diff --git a/lib/node_modules/@stdlib/math/base/special/beta/README.md b/lib/node_modules/@stdlib/math/base/special/beta/README.md new file mode 100644 index 000000000000..57a8bc8c20de --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/README.md @@ -0,0 +1,76 @@ +beta +=== +> [Beta function][beta-function]. + + +The [Beta function][beta-function], also called the Euler integral, is defined as + + +
+ Equation for the beta function. +
+
+ + +It is related to the [Gamma function][gamma-function] via the following equation + + +
+ Beta function expressed in terms of the Gamma function. +
+
+ + + + +## Usage + +``` javascript +var beta = require( '@stdlib/math/base/special/beta' ); +``` + + +#### beta( x, y ) + +Evaluates the the [Beta function][beta-function]. + +``` javascript +var val = beta( 0, 0 ); +// returns +Infinity + +val = beta( 1, 1 ); +// returns 1 + +val = beta( -1, 2 ); +// return NaN + +val = beta( 5, 0.2 ); +// returns ~3.382 + +val = beta( 4, 1 ); +// returns 0.25 +``` + + + +## Examples + +``` javascript +var beta = require( '@stdlib/math/base/special/beta' ); + +for ( var x = 0; x < 10; x++ ) { + for ( var y = 10; y > 0; y-- ) { + console.log( 'x: %d, \t y: %d, \t f(x,y): %d', x, y, beta( x, y ) ); + } +} +``` + + + +[beta-function]: http://en.wikipedia.org/wiki/Beta_function +[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function + diff --git a/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/arg1.json b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/arg1.json new file mode 100644 index 000000000000..d278951545a1 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/arg1.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/arg2.json b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/arg2.json new file mode 100644 index 000000000000..3886d24ad6bd --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/arg2.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/expected.json b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/expected.json new file mode 100644 index 000000000000..cfdd2d848f42 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/expected.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/runner.R b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/runner.R new file mode 100644 index 000000000000..4fadaab97c29 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/fixtures/runner.R @@ -0,0 +1,15 @@ +# To run this script, `cd` to the `./benchmark/fixtures` directory and then, from the R shell, `source("./runner.R")`. +options( digits = 16 ); +library( jsonlite ); + +set.seed( 329 ) + +x = sample( seq( 0.5, 100, by = 0.25 ), 1000, replace = TRUE ) +y = sample( seq( 0.5, 100, by = 0.25 ), 1000, replace = TRUE ) +v = beta( x, y ) + +cat( v, sep = ",\n" ) + +write( toJSON( x, digits = 16, auto_unbox = TRUE ), "./arg1.json" ) +write( toJSON( y, digits = 16, auto_unbox = TRUE ), "./arg2.json" ) +write( toJSON( v, digits = 16, auto_unbox = TRUE ), "./expected.json" ) diff --git a/lib/node_modules/@stdlib/math/base/special/beta/benchmark/index.js b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/index.js new file mode 100644 index 000000000000..876106e7cc93 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/index.js @@ -0,0 +1,69 @@ +'use strict'; + +// MODULES // + +var betaOld = require( './naive.js' ); +var beta = require( './../lib/index.js' ); + + +// VARIABLES // + +var len; +var i; +var res = new Array( 2 ); +var start; +var stop; +var x; +var y; +var out; + + +// FIXTURES // + +var arg1 = require( './fixtures/arg1.json' ); +var arg2 = require( './fixtures/arg2.json' ); + + +// -------------------------------------- +// WARM-UP + +len = arg1.length; +for ( i = 0; i < len; i++ ) { + i = i; +} + +// -------------------------------------- +// BENCHMARK + +// Beta( old ) + + +start = process.hrtime(); +for ( i = 0; i < len; i++ ) { + x = arg1[ i ]; + y = arg2[ i ]; + out = betaOld( x, y ); +} +stop = process.hrtime( start ); + +res[ 0 ] = stop[ 0 ] + stop[ 1 ]*1e-9; + + +// Beta( new ) + +start = process.hrtime(); +for ( i = 0; i < len; i++ ) { + x = arg1[ i ]; + y = arg2[ i ]; + out = beta( x, y ); +} +stop = process.hrtime( start ); + +res[ 1 ] = stop[ 0 ] + stop[ 1 ]*1e-9; + +// -------------------------------------- +// RESULTS + +console.log( 'Beta( old ):\t%d ops/sec', Math.floor( len/res[ 0 ] ) ); +console.log( 'Beta( new ):\t%d ops/sec', Math.floor( len/res[ 1 ] ) ); +console.log( '\n' ); diff --git a/lib/node_modules/@stdlib/math/base/special/beta/benchmark/naive.js b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/naive.js new file mode 100644 index 000000000000..c67f89f4d547 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/benchmark/naive.js @@ -0,0 +1,41 @@ +'use strict'; + +// MODULES // + +var betaln = require( '@stdlib/math/base/special/betaln' ); +var exp = require( '@stdlib/math/base/special/exp' ); +var gamma = require( '@stdlib/math/base/special/gamma' ); + + +// CONSTANTS // + +var GAMMA_XMAX = 171.61447887182298; + + +// BETA // + +/** +* FUNCTION: beta( x, y ) +* Evaluates the beta function. +* +* @param {Number} x - input value +* @param {Number} y - input value +* @returns {Number} evaluated beta function +*/ +function beta( x, y ) { + if ( x < 0 || y < 0 ) { + return NaN; + } + if ( x === 0 || y === 0 ) { + return Number.POSITIVE_INFINITY; + } + if ( x + y > GAMMA_XMAX ) { + return exp( betaln( x, y ) ); + } + return gamma( x ) * gamma( y ) / gamma( x + y ); +} // end FUNCTION beta() + + +// EXPORTS // + +module.exports = beta; diff --git a/lib/node_modules/@stdlib/math/base/special/beta/examples/index.js b/lib/node_modules/@stdlib/math/base/special/beta/examples/index.js new file mode 100644 index 000000000000..069ac1dfb986 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/examples/index.js @@ -0,0 +1,9 @@ +'use strict'; + +var beta = require( './../lib' ); + +for ( var x = 0; x < 10; x++ ) { + for ( var y = 10; y > 0; y-- ) { + console.log( 'x: %d, \t y: %d, \t beta(x,y): %d', x, y, beta( x, y ) ); + } +} diff --git a/lib/node_modules/@stdlib/math/base/special/beta/lib/beta.js b/lib/node_modules/@stdlib/math/base/special/beta/lib/beta.js new file mode 100644 index 000000000000..f8a17c5aa8d6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/lib/beta.js @@ -0,0 +1,177 @@ +'use strict'; + +/** +* NOTE: the original C++ code and copyright notice is from the [Boost library]{http://www.boost.org/doc/libs/1_52_0/boost/math/special_functions/beta.hpp}. +* +* The implementation has been modified for JavaScript. +*/ + +/** +* (C) Copyright John Maddock 2006. +* Use, modification and distribution are subject to the +* Boost Software License, Version 1.0. (See accompanying file +* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) +*/ + +// MODULES // + +var abs = require( '@stdlib/math/base/special/abs' ); +var exp = require( '@stdlib/math/base/special/exp' ); +var evalrational = require( '@stdlib/math/base/tools/evalrational' ).factory; +var gamma = require( '@stdlib/math/base/special/gamma' ); +var log1p = require( '@stdlib/math/base/special/log1p' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var sqrt = require( '@stdlib/math/base/special/sqrt' ); +var isnan = require( '@stdlib/math/base/utils/is-nan' ); + + +// CONSTANTS // + +var E = require( '@stdlib/math/constants/float64-e' ); +var EPSILON = require( '@stdlib/math/constants/float64-eps' ); + +// LANCZOS APPROXIMATION CONSTANTS // + +var G = 10.90051099999999983936049829935654997826; +var NUM = [ + 709811.662581657956893540610814842699825, + 679979.847415722640161734319823103390728, + 293136.785721159725251629480984140341656, + 74887.5403291467179935942448101441897121, + 12555.29058241386295096255111537516768137, + 1443.42992444170669746078056942194198252, + 115.2419459613734722083208906727972935065, + 6.30923920573262762719523981992008976989, + 0.2266840463022436475495508977579735223818, + 0.004826466289237661857584712046231435101741, + 0.4624429436045378766270459638520555557321e-4 +]; +var DENOM = [ + 0, + 362880, + 1026576, + 1172700, + 723680, + 269325, + 63273, + 9450, + 870, + 45, + 1 +]; + + +// FUNCTIONS // + +/** +* Calculate the Lanczos approximation scaled by exp(G). +* +* @private +* @param {Number} z - input value +* @returns {Number} Lanczos approximation +*/ +var lanczos_sum_expG_scaled = evalrational( NUM, DENOM ); + + +// BETA // + +/** +* Evaluate the beta function. +* +* @param {Number} x - input value +* @param {Number} y - input value +* @returns {Number} evaluated beta function +* +* @example +* var v = beta( 0, 0 ); +* // returns +Infinity +* @example +* var v = beta( 1, 1 ); +* // returns 1 +* @example +* var v = beta( -1, 2 ); +* // return NaN +* @example +* var v = beta( 5, 0.2 ); +* // returns ~3.382 +* @example +* var v = beta( 4, 1 ); +* // returns 0.25 +* @example +* var v = beta( NaN, 2 ); +* // returns NaN +*/ +function beta( a, b ) { + if ( isnan( a ) || isnan( b ) ) { + return NaN; + } + if ( a < 0 || b < 0 ) { + return NaN; + } + if ( b === 1 ) { + return 1 / a; + } else if( a === 1 ) { + return 1 / b; + } + var result; + var prefix = 1; + var tmp; + var agh, bgh, cgh; + var ambh; + var c = a + b; + + // Special cases: + if ( (c === a) && (b < EPSILON) ) { + return gamma( b ); + } else if ( (c === b) && (a < EPSILON) ) { + return gamma( a ); + } + + // Shift to a and b > 1 if required: + if ( a < 1 ) { + prefix *= c / a; + c += 1; + a += 1; + } + if ( b < 1 ) { + prefix *= c / b; + c += 1; + b += 1; + } + if ( a < b ) { + // Swap a and b: + tmp = b; + b = a; + a = tmp; + } + + // Lanczos calculation: + agh = a + G - 0.5; + bgh = b + G - 0.5; + cgh = c + G - 0.5; + result = lanczos_sum_expG_scaled( a ) * lanczos_sum_expG_scaled( b ) / lanczos_sum_expG_scaled( c ); + ambh = a - 0.5 - b; + if( ( abs( b * ambh ) < (cgh * 100) ) && (a > 100) ) { + // Special case where the base of the power term is close to 1 + // compute (1+x)^y instead: + result *= exp( ambh * log1p( -b / cgh ) ); + } else { + result *= pow( agh / cgh, a - 0.5 - b ); + } + if ( cgh > 1e10 ) { + // This avoids possible overflow, but appears to be marginally less accurate: + result *= pow( (agh / cgh) * (bgh / cgh), b); + } else { + result *= pow((agh * bgh) / (cgh * cgh), b); + } + result *= sqrt( E / bgh); + + // If a and b were originally less than 1 we need to scale the result: + result *= prefix; + return result; +} // end FUNCTION beta() + + +// EXPORTS // + +module.exports = beta; diff --git a/lib/node_modules/@stdlib/math/base/special/beta/lib/index.js b/lib/node_modules/@stdlib/math/base/special/beta/lib/index.js new file mode 100644 index 000000000000..d0c68e55edf2 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/lib/index.js @@ -0,0 +1,37 @@ +'use strict'; + +/** +* Evaluate the beta function. +* +* @module @stdlib/math/base/special/beta +* +* @example +* var beta = require( '@stdlib/math/base/special/beta' ); +* +* var v = beta( 0, 0 ); +* // returns +Infinity +* +* v = beta( 1, 1 ); +* // returns 1 +* +* v = beta( -1, 2 ); +* // return NaN +* +* v = beta( 5, 0.2 ); +* // returns ~3.382 +* +* v = beta( 4, 1 ); +* // returns 0.25 +* +* v = beta( NaN, 2 ); +* // returns NaN +*/ + +// MODULES // + +var beta = require( './beta.js' ); + + +// EXPORTS // + +module.exports = beta; diff --git a/lib/node_modules/@stdlib/math/base/special/beta/package.json b/lib/node_modules/@stdlib/math/base/special/beta/package.json new file mode 100644 index 000000000000..9e584e4e9572 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/package.json @@ -0,0 +1,26 @@ +{ + "name": "", + "version": "", + "description": "Beta function.", + "author": {}, + "contributors": [], + "scripts": {}, + "main": "./lib", + "repository": {}, + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "special function", + "special", + "function", + "beta", + "gamma", + "number" + ], + "bugs": {}, + "dependencies": {}, + "devDependencies": {}, + "license": "MIT AND BSL-1.0" +} diff --git a/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/DESCRIPTION b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/DESCRIPTION new file mode 100644 index 000000000000..79829374d5e2 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/DESCRIPTION @@ -0,0 +1,9 @@ +Package: betafixtures +Title: beta test fixtures +Version: 0.0.0 +Authors@R: person("stdlib", "js", role = c("aut","cre")) +Description: Generates beta test fixtures. +Depends: R (>=3.0.0) +Imports: + jsonlite +LazyData: true diff --git a/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/arg1.json b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/arg1.json new file mode 100644 index 000000000000..60e2f0dae008 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/arg1.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/arg2.json b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/arg2.json new file mode 100644 index 000000000000..428c3d83583e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/arg2.