diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/README.md b/lib/node_modules/@stdlib/math/base/special/hyp2f1/README.md new file mode 100644 index 000000000000..d041ea732e03 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/README.md @@ -0,0 +1,140 @@ + + +# Gaussian hypergeometric function + +> Evaluates the [Gaussian hypergeometric function][hypergeometric-function]. + +
+ +The [Gaussian hypergeometric function][hypergeometric-function] is defined for `|x| < 1` by the power series: + + + +```math +{}_2F_1(a, b; c; x) = \sum_{n=0}^{\infty} \frac{(a)_n (b)_n}{(c)_n} \frac{x^n}{n!} = 1 + \frac{a b}{c} x + \frac{a(a+1) b(b+1)}{c(c+1)} \frac{x^2}{2!} + \frac{a(a+1)(a+2) b(b+1)(b+2)}{c(c+1)(c+2)} \frac{x^3}{3!} + \cdots +``` + + + + + +and is undefined (or infinite) if `c` equals a non-positive integer. + +Here `(q)ₙ` is the (rising) [Pochhammer symbol][pochhammer-symbol], which is defined by: + + + +```math +(q)_n = \begin{cases} 1 & n = 0 \\ q(q+1) \cdots (q+n-1) & n > 0 \end{cases} +``` + + + + + +For `|x| >= 1`, the function can be [analytically continued][analytic-continuation] using functional identities and transformation formulas. + +
+ + + +
+ +## Usage + +```javascript +var hyp2f1 = require( '@stdlib/math/base/special/hyp2f1' ); +``` + +#### hyp2f1( a, b, c, x ) + +Evaluates the [Gaussian hypergeometric function][hypergeometric-function]. + +```javascript +var v = hyp2f1( 1.0, 1.0, 1.0, 0.0 ); +// returns 1.0 + +v = hyp2f1( 10.0, 7.4, -1.8, -0.99 ); +// returns ~0.423 + +v = hyp2f1( 3.0, 4.0, 7.0, 1.0 ); +// returns +Infinity + +v = hyp2f1( NaN, 3.0, 2.0, 0.5 ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var linspace = require( '@stdlib/array/base/linspace' ); +var hyp2f1 = require( '@stdlib/math/base/special/hyp2f1' ); + +var a = linspace( -50.0, 50.0, 100 ); +var b = linspace( -50.0, 50.0, 100 ); +var c = linspace( -50.0, 50.0, 100 ); +var x = linspace( -50.0, 50.0, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( 'a: %d, b: %d, c: %d, x: %d, 2F1(a,b;c;x): %d', a[ i ], b[ i ], c[ i ], x[ i ], hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ) ); +} +``` + +
+ + + + + +
+ +
+ + + + + +
+ +[hypergeometric-function]: https://en.wikipedia.org/wiki/Hypergeometric_function + +[pochhammer-symbol]: https://en.wikipedia.org/wiki/Falling_and_rising_factorials + +[analytic-continuation]: https://en.wikipedia.org/wiki/Analytic_continuation + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/benchmark/benchmark.js new file mode 100644 index 000000000000..d2abf5406cff --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/benchmark/benchmark.js @@ -0,0 +1,59 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 pkg = require( './../package.json' ).name; +var hyp2f1 = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( bm ) { + var x; + var a; + var b; + var c; + var z; + var i; + + a = uniform( 100, -50.0, 50.0 ); + b = uniform( 100, -50.0, 50.0 ); + c = uniform( 100, -50.0, 50.0 ); + x = uniform( 100, -50.0, 50.0 ); + + bm.tic(); + for ( i = 0; i < bm.iterations; i++ ) { + // eslint-disable-next-line max-len + z = hyp2f1( a[ i % x.length ], b[ i % x.length ], c[ i % x.length ], x[ i % x.length ] ); + if ( isnan( z ) ) { + bm.fail( 'should not return NaN' ); + } + } + bm.toc(); + if ( isnan( z ) ) { + bm.fail( 'should not return NaN' ); + } + bm.pass( 'benchmark finished' ); + bm.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_hypergeometric_function.svg b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_hypergeometric_function.svg new file mode 100644 index 000000000000..f9a9b263b15e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_hypergeometric_function.svg @@ -0,0 +1,208 @@ + +Subscript 2 Baseline upper F 1 left-parenthesis a comma b semicolon c semicolon x right-parenthesis equals sigma-summation Underscript n equals 0 Overscript normal infinity Endscripts StartFraction left-parenthesis a right-parenthesis Subscript n Baseline left-parenthesis b right-parenthesis Subscript n Baseline Over left-parenthesis c right-parenthesis Subscript n Baseline EndFraction StartFraction x Superscript n Baseline Over n factorial EndFraction equals 1 plus StartFraction a b Over c EndFraction x plus StartFraction a left-parenthesis a plus 1 right-parenthesis b left-parenthesis b plus 1 right-parenthesis Over c left-parenthesis c plus 1 right-parenthesis EndFraction StartFraction x squared Over 2 factorial EndFraction plus StartFraction a left-parenthesis a plus 1 right-parenthesis left-parenthesis a plus 2 right-parenthesis b left-parenthesis b plus 1 right-parenthesis left-parenthesis b plus 2 right-parenthesis Over c left-parenthesis c plus 1 right-parenthesis left-parenthesis c plus 2 right-parenthesis EndFraction StartFraction x cubed Over 3 factorial EndFraction plus midline-horizontal-ellipsis + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_pochhammer_symbol.svg b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_pochhammer_symbol.svg new file mode 100644 index 000000000000..aaf8b08bab18 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_pochhammer_symbol.svg @@ -0,0 +1,63 @@ + +left-parenthesis q right-parenthesis Subscript n Baseline equals StartLayout Enlarged left-brace 1st Row 1st Column 1 2nd Column n equals 0 2nd Row 1st Column q left-parenthesis q plus 1 right-parenthesis midline-horizontal-ellipsis left-parenthesis q plus n minus 1 right-parenthesis 2nd Column n greater-than 0 EndLayout + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/repl.txt new file mode 100644 index 000000000000..a8f20d2304e6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/repl.txt @@ -0,0 +1,40 @@ + +{{alias}}( a, b, c, x ) + Evaluates the Gaussian hypergeometric function. + + Parameters + ---------- + a: number + Input value. + b: number + Input value. + c: number + Input value. + x: number + Input value. + + Returns + ------- + y: number + Function value. + + Examples + -------- + > var y = {{alias}}( 1.0, 1.0, 1.0, 0.0 ) + 1.0 + > y = {{alias}}( 10.0, 7.4, -1.8, -0.99 ) + ~0.423 + > y = {{alias}}( 10.0, 1.0, -1.8, -0.99 ) + ~-0.875 + > y = {{alias}}( 2.0, 3.0, 5.0, 0.99 ) + ~27.699 + > y = {{alias}}( 3.0, 4.0, 7.0, 1.0 ) + +Infinity + > y = {{alias}}( NaN, 3.0, 2.0, 0.5 ) + NaN + > y = {{alias}}( 1.0, NaN, 2.0, 0.5 ) + NaN + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/types/index.d.ts new file mode 100644 index 000000000000..bc901412f3d5 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/types/index.d.ts @@ -0,0 +1,63 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 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 Gaussian hypergeometric function. +* +* @param a - input value +* @param b - input value +* @param c - input value +* @param x - input value +* @returns function value +* +* @example +* var v = hyp2f1( 1.0, 1.0, 1.0, 0.0 ); +* // returns 1.0 +* +* @example +* var v = hyp2f1( 10.0, 7.4, -1.8, -0.99 ); +* // returns ~0.423 +* +* @example +* var v = hyp2f1( 10.0, 1.0, -1.8, -0.99 ); +* // returns ~-0.875 +* +* @example +* var v = hyp2f1( 2.0, 3.0, 5.0, 0.99 ); +* // returns ~27.699 +* +* @example +* var v = hyp2f1( 3.0, 4.0, 7.0, 1.0 ); +* // returns +Infinity +* +* @example +* var v = hyp2f1( NaN, 3.0, 2.0, 0.5 ); +* // returns NaN +* +* @example +* var v = hyp2f1( 1.0, NaN, 2.0, 0.5 ); +* // returns NaN +*/ +declare function hyp2f1( a: number, b: number, c: number, x: number ): number; + + +// EXPORTS // + +export = hyp2f1; diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/types/test.ts new file mode 100644 index 000000000000..086f16297485 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/types/test.ts @@ -0,0 +1,76 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 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 hyp2f1 = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + hyp2f1( 1.0, 1.0, 1.0, 0.0 ); // $ExpectType number + hyp2f1( 10.0, 7.4, -1.8, -0.99 ); // $ExpectType number + hyp2f1( 10.0, 1.0, -1.8, -0.99 ); // $ExpectType number + hyp2f1( 2.0, 3.0, 5.0, 0.99 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a first argument which is a not a number... +{ + hyp2f1( true, 1.0, 1.0, 0.0 ); // $ExpectError + hyp2f1( false, 7.4, -1.8, -0.99 ); // $ExpectError + hyp2f1( '5', 1.0, -1.8, -0.99 ); // $ExpectError + hyp2f1( [], 3.0, 5.0, 0.99 ); // $ExpectError + hyp2f1( {}, 3.0, 5.0, 0.99 ); // $ExpectError + hyp2f1( ( x: number ): number => x, 1.0, 1.0, 0.0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is a not a number... +{ + hyp2f1( 1.0, true, 1.0, 0.0 ); // $ExpectError + hyp2f1( 7.4, false, -1.8, -0.99 ); // $ExpectError + hyp2f1( 1.0, '5', -1.8, -0.99 ); // $ExpectError + hyp2f1( 3.0, [], 5.0, 0.99 ); // $ExpectError + hyp2f1( 3.0, {}, 5.0, 0.99 ); // $ExpectError + hyp2f1( 1.0, ( x: number ): number => x, 1.0, 0.0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a third argument which is a not a number... +{ + hyp2f1( 1.0, 1.0, true, 0.0 ); // $ExpectError + hyp2f1( 7.4, -1.8, false, -0.99 ); // $ExpectError + hyp2f1( 1.0, -1.8, '5', -0.99 ); // $ExpectError + hyp2f1( 3.0, 5.0, [], 0.99 ); // $ExpectError + hyp2f1( 3.0, 5.0, {}, 0.99 ); // $ExpectError + hyp2f1( 1.0, 1.0, ( x: number ): number => x, 0.0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fourth argument which is a not a number... +{ + hyp2f1( 1.0, 1.0, 0.0, true ); // $ExpectError + hyp2f1( 7.4, -1.8, -0.99, false ); // $ExpectError + hyp2f1( 1.0, -1.8, -0.99, '5' ); // $ExpectError + hyp2f1( 3.0, 5.0, 0.99, [] ); // $ExpectError + hyp2f1( 3.0, 5.0, 0.99, {} ); // $ExpectError + hyp2f1( 1.0, 1.0, 0.0, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an invalid number of arguments... +{ + hyp2f1(); // $ExpectError + hyp2f1( 2.0, 3.0, 5.0 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/examples/index.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/examples/index.js new file mode 100644 index 000000000000..a666b43d65e3 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/examples/index.js @@ -0,0 +1,32 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 linspace = require( '@stdlib/array/base/linspace' ); +var hyp2f1 = require( './../lib' ); + +var a = linspace( -50.0, 50.0, 100 ); +var b = linspace( -50.0, 50.0, 100 ); +var c = linspace( -50.0, 50.0, 100 ); +var x = linspace( -50.0, 50.0, 100 ); + +var i; +for ( i = 0; i < x.length; i++ ) { + console.log( 'a: %d, b: %d, c: %d, x: %d, 2F1(a,b;c;x): %d', a[ i ], b[ i ], c[ i ], x[ i ], hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ) ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/config.json b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/config.json new file mode 100644 index 000000000000..25be968b2a4e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/config.json @@ -0,0 +1,6 @@ +{ + "MACHEP": 1.11022302462515654042e-16, + "EPS": 1.0e-13, + "ETHRESH": 1.0e-12, + "MAX_ITERATIONS": 10000 +} diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/hys2f1.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/hys2f1.js new file mode 100644 index 000000000000..ec8ced0d0691 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/hys2f1.js @@ -0,0 +1,239 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +* +* +* ## Notice +* +* The original C code and copyright notice are from the [Cephes Mathematical Library]{@link https://www.netlib.org/cephes/}. The implementation has been modified for JavaScript. +* +* ```text +* (C) Copyright Stephen L. Moshier 1984, 1987, 1992, 2000. +* +* Use, modification and distribution are subject to the +* Cephes Mathematical Library License. (See accompanying file +* LICENSE or copy at https://smath.com/en-US/view/CephesMathLibrary/license) +* ``` +*/ + +'use strict'; + +// MODULES // + +var PINF = require( '@stdlib/constants/float64/pinf' ); +var round = require( '@stdlib/math/base/special/round' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var isNonPositiveInteger = require( './isnonpositiveinteger.js' ); +var config = require( './config.json' ); + + +// VARIABLES // + +var MACHEP = config.MACHEP; +var EPS = config.EPS; +var MAX_ITERATIONS = config.MAX_ITERATIONS; + + +// FUNCTIONS // + +/** +* Evaluates the Gaussian hypergeometric function by two-term recurrence in `a`. +* +* ## Notes +* +* - This function helps prevent losing accuracy in the highly alternating hypergeometric series and allows a and b to be reduced to smaller values. +* +* ## References +* +* - AMS55 #15.2.10 +* +* @private +* @param {number} a - input value +* @param {number} b - input value +* @param {number} c - input value +* @param {number} x - input value +* @param {number} loss - starting loss of significance +* @returns {Object} the function value and error +*/ +function hyp2f1ra( a, b, c, x, loss ) { + var f2Val; + var f1Val; + var f0Val; + var err; + var da; + var f1; + var f0; + var t; + var n; + + loss = 0.0; + err = 0.0; + + if ( ( c < 0.0 && a <= c ) || ( c >= 0.0 && a >= c ) ) { + da = round( a-c ); + } else { + da = round( a ); + } + + t = a - da; + if ( abs( da ) > MAX_ITERATIONS ) { + // Too expensive to compute, so return `NaN`: + loss = 1.0; + return { + 'value': NaN, + 'error': loss + }; + } + + if ( da < 0.0 ) { + // Backward recurrence... + f2Val = 0.0; + f1 = hys2f1( t, b, c, x, err ); + loss += f1.error; + err = f1.error; + f0 = hys2f1( t-1.0, b, c, x, err ); + loss += f0.error; + t -= 1.0; + f1Val = f1.value; + f0Val = f0.value; + for ( n = 1; n < -da; n++ ) { + f2Val = f1Val; + f1Val = f0Val; + + // eslint-disable-next-line max-len + f0Val = -( ( ( ( (2.0*t)-c )-( t*x )+( b*x ) ) * f1Val ) + ( ( t*(x-1.0) ) * f2Val ) ) / ( c-t ); + t -= 1.0; + } + } else { + // Forward recurrence... + f2Val = 0.0; + f1 = hys2f1( t, b, c, x, err ); + loss += f1.error; + err = f1.error; + f0 = hys2f1( t+1.0, b, c, x, err ); + loss += f0.error; + t += 1.0; + f1Val = f1.value; + f0Val = f0.value; + for ( n = 1; n < da; n++ ) { + f2Val = f1Val; + f1Val = f0Val; + + // eslint-disable-next-line max-len + f0Val = -( ( ( ( (2.0*t)-c )-( t*x )+( b*x ) ) * f1Val ) + ( (c-t)*f2Val ) ) / ( t*(x-1.0) ); + t += 1.0; + } + } + + return { + 'value': f0Val, + 'error': loss + }; +} + + +// MAIN // + +/** +* Evaluates the power series expansion of Gaussian hypergeometric function. +* +* @private +* @param {number} a - input value +* @param {number} b - input value +* @param {number} c - input value +* @param {number} x - input value +* @param {number} loss - starting loss of significance +* @returns {Object} the function value and error +*/ +function hys2f1( a, b, c, x, loss ) { + var intFlag; + var umax; + var f; + var g; + var h; + var k; + var m; + var s; + var u; + var i; + + intFlag = 0; + + if ( abs( b ) > abs( a ) ) { + f = b; + b = a; + a = f; + } + + if ( isNonPositiveInteger( b ) && ( abs( b ) < abs( a ) ) ) { + f = b; + b = a; + a = f; + intFlag = 1; + } + + // eslint-disable-next-line max-len + if ( ( ( abs( a ) > abs( c ) + 1.0 ) || intFlag ) && ( abs( c-a ) > 2.0 ) && ( abs( a ) > 2.0 ) ) { + return hyp2f1ra( a, b, c, x, loss ); + } + + i = 0.0; + umax = 0.0; + f = a; + g = b; + h = c; + s = 1.0; + u = 1.0; + k = 0.0; + + do { + if ( abs( h ) < EPS ) { + loss = 1.0; + return { + 'value': PINF, + 'error': loss + }; + } + m = k + 1.0; + u *= ( ( f+k ) * ( g+k ) * x / ( ( h+k ) * m ) ); + s += u; + k = abs( u ); + if ( k > umax ) { + umax = k; + } + k = m; + i += 1.0; + if ( i > MAX_ITERATIONS ) { + loss = 1.0; + return { + 'value': s, + 'error': loss + }; + } + } while ( s === 0.0 || abs( u/s ) > MACHEP ); + + // Estimate the relative error due to truncation by the series: + loss = ( ( MACHEP*umax ) / abs( s ) ) + ( MACHEP*i ); + return { + 'value': s, + 'error': loss + }; +} + + +// EXPORTS // + +module.exports = hys2f1; diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/hyt2f1.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/hyt2f1.js new file mode 100644 index 000000000000..99ebf12a4314 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/hyt2f1.js @@ -0,0 +1,242 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +* +* +* ## Notice +* +* The original C code and copyright notice are from the [Cephes Mathematical Library]{@link https://www.netlib.org/cephes/}. The implementation has been modified for JavaScript. +* +* ```text +* (C) Copyright Stephen L. Moshier 1984, 1987, 1992, 2000. +* +* Use, modification and distribution are subject to the +* Cephes Mathematical Library License. (See accompanying file +* LICENSE or copy at https://smath.com/en-US/view/CephesMathLibrary/license) +* ``` +*/ + +'use strict'; + +// MODULES // + +var abs = require( '@stdlib/math/base/special/abs' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var max = require( '@stdlib/math/base/special/max' ); +var exp = require( '@stdlib/math/base/special/exp' ); +var ln = require( '@stdlib/math/base/special/ln' ); +var round = require( '@stdlib/math/base/special/round' ); +var gamma = require( '@stdlib/math/base/special/gamma' ); +var gammaln = require( '@stdlib/math/base/special/gammaln' ); +var gammasgn = require( '@stdlib/math/base/special/gammasgn' ); +var digamma = require( '@stdlib/math/base/special/digamma' ); +var isNonPositiveInteger = require( './isnonpositiveinteger.js' ); +var isInteger = require( './isinteger.js' ); +var hys2f1 = require( './hys2f1.js' ); +var config = require( './config.json' ); + + +// VARIABLES // + +var MACHEP = config.MACHEP; +var EPS = config.EPS; +var ETHRESH = config.ETHRESH; +var MAX_ITERATIONS = config.MAX_ITERATIONS; + + +// MAIN // + +/** +* Applies transformations for `|x|` near unity before performing a power series expansion. +* +* @private +* @param {number} a - input value +* @param {number} b - input value +* @param {number} c - input value +* @param {number} x - input value +* @param {number} loss - starting loss of significance +* @returns {Object} the function value and error +*/ +function hyt2f1( a, b, c, x, loss ) { + var negIntA; + var negIntB; + var qVal; + var rVal; + var sign; + var err1; + var err; + var val; + var aid; + var ax; + var id; + var d1; + var d2; + var y1; + var i; + var p; + var q; + var r; + var t; + var y; + var w; + var d; + var e; + var s; + + negIntA = isNonPositiveInteger( a ); + negIntB = isNonPositiveInteger( b ); + err = 0.0; + err1 = 0.0; + s = 1.0 - x; + + if ( x < -0.5 && !( negIntA || negIntB ) ) { + if ( b > a ) { + // Transformation based on AMS55 #15.3.4: + y = hys2f1( a, c-b, c, -x/s, err ); + val = pow( s, -a ) * y.value; + } else { + // Transformation based on AMS55 #15.3.5: + y = hys2f1( c-a, b, c, -x/s, err ); + val = pow( s, -b ) * y.value; + } + loss = y.error; + return { + 'value': val, + 'error': loss + }; + } + + d = c - a - b; + id = round( d ); + + if ( x > 0.9 && !negIntA && !negIntB ) { + if ( isInteger( d ) === false ) { + // Try the power series first: + y = hys2f1( a, b, c, x, err ); + if ( y.error < ETHRESH ) { + return y; + } + // If the power series fails, then apply AMS55 #15.3.6... + err = y.error; + q = hys2f1( a, b, 1.0-d, s, err ); + qVal = q.value; + err = q.error; + sign = 1.0; + w = gammaln( d ); + sign *= gammasgn( d ); + w -= gammaln( c-a ); + sign *= gammasgn( c-a ); + w -= gammaln( c-b ); + sign *= gammasgn( c-b ); + qVal *= sign * exp( w ); + + r = hys2f1( c-a, c-b, d+1.0, s, err1 ); + err1 = r.error; + rVal = pow( s, d ) * r.value; + sign = 1.0; + w = gammaln( -d ); + sign *= gammasgn( -d ); + w -= gammaln( a ); + sign *= gammasgn( a ); + w -= gammaln( b ); + sign *= gammasgn( b ); + rVal *= sign * exp( w ); + + y = qVal + rVal; + err += err1 + ( ( MACHEP * max( abs( qVal ), abs( rVal ) ) ) / y ); + y *= gamma( c ); + } else { + // Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12... + if ( id >= 0.0 ) { + e = d; + d1 = d; + d2 = 0.0; + aid = id; + } else { + e = -d; + d1 = 0.0; + d2 = d; + aid = -id; + } + ax = ln( s ); + + // eslint-disable-next-line max-len + y = digamma( 1.0 ) + digamma( 1.0+e ) - digamma( a+d1 ) - digamma( b+d1 ) - ax; + y /= gamma( e+1.0 ); + p = ( a+d1 ) * ( b+d1 ) * s / gamma( e+2.0 ); + t = 1.0; + do { + // eslint-disable-next-line max-len + r = digamma( 1.0+t ) + digamma( 1.0+t+e ) - digamma( a+t+d1 ) - digamma( b+t+d1 ) - ax; + q = p * r; + y += q; + p *= s * ( a+t+d1 ) / ( t+1.0 ); + p *= ( b+t+d1 ) / ( t+1.0+e ); + t += 1.0; + if ( t > MAX_ITERATIONS ) { + loss = 1.0; + return { + 'value': NaN, + 'error': loss + }; + } + } while ( y === 0.0 || abs( q/y ) > EPS ); + + if ( id === 0.0 ) { + y *= gamma( c ) / ( gamma( a ) * gamma( b ) ); + return { + 'value': y, + 'error': err + }; + } + + y1 = 1.0; + if ( aid !== 1.0 ) { + t = 0.0; + p = 1.0; + for ( i = 1; i < aid; i++ ) { + r = 1.0 - e + t; + p *= s * ( a+t+d2 ) * ( b+t+d2 ) / r; + t += 1.0; + p /= t; + y1 += p; + } + } + + p = gamma( c ); + y1 *= gamma( e ) * p / ( gamma( a+d1 ) * gamma( b+d1 ) ); + y *= p / ( gamma( a+d2 ) * gamma( b+d2 ) ); + if ( aid % 2.0 !== 0.0 ) { + y = -y; + } + q = pow( s, id ); + y = ( id > 0.0 ) ? y*q : y1*q; + y += y1; + } + return { + 'value': y, + 'error': err + }; + } + // Perform power series if no special cases: + y = hys2f1( a, b, c, x, err ); + return y; +} + + +// EXPORTS // + +module.exports = hyt2f1; diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/index.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/index.js new file mode 100644 index 000000000000..09e590b4624e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/index.js @@ -0,0 +1,58 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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'; + +/** +* Evaluate the Gaussian hypergoemetric function. +* +* @module @stdlib/math/base/special/hyp2f1 +* +* @example +* var hyp2f1 = require( '@stdlib/math/base/special/hyp2f1' ); +* +* var v = hyp2f1( 1.0, 1.0, 1.0, 0.0 ); +* // returns 1.0 +* +* v = hyp2f1( 10.0, 7.4, -1.8, -0.99 ); +* // returns ~0.423 +* +* v = hyp2f1( 10.0, 1.0, -1.8, -0.99 ); +* // returns ~-0.875 +* +* v = hyp2f1( 2.0, 3.0, 5.0, 0.99 ); +* // returns ~27.699 +* +* v = hyp2f1( 3.0, 4.0, 7.0, 1.0 ); +* // returns +Infinity +* +* v = hyp2f1( NaN, 3.0, 2.0, 0.5 ); +* // returns NaN +* +* v = hyp2f1( 1.0, NaN, 2.0, 0.5 ); +* // returns NaN +*/ + +// MODULES // + +var hyp2f1 = require( './main.js' ); + + +// EXPORTS // + +module.exports = hyp2f1; diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/isinteger.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/isinteger.js new file mode 100644 index 000000000000..71439f3be6f7 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/isinteger.js @@ -0,0 +1,67 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +* +* +* ## Notice +* +* The original C code and copyright notice are from the [Cephes Mathematical Library]{@link https://www.netlib.org/cephes/}. The implementation has been modified for JavaScript. +* +* ```text +* (C) Copyright Stephen L. Moshier 1984, 1987, 1992, 2000. +* +* Use, modification and distribution are subject to the +* Cephes Mathematical Library License. (See accompanying file +* LICENSE or copy at https://smath.com/en-US/view/CephesMathLibrary/license) +* ``` +*/ + +'use strict'; + +// MODULES // + +var round = require( '@stdlib/math/base/special/round' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var config = require( './config.json' ); + + +// VARIABLES // + +var EPS = config.EPS; + + +// MAIN // + +/** +* Tests if a finite double-precision floating-point number is a "close enough" integer. +* +* @private +* @param {number} x - input value +* @returns {boolean} boolean indicating whether the value is a "close enough" integer +*/ +function isInteger( x ) { + var diff; + var ix; + + ix = round( x ); + diff = abs( x - ix ); + return ( diff < EPS ); +} + + +// EXPORTS // + +module.exports = isInteger; diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/isnonpositiveinteger.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/isnonpositiveinteger.js new file mode 100644 index 000000000000..eda458f8acf4 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/isnonpositiveinteger.js @@ -0,0 +1,67 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +* +* +* ## Notice +* +* The original C code and copyright notice are from the [Cephes Mathematical Library]{@link https://www.netlib.org/cephes/}. The implementation has been modified for JavaScript. +* +* ```text +* (C) Copyright Stephen L. Moshier 1984, 1987, 1992, 2000. +* +* Use, modification and distribution are subject to the +* Cephes Mathematical Library License. (See accompanying file +* LICENSE or copy at https://smath.com/en-US/view/CephesMathLibrary/license) +* ``` +*/ + +'use strict'; + +// MODULES // + +var round = require( '@stdlib/math/base/special/round' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var config = require( './config.json' ); + + +// VARIABLES // + +var EPS = config.EPS; + + +// MAIN // + +/** +* Tests if a finite double-precision floating-point number is a "close enough" nonpositive integer. +* +* @private +* @param {number} x - input value +* @returns {boolean} boolean indicating whether the value is a "close enough" nonpositive integer +*/ +function isNonPositiveInteger( x ) { + var diff; + var ix; + + ix = round( x ); + diff = abs( x - ix ); + return ( ( ix <= 0.0 ) && ( diff < EPS ) ); +} + + +// EXPORTS // + +module.exports = isNonPositiveInteger; diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/main.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/main.js new file mode 100644 index 000000000000..32ae742b1c62 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/main.js @@ -0,0 +1,279 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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. +* +* +* ## Notice +* +* The original C code and copyright notice are from the [Cephes Mathematical Library]{@link https://www.netlib.org/cephes/}. The implementation has been modified for JavaScript. +* +* ```text +* (C) Copyright Stephen L. Moshier 1984, 1987, 1992, 2000. +* +* Use, modification and distribution are subject to the +* Cephes Mathematical Library License. (See accompanying file +* LICENSE or copy at https://smath.com/en-US/view/CephesMathLibrary/license) +* ``` +*/ + +'use strict'; + +// MODULES // + +var isnan = require( '@stdlib/assert/is-nan' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var round = require( '@stdlib/math/base/special/round' ); +var gamma = require( '@stdlib/math/base/special/gamma' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var isNonPositiveInteger = require( './isnonpositiveinteger.js' ); +var isInteger = require( './isinteger.js' ); +var hys2f1 = require( './hys2f1.js' ); +var hyt2f1 = require( './hyt2f1.js' ); +var config = require( './config.json' ); + + +// VARIABLES // + +var ETHRESH = config.ETHRESH; + + +// MAIN // + +/** +* Evaluates the Gaussian hypergeometric function. +* +* @param {number} a - input value +* @param {number} b - input value +* @param {number} c - input value +* @param {number} x - input value +* @returns {number} function value +* +* @example +* var v = hyp2f1( 1.0, 1.0, 1.0, 0.0 ); +* // returns 1.0 +* +* @example +* var v = hyp2f1( 10.0, 7.4, -1.8, -0.99 ); +* // returns ~0.423 +* +* @example +* var v = hyp2f1( 10.0, 1.0, -1.8, -0.99 ); +* // returns ~-0.875 +* +* @example +* var v = hyp2f1( 2.0, 3.0, 5.0, 0.99 ); +* // returns ~27.699 +* +* @example +* var v = hyp2f1( 3.0, 4.0, 7.0, 1.0 ); +* // returns +Infinity +* +* @example +* var v = hyp2f1( NaN, 3.0, 2.0, 0.5 ); +* // returns NaN +* +* @example +* var v = hyp2f1( 1.0, NaN, 2.0, 0.5 ); +* // returns NaN +*/ +function hyp2f1( a, b, c, x ) { + var negIntCaOrCb; + var negIntC; + var negIntB; + var negIntA; + var isIntD; + var aid; + var err; + var ax; + var d2; + var d1; + var id; + var ic; + var ia; + var ib; + var t1; + var y1; + var y2; + var q; + var r; + var p; + var e; + var s; + var d; + var y; + var i; + + err = 0.0; + ax = abs( x ); + ia = round( a ); + ib = round( b ); + id = round( d ); + ic = round( c ); + s = 1.0 - x; + d = c - a - b; + negIntA = isNonPositiveInteger( a ); + negIntB = isNonPositiveInteger( b ); + negIntC = isNonPositiveInteger( c ); + isIntD = isInteger( d ); + t1 = abs( b-a ); + + if ( isnan( a ) || isnan( b ) || isnan( c ) || isnan( x ) ) { + return NaN; + } + + if ( x === 0.0 ) { + return 1.0; + } + + if ( ( a === 0.0 || b === 0.0 ) && c !== 0.0 ) { + return 1.0; + } + + // The transformation for c - a or c - b negative integer (AMS55 #15.3.3)... + if ( d <= -1.0 && !( !isIntD && s < 0.0 ) && !( negIntA || negIntB ) ) { + return pow( s, d ) * hyp2f1( c-a, c-b, c, x ); + } + + // Check whether the series diverges... + if ( d <= 0.0 && x === 1.0 && !( negIntA || negIntB ) ) { + return PINF; + } + + if ( ax < 1.0 || x === -1.0 ) { + if ( b === c ) { + // 2F1(a,b;b;x) = (1-x)**(-a): + return pow( s, -a ); + } + if ( a === c ) { + // 2F1(a,b;a;x) = (1-x)**(-b): + return pow( s, -b ); + } + } + + if ( negIntC ) { + // Check if termination before explosion... + if ( negIntA && ( ia > ic ) ) { + y = hyt2f1( a, b, c, x, err ); + return y.value; + } + if ( negIntB && ( ib > ic ) ) { + y = hyt2f1( a, b, c, x, err ); + return y.value; + } + return PINF; + } + + // Check whether the function is a polynomial before trying the power series expansion... + if ( negIntA || negIntB ) { + y = hyt2f1( a, b, c, x, err ); + return y.value; + } + + // The following transform has a pole for integer b - a and may cause large cancellation errors near |1/x| = 1 (AMS55 #15.3.7)... + if ( x < -2.0 && !isInteger( t1 ) ) { + p = hyp2f1( a, 1.0-c+a, 1.0-b+a, 1.0/x ); + q = hyp2f1( b, 1.0-c+b, 1.0-a+b, 1.0/x ); + p *= pow( -x, -a ); + q *= pow( -x, -b ); + t1 = gamma( c ); + s = t1 * gamma( b-a ) / ( gamma( b ) * gamma( c-a ) ); + y = t1 * gamma( a-b ) / ( gamma( a ) * gamma( c-b ) ); + return ( s*p ) + ( y*q ); + } + if ( x < -1.0 ) { + // Transformation based on AMS55 #15.3.4... + if ( abs( a ) < abs( b ) ) { + return pow( s, -a ) * hyp2f1( a, c-b, c, x/( x-1.0 ) ); + } + // Transformation based on AMS55 #15.3.5: + return pow( s, -b ) * hyp2f1( b, c-a, c, x/( x-1.0 ) ); + } + + // The series diverges for `|x|` greater than unity if above checks fail... + if ( ax > 1.0 ) { + return PINF; + } + + p = c - a; + r = c - b; + negIntCaOrCb = isNonPositiveInteger( p ) || isNonPositiveInteger( r ); + + // If `|x|` is equal to unity, the function is a polynomial... + if ( ax === 1.0 ) { + if ( x > 0.0 ) { + if ( negIntCaOrCb ) { + if ( d >= 0.0 ) { + // Transformation based on AMS55 #15.3.3: + y = hys2f1( c-a, c-b, c, x, err ); + return pow( s, d ) * y.value; + } + return PINF; + } + if ( d <= 0.0 ) { + return PINF; + } + // Transformation based on AMS55 #15.3.6: + return gamma( c ) * gamma( d ) / ( gamma( p ) * gamma( r ) ); + } + if ( d <= -1.0 ) { + return PINF; + } + } + + // Conditionally make `d > 0` by recurrence on `c` (AMS55 #15.2.27)... + if ( d < 0.0 ) { + // Try the power series first: + y = hyt2f1( a, b, c, x, err ); + if ( y.error < ETHRESH ) { + return y.value; + } + // If the power series fails, then apply the recurrence... + y = y.value; + err = 0.0; + aid = 2.0 - id; + e = c + aid; + d2 = hyp2f1( a, b, e, x ); + d1 = hyp2f1( a, b, e+1.0, x ); + q = a + b + 1.0; + for ( i = 0; i < aid; i++ ) { + r = e - 1.0; + y1 = ( e-a ) * ( e-b ) * x; + y2 = r - ( ( (2.0*e)-q ) * x ); + y2 *= e; + y = ( ( y2*d2 ) + ( y1*d1 ) ) / ( e*r*s ); + e = r; + d1 = d2; + d2 = y; + } + return y; + } + + // The transformation for c - a or c - b negative integer (AMS55 #15.3.3)... + if ( negIntCaOrCb ) { + y = hys2f1( c-a, c-b, c, x, err ); + return pow( s, d ) * y.value; + } + + // Try the power series: + y = hyt2f1( a, b, c, x, err ); + return y.value; +} + + +// EXPORTS // + +module.exports = hyp2f1; diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/package.json b/lib/node_modules/@stdlib/math/base/special/hyp2f1/package.json new file mode 100644 index 000000000000..7a7001f392ee --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/package.json @@ -0,0 +1,66 @@ +{ + "name": "@stdlib/math/base/special/hyp2f1", + "version": "0.0.0", + "description": "Evaluates the Gaussian hypergeometric function.", + "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", + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "lib": "./lib", + "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", + "special function", + "special", + "function", + "hypergeometric", + "gaussian", + "special functions", + "hyp2f1", + "hypergeometric function", + "number" + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/basic.json b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/basic.json new file mode 100644 index 000000000000..65c16efd72f9 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/basic.json @@ -0,0 +1 @@ +{"a": [-50, -50, -50, -50, -50, -50, -50, -50, -50, -50, -49, -49, -49, -49, -49, -49, -49, -49, -49, -49, -48, -48, -48, -48, -48, -48, -48, -48, -48, -48, -47, -47, -47, -47, -47, -47, -47, -47, -47, -47, -46, -46, -46, -46, -46, -46, -46, -46, -46, -46, -45, -45, -45, -45, 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0.9305650836976463, 0.7365814611655741, 1.2054216069215589, 1.352186856525951, 1.8913331589411715, -26.331668749748037, 0.9855249949815079, 2.2677201840029673]} diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/outliers.json b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/outliers.json new file mode 100644 index 000000000000..6cbfb31e9cb0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/outliers.json @@ -0,0 +1 @@ +{"a": [-1.8, 1.8, 1.8, 1.8, 1.8, 5.0, 10.0, 10.0, 2.0, 2.0, -1.8, 1.8, 10.0, 10.0, -8.0, -0.1156544430516313, -27.911722328444608, -10.184355055477743, -5.0083982772911, -0.7429095709749414, -14.55029516886238, -5.428179853908536, -1.8190858888165087, -0.9534205693212994, -31.70680212982947, -0.18350917503602782, -200.19574300099214, -8.837706832399117, -3.2052905962805456, -13.37614633859299], "b": [7.4, -2.5, 1.0, 7.4, 7.4, 7.4, 7.4, 7.4, 3.0, 2.5, -2.5, 7.4, 1.0, 7.4, 18.016500331508873, 12.722140489351698, 14.018736008860946, 6.5450429328481174, 171.09919289684245, 11.725525989335528, 0.46553367087834685, 26.782963689614604, 21.025202609254364, 10.024920055648606, 0.11445767340979862, 14.696533286274349, 1.9444493115386567, 0.19096384651567044, 0.3048596186043564, 1.337786902832312], "c": [20.4, 20.4, 20.4, -1.8, 20.4, 20.4, 20.4, 20.4, 5.0, -3.25, 20.4, -1.8, -1.8, -1.8, 10.805295997850628, -0.6030985338257255, -1.0168630024136034, -0.44051751620383994, -1.4923865283013589, -7.299203351011158, -0.5349901418098844, -4.162402828198655, -0.6960141045675334, -0.23845367675425955, -0.5570625216964069, -6.338990250643928, -0.6933677849479691, -2.3808990396202425, -0.7039276707364683, -0.05015281580946018], "x": [-10.0, -10.0, -10.0, -10.0, -10.0, -10.0, -10.0, 0.95, 0.99, 0.999, -10.0, -1.01, -0.99, -0.99, 0.90875647507, -0.0005448214561780684, 0.6228483452847298, 0.6555896492302491, 0.7073764056574465, 0.11534401417791407, 0.6086682776938632, 0.10047548647104909, 0.2570211738060222, 0.4419851803780206, 0.020574313007314604, -0.9003519736816863, 0.24492811068225362, -0.27624718180517105, 0.8496565195400692, -0.0022109253176725296], "expected": [16.334204105729413, 5.883122144128727, 0.5820646473844754, 0.010147094307759376, 0.07291374137469146, 0.0011628419587190388, 8.042653908304492e-06, 566.0092271657466, 27.699347904322664, 2.183739328012162e+26, -0.5786871007671348, 0.10921062752340924, -0.8752587026378827, 0.4234752106080307, -3.566216341436626e-09, 0.998681836639102, 5.33299803869569, 1.1177709865124041, 3.491332086988064e+82, 1.132062691110089, -0.0006927158077474787, 98.41698380414908, -221.57018712798285, 43.53554136829992, 1.0540592696289446, 0.5371016318543966, 0.0028040224553278668, -2.4067466563131665, 0.028751519134363426, 0.18419839456905535]} diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/runner.py b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/runner.py new file mode 100644 index 000000000000..8127f44d4a68 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/runner.py @@ -0,0 +1,260 @@ +#!/usr/bin/env python +# +# @license Apache-2.0 +# +# Copyright (c) 2025 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 fixtures.""" + +import os +import json +import numpy as np +from scipy.special import hyp2f1 + +# For reproducibility: +np.random.seed(1234) + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + +# Outliers: +outliers = [ + (-1.8, 7.4, 20.4, -10), + (1.8, -2.5, 20.4, -10), + (1.8, 1, 20.4, -10), + (1.8, 7.4, -1.8, -10), + (1.8, 7.4, 20.4, -10), + (5, 7.4, 20.4, -10), + (10, 7.4, 20.4, -10), + (10, 7.4, 20.4, 0.95), + (2, 3, 5, 0.99), + (2, 2.5, -3.25, 0.999), + (-1.8, -2.5, 20.4, -10), + (1.8, 7.4, -1.8, -1.01), + (10, 1, -1.8, -0.99), + (10, 7.4, -1.8, -0.99), + (-8, 18.016500331508873, 10.805295997850628, 0.90875647507), + ( + -0.1156544430516313, + 12.722140489351698, + -0.6030985338257255, + -0.0005448214561780684, + ), + (-27.911722328444608, 14.018736008860946, -1.0168630024136034, 0.6228483452847298), + (-10.184355055477743, 6.5450429328481174, -0.44051751620383994, 0.6555896492302491), + (-5.0083982772911, 171.09919289684245, -1.4923865283013589, 0.7073764056574465), + (-0.7429095709749414, 11.725525989335528, -7.299203351011158, 0.11534401417791407), + (-14.55029516886238, 0.46553367087834685, -0.5349901418098844, 0.6086682776938632), + (-5.428179853908536, 26.782963689614604, -4.162402828198655, 0.10047548647104909), + (-1.8190858888165087, 21.025202609254364, -0.6960141045675334, 0.2570211738060222), + (-0.9534205693212994, 10.024920055648606, -0.23845367675425955, 0.4419851803780206), + ( + -31.70680212982947, + 0.11445767340979862, + -0.5570625216964069, + 0.020574313007314604, + ), + (-0.18350917503602782, 14.696533286274349, -6.338990250643928, -0.9003519736816863), + (-200.19574300099214, 1.9444493115386567, -0.6933677849479691, 0.24492811068225362), + ( + -8.837706832399117, + 0.19096384651567044, + -2.3808990396202425, + -0.27624718180517105, + ), + (-3.2052905962805456, 0.3048596186043564, -0.7039276707364683, 0.8496565195400692), + ( + -13.37614633859299, + 1.337786902832312, + -0.05015281580946018, + -0.0022109253176725296, + ), +] + + +def gen(a, b, c, x, name): + """Generate fixture data and write to file. + + # Arguments + + * `a`: domain + * `b`: domain + * `c`: domain + * `x`: domain + * `name::str`: output filename + + # Examples + + ``` python + python> a = linspace(-50, 50, 1000) + python> b = linspace(-50, 50, 1000) + python> c = linspace(-50, 50, 1000) + python> x = linspace(-50, 50, 1000) + python> gen(a, b, c, x, './data.json') + ``` + """ + filtered_data = [ + (ai, bi, ci, xi) + for ai, bi, ci, xi in zip(a, b, c, x) + if (ai, bi, ci, xi) not in outliers + ] + a_f, b_f, c_f, x_f = map(np.array, zip(*filtered_data)) + y = hyp2f1(a_f, b_f, c_f, x_f) + y_f = ["PINF" if np.isinf(val) else val for val in y] + data = { + "a": a_f.tolist(), + "b": b_f.tolist(), + "c": c_f.tolist(), + "x": x_f.tolist(), + "expected": y_f, + } + + # 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 gen_outliers(name): + """Generate a test fixture including only outlier points. + + # Arguments + + * `name::str`: output filename + + # Examples + + ``` python + python> gen_outliers('./data.json') + ``` + """ + a = np.array([o[0] for o in outliers]) + b = np.array([o[1] for o in outliers]) + c = np.array([o[2] for o in outliers]) + x = np.array([o[3] for o in outliers]) + y = hyp2f1(a, b, c, x) + y = ["PINF" if np.isinf(val) else val for val in y] + data = { + "a": a.tolist(), + "b": b.tolist(), + "c": c.tolist(), + "x": x.tolist(), + "expected": y, + } + + # 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.""" + # Basic values: + n = 1000 + a = np.linspace(-50, 50, n, dtype=int) + b = np.linspace(-50, 50, n, dtype=int) + c = np.linspace(-50, 50, n, dtype=int) + x = np.linspace(-50, 50, n) + gen(a, b, c, x, "basic.json") + + # Edge Cases #1 + pts = [ + (1, 2, 3, 0), + (1.0 / 3, 2.0 / 3, 5.0 / 6, 27.0 / 32), + (1.0 / 4, 1.0 / 2, 3.0 / 4, 80.0 / 81), + (2, -2, -3, 3), + (2, -3, -2, 3), + (2, -1.5, -1.5, 3), + (1, 2, 3, 0), + (0.7235, -1, -5, 0.3), + (0.25, 1.0 / 3, 2, 0.999), + (0.25, 1.0 / 3, 2, -1), + (2, 3, 5, 0.99), + (3.0 / 2, -0.5, 3, 0.99), + (2, 2.5, -3.25, 0.999), + (-8, 18.016500331508873, 10.805295997850628, 0.90875647507000001), + (-10, 900, -10.5, 0.99), + (-10, 900, 10.5, 0.99), + (-1, 2, 1, 1.0), + (-1, 2, 1, -1.0), + (-3, 13, 5, 1.0), + (-3, 13, 5, -1.0), + (0.5, 1 - 270.5, 1.5, 0.999**2), + ] + a, b, c, x = zip(*pts) + a = np.array(a) + b = np.array(b) + c = np.array(c) + x = np.array(x) + gen(a, b, c, x, "edge_cases1.json") + + # Edge Cases #2 + pts = [ + (112, 5.1, -0.9, -0.99999), + (10, -900, 10.5, 0.99), + (10, -900, -10.5, 0.99), + ] + a, b, c, x = zip(*pts) + a = np.array(a) + b = np.array(b) + c = np.array(c) + x = np.array(x) + gen(a, b, c, x, "edge_cases2.json") + + # Edge Cases #3 + a_values = [-10, -5, -1.8, 1.8, 5, 10] + b_values = [-2.5, -1, 1, 7.4] + c_values = [-9, -1.8, 5, 20.4] + x_values = [-10, -1.01, -0.99, 0, 0.6, 0.95] + + a_list, b_list, c_list, x_list = [], [], [], [] + + for a in a_values: + for b in b_values: + for c in c_values: + for x in x_values: + a_list.append(a) + b_list.append(b) + c_list.append(c) + x_list.append(x) + + a = np.array(a_list) + b = np.array(b_list) + c = np.array(c_list) + x = np.array(x_list) + gen(a, b, c, x, "edge_cases3.json") + + # Edge Cases #4 + n = 500 + a = np.random.pareto(1.5, n) * (-1) ** np.random.randint(2, n) + b = np.random.pareto(1.5, n) * (-1) ** np.random.randint(2, n) + c = np.random.pareto(1.5, n) * (-1) ** np.random.randint(2, n) + x = 2 * np.random.rand(n) - 1 + gen(a, b, c, x, "edge_cases4.json") + + # Outliers: + gen_outliers("outliers.json") + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/test.