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..ebaeaf20354d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/README.md @@ -0,0 +1,105 @@ + + +# hyp2f1 + +> Evaluate Gaussian hypergeometric function + + + +
+ +The Gaussian hypergeometric function is defined as + + + +
+ Equation for Gaussian hypergeometric function. +
+
+ + + +
+ + + + + +
+ +## Usage + +```javascript +var hyp2f1 = require( '@stdlib/math/base/special/hyp2f1' ); +``` + +#### hyp2f1( a, b, c, z ) + +Evaluates the Gaussian hypergeometric function. + +```javascript +var v = hyp2f1( 1.0, 1.0, 1.0, 0.0 ); +// returns 1.0 +``` + +
+ + + + + +
+ +
+ + + + + +
+ +## Examples + + + +```javascript +var hyp2f1 = require( '@stdlib/math/base/special/hyp2f1' ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +
+ + 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..a65bc19464fc --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/benchmark/benchmark.js @@ -0,0 +1,45 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 isnan = require( '@stdlib/random/base/randu' ); +var pkg = require( './../package.json' ).name; +var hyp2f1 = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var i; + var y; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = hyp2f1( 1.0, 1.0, 1.0, 0.0 ); + if ( isnan( y ) ) { + b.fail( 'something went wrong' ); + } + } + b.toc(); + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_gaussian_hypergeometric_function.svg b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_gaussian_hypergeometric_function.svg new file mode 100644 index 000000000000..45b85e13b467 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/img/equation_gaussian_hypergeometric_function.svg @@ -0,0 +1,91 @@ + +h y p Baseline 2 f Baseline 1 left-parenthesis a comma b comma c comma z 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 z Superscript n Baseline Over n factorial EndFraction + + + \ 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..462cd73ba037 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/docs/repl.txt @@ -0,0 +1,36 @@ + +{{alias}}( a, b, c, x ) + TODO: short desc. + + TODO: longer desc/bkgd. + + List: + + - item 1 + - item 2 + + Parameters + ---------- + a: number + TODO: desc + b: number + c: number + x: number + + Returns + ------- + y: number + TODO: desc + + Examples + -------- + > var TODO = {{alias}}() + TODO: abbrev output + + References + ---------- + - TODO: only include reference(s) if usage requires citation(s) + + See Also + -------- + 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..78864b0fdffe --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/examples/index.js @@ -0,0 +1,26 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 hyp2f1 = require( './../lib' ); + +var y; + +y = hyp2f1( 1.0, 1.0, 1.0, 0.0 ); +console.log( 'hyp2f1( 1.0, 1.0, 1.0, 0.0) = %d', y ); 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..a39ea366830a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/index.js @@ -0,0 +1,40 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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'; + +/** +* Evaulation of 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 +*/ + +// MODULES // + +var hyp2f1 = require( './main.js' ); + + +// EXPORTS // + +module.exports = hyp2f1; 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..f9174490ed3a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/main.js @@ -0,0 +1,275 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 abs = require( '@stdlib/math/base/special/abs' ); +var gamma = require( '@stdlib/math/base/special/gamma' ); +var round = require( '@stdlib/math/base/special/round' ); +var isNegInt = require( '@stdlib/math/base/assert/is-negative-integer' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var PINF = require( '@stdlib/constants/math/float64-pinf' ); +var max = require( '@stdlib/math/base/special/max' ); +var hys2f1 = require( './support.js' ).hys2f1; +var hyt2f1 = require( './support.js' ).hyt2f1; + + +// VARIABLES // + +var EPS = 1.0e-13; +var ETHRESH = 1.0e-12; + + +// 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 +*/ +function hyp2f1( a, b, c, x ) { + var negIntCaOrCb; + var negIntA; + var negIntB; + var err; + var aid; + var ax; + var ia; + var ib; + var ic; + var id; + var t1; + var d1; + var d2; + var i; + var d; + var e; + var p; + var q; + var r; + var s; + var y; + + if ( x === 0.0 ) { + return 1.0; + } + + if ( ( a === 0 || b === 0 ) && c !== 0 ) { + return 1.0; + } + + negIntA = isNegInt(a); + negIntB = isNegInt(b); + + negIntCaOrCb = 0; + err = { + 'v': 0.0 + }; + ax = abs( x ); + s = 1.0 - x; + ia = round( a ); + ib = round( b ); + + d = c - a - b; + id = round( d ); + + // eslint-disable-next-line max-len + if ( d <= -1 && !( abs( d - id ) > EPS && s < 0) && !( negIntA || negIntB ) ) { + return pow( s, d ) * hyp2f1( c-a, c-b, c, x ); + } + + if ( d <= 0 && x === 1 && !( negIntA || negIntB )) { + // CEPHES: goto hypdiv + return PINF; + } + if ( ax < 1.0 || x === -1.0 ) { // 2F1(a,b;b;x) = (1-x)**(-a) + if ( abs( b-c ) < EPS ) { // b = c + if ( negIntB ) { + y = hyp2f1NegCEqualBC( a, b, x ); + } else { + y = pow( s, -a ); + } + // CEPHES: goto hypdon + return y; + } + if ( abs( a - c ) < EPS ) { // a = c + y = pow( s, -b ); + return y; + } + } + if ( c <= 0.0 ) { + ic = round( c ); + if ( abs( c - ic ) < EPS ) { // c is negative integer + // Check termination before explosion + if ( negIntA && ( ia > ic ) ) { + // CEPHES: goto hypok + y = hyt2f1( a, b, c, x, err ); + return y; + } + if ( negIntB && ( ib > ic ) ) { + // CEPHES: goto hypok + y = hyt2f1( a, b, c, x, err ); + return y; + } + // CEPHES: goto hypdiv + return PINF; + } + } + + if ( negIntA || negIntB ) { // function in polynomial + // CEPHES: goto hypok + y = hyt2f1( a, b, c, x, err ); + return y; + } + t1 = abs( b - a ); + if ( x < -2.0 && abs( t1 - round(t1) ) > EPS ) { + // This transform has a pole for b-a integer, and may produce large cancellation errors for |1/x| close to 1 + p = hyp2f1( a, 1 - c + a, 1 - b + a, 1.0 / x ); + q = hyp2f1( b, 1 - c + b, 1 - 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 ) { + if ( abs( a ) < abs( b ) ) { + return pow( s, -a ) * hyp2f1( a, c-b, c, x / ( x-1 ) ); + } + return pow( s, -b ) * hyp2f1( b, c-a, c, x / ( x-1 ) ); + } + if ( ax > 1.0 ) { // series diverges + // CEPHES: goto hypdiv + return PINF; + } + + p = c - a; + ia = round( p ); // Nearest integer to c-a + if ( ( ia <= 0.0 ) && ( abs( p - ia ) < EPS ) ) { // negative int c-a + negIntCaOrCb = 1; + } + + r = c - b; + ib = round( r ); // Nearest integer to c-b + if ( ( ib <= 0.0 ) && ( abs( r - ib ) < EPS ) ) { // negative int c-b + negIntCaOrCb = 1; + } + + id = round( d ); + q = abs( d - id ); + + if ( abs( ax - 1.0 ) < EPS ) { // |x| = 1.0 + if ( x > 0.0 ) { + if ( negIntCaOrCb === 1 ) { + if ( d >= 0.0 ) { // goto hypf + y = pow( s, d ) * hys2f1( c-a, c-b, c, x, err ); + return y; + } + // CEPHES: goto hypdiv + return PINF; + } + if ( d <= 0.0 ) { // goto hypdiv + return PINF; + } + y = gamma( c ) * gamma( d ) / ( gamma( p ) * gamma( r ) ); + return y; + } + if ( d <= -1.0 ) { + return PINF; + } + if ( d < 0.0 ) { + y = hyt2f1( a, b, c, x, err ); + if ( err.v < ETHRESH ) { + return y; + } + err.v = 0.0; + aid = 2 - 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; + + // eslint-disable-next-line max-len + y = ( e * ( r - ( ( ( 2.0 * e ) - q ) * x ) ) * d2 ) + ( ( ( e - a ) * ( e - b ) * x * d1 ) / ( e * r * s ) ); + e = r; + d1 = d2; + d2 = y; + } + return y; + } + + if ( negIntCaOrCb ) { + y = pow( s, d ) * hys2f1( c - a, c - b, c, x, err ); + return y; + } + } +} + +/** +* Evaluates the Gaussian hypergeometric function. +* +* @param {number} a - input value +* @param {number} b - input value +* @param {number} x - input value +* @returns {number} function value +* +*/ +function hyp2f1NegCEqualBC( a, b, x ