0 +1,82 @@ +{ + "options": { + "task": "build", + "wasm": false + }, + "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", + "wasm": false, + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/napi/ternary", + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/cos", + "@stdlib/constants/float64/pi" + ] + }, + { + "task": "benchmark", + "wasm": false, + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/cos", + "@stdlib/constants/float64/pi" + ] + }, + { + "task": "examples", + "wasm": false, + "src": [ + "./src/main.c" + ], + "include": [ + "./include" + ], + "libraries": [], + "libpath": [], + "dependencies": [ + "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/cos", + "@stdlib/constants/float64/pi" + ] + } + ] +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/package.json b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/package.json new file mode 100644 index 000000000000..d1e1d6bc609a --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/package.json @@ -0,0 +1,71 @@ +{ + "name": "@stdlib/stats/base/dists/anglit/pdf", + "version": "0.0.0", + "description": "Anglit distribution probability density function (PDF).", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "gypfile": true, + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "include": "./include", + "lib": "./lib", + "src": "./src", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "statistics", + "stats", + "dist", + "distribution", + "probability", + "continuous distribution", + "probability density", + "probability density function", + "pdf", + "anglit", + "random variable" + ] +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/src/Makefile b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/src/Makefile new file mode 100644 index 000000000000..2caf905cedbe --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/src/Makefile @@ -0,0 +1,70 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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/stats/base/dists/anglit/pdf/src/addon.c b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/src/addon.c new file mode 100644 index 000000000000..aab0f6147c84 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/src/addon.c @@ -0,0 +1,22 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/stats/base/dists/anglit/pdf.h" +#include "stdlib/math/base/napi/ternary.h" + +STDLIB_MATH_BASE_NAPI_MODULE_DDD_D( stdlib_base_dists_anglit_pdf ) diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/src/main.c new file mode 100644 index 000000000000..be9a53dd5cdc --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/src/main.c @@ -0,0 +1,56 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/stats/base/dists/anglit/pdf.h" +#include "stdlib/math/base/assert/is_nan.h" +#include "stdlib/math/base/special/cos.h" +#include "stdlib/constants/float64/pi.h" + +static const double PI_OVER_4 = STDLIB_CONSTANT_FLOAT64_PI / 4.0; + +/** +* Evaluates the probability density function (PDF) for an anglit distribution with location parameter `mu` and scale parameter `sigma` at a value `x`. +* +* @param x input value +* @param mu location parameter +* @param sigma scale parameter +* @return evaluated PDF +* +* @example +* double y = stdlib_base_dists_anglit_pdf( 0.0, 0.0, 1.0 ); +* // returns 1.0 +*/ +double stdlib_base_dists_anglit_pdf( const double x, const double mu, const double sigma ) { + double y; + + if ( + stdlib_base_is_nan( x ) || + stdlib_base_is_nan( mu ) || + stdlib_base_is_nan( sigma ) || + sigma <= 0.0 + ) { + return 0.0 / 0.0; // NaN + } + + // Standardize + y = ( x - mu ) / sigma; + if ( y < -PI_OVER_4 || y > PI_OVER_4 ) { + return 0.0; + } + return stdlib_base_cos( 2.0 * y ) / sigma; +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/fixtures/python/data.json b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/fixtures/python/data.json new file mode 100644 index 000000000000..fef5d48c5608 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/fixtures/python/data.json @@ -0,0 +1 @@ +{"x":[-6.361859466873372,-3.5388146767965196,-7.347424446304707,0.9705669418157505,4.7442517291432384,-7.968847072228362,4.56351816153882,-8.232910530752422,9.239414010530076,-9.811058423754373,-9.088779659266956,3.2309104157066404,6.8269648571446275,5.198426764698613,-8.116086772606295,8.999208436955804,5.835079041228326,-9.891053710232198,0.6399090790260367,-8.841537528475914,-3.9148494820254776,6.1104659261694785,-6.69829860633847,6.192681508108848,2.351997332772184,2.4344275910415334,-8.223178744238382,2.2400929609486475,-4.094612016980522,9.861807284896052,4.756678340679457,0.349726314226551,1.3344304018309572,-7.038910847625646,-9.638488509411545,3.8749862929967165,-0.12300817545036047,-2.3777409815713124,-1.9951170357276418,-2.212092916724952,-9.241004196554757,2.5667759104241394,-1.3115256947671448,6.439107247692025,-3.1107502593394587,-1.7918910438770155,-3.1113743851729536,-5.090200421878663,-7.685116967373736,6.585064297828488,4.1614707190743605,6.940980579670562,-0.13977371652091364,-4.982907349221046,0.14168768164680046,-8.88850845621324,-5.594286875303494,-4.811324429600068,-6.890794821520762,-9.520156573183217,-0.6813662848539774,-4.989353476180627,4.941694096605749,-5.044856720253881,-9.10062087425477,-5.575355335624954,-1.6728367789923695,3.461083404460574,4.656266949699283,-2.192340818672851,-3.1691244410103847,1.663570647013346,2.6769110037928954,6.253057590435041,1.170172338085706,9.92867459293575,6.7813802143311435,3.7624834661507407,-9.754663205070592,4.202325695852082,1.6035734097425003,-1.3713924429984239,-7.108788970335704,9.244143867481533,3.361274303686571,4.141440812727652,7.5994506718496595,6.027649201274926,8.60668270996904,6.388252733935985,7.167387352700633,-0.5693057374368173,-6.277390291631537,-6.099878609962152,-8.286584413523705,7.20941861370126,-7.957363207613399,5.535946585313237,-4.911020419190177,-8.20614361102973,6.934425247867065,-9.835748216631208,3.3571930307341074,6.5807821752705955,3.512585062745311,-1.1696291595122315,-0.20005514374751776,8.59389512766333,2.733215429394493,5.116513420199469,-4.30672751263349,-4.731693437353901,-6.282633619043196,-9.425023965491786,-4.042307123782747,1.316134560659922,-2.6757458693887397,0.20732331375076285,-0.6519771808063588,5.524468519057216,0.64311885272941,5.970025801153859,1.214234954616444,1.291230813687239,8.731287344990392,-6.038453093121701,-5.433524512843495,0.257213488916042,5.93001217554731,-3.9533847589462585,0.5498403656447497,0.014663255146755816,-7.136392150646797,8.737413501201733,7.528672533905677,-1.4336906826312994,-6.771245604561596,9.933869531388247,4.755018481716611,5.781221285284094,-7.044424484211471,-8.310453434452633,-3.550316439130288,-4.283282585026395,-3.1383363237082857,7.424321215585522,1.7013936315253773,8.623714230004577,-6.804543985638967,4.548389077856408,-4.31951485703844,2.854584825148663,3.805929508888541,7.312369078561321,-6.596168473533406,3.254559796172531,9.933501279288286,-9.861893044551838,-4.450377694780887,-6.867128893157437,0.7424932607710293,4.791115537136765,4.350197556608968,2.3004772356836245,-1.3185365910071862,-8.886163996853217,1.8458714625848476,-9.04187352439238,9.279307867580222,2.7399609515117653,0.45672925859522273,-4.630853128301123,-3.890296726314018,-0.5370097226730248,8.224152149407605,-9.021741408671058,-8.866344345458579,6.352181611799871,-2.496820412360239,-7.415427118379377,-7.093553014781673,9.850502544264195,4.571357717462012,7.250557752143866,7.0841870273957,2.316749909703713,3.6932700038560817,-9.770792945367896,9.786153062959858,5.583811848095195,0.15152203038025824,-5.33600522064825,3.454899379575785,-3.3488919540521085,-3.397178032304149,-9.56523612865021,2.9053429198675023,4.4206121435920505,8.919930818219015,-1.2067712042347818,3.2766446184363023,9.873915525531473,0.8182790101830335,-8.467456643334915,9.260992781574735,3.189535592963079,-6.197471408187745,2.766870509257524,6.265182381116997,-8.45604642473849,1.8398659715386465,-9.618172333108104,9.787207276994213,-0.8599674168883737,-7.519986729268209,1.7794683975686105,9.376064137480565,-6.444414044250266,-4.453552683235595,9.587686709972516,-4.838120765445224,6.624881232496524,5.143108988381206,-9.671311938479946,7.707086008905502,9.070983573383376,-8.805384053785927,6.458796009876874,4.203963661354589,6.476448857219626,-4.964458109743077,9.412777827320834,3.46834247126589,4.376242251128517,-4.179372161098344,-2.301750157154247,-8.535947122060692,2.3915111293792783,-6.887938001095833,3.5589873943637897,9.654105148726845,2.9163981759756332,-3.8031623044808356,7.9339663550757535,6.268099768551849,7.792562447946587,-4.770494783034591,-8.64662114045342,-1.459668817890055,-6.738621816692783,-6.653129470144283,6.053647108842959,-3.044872139269188,-4.2310848294672,7.250957231500706,-7.91281930372866,-1.9171742047118219,-8.379178201691278,6.793029739170237,-3.2844653784727873,7.430090322054713,2.9590225210291994,-6.747913253485356,9.990934007954863,-7.499484641898824,8.812902296117361,-7.097901640433553,3.22049902382968,-7.475922318292387,5.575551177977813,5.330400104881308,-8.706540432891206,3.7729394874535807,3.192346323143031,-6.322927075561129,4.385253907606359,3.361028968694921,-1.3664794816798391,-0.8120056338099264,-9.380556038611108,7.699021430543404,8.60155440162972,6.8018040355491785,0.31352247179910364,5.094383615741682,1.2660140165634068,3.977230906077743,-0.6328306737832214,8.495265611376823,0.18076240208587535,-1.2103756805759591,-5.556715806587538,-0.7391732455982485,7.473887514734802,7.524356512425992,-2.469852577822394,8.73633121133619,-9.631836979797157,8.900053979504847,-6.028048847020937,-16.657638482139422,0.25403833559474975,-3.096107468775365,-16.911715580778157,15.56702900440962,17.425006247842752,-19.13748972091154,1.8671729222317879,2.3008295018093996,14.626640903223596,7.628630416060712,-14.168139450706473,17.931533941740355,-17.133710290061078,-14.375871201957903,15.481140428035438,-16.609056619012236,12.590860433749228,-2.456956798528239,10.413780758928155,7.199894574470989,-17.61983441488376,9.512335759192837,-1.3310868934405278,12.176831171715655,3.4835209946213794,-7.051419016261482,-17.247359057472895,19.66123270815752,-0.9820325911243124,-17.332106412167416,6.861186707221691,-0.9681340251228079,-8.496612247222167,-4.326877217739629,-14.971674326536665,-15.983426324070663,12.342255283468269,7.578160472768637,-12.227110699128323,-2.377229409851914,-3.7487863642144745,1.935169713937075,-2.1615450924054436,-15.103749015699819,-12.603659201378385,-7.04530677603131,13.246128726771907,-3.047313068810702,-17.28053566129713,-12.013253634196573,5.563351993569867,2.3036849222462976,5.47170546115413,-8.39092638002481,18.2196373970488,8.023461355032158,19.14659829744639,8.896933751413656,4.116246533764901,-14.430658225341473,19.06925575409288,-14.530420997693527,14.040528235726207,7.203070932687929,-18.532920676099923,-7.4636048157415935,-13.4720380336041,-4.927008028553143,-13.730476232146476,1.6726320420987193,-0.8153965327903698,-8.580317495354013,4.062663076067906,-14.732835447988464,-13.974374375262473,11.895643240129395,19.83220951736773,3.678759216631331,0.04038190210520298,10.15433088975296,18.713258280551265,-11.504923607431632,3.752612598235835,7.419087338435531,7.0882081160273955,14.433771948373469,-11.076580296961339,5.8835715997348,9.843663130926494,12.864347469884187,8.871569298271197,1.317794228704301,-14.479929061756351,8.777925760848028,-1.268459802455343,-2.6729030949052976,-15.431817237158544,15.661448242550804,7.077480296835162,9.49635880678549,-9.112063789850616,-8.251478932539174,-13.818145027223604,-10.640273413646856,-14.090074263390369,-4.34084822976188,15.833989145486399,-18.959068691863603,-0.47085737842821374,-8.091211079804005,-4.933909301486498,7.977439997713141,-12.706280735262068,-6.902964715703304,-16.11891884341734,1.567804802139797,-17.63966616467975,7.246623395904326,-8.432818552986504,11.779342813750912,-12.400762012957252,-15.172109192077272,-12.949848251850572,17.542448094996082,9.315356756389725,-19.309422194948137,-17.31283851629826,-19.316859890940655,16.52868547097033,10.209080233251633,-15.634005967368472,1.3228763525754736,1.9962558584994952,-0.40717973913872996,-18.900876934446764,-19.03373008891137,-0.3130324399897759,17.611257813429297,0.957382031169093,11.032997208850752,0.5916682010457208,9.274746442739211,-11.358152795793561,13.147204991607978,6.814163292336467,-18.213808737319805,9.919449535455765,-2.0289118836168285,-5.424367453806958,-19.9361538415597,-8.807165237157516,1.8347293090872867,-16.343298327158426,-1.4938232674510878,4.815789922843461,16.681472871025164,-7.05474358863154,7.455832332558746,4.632050063702103,-17.070884478365237,4.893137662160946,-19.677533805601012,-19.60112826189753,7.454380120284977,17.849945302921377,-7.89905241785247,-9.698676467046017,5.283543363863309,-8.621175811511357,14.702310218839685,-2.077031014597722,19.02039007306385,16.582557935258684,1.9139700024106965,-5.192363310438996,3.8782266238068175,3.4001483248530064,-13.18153277432554,0.5244395953319554,-10.114845277046456,19.22536269706748,19.17502574443325,-1.9984569855765884,15.749984958692949,5.89015443304071,-16.8780130085515,3.8401158290940742,15.841731426828389,-14.887254093514324,-16.40782326453898,-15.772150398817097,16.462962438308843,-5.941542023789337,-7.2709703822016145,2.1158429785795185,-17.5828163284147,17.57168429312855,-6.026838003560847,10.711731513697636,-16.636848774403333,6.999721405593409,17.3713042590635,-18.255339499280474,6.471598607267076,-10.913493568684768,12.599049840220438,-6.266161162227192,-3.1162670027080885,14.533221287549068,-16.594681161433158,17.962270781959376,0.5110106309088636,-4.465921479925697,18.372347304287864,16.080502879235866,-4.884730328336261,-19.308184890691663,-12.130679622098196,5.130638467093288,-8.730197217692757,-12.896868510586739,17.275623935937126,10.05510288772556,-10.748611050997635,8.304706620193912,15.963180489355821,14.976012252119048,-18.680766011579294,-4.114062248845807,-18.938513689848282,-10.79086592576246,13.615646211600968,-4.753765156532426,4.903223160622282,0.015006168973783929,-4.778963138323409,11.167022301838891,16.9883788906199,11.106783655971135,17.236800219801268,-0.5995063705240895,0.8757305202623442,13.577620493067073,17.713049564278172,0.016195429867064348,6.775091150233472,17.107834390845873,16.27591059919873,-15.386949529067948,19.700292376029736,17.56702510806467,17.46664970855018,9.659411886787304,-7.03791086453737,4.887828113427382,10.222010911267198,-2.8599984009988404,-4.644645719725338,-15.098871405734325,4.1580544038640745,4.417820237938088,-7.599151246248068,16.617857164968164,-3.4978036368405405,-1.4142191370475103,-8.740942850276646,-19.488738029577398,-4.434364510721265,-1.67138542999637,-19.45629101121822,-18.481553515647093,-1.2068375212849922,-15.998532646477543,-8.238125447803842,18.738999812483257,1.2803414415040208,11.944916273241954,3.369079778557598,-12.683852434838489,11.943558146832292,19.43772885108786,-13.33250883298788,9.484260794034963,-5.699264493162314,3.8681599869452796,-1.6919874711128458,3.4522129030071724,3.605949585328414,1.3629818980263089,15.146871138587144,-17.151175068969483,6.453150279403275,14.409674729968593,-7.335455746043706,5.302345142767557,8.221295339836786,-8.717354408909369,-12.668297357701306,-14.27472133426216,-36.3701219418905,-9.664376827169917,13.247149397774294,-48.80309173656079,6.747928761203362,-0.855520633167103,40.4961712418842,20.062298212012635,-30.478602358370676,16.34141767811748,28.179821825564716,9.444885395563261,-36.3500495885003,-45.62042468556909,30.163549733827097,-23.072973567590218,4.688526178802718,26.52357033114727,20.852239713376648,-45.58983591455379,-1.0262238996434974,33.718983399321516,30.287652395939702,-43.963387545165304,46.28003859904912,24.40066749412331,-16.4915295383856,-33.22993903626266,13.14432590960174,-32.59686824318564,-17.95609305402406,35.961084428634294,30.32429406698907,-15.853329773309888,10.226909073633792,-13.44113631974254,-48.46538649888246,44.677244692656515,-34.90797024748768,9.75083709950286,37.77438771339054,-10.585335654904192,38.48694121723757,-40.92847738061698,1.9415699798322166,34.79067536275427,-37.918858680307,-7.001495568369755,9.595381584734199,-32.51871306378483,29.21373920304532,36.9258822002958,-15.02738446311568,47.40996757279028,-26.826645194937015,-23.079837924132097,-8.169669520052182,-24.94931224899166,-23.503505479059093,4.039214957744477,7.049107473671953,1.142004656646833,10.400296981252069,42.48962173346162,17.339170616735544,-5.738462335494141,12.152022959541554,-24.340776898303307,14.552003611115552,38.973950195734346,13.288056985677287,2.256797238144891,-4.341054690781711,-3.907746305734939,-49.310956266979765,37.772386520044975,-46.17147100409992,-31.601104626707542,-28.858389226740833,-24.112606648952084,-6.6759970991165005,-2.834003277557869,24.668810088863523,-39.029593799742344,34.973767247900696,11.34361901881499,18.28924732020792,28.929207885543136,-37.11841206036086,-15.361737483446866,-11.462387513363538,-0.8848895931461129,-49.80289962739932,-6.464443337497649,-39.96506412273095,18.960134769746944,34.095857713982824,-32.694892819681,24.856131042086616,-4.941099302970855,-45.57540470359493,-34.9913792870631,30.50991436769729,-49.544247339942096,-47.19065925470085,-33.12933556565413,-41.45186366532596,-30.62230873180255,33.98442628150761,-32.41840289780272,-7.765758174232154,-27.6444681846861,36.933894822147465,33.11419458534196,-17.902808591251308,-20.008405691356334,43.727264653300125,42.846103567746326,-31.071028774244024,31.360288916290017,9.542313081863774,-42.118402193625556,27.223678903152432,15.07801237222904,-4.759804363047074,1.9816414913602074,-49.65507005223932,-20.73375670142449,-46.492490714662836,45.25172201076582,-32.07221818996334,25.71416999097437,25.197790001121987,-47.38651327614595,18.395453826448843,-24.137425979563996,38.232399403448156,-42.298077159133086,17.553725047535778,-14.62817508745895,-44.64384056988689,-38.27872531542861,-23.01313815487194,46.85298322376829,-28.19545396573382,42.62472566891718,49.69549868370255,-16.164961918815294,44.26466263450244,12.620857058116151,3.464483599248389,-26.14758155057293,-2.896326035017161,-1.7507819763950465,-44.46530577712814,8.387177206197471,48.79462710960276,6.960604579592967,-38.75049265200388,-16.535474520930215,-40.91025611197108,31.965407092803886,7.659858642740211,-22.652708867097914,2.3116993959486436,-29.470735946228586,-24.867304012659396,25.058392869177098,34.392213095917455,-33.77325477950859,-1.925028569257826,-46.705310326287496,-27.498631113997774,26.86081695358071,-17.078836936298543,26.804448212301295,-21.83485090755013,9.937846130300898,16.17011943137068,-27.642212928124856,4.8509436951325355,-22.651730509691003,-46.20949890477618,-47.87725916241799,25.58533956304001,-35.70733608361262,9.945674312722865,-2.6909276095811165,-44.23054981233317,-18.177357053255704,23.703847414135765,11.266751600998418,39.36262646130902,-43.998333957305455,-48.13329680570316,23.699656995176127,22.36948061455722,-0.21367738954464244,37.22750939975538,2.998171607601172,-0.147442138500665,-15.694245927515617,-25.923901818283845,-25.21640008380427,6.4843094145487825,-3.3693652742115034,-8.962700583725002,-33.86631923443883,7.130945012491395,3.830453515164656,13.483613762732816,-34.90099218131071,-34.20884597575366,29.20971101009347,8.161545680707604,-6.9917462005683575,-5.3558143199701504,38.58050344469763,-23.793761113232737,11.213862759053072,2.183534251725881,-38.150437365289356,47.32071714376197,23.131241790367767,-42.419017587869355,-26.32311638024616,-14.63336395270143,49.2277004347776,-13.850603656707328,-16.073620987426516,2.463357103052374,37.189639881370795,31.92326810761341,-15.152376668696945,-37.34870025764073,-39.914084807622885,23.378771537635487,-29.161330545327722,-21.12758542246803,-23.78907967249243,8.69764937083928,-3.4853902299168382,26.08782372486955,-23.932054845150397,-12.494787913910997,-24.776094821594697,-41.93021785276393,37.52084570551477,-4.086309418298107,-26.296681707945325,2.432190633826572,-37.594636287063224,-31.624339421623127,48.75141805906124,-15.318610402219804,-49.07845193973864,23.341841000518144,4.08670241864565,37.013461843971925,-14.875512233046571,16.80693924550674,37.56216784084653,46.63428254024123,44.60096571317442,10.785490884934688,-4.711642259151979,48.89181859374615,36.0535868896835,-19.771689716560026,-36.40696524378081,22.07528617682958,17.655807778685002,14.620688954657894,-29.38198438920948,-16.33151979830837,-19.20829599491617,-2.360949104177358,-24.671768014072583,14.342040022320617,-2.8956809431158206,-14.45358917501607,-34.5160722206169,-42.39072664433108,25.21834577469214,8.645770462003057,-2.5434485639439757,-22.911063586269798,46.06667594307811,12.54773516330522,-47.728788387720144,20.346869386672424,4.270157694657627,-37.12123996727817,42.64753896583801,28.277991529455434,-2.779208581700132,45.644192063188825,-3.6443049319295895,27.38967858955739,41.68622805844342,-15.48879987126277,-9.127424844754614,44.01404789731079,17.462791043636912,-29.09183691262878,-45.94929680039017,-18.526280008431982,46.36819071718736,-44.787360632260054,28.078703621183948,-19.3862014092381,36.85106386724996,-4.940790229719575,-39.420515610443445,-29.61712019374566,-49.519961039531836,-24.66897294652537,-23.10302542362055,-27.60640236936852,-24.340389064961588,-30.76384026673711,-47.50874688725251,24.775696159683292,22.228247345981416,-47.11729058700851,-42.65596982733303,24.026222274115966,-18.266130076304286,33.17354768866831,14.471966199334659,8.683381056164166,-16.84963246972896,11.447832328197748,-16.13731064386689,4.991203944413627,-37.44357978358373,30.3781840429384,-40.422013748921785,12.897570510706956,-33.692441233297465,-37.296717978418684,29.602842138165087,24.884343085123277,-6.23794354599525,-19.519409983056534,23.499877004756456,-7.104926106411057,-7.946704098655509,-16.50942276670075,9.286217464506372,37.36415343575534,-28.687359922355625,-22.121960129118477,-4.238601951895703,31.601560767966205,-34.12036873074858,2.1882687392821865,-13.995504539968437,-7.2766269520436,-29.445321456147376,8.66540739104751,36.53578132130228,13.408827224245435,-25.419372295955668,-22.520503481204447,-6.534512243269738,6.337554544987512,8.88518986529435,-30.851744620506928,13.152349633095461,32.127265031892875,35.3197157154426,-40.346353417964295,5.330655776466443,-48.21861704766008,35.0570153220592,-32.2379398124743,47.174052991059455,-28.964293521408102,0.1519638568634818,0.47037020003064356,16.032709852990138,12.33316110175545,46.269607499654114,-44.4703264440362,-10.766133150204837,-0.47083894967789064,24.652985595192007,-29.286164455411367,16.379294389261773,-36.731903905940854,9.69768600762405,8.488650310729327,-14.20173413416719,-39.24961269184307,-48.28148601821166,-33.393174077346,-39.09012692350233,30.74679223257094,18.770028668287836],"mu":[2.714242172522976,0.610079066119793,-1.196388274898049,-4.325040297827737,4.425761990124997,3.372592551399194,-3.0887213872393637,-2.9257979422108074,-3.131906253534517,-2.6497422017301933,-3.5383214089033324,4.191477755675159,-0.8446806979962069,-2.7612852162240165,-3.887747786017429,2.6957958355011655,-0.6735025994113508,0.8425169528713141,1.515689713395318,-4.473747468070291,3.364049917170526,-3.4735061763151895,-2.5717175869207507,-2.9881353325030413,3.613932932569334,-3.2173918671743484,1.388353241688776,-4.452052217284025,-1.8996699858204567,-4.383216795214503,2.7265572495951105,0.7505472594984672,2.484253383949971,0.8588680758722669,-1.594118263557692,-4.264804143254249,-3.8179206128071383,1.8367871658817556,4.461574368271698,3.7488784512597455,3.8100062737683587,-1.494215353911179,0.5881965883032887,4.914012277226483,-0.7957666909789207,-3.0733271175592956,-2.9824925100843136,2.877712592086846,0.5698886001947567,2.1422656770527224,1.8361026179952988,0.653778568714344,-4.04353488305245,-3.732768446201259,-3.1011774477425122,-4.766180728547409,-4.516667170493277,-4.078066333988172,4.589048665652562,-0.7594919259157686,2.6435633249266868,-2.177459355920792,4.172534236840757,-4.140489301102013,-2.1200091686041156,1.7161741015291012,-3.186950394224477,-3.1268292767711845,-3.802834694721009,3.577492114254378,0.8956615595227637,-3.229184391142618,-1.4366526198907148,-1.6249820151499481,3.6227523931284065,3.3492513706408875,0.748209614388494,4.327010454160593,-4.5230346678812685,-4.107319591677062,-0.5509065473886832,0.07804949255776439,-2.2449061994396233,-0.20105634729127964,2.7815924465285917,-4.076824276877583,3.544603303997093,-2.9005891913209956,3.4922278445327066,1.778444238105962,0.0414636931216128,-2.5326325891773225,-1.8608969798497368,-2.789358828856442,-0.4296312251299774,-1.6937521054334495,3.0637949321389755,3.475319152608872,-4.194800211371859,-2.439400606981396,-4.607823720221848,-1.2131654757542707,-0.9389647047657848,1.9642678813395644,1.5348558687194842,0.4491452056557854,3.6980890137214057,-1.9519901597663658,3.3494253676682924,4.315508161717441,1.6148684240834745,-1.3340562784916465,0.7391548240168309,4.070728311398792,3.370696628153979,4.5159818190772345,2.31532118952519,-3.8633251098329993,0.9914386971055675,-4.618465998147197,3.368541429365763,1.9906690310029767,-0.269016987930943,3.766776907431879,3.598490423534992,-2.358011479575932,0.22527549894522547,-2.6264171133523764,-2.1234894808742624,2.6561147396499463,3.9948501277871564,-4.169329003528707,3.8913617303045633,0.2833438699138142,-2.6142523065462573,-3.0244223374869317,1.3879450953817072,-2.5358590443394693,-1.334178022352729,3.5794861803799645,-2.86908584586698,-0.8529803328614607,-0.45963486997156355,1.3261484645898447,-3.0767824583930183,-3.644480017229718,4.897020353591172,1.0171322475633442,3.2289500727613643,-2.9221658108552684,1.2212730924489277,2.2415737800207927,-3.919323541287084,-2.1789457752818087,1.1290985744065152,-2.4828251484798916,1.3455823364075625,1.4611341113313125,2.890796892455211,0.4562348693769289,2.815034513659124,-2.147186644451579,4.502844716985614,1.9528146671857698,2.23464680313465,-0.09375845844202679,2.0235976853726445,0.24275625918182087,0.25873362745049455,4.51642043724123,1.9182660198007753,2.2937658425489262,0.8138335214057646,4.312488522764385,-2.160488330658036,0.3802286411990341,-2.9050450928115747,1.123843982195596,2.756452632484492,-4.2223401250476655,4.931588398363241,2.498495213490468,1.276013923957401,-3.8193980774170724,-2.9937519111619846,0.7964550502271894,-2.406148196686223,-3.9544799612750783,-3.897739610841814,0.8231326642896946,4.037564761308376,4.698574910603735,-4.269860994710342,2.986783836080095,2.257682733987081,4.563259969877096,-4.13172321319741,-1.4480526815523955,-4.545843635277662,1.2611051451743727,3.898775342316469,1.3600919176116193,-4.130784384017589,-1.6630484580960148,-4.717020777725205,3.742805065687456,4.331082670026511,-3.8624588973119236,3.2991520598143875,-0.5391070762602279,-0.773123107450254,4.4468751648473095,2.0031146938222575,3.6665666532230787,3.5034025686768615,-0.07642565203881801,2.1007438507167544,1.6478682822524906,2.6245488309734855,1.0426438448183353,2.2834928537598707,-2.390526277021896,1.283529128855867,0.4874719848671072,0.78163965050957,-0.8456747122980435,-4.422620134473823,-3.4717432909550383,4.496620400705748,3.766612810420364,-3.2510580348058413,-2.3671126403947182,-3.2725236829760274,-1.8226387413389409,4.246322727588819,-1.0207735265847395,1.2928919082974408,-1.3552238051724972,-3.4771079648924297,-3.895016618599847,0.6456421518056601,0.3090355755450327,2.433853020671691,1.1140776700146162,0.947172044794879,3.5642067888047517,-2.54458536835402,1.3362471082670702,-4.660906743889695,-2.5734736044054096,-4.634711376273888,-0.6102633308112084,-2.1137743728864686,2.813723937792414,-0.3249435007612327,-2.8577673716260543,3.245821695140709,3.681817648397484,-2.0183209024403173,0.6341342486922077,1.966828988585899,2.638179961764539,1.6733745526269246,-1.2974902256599274,4.280966323663865,-4.154073104840041,-1.6135215025627803,-2.7492039753319384,1.6222601825848386,3.0328885049340766,-2.62278156422161,-2.9791495938380654,2.068167173322509,1.4858024405959904,-1.6641650809622464,-2.239063595918589,0.08474494250878806,2.817564153852489,1.8244869080709156,-1.7673514650378364,-3.2892738868110727,0.34557773171858397,3.408619367460089,-0.8611323228588184,4.780303166531684,-2.1858029467813944,3.807656147611361,-0.5130555105857226,-2.408048370792998,-3.3936257018974434,1.7336204809942686,-4.534431766985627,2.782124222823245,1.6315912686664413,-4.810904062377758,0.9515656713552367,1.678538827840983,0.6020006738653763,2.8049932933011137,-0.3634807756606655,-1.8412107744402242,-0.13814311277916858,-0.5069064748682646,-4.228700759374893,-3.0647148083185627,3.009014394000797,-2.7106423840496134,-2.783990227212403,-8.809284399491048,-0.5899828716999806,7.136194790272587,-4.810876494738718,-2.995894756991884,-6.9010513068856705,-6.791648723313665,-0.46952759348675244,4.620120329543582,2.7047540378004182,6.6070422998690574,7.670307471875056,1.5231984555777025,7.055187474592653,3.81456358322675,-4.633002813632587,7.846229313829674,-9.242337338889026,-3.784269088098138,-3.610615327279321,3.6584782081861498,-1.4591991573507066,-4.459917304545105,-9.377641738368986,5.850368265071392,-5.548155501459133,-1.5147420404521021,0.8526170476961923,-4.513264885053414,7.307780258836001,8.549087714666726,-8.897856455828508,8.167091032620736,-9.837099577951658,8.19268475079781,1.6217628766374208,3.2192287158007016,8.045077133681936,5.7728300221727125,0.9861231832525785,2.0232714597031034,1.0477551313012778,0.6213278424719206,2.9932280654565027,-4.410611535327302,0.9069387289292781,8.286144342225064,5.102141059556779,-7.756136449761872,8.797493686419344,-3.5235269478457587,-9.060535995732392,3.0701714727695784,-9.95391438885677,0.22271188219876237,-9.199586845975482,-0.6448630135724223,4.909106814372258,-2.541393759341495,7.160435013062564,5.899530466032399,8.822564634844984,-5.309814370939403,9.85433807218228,-5.220528439351336,9.696977800932181,-8.422612760650939,7.873794254787665,4.121278108732369,-8.556047221103903,-1.5489449850000732,4.1546385665917125,-7.304478053348689,6.4728963320174095,-1.538840486323135,2.6602520519786115,-5.5865132853768955,-9.650752439135095,0.14634289724325278,-9.953789875340098,2.8680071107159595,6.873743640924172,-5.2216667254875855,-0.9796184101923888,-5.356616967648977,0.2106226309330932,6.863661940498616,-2.7531068983970304,9.801346316480004,6.806750849388962,-6.209627414595975,7.742093641813032,8.332511858622645,7.12603164470071,0.2958581258556805,6.895779840095237,-9.330619758047511,4.7833003791223945,-8.455381402413504,-0.6870974130579199,6.872031752553781,8.220441292853206,-1.5205611919029351,5.36671484361497,-2.2613346451088105,6.994998171300669,7.122072908638103,-1.6269365239219091,-8.87933085008708,4.125773104299741,-3.530012601457832,-9.713251209079823,1.7356581141159406,-8.2612373873953,-7.69069794490515,-2.9414884009311244,9.805515532877283,4.472715162735177,4.112769808085535,5.934230333198972,6.161362372167503,6.999652657757963,3.3268101415236693,-8.23815244130044,3.5681589080219958,-8.301099206470386,2.5894735031925116,-4.482626046789308,7.994707172035682,4.911270083459607,-1.4316572079853795,-6.057114065042619,9.641915869616543,8.47233924504171,-5.718892705688665,0.5571158698654504,-5.488594402287701,-1.2502317717386298,3.491040302516561,-0.5944051139280919,6.026926423628705,-0.6722662956617853,-8.432156738785451,0.9884280885153771,8.008105961458359,-1.2360988687667493,-9.383070141365174,9.254372549539866,-4.301103820531306,-8.28656768073202,-6.1096375004777865,-5.882009218311399,8.055001575152922,-7.869128798936023,-5.696542800696374,-2.4357701928109705,-0.02137648875665832,-3.6367250958872237,-6.167629816810245,5.232882438340917,-6.7601031303805925,1.8966638461797984,0.01691811085356143,6.564815110092187,-5.275746013877381,7.854382193300999,0.7626808356013708,6.16244938341957,-9.356543801852988,-2.871158974815362,9.828540017517227,6.779821002146594,-3.71588605880536,8.06460805896075,9.425936714330085,-0.2929362242006519,-3.6617959860816303,0.5091579027663666,-9.878254754096488,-9.63344339439759,-6.1858665205372905,-9.366284843594663,2.521150464671532,-4.627723842959073,-9.604723643845062,-3.912974517587142,6.934733422853057,4.192038924571248,5.275352863615918,4.918677590142996,-0.7311101811549925,2.9936059498987255,6.529372524331855,5.9202461581931605,6.855705687682089,-7.09558957835495,-6.888710515967236,-5.154341683092478,-0.059869810131845114,8.281179870683168,0.7822539580393251,-7.945791349011335,0.8112429241457786,4.719038105070787,-0.9274562983652359,-3.75175967999507,0.7117317384041009,-4.258516001883277,-8.319135888327523,-3.1026793392666114,-0.3252069726636968,0.9035219948804922,0.25619747642726765,0.21957580778069463,-7.32644357602153,-2.1494925713146307,-4.688523914164556,-0.15410181837121684,2.4197831279529467,-1.670014962358957,1.6376253264048994,-0.055867145708013766,-1.7226782872789297,5.901404557338337,-6.440013174050105,6.540127467709002,5.026541798904589,-7.505750546550227,-8.130465254167113,2.6891332621141917,2.9906618364179067,-9.174583344769909,-4.808162906077261,7.8532113259394905,4.808431071868984,-7.487900725158072,2.289500126558739,-5.315906447017138,-7.912706419102378,-8.577011570891088,-5.054503780317892,0.9090838980350746,4.521229836878078,-0.0834991923636057,-8.16112143851891,-0.886264063124834,6.688137755956134,-7.730976795302089,-2.196069086949146,2.210786021590911,6.433036706977205,4.650468010121996,0.631219307426127,-4.012970532620956,-0.5800069809518256,4.551696801609218,5.586444385124631,-0.3864524446469133,7.861250808847835,6.070405873884628,-4.206469159679278,9.778230600491014,-2.2383635876918166,5.5360763401188535,3.201207696462019,-1.4830567598328415,-7.676758707008922,-5.38901062250509,-4.447258141378525,9.221628506435419,3.027470303299758,4.264608468302933,7.538813132224938,6.70490623322592,4.041433434328972,3.7321397912925534,-4.57983228478442,5.002138777010021,4.895329644320107,-3.5784188233288443,4.9866931806614545,-3.28142490863039,6.4705012873560825,4.4682977498319065,-8.248272903728825,1.3152868147995473,-7.145740945583363,-2.8383883876890454,9.605709996661854,-6.758180825252316,1.127144071347761,4.210715629968851,6.887090696281032,-15.756637965999701,13.65091365976199,-0.7956486999568533,-10.63016072801795,-15.775074914244414,7.177654531225379,-16.668810157261422,9.940664614269373,4.335607227634647,9.113188172344898,-14.954240251924734,2.7212720240456356,-4.277130172024496,0.23457541904070212,-15.615497189147792,-2.2192343228732696,-6.678619738110768,-13.45126586470422,-13.336883148285224,19.168365658348648,-8.717028523672074,6.6886261281768675,6.424103131386385,-4.365864777735769,1.7047372878723834,-9.117446036205408,2.3541252568364754,-5.166534256647942,6.691523892675065,-8.682425039038826,8.618566936197233,-6.7221284907430565,7.450558779129199,-2.016760709124661,-2.1547548812618267,-6.3149357179581,-16.23122531024633,-19.07646076636402,-8.52248462839944,-13.243956708282303,9.492567956602844,4.864326291785538,-6.641890917470743,8.654009170810681,-18.050005312719332,11.7142444690503,-15.346090884682715,-4.4384506209328745,-13.765809488541812,-14.104712634010852,-8.347312004965989,-0.03849891323410759,10.542538368105909,-12.987005243221198,-7.885973863090721,1.9414687420571113,-9.273985243093325,-0.5358512620346474,-6.488259631231813,10.473959265862497,-17.404207560580378,-0.02255134974816997,11.915748290031352,1.0828645229479328,-1.1541368168933666,-5.544382880531021,5.268892245546052,1.028027768890773,-2.1210027146956705,-8.826982599132194,-19.18766296415289,2.424787071983779,-0.8151161059757683,13.18885642359146,13.445995769277793,2.9527119084716773,-12.306563254436313,10.070420879559158,17.961285143977214,-11.373481412392362,15.98622726232243,-13.499350284934884,-7.678584664930463,6.523710321593676,8.70044532394056,-14.59885910293153,13.046596881945732,-2.2600511253850186,1.0825352047573844,14.981357248689882,-3.038207919547421,-14.052137522733968,-18.125485977459558,-2.136317646544967,12.847809820245878,-18.175829192548054,17.306248052507925,-17.159353452847522,14.210852537503428,-11.870464433889074,-10.249227372039705,10.815968037794242,8.531366356889961,19.007036411910143,-4.100309782480412,0.07715630332178236,10.23452694342906,3.125362598431593,14.866471380500329,-13.283133726752045,-18.041418027971833,13.703521040056678,-6.839314547465239,-4.159362583978851,19.603103543343245,-17.16632968625527,19.729295078026162,1.2317947881976998,16.075809372884528,6.442153603658763,-8.468581341631403,-18.96884663486702,-16.020251333409256,9.157632410566755,-6.109413516835392,-13.762241143491742,5.230231855243446,-12.373687799437585,0.5119212411738161,-13.949841917018567,11.973247378069978,-0.05114679149551904,1.6864548307318863,3.667463992427141,-15.799899988092921,-7.018951117838025,18.471175024723664,17.486918963373718,-6.9291676839697836,-15.355427830050722,-2.6421868038478493,11.509166567499495,3.1594866890358446,13.108221210768711,8.96173100789063,5.072442625311375,16.537871941528948,16.36670609150481,-3.355385492267704,10.099459499757412,11.688455287345285,12.801128162321604,-12.026024593290838,-3.842231851581417,-7.8754495047001924,-18.849962243371834,5.329613240176187,-12.84971984152643,-10.211804691601415,-9.324142798557187,14.39688957871531,-0.12252577609895354,-0.9300395969102908,6.847982653040525,7.409860076422984,12.407495867336507,-15.64202591058821,1.3028275317342306,-10.345966010700565,0.4800897526391914,19.211520795027333,8.748121530851623,-15.024679708553679,-11.900191438490658,-12.294002431555931,-15.204075570333861,19.96727774194168,19.12433812877468,12.883030924450992,3.048007939133921,-12.789539234509721,-15.101890185840162,14.986345734361628,-19.979175701991956,12.550356247758884,-5.070945359967132,-13.950880031740072,-11.09214146225101,7.837868560314078,-14.060884400508339,9.49702750119421,-17.9054908054162,-4.1425645030944445,2.265827948110932,-4.757861074742156,-9.15557864566031,10.86473221945543,4.205562962638773,11.027659553389732,8.514275041348366,10.000971256480597,8.189036366861721,3.483259522819047,-18.05357424525223,18.07425803537018,-18.02517737320445,3.188805282729138,17.341397915611495,-13.866568324218186,1.5733899799068176,-5.514172340723867,6.232060484076296,12.943830481024577,13.09233073073198,8.444051314158045,-7.424504637351323,8.521430363134627,-18.136699352326076,-10.926991988806204,-13.960445720792357,14.973647728098442,19.000722470223877,2.8555877595124457,-10.027928182042425,19.653070991344556,6.004936983888104,16.88477170787037,-5.966161660149677,-6.951465087851702,9.80079626818096,-8.668393442204962,-18.48069133673843,16.311910874709746,-6.707941419593713,-17.825738835571144,-5.064962644957557,8.054439293605064,-16.055120380163906,8.01750509312338,6.458883254868148,-13.409999529924557,8.045463079568304,7.34969029025423,-5.840349020870637,2.9428200842885843,9.010547315125041,6.620168536385485,-6.129228627925283,-3.0856286978852445,-15.539162174792764,9.089716430041793,2.7040151229956635,-8.641377393276791,4.834536500639366,17.095059222433086,-0.9988055060429382,1.7994879327655084,4.30675771247493,-9.085769892040236,-0.5945292955228645,9.583563950773168,-15.869660250309202,10.102918782901313,-1.9568047627251808,-10.639934695707577,-15.692263173437762,-1.7113509255051262,10.660892232075575,-2.0163779460339235,-3.035139085204854,9.703030505661332,12.79258152266975,-9.582813189427757,-4.592871432681008,-5.052952936242519,11.665673180971801,0.7695755570033924,3.2445685317917423,11.946972120426459,-3.410633562822241,19.928768714503192,12.193851751118807,11.93577724299887,19.39071064847922,17.49027342320541,8.596587839398833,8.240276645023009,5.3540129479063125,-3.86251989222459,-5.641341342980795,-16.917595323542464,-16.240392036398298,13.903797051855612,-17.330046083880283,17.795581711989314,-16.34828154033623,18.32657450651326,2.1854755010629816,13.894996132248124,10.628054373658994,-10.174612616963902,-7.699157436461771,15.252128745201752,-1.200985441384809,5.182405932206763,-4.144858263168199,-12.652001692405946,-5.081810015146896,1.5449922950771509,7.004622913174593,-0.3138443590854898,-19.307177553782275,14.491936654479012,12.278189796746304,10.938435331397859,12.55546868599086,-19.67567707059727,18.58367574244091,-4.870960764699316,-7.928236580908695,11.554155283244576,-16.4057501085107,10.461210035772321,4.269893817389075,-18.243290426623417,6.002183035133545,4.292022133909043,-18.899718696012897,19.04461778156451,0.37355016762166215,-4.535203383857924,18.527305275518692,-10.903015489447828,-10.186179465565521,11.710509280207958,8.158464740773361,15.410962502114394,15.6772283164035,2.1838764301098657,-11.678592558703716,3.987710926383624,-2.4747515225436203,11.950304539268608,-18.77619212094821,-10.749025494804538,14.537043951193752,-9.539309510553204,-8.195084261242993,5.367342049946437,4.6862065009048415,-6.268121796736473,15.458975467719462,13.046134361682917,-2.0182296541773823,10.533569851180168,-14.64647395154234,1.3657059356058063,13.214978092804031,-13.009136905717389,-5.7571059613048945,-3.6347077358005784,5.8534666092058,3.4764179237320327,-19.2249222453859,8.06523153871456,-4.559510542438371,-0.17485495810196738,1.9957415671667853,11.215975159369652,9.92784295202825,-19.712878856338172,-9.421514093503177,-4.164704305147664,4.695954569151301,14.691081401772138,9.34832349220239,-14.665159858723316,2.040087174324789,-0.06837145466013794,4.757288111161056,-16.40583050501395,-10.240412169048545,-18.428265333635437,-16.371878769298554,-1.2912570947075785,-7.841863813030763,2.744943291052362,-4.662999651041876,-19.643455664980326,5.989730427685089,-15.221187465628798,17.598286108005723,13.980188896601142,19.691240228546498,-10.249821588257625,-14.207300430993183,8.834246285642678,-13.975088503196593,19.25943693465947],"sigma":[3.856632912544532,1.7441945432215844,2.2922703014255563,4.157138241206321,0.894373013711918,1.76818966231643,4.15651361140432,1.98793500013077,2.802617848289078,2.7195869906021275,0.8663649746406468,4.720930170685998,3.471597145649977,3.168466009275196,4.970193102366511,1.194768129952813,2.8170275513789615,0.16440750719279407,1.9288661693934372,0.1732355776089948,4.82844358045215,0.3414376919235621,1.5057358394491864,1.4242016966702793,1.975942652089347,3.3887289964179144,0.2858731044358732,3.6789008012000495,3.766473025135317,2.672691446340385,1.3853701521742074,4.499759843063209,2.2020642929053915,2.452508886445828,1.6678089366382929,3.988066113386456,4.445191757439674,3.2398591522119546,2.8424845946917916,1.0532607279640755,3.0370056127040903,2.3518958278859707,2.042313685577001,4.00233559677752,1.332475382597026,0.9849228891079734,2.706452656475256,4.729068159478658,0.9308525606206398,3.579918418447298,3.707124581329154,1.9572252157262107,4.3717195085774065,3.260082437447734,4.700705903746054,2.1319573154181874,4.161321762785032,0.4144311711890637,0.6034168846152212,0.956130022855073,3.2379835648011035,1.2303789323153096,1.1293852153730732,4.162942966156894,1.4154329406184578,3.378895546956696,4.0362711090894,2.2022199797871482,1.942450112897543,3.984156393155894,4.54434527540465,2.0296996414999353,0.13737607943505006,1.9185752702238905,1.936178236004043,1.09217181982563,0.8296851802497076,3.1482133543529707,0.34509134778804684,3.3480802319099694,1.1078935734002084,2.7552541518661524,0.8147713841376285,4.509722103959296,3.952001662903325,2.862176064518243,2.634180128376391,4.045006398294805,2.233942391792399,4.895704495255507,3.947209414602201,4.404214497895229,1.9917633413984106,4.616295983990324,0.7287478002805133,2.6846404509589927,2.768405403916144,2.3081721226484744,1.2056415740325195,4.276061772173444,0.38608167863926557,3.127834801738098,0.34733171194649737,4.032776605508736,3.018735782252432,0.958056303151363,1.944034657641442,3.544728454557521,3.416361188534777,2.8309846909525125,4.688893925766011,4.336980852997742,2.890433830474783,0.483773475277106,1.5377445714383127,1.6076693345876283,4.865063326490639,0.9116093803931797,1.0202108208615073,0.12793447547392275,3.61287728323144,1.5141230689116443,3.457223668125272,2.941604169085093,0.4945370195895873,4.9781305162838905,1.5131255148075629,1.8449295627025688,4.860386196085528,4.183459076470115,3.988294500977622,2.9717959466400514,0.7654798140672716,1.4709425263733704,0.41357114135848805,1.872111952016558,3.400000859154829,2.909011099817953,1.384422894668586,1.6537472567364553,2.219100889550292,3.2416117014327765,3.57615220926095,2.0309693539631217,3.2068577753433316,1.27743854282053,2.7017490767018417,3.7135331556132463,3.3833884830467476,3.2089617343037453,3.8300690341058186,1.2116861030437085,4.093706751465051,2.0518018677523457,1.3621688091055524,3.764439142459866,3.5712726199782034,4.086043637762303,2.9030996488041945,4.132851315560687,1.0527077358558408,0.20765125865383044,1.3340274063381075,1.6920763505996734,4.866398311337427,0.5838723305254645,0.624657552564573,2.755672305925562,1.6707200381584741,0.9597058226192126,4.1014169966731275,0.8686689621800691,3.4893803493351108,3.9927061441603793,4.597437111029905,3.890544934598083,2.980876024040234,1.287169557924301,4.2004899842665475,3.099814874817672,1.6851987532354062,2.1828693241626635,2.4754176348471066,4.3548300750342035,0.5078217449731308,1.8755431437393473,3.943437669771931,2.398776733489535,1.6439987988857732,3.6542014080834866,2.6780474654324937,4.8146413276839795,2.230561092328039,4.1978794146778275,2.8146463689779524,1.0797798276548485,3.368245341240017,2.9924985472893675,1.5764445340559499,0.8077668460985579,0.5091687245454327,4.432911403422255,0.1924343781227077,1.6929681757307122,2.287119578132105,4.728529013077248,2.8222398939455196,2.806476185244594,0.5290226056103666,1.8881759018392856,0.4900939067863139,3.3065747873402787,2.0803824810734586,1.77875752033172,4.11980676524544,0.22444119690383058,3.5506200669178636,2.3313656818867283,3.03589272795927,4.529423414883472,3.5624160954858337,0.20401285715525494,2.3050941940035106,2.601467214558397,3.1017487752446167,3.0235483440044213,2.770986729596427,4.769946986807908,1.236998894240379,2.7488099511593287,1.1176201528987224,2.091717088304415,2.4827895488461635,0.18922848158810124,4.770645696033097,2.901076239848119,0.4362518313823823,0.2731127620254782,0.720240684461033,1.1792149393671665,3.9182685722132216,4.623781710361254,1.8426781788336506,4.574008275153989,2.272289081006674,2.7106393859993427,4.836886522673628,2.4784081774321822,2.0393401994909626,4.704185570116163,3.1451116457835453,3.9456946808665765,3.806693689467229,3.053719884538551,3.2003348794867787,0.8045477513506469,4.564904417578839,3.1870076453847425,4.616407621996272,3.6688487430897885,0.9144441932500731,4.520318176982046,4.17268914749962,3.9362871840098856,3.51833511111574,3.260525129981629,0.583622596621965,0.8088530819227582,4.622563766436512,4.195513995670356,2.2818878323308995,3.7636852155481844,1.8753027046246453,3.994333654032276,0.8435935908669122,4.224163548662894,1.2882339569363044,1.651320321566642,4.31570045960744,2.5014730937003398,4.378563060614963,2.5104978190512606,4.248952964228099,2.3299703226096997,4.634273164183228,4.400466121861999,4.422461279244911,1.4309329564421152,3.801419564304524,4.5916472952279515,1.5676836273899855,1.6816016350824257,2.9805200040365056,0.24115458482847896,4.611421768000086,4.598066059787913,2.251069125598536,1.4015063044059188,0.23731498155691153,4.819048308733043,7.232733616880444,2.533111800569592,6.60381127017283,5.147099727396481,9.293573078690427,3.184806175238288,8.115912044141677,4.740897536432149,3.0616118889759982,4.677962865474118,9.009207397803483,8.28494696070872,1.0313615205349562,8.570262009976707,6.991385188217314,8.739600196893877,1.9386013520433374,1.1273431869410493,4.070537847867976,8.768612894710687,5.155920655205335,2.83418863138213,1.1372129804623297,9.825416183262181,2.9267405943651634,4.034675253931404,9.028141790979074,6.087746400512909,4.794663738154241,8.431060905223804,5.290579512494004,6.764046536651738,6.904776404422832,8.033312145826923,0.9851392432431879,8.78728485908573,6.443915573475752,1.7428536425034624,9.804481615278672,5.999957159407062,5.554971899352366,2.8471916807229194,9.519295489184119,0.5704425057916753,6.45406475643271,2.456798757900435,4.205681212462079,0.8335415161269649,5.72319752184499,2.879527188760722,4.732833040396941,9.60060920389196,2.2086520999040173,5.658204166693851,6.863061621350478,8.224031538483809,3.2382765804207607,0.14284294690095176,3.039611980013721,7.434901821160154,0.12747358090665342,8.194768394677691,8.612338824349528,1.3671064142527767,6.124028005979855,1.7161828526275404,5.791224469026451,6.430997270239341,8.146533530406627,9.702983880402888,5.459659462015682,1.606653689447649,4.347607039062061,0.946180947218237,9.464191900834974,9.606574548651139,2.6374972914223442,7.774890230463125,1.9667559772552694,6.115118159291711,9.501884248905267,3.504169656184825,2.7865315678653366,4.804728469816138,2.751517178752255,0.837971406923037,7.766383235566463,0.9386162170187087,6.422167718597173,5.007532807918477,5.460178486156501,0.6130181813568532,5.10051399070061,2.371732619102601,6.871059593905311,7.278206322094659,1.7212019714769142,7.263377062619343,5.231325907537357,5.614613891670651,9.705919991086185,7.966271403255717,3.11382885935385,7.806377164803533,5.136408739142448,0.8555404640320902,6.653387966882222,9.81300774911406,7.130694505751762,6.2546763135369305,5.215105707520266,6.226109726421377,3.932054232299519,5.346218247814574,7.9681830356159855,3.4934481546166722,3.8733570420015053,7.060098438448211,6.581658631945784,1.4002759420187445,1.5590463808429718,2.7707317146117414,9.528699568712069,0.8150290676077246,5.84299043802833,1.6654147342277228,4.912318266075021,6.308885050813022,3.2188638754975516,9.528707123594913,5.149937309427563,7.913482924322635,8.692902847789044,0.3102091148840749,6.003210334635903,6.15177505346721,2.6383981135014323,1.2944672879217927,8.989304123924509,2.8129983662749636,6.890243875651178,6.5665151524343175,4.844754727240412,6.010515986854159,9.809394867810944,0.228036872442257,5.09226192893818,6.420570417002566,6.928004194243381,5.832508050004096,7.259486366933047,3.7562519424007337,7.65273943918663,4.0848237217001655,1.0004632924119004,5.709985736790666,1.1172895986295797,8.73360099254275,3.9718258257010968,4.89833478041313,4.356786553960766,2.3261756075407325,4.968508722146639,0.5973107179000369,5.643084131388838,2.9002022911982888,5.774864747490652,4.549850219449262,8.94572027966873,5.797162694202454,1.900013769290238,0.5087193025478022,0.5298451351445583,9.618664007864357,6.230120935646064,5.78828085882897,3.732446860225619,5.365161110287824,5.938149754998237,6.508765201269616,9.695369774355834,3.495003610354574,7.000555788298965,1.4653663886942265,8.177279877112449,1.2133087019114572,3.6530015459003096,5.457932039196003,4.066024137037369,1.3862087663601872,3.524805829273854,2.9376823328948998,7.491693383515092,9.328405571120616,2.608505710528546,3.991993074504725,1.6854081338796227,9.463366145374465,3.493233574338961,5.639555449328145,6.814532330837989,5.745244556935825,3.7892133796800636,3.2876391586924325,7.184706442389635,2.167547989836429,3.4128787631732638,4.841870300386654,6.588786873455122,6.349341876811372,3.6049256714213054,7.624767658342103,7.317804309421252,3.936052515699401,7.318975868126769,9.135590911520866,4.234176281891258,8.206366044691146,6.185098671768452,8.480453035150756,3.1839361619327917,6.366998057041344,0.6370602734667473,5.137942899753513,1.8118353712978943,0.3777685243347878,6.170684720688212,7.0884082258942,4.673928865042752,7.576123727581204,6.333105751419154,7.078398782413202,8.71475983985103,4.116186559768981,5.570659774589501,8.457038355575456,7.615160629293223,5.660965227654607,1.0231946302825237,1.3290210518149135,0.36507860653529645,2.3229429195737663,9.450806656601932,9.842189137947067,7.104382623952973,9.305623408856244,4.922466511252683,8.808157989438273,1.5086911623911632,8.339686222698198,1.709235290263497,5.770382285928762,7.626794490394179,6.220151239423588,7.952076190910719,9.855454494856692,3.6682477029758656,5.198654144229501,2.560072091399588,8.872719005206637,7.635558985913849,9.24314107840022,7.432145981648243,0.18485028073403253,1.6459280485263623,7.891931834261916,1.770344010465757,9.30860445888164,6.174282691685972,0.9185872023219771,3.1399983262474027,2.6859662720743147,7.821525057641827,5.298542457829873,1.8634265301235826,5.413931471530988,5.048688803107006,3.4083537240355324,0.16392958277103947,1.1709465103704848,0.4965553208620864,1.8628180256065152,1.490988154549092,4.1132562492845635,2.3920698577476043,4.408591104915289,8.314777635251332,7.315321012326411,2.3127451462527646,1.8338419004821624,3.532098010844675,1.1380786660719255,1.0606225038121837,5.264834860146312,4.619229010023929,1.9869839111407939,4.798355733070753,7.12889923733184,4.461394560610918,5.306204411858702,15.105568588259036,18.172730649785116,17.69768942511893,10.87231278625956,17.695909497055194,2.0858595540482328,16.952807551034844,17.827820269004558,12.685703649034117,19.35201659169696,5.803088244094236,18.45098635009139,15.680537675592356,4.798434519567318,13.854708588528274,16.19721574184127,5.562025313397971,2.2955148131949823,19.184863182072867,11.19256893738697,6.670904934584413,9.15369978061187,2.17712187631296,17.45633424788726,13.140852007638877,16.070413723564993,17.63296670003273,14.404483350733067,10.380287032430362,18.870088392293113,18.699766413870115,18.200916705548817,14.800311313845073,9.50198483661651,0.1961024420208615,0.26432353445974055,10.871168920705298,13.49853440353579,5.932578378230339,9.151546373904537,2.2365781644739524,18.48048031072377,6.730074568848324,11.464650459789624,15.434288176218327,12.773278618717134,14.668226955209382,4.752562378803772,10.16399243414975,13.889551679602091,12.799284214198833,17.356176243621633,12.730815022490226,12.20469419910514,13.890335797747209,13.064842074143359,17.728922416446522,14.735194770704856,5.55745556190767,16.439543015023045,17.817899604909098,2.445114038149453,13.847852197392937,7.41215111874882,11.132818568511668,7.874387217083624,7.7380562615598825,15.901013816465122,13.190505570747064,16.382399748895274,19.29532748282334,14.444186871301103,19.20370076465012,3.9567726770535154,1.7520686483029762,17.649925492560175,2.4272225051361795,4.660145435263661,6.8214760230114795,8.007939183989047,2.217783782020216,1.090312807809837,4.449533021909361,12.767000075722871,12.696972066297144,18.562335081121745,7.491436369916795,15.869789206731,8.814864168681968,19.99830435301551,6.329829792758884,6.675215655409495,8.765518298388688,19.634402589986518,11.484019535718438,18.462459274728694,17.78735785749913,6.7179010540824144,15.788087536575892,9.641448771081281,18.18294539934914,16.896813127653967,7.358262306170094,2.1406948803061554,3.8061518944266726,17.33518657891634,11.820425177417292,1.4980073780921068,9.227321163546216,0.9097719244366363,5.221500937482935,4.920988783692519,5.193496784307989,7.349999614932051,15.373819275912576,0.14430214695835317,3.783482536971065,7.274382959731691,7.682226564619069,10.304560125508257,16.540592584426427,13.057440983104053,7.860302744867465,2.859154605295148,4.719548539652955,16.99165400695512,8.376704567902468,15.952274725658256,5.460657253338596,4.967584663418241,9.637664753188119,4.540072403974982,18.474062711722606,11.613467450954047,9.329595095287777,19.299950955824034,8.967770655554506,14.303853221286419,15.084082741538358,19.139095424774112,19.868913501248528,2.6730809571240672,19.618879884190374,1.2244666915503633,16.136242259367506,4.403033130424545,3.587001269590104,5.6577438643425735,1.383680706857922,4.466253753600737,4.439713104002936,4.261982610767225,13.158166649258712,6.4354180905887715,4.3882083355289625,17.179282128890172,13.856975042936826,8.041777579955303,12.753861920620187,12.139884567850771,2.3239973882877756,14.316658210289939,5.7848172503351085,9.464319521987585,4.480768085582558,19.79170994487254,6.060273963780888,8.493703424419424,7.354541201425219,15.185860563368808,13.874989261363918,18.762767842359647,10.234846883402618,0.1863665494070389,2.546966723741308,9.626524227599095,16.927549088581966,15.810228462712674,2.413934446638952,13.979354507553607,5.306796075040392,17.459426429605546,13.829105264384244,16.370077783510705,19.042672541548566,14.251034195845074,1.8255873269354532,13.280163508806869,2.579792087958739,19.256691563331753,19.732158644831788,10.678709702689064,12.910281727386613,12.133095093472338,8.005939452743183,2.8554155655392703,15.572709363533647,3.013115274326549,7.694088103417794,1.8414308140993643,7.24061499057059,1.4312368833715676,1.5269277890660922,1.16679608092624,16.108115809090727,5.0107435418324435,16.466157462638684,7.188803327050215,12.768807908096056,2.4942341839418356,5.320535215810323,12.01977481764481,7.014850217148017,14.218833136678153,13.896578040869839,8.705588740768716,0.6974443868487711,7.418017479545383,16.632959425996614,11.863033816330244,4.0176594238926535,15.018834046876412,13.99557009823033,12.823250768211029,19.771139068268518,8.859349682937493,10.25495994518089,15.186914529539832,9.755126085534645,4.787187531361194,2.5478788763733764,9.967864006888048,5.9213881300851785,9.196194151751307,7.145258425523292,12.745708338437689,8.500141521390834,12.74405011932035,9.090139011315456,3.373476968839762,7.3267470424629995,0.6489255959856487,13.39708031886753,13.90667897017658,3.1847598132621555,1.7999923324699305,0.7013543404674435,18.669377484853904,3.7080857212791978,3.201165217462127,4.207811944371462,14.115168796764372,13.091005032499341,12.705904142396582,11.373243299302196,4.131280874751754,11.391152508385058,17.81390450110983,1.260006165605522,6.406614509059932,17.555907328784457,4.324657793400211,10.280590807691029,4.351972682348412,0.33940779847077857,19.535233791411198,19.887792552400956,12.641744456873731,15.85089110931164,19.97678514742204,9.67491692897622,1.4361375965553422,2.5227697627852623,16.09237263791612,5.4183870455298795,0.8835480350254572,17.729392714391334,13.889161485515741,13.574169248501617,0.3712903240334786,9.022568886094694,6.673569504905864,9.86279002407333,4.788868413330838,5.065822267905727,6.680260169274106,11.929625070548957,14.42127204024335,13.737797369799601,19.024989472284936,14.32395258229531,2.407261324685206,17.475952361358377,19.667023304943076,17.957879893356065,10.640284868152406,6.854165282988872,12.979075057976049,16.3252537500453,12.496576834569307,4.965915491499896,19.812896130426232,15.826630242092172,14.697046137924833,10.190520443897253,17.5101620303848,1.786143251293094,4.1284146103775345,15.718249870319305,5.75091979908366,11.745646066118077,13.600109525407268,17.735167639697636,2.5997145164175484,7.476458917094795,19.30505407743273,15.847417121132198,9.135957712758023,5.219423279040718,6.884347752485269,14.428177561207406,4.822403766595187,8.839283217801258,2.43363574252294,12.111709224126285,0.6949458871240134,13.520071627450191,1.6724517230328868,5.596998890470679,4.184208179351566,9.462014938712345,11.408859626452697,11.094724427638113,2.406657479608215,5.91252503916684,6.673125769546815,6.3255426041160066,10.743176189447711,19.030833487462598,4.0463164936588,16.788558824319054,10.47277934029046,2.10782820418945,10.247038530226142,15.82264473108352,4.614667257175094,1.5123997210557334,17.259693267851503,11.532048518811452,12.340108940279313,12.882175923891653,1.4806565374492298,0.6517827895692471,4.797869197030258,8.692019697104323,2.869695543048978,6.494946381446894,7.463879740315233,16.77832504375182,15.097767739279162,6.139394324067882,0.8058231966920184,19.87773634736269,8.410746492101904,15.096619579743768,16.011690462926627,14.634106217330707,0.9696911743961955,11.289805417281972,10.125073328873482,10.201892116441607,15.627630847211066,10.95247480224291,15.61092563852357,18.784885196394317,4.568752245772708,6.296600313880429,17.489359640972495,0.5205467321157897,15.28371503244666,18.820119134350218,11.964444632978415,7.899272180022857,11.150014758796509,10.43099911483914,11.623015963416064,7.0737472629967435,11.426116559528602,19.632398643728763,19.447185210094343,2.74483122614334,18.65604797510561,10.879276863367618,8.585409008195693,14.958880361863304,7.7757437225732,7.647446123733779,19.42656404736823,7.973916340976721,13.310117824391675],"expected":[0,0,0,0,0.8463145335508915,0,0,0,0,0,0,0.19452444591438392,0,0,0,0,0,0,0.31897594235778454,0,0,0,0,0,0.14641162457166765,0,0,0,0.10468056354543429,0,0,0.21871674645536873,0.22819287604843136,0,0,0,0,0,0,0,0,0,0,0.1807409546031063,0,0,0.3678128467711849,0,0,0,0.0838954012078354,0,0,0.22086544827418578,0.04039832400363158,0,0.20879181007392397,0,0,0,0,0,0.1834612718465585,0.21789563320879177,0,0,0.18123557889442318,0,0,0,0,0,0,0,0,0,0,0.29743137329998565,0,0,0,0.17991909683595134,0,0,0.24222594539802467,0,0,0,0,0,0,0.1426345915997203,0,0.029481924032776097,0,0,0,0,0.3097185100614857,0,0,0,0,0,0.08531959655236868,0,0,0,0.2738690826208324,0.298169985551804,0,0.0009165219236778883,0,0,0,0,0,0,0,0,0.017169024026624746,0,0.18914216590126748,0,0,0.018485227176959967,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.31160198138213446,0,0,0,0,0,0,0.43766195730797186,0,0,0,0,0,0,0,0,0,0,0.7300656307498341,0.5417897788807962,0.022661255272120172,0,1.3486124504459722,0,0,0,0.18447287341531185,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.20571801468894105,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.7195860614847046,0,0,0,0,0,0,0.21879996429079995,0,0,0,0,0,0.09270415024608324,0,0,0,0,0.125185972957126,0,0,0,0.09008722081936049,0,0.2318846657390104,0,0,0,0,0,0,0,0,0.21899812217202366,0,0,0,0,0,0,0,0.08367665791542722,0,0,0,0.16438511464671657,0,0,0,0,0.07923192483916454,0,0,0,0,0.22888676943281328,0.21380431277312995,0.00044422861428098054,0.2254538494647244,0.6890748375554138,0,0.0030244162356903095,0,0.20667444898698742,0,0,0,0.017943112731387018,0,0,0,0,0,0.3759968695514802,0.10720874441327662,0,0,0,0,0,0,0,0.11033497829478744,0,0,0,0,0,0,0,0,0.09243479474959003,0,0,0,0.07964091334998114,0,0,0.08299763194241767,0,0,0.11785000412667995,0,0,0,0.09242295086922633,0,0,0,0,0.10000024627952703,0.07414670679790691,0,0,0.026609624939870145,0,0,0,0,0,0,0,0,0.08958392793073112,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.005799241023717062,0,0.024839012416335318,0,0,0,0,0.036515416873935926,0,0,0,0.18698076725056814,0,0,0,0,0.09194802405918436,0.07492768361207598,0,0,0,0,0.12352405876783476,0.1261200674033477,0,0,0,0.17313866646091497,0.10008121363194473,0,0,0,0.16991819981518913,0,0.0492679760010395,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.00005312768161656613,0,0,0,0,0,0,0,0,0,0.1000257656642096,0,0.09023335249962933,0,0,0,0,0,0.1334613537231389,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.002823443668335631,0,0.10997481815235509,0,0,0,0,0,0,0,0,0.14295370547927283,0,0,0,0,0,0,0,0.14967225173152887,0,0,0,0,0,0.025597004195318775,0,0,0,0,0,0,0,0,0,0,0,0,0.09721946825658397,0,0.12676998458560806,0,0,0,0,0,0.16191155619224706,0,0,0,0,0,0,0.05733939009272669,0,0,0,0.12622776300929042,0.23751654504430672,0,0,0,0,0,0.06401797161221949,0,0,0,0,0,0,0,0,0,0.06322140247182924,0,0,0,0,0.17933603773893791,0,0.08364666988584978,0,0,0,0,0,0.07123373627747905,0,0,0.04428926286974858,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.07894624230204624,0,0,0,0,0.12243790397586955,0,0,0.16152102667458348,0,0,0,0.05487790319269133,0,0.4421508657568099,0,0,0,0,0,0,0,0,0,0.24792401221127186,0.19747083921130731,0,0,0.159081728618727,0,0,0,0,0,0.21575641637724255,0,0.1746603958851553,0.11961331115318578,0,0,0,0.043115210902188256,0.05644574001169157,0,0,0,0,0,0,0.016745397754130968,0,0,0,0,0,0.0373617379074685,0,0,0,0,0,0,0,0,0,0,0.03800501482785702,0,0,0,0.029259375962122948,0,0,0,0,0,0,0,0,0,0,0,0,0,0.04178830483944883,0,0,0,0,0,0,0,0,0,0,0,0.023521735438718376,0,0,0.017396855670118637,0.052027064673997196,0,0.004723598710275674,0,0,0.05020518149766379,0,0,0,0,0,0,0.039671791120161976,0.0019176803484242768,0,0,0,0,0,0,0,0,0,0,0,0.05170259955738721,0,0,0,0,0,0.11969630567544855,0,0.019032167147965726,0,0.042718096320313856,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.056259219544222444,0,0,0,0,0.03412056084068833,0,0,0,0,0,0,0,0,0,0.033648015503465314,0,0,0.06629244793050171,0.03623204175497126,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.11426008100330845,0,0.04157095107754705,0,0,0,0,0,0,0,0,0,0,0.067784167673367,0,0,0,0,0,0.04185467556651881,0.01881671141111436,0,0,0.14658532655393158,0.024451367176843125,0,0,0,0,0,0,0,0,0,0.08854738276770181,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.027507131108260842,0,0,0,0,0,0,0,0.054588717414497216,0,0,0,0.04674047380646887,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.04832118081631429,0,0.11178290434824373,0,0,0,0,0,0,0,0.12187592156087913,0,0,0,0,0,0,0,0,0.05429524320014127,0,0,0,0,0,0,0,0.042047152041949865,0,0,0,0,0,0,0.04804701206209943,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.03639016974087764,0,0,0,0,0,0,0,0,0,0,0,0,0.05019044847649928,0,0.0649852101734583,0,0,0,0,0,0,0,0,0,0,0,0,0,0.08006662139203026,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.02617151875999858,0,0,0,0,0,0.05032018554205387,0,0,0,0,0,0.06292187963272997,0,0,0.05695464043924793,0.011141707245646403,0.06523330139372947,0,0,0,0,0,0,0,0,0,0,0,0,0.036458366050297064,0,0.060026367255215915,0,0.005564835857110959,0,0,0.09162776207212839,0,0,0,0.022223456879794233,0,0,0,0,0,0.06540192385531349,0.04771550351271556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.07492775183648416]} diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/fixtures/python/runner.py b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/fixtures/python/runner.py new file mode 100644 index 000000000000..bead71752960 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/fixtures/python/runner.py @@ -0,0 +1,98 @@ +#!/usr/bin/env python +# +# @license Apache-2.0 +# +# Copyright (c) 2026 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. + +"""Generate PDF fixtures for Anglit distribution.""" + +import os +import json +import numpy as np +from scipy.stats import anglit + + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + + +def gen(x, loc, sigma, name): + """Generate fixture data and write to file. + + # Arguments + + * `x`: input values + * `loc`: location parameter + * `sigma`: scale parameter + * `name::str`: output filename + + # Examples + + ``` python + python> x = np.random.uniform(0.0, 10.0, 300) + python> loc = np.random.uniform(0.0, 10.0, 300) + python> sigma = np.random.uniform(0.1, 5.0, 300) + python> gen(x, loc, sigma, './data.json') + ``` + """ + z = anglit.pdf(x, loc=loc, scale=sigma) + + # Store data to be written to file as a dictionary: + data = { + "x": x.tolist(), + "mu": loc.tolist(), + "sigma": sigma.tolist(), + "expected": z.tolist() + } + + # Based on the script directory, create an output filepath: + filepath = os.path.join(DIR, name) + + # Write the data to the output filepath as JSON: + with open(filepath, "w", encoding="utf-8") as outfile: + json.dump(data, outfile) + + +def main(): + """Generate fixture data.""" + # Set seed for reproducibility: + np.random.seed(457) + + # Generate data for three different ranges of input values and parameters: + x_small = np.random.uniform(-10.0, 10.0, 300) + loc_small = np.random.uniform(-5.0, 5.0, 300) + sigma_small = np.random.uniform(0.1, 5.0, 300) + + x_med = np.random.uniform(-20.0, 20.0, 300) + loc_med = np.random.uniform(-10.0, 10.0, 300) + sigma_med = np.random.uniform(0.1, 10.0, 300) + + x_large = np.random.uniform(-50.0, 50.0, 400) + loc_large = np.random.uniform(-20.0, 20.0, 400) + sigma_large = np.random.uniform(0.1, 20.0, 400) + + # Concatenate arrays + x = np.concatenate([x_small, x_med, x_large]) + loc = np.concatenate([loc_small, loc_med, loc_large]) + sigma = np.concatenate([sigma_small, sigma_med, sigma_large]) + + gen(x, loc, sigma, "data.json") + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.factory.js new file mode 100644 index 000000000000..8c38761b5c06 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.factory.js @@ -0,0 +1,142 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var factory = require( './../lib/factory.js' ); + + +// FIXTURES // + +var data = require( './fixtures/python/data.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof factory, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns a function', function test( t ) { + var pdf = factory( 0.0, 1.0 ); + t.strictEqual( typeof pdf, 'function', 'returns expected value' ); + t.end(); +}); + +tape( 'if provided `NaN` for any parameter, the created function returns `NaN`', function test( t ) { + var pdf; + var y; + + pdf = factory( 0.0, 1.0 ); + y = pdf( NaN ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + pdf = factory( NaN, 1.0 ); + y = pdf( 0.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + pdf = factory( 1.0, NaN ); + y = pdf( 0.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + pdf = factory( NaN, NaN ); + y = pdf( 0.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided finite `mu` and `sigma`, the created function returns `0` when provided `+infinity` for `x`', function test( t ) { + var pdf; + var y; + + pdf = factory( 0.5, 1.0 ); + y = pdf( PINF ); + t.strictEqual( y, 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided finite `mu` and `sigma`, the created function returns `0` when provided `-infinity` for `x`', function test( t ) { + var pdf; + var y; + + pdf = factory( 0.5, 1.0 ); + y = pdf( NINF ); + t.strictEqual( y, 0.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided `sigma <= 0`, the created function always returns `NaN`', function test( t ) { + var pdf; + var y; + + pdf = factory( 0.0, -1.0 ); + + y = pdf( 2.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + pdf = factory( 0.0, 0.0 ); + y = pdf( 2.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + pdf = factory( 0.0, NINF ); + y = pdf( 2.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the created function evaluates the pdf for `x` given `mu` and `sigma`', function test( t ) { + var expected; + var sigma; + var pdf; + var mu; + var x; + var y; + var i; + + expected = data.expected; + x = data.x; + mu = data.mu; + sigma = data.sigma; + + for ( i = 0; i < x.length; i++ ) { + pdf = factory( mu[i], sigma[i] ); + y = pdf( x[i] ); + if ( y === expected[i] ) { + t.strictEqual(y, expected[i], 'x: '+x[i]+', mu: '+mu[i]+', sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i]); + } else { + t.ok( isAlmostSameValue( y, expected[i], 1 ), 'within tolerance. x: '+x[i]+'. mu: '+mu[i]+'. sigma: '+sigma[i]+'. y: '+y+'. expected: '+expected[i]+'.' ); + } + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.js new file mode 100644 index 000000000000..e2e51b8221dd --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.js @@ -0,0 +1,38 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 tape = require( 'tape' ); +var pdf = require( './../lib' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof pdf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'attached to the main export is a factory method for generating `pdf` functions', function test( t ) { + t.strictEqual( typeof pdf.factory, 'function', 'exports a factory method' ); + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.main.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.main.js new file mode 100644 index 000000000000..f81edc7c26b0 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.main.js @@ -0,0 +1,106 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var pdf = require( './../lib' ); + + +// FIXTURES // + +var data = require( './fixtures/python/data.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof pdf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'if provided `NaN` for any parameter, the function returns `NaN`', function test( t ) { + var y = pdf( NaN, 0.0, 1.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0, NaN, 1.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0, 0.0, NaN ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided `+infinity` for `x` and finite `mu` and `sigma`, the function returns `0`', function test( t ) { + var y = pdf( PINF, 0.0, 1.0 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided `-infinity` for `x` and finite `mu` and `sigma`, the function returns `0`', function test( t ) { + var y = pdf( NINF, 0.0, 1.0 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided `sigma <= 0`, the function returns `NaN`', function test( t ) { + var y; + + y = pdf( 0.0, 0.0, -1.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0, 0.0, 0.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0, 0.0, NINF ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function evaluates the pdf for `x` given `mu` and `sigma`', function test( t ) { + var expected; + var sigma; + var mu; + var x; + var y; + var i; + + expected = data.expected; + x = data.x; + mu = data.mu; + sigma = data.sigma; + + for ( i = 0; i < x.length; i++ ) { + y = pdf( x[i], mu[i], sigma[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i], 'x: '+x[i]+', mu: '+mu[i]+', sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] ); + } else { + t.ok( isAlmostSameValue( y, expected[i], 1 ), 'within tolerance. x: '+x[i]+'. mu: '+mu[i]+'. sigma: '+sigma[i]+'. y: '+y+'. expected: '+expected[i]+'.' ); + } + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.native.js new file mode 100644 index 000000000000..b3e29011fe83 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/anglit/pdf/test/test.native.js @@ -0,0 +1,115 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 tape = require( 'tape' ); +var tryRequire = require( '@stdlib/utils/try-require' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); + + +// FIXTURES // + +var data = require( './fixtures/python/data.json' ); + + +// VARIABLES // + +var pdf = tryRequire( resolve( __dirname, './../lib/native.js' ) ); +var opts = { + 'skip': ( pdf instanceof Error ) +}; + + +// TESTS // + +tape( 'main export is a function', opts, function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof pdf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'if provided `NaN` for any parameter, the function returns `NaN`', opts, function test( t ) { + var y = pdf( NaN, 0.0, 1.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0, NaN, 1.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0, 0.0, NaN ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'if provided `+infinity` for `x` and finite `mu` and `sigma`, the function returns `0`', opts, function test( t ) { + var y = pdf( PINF, 0.0, 1.0 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided `-infinity` for `x` and finite `mu` and `sigma`, the function returns `0`', opts, function test( t ) { + var y = pdf( NINF, 0.0, 1.0 ); + t.strictEqual( y, 0.0, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided `sigma <= 0`, the function returns `NaN`', opts, function test( t ) { + var y; + + y = pdf( 0.0, 0.0, -1.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0, 0.0, 0.0 ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + y = pdf( 0.0, 0.0, NINF ); + t.strictEqual( isnan( y ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function evaluates the pdf for `x` given `mu` and `sigma`', opts, function test( t ) { + var expected; + var sigma; + var mu; + var x; + var y; + var i; + + expected = data.expected; + x = data.x; + mu = data.mu; + sigma = data.sigma; + + for ( i = 0; i < x.length; i++ ) { + y = pdf( x[i], mu[i], sigma[i] ); + if ( y === expected[i] ) { + t.strictEqual( y, expected[i], 'x: '+x[i]+', mu: '+mu[i]+', sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] ); + } else { + t.ok( isAlmostSameValue( y, expected[i], 1 ), 'within tolerance. x: '+x[i]+'. mu: '+mu[i]+'. sigma: '+sigma[i]+'. y: '+y+'. expected: '+expected[i]+'.' ); + } + } + t.end(); +});