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/expected.json b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/expected.json new file mode 100644 index 000000000000..0e0b0d3786a9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/expected.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/runner.R b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/runner.R new file mode 100644 index 000000000000..f32b4cc266eb --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/test/fixtures/r/runner.R @@ -0,0 +1,53 @@ +#!/usr/bin/env Rscript + +# Set the precision to 16 digits: +options( digits = 16 ); + +#' Get the script filepath. +#' +#' @return full path to this script +#' +#' @examples +#' filepath <- get_script_path() +get_script_path <- function() { + cmdArgs <- commandArgs( trailingOnly = FALSE ); + needle <- "--file="; + match <- grep( needle, cmdArgs ); + if ( length( match ) > 0 ) { + # Rscript: + filepath <- sub( needle, "", cmdArgs[match] ); + } else { + ls_vars <- ls( sys.frames()[[1]] ) + if ( "fileName" %in% ls_vars ) { + # Source'd via RStudio: + filepath <- sys.frames()[[1]]$fileName; + } else { + # Source'd via R console: + filepath <- sys.frames()[[1]]$ofile; + } + } + return( normalizePath( filepath ) ); +} + +# TODO: better and more comprehensive tests + +# Generate test fixture data: +x <- sample( seq( 0.5, 100, by = 0.25 ), 1000, replace = TRUE ) +y <- sample( seq( 0.5, 100, by = 0.25 ), 1000, replace = TRUE ) +z <- beta( x, y ) + +# Deal with NaNs: +cat( y, sep = ",\n" ); + +# Get the directory of this script: +sourceDir <- dirname( get_script_path() ); + +# Write the data to file... +out <- paste( sourceDir, "/arg1.json", sep = "" ); +write( jsonlite::toJSON( x, digits = 16, auto_unbox = TRUE ), out ); + +out <- paste( sourceDir, "/arg2.json", sep = "" ); +write( jsonlite::toJSON( y, digits = 16, auto_unbox = TRUE ), out ); + +out <- paste( sourceDir, "/expected.json", sep = "" ); +write( jsonlite::toJSON( z, digits = 16, auto_unbox = TRUE ), out ); diff --git a/lib/node_modules/@stdlib/math/base/special/beta/test/test.js b/lib/node_modules/@stdlib/math/base/special/beta/test/test.js new file mode 100644 index 000000000000..d0f2f093c203 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/beta/test/test.js @@ -0,0 +1,83 @@ +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var PINF = require( '@stdlib/math/constants/float64-pinf' ); +var isInfinite = require( '@stdlib/math/base/utils/is-infinite' ); +var isnan = require( '@stdlib/utils/is-nan' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var beta = require( './../lib' ); + + +// FIXTURES // + +var arg1 = require( './fixtures/r/arg1.json' ); +var arg2 = require( './fixtures/r/arg2.json' ); +var expected = require( './fixtures/r/expected.json' ); +var i; +var v; +for ( i = 0; i < expected.length; i++ ) { + v = expected[ i ]; + if ( v === 'Inf' ) { + expected[ i ] = Number.POSITIVE_INFINITY; + } + else if ( v === 'NaN' ) { + expected[ i ] = NaN; + } +} + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.ok( typeof beta === 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided a `NaN`', function test( t ) { + var val = beta( NaN, 2 ); + t.notOk( val === val, 'returns NaN' ); + val = beta( 2, NaN ); + t.notOk( val === val, 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided negative values', function test( t ) { + var val = beta( -2, 5 ); + t.notOk( val === val, 'returns NaN' ); + val = beta( 4, -3 ); + t.notOk( val === val, 'returns NaN' ); + t.end(); +}); + +tape( 'the function returns +Infinity if at least one argument is zero', function test( t ) { + var val = beta( 0, 2 ); + t.equal( val, PINF, 'returns +Infinity' ); + val = beta( 1, 0 ); + t.equal( val, PINF, 'returns +Infinity' ); + t.end(); +}); + +tape( 'the function evaluates the beta function', function test( t ) { + var actual; + var b1; + var b2; + var i; + for ( i = 0; i < arg1.length; i++ ) { + actual = beta( arg1[ i ], arg2[ i ] ); + + b1 = isInfinite( actual ); + b2 = isInfinite( expected[ i ] ); + t.equal( b1, b2, 'returned result is ' + ( (b2) ? 'not finite' : 'finite' ) ); + + b1 = isnan( actual ); + b2 = isnan( expected[ i ] ); + t.equal( b1, b2, 'returned result is ' + ( (b1) ? '' : 'not' ) + ' NaN' ); + if ( !b1 ) { + t.ok( abs( actual - expected[ i ] ) < 1e-14, 'returned result is within tolerance. actual: ' + actual + '; expected: ' + expected[ i ] + '.' ); + } + } + t.end(); +});