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/test.js new file mode 100644 index 000000000000..115ab92ba165 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/test.js @@ -0,0 +1,296 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 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 abs = require( '@stdlib/math/base/special/abs' ); +var isnanf = require( '@stdlib/math/base/assert/is-nanf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var hyp2f1 = require( './../lib' ); + + +// FIXTURES // + +var basic = require( './fixtures/python/basic.json' ); +var edgeCases1 = require( './fixtures/python/edge_cases1.json' ); +var edgeCases2 = require( './fixtures/python/edge_cases2.json' ); +var edgeCases3 = require( './fixtures/python/edge_cases3.json' ); +var edgeCases4 = require( './fixtures/python/edge_cases4.json' ); +var outliers = require( './fixtures/python/outliers.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof hyp2f1, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `1` if `x` is 0', function test( t ) { + var v; + + v = hyp2f1( 1.0, 1.0, 1.0, 0.0 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + v = hyp2f1( 1.5, 2.5, 3.5, 0.0 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + v = hyp2f1( -1, 4, 2, 0.0 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN`', function test( t ) { + var v; + + v = hyp2f1( NaN, 3.0, 2.0, 0.5 ); + t.equal( isnanf( v ), true, 'returns expected value' ); + + v = hyp2f1( 0.0, NaN, 2.0, 0.5 ); + t.equal( isnanf( v ), true, 'returns expected value' ); + + v = hyp2f1( 0.0, 3.0, NaN, 0.5 ); + t.equal( isnanf( v ), true, 'returns expected value' ); + + v = hyp2f1( 0.0, 3.0, 2.0, NaN ); + t.equal( isnanf( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `1` if either `a` or `b` is 0 and `c` is not 0', function test( t ) { + var v; + + v = hyp2f1( 0.0, 3.0, 2.0, 0.5 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + v = hyp2f1( 0.0, -2.0, 4.0, 0.3 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + v = hyp2f1( 3.0, 0.0, 2.0, 0.5 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + v = hyp2f1( -2.0, 0.0, 4.0, 0.3 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `PINF` when `c <= a + b`, `x === 1`, and neither `a` nor `b` are nonpositive integers', function test( t ) { + var v; + + v = hyp2f1( 3.0, 4.0, 7.0, 1.0 ); + t.strictEqual( v, PINF, 'returns expected value' ); + + v = hyp2f1( 3.5, 4.5, 8.0, 1.0 ); + t.strictEqual( v, PINF, 'returns expected value' ); + + v = hyp2f1( 3.5, 4.5, 8.0, 1.0 ); + t.strictEqual( v, PINF, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function correctly evaluates the hypergeometric function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = basic.a; + b = basic.b; + c = basic.c; + x = basic.x; + expected = basic.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.equal( v, PINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. a: ' + a[ i ] + ' b: ' + b[ i ] + ' c: ' + c[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the hypergeometric function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = edgeCases1.a; + b = edgeCases1.b; + c = edgeCases1.c; + x = edgeCases1.x; + expected = edgeCases1.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.equal( v, PINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. a: ' + a[ i ] + ' b: ' + b[ i ] + ' c: ' + c[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the hypergeometric function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = edgeCases2.a; + b = edgeCases2.b; + c = edgeCases2.c; + x = edgeCases2.x; + expected = edgeCases2.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.equal( v, PINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = 7.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. a: ' + a[ i ] + ' b: ' + b[ i ] + ' c: ' + c[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the hypergeometric function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = edgeCases3.a; + b = edgeCases3.b; + c = edgeCases3.c; + x = edgeCases3.x; + expected = edgeCases3.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.equal( v, PINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = 10.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. a: ' + a[ i ] + ' b: ' + b[ i ] + ' c: ' + c[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the hypergeometric function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = edgeCases4.a; + b = edgeCases4.b; + c = edgeCases4.c; + x = edgeCases4.x; + expected = edgeCases4.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.equal( v, PINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = 20.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. a: ' + a[ i ] + ' b: ' + b[ i ] + ' c: ' + c[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the hypergeometric function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = outliers.a; + b = outliers.b; + c = outliers.c; + x = outliers.x; + expected = outliers.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + delta = abs( v - expected[ i ] ); + + /* + * NOTE: the tolerance is set high in this case due to: + * + * 1. The expected values having a very large range, being either very small or very large. + * 2. The function making a large number of internal calls, leading to accumulated numerical errors. + */ + tol = 260000.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. a: ' + a[ i ] + ' b: ' + b[ i ] + ' c: ' + c[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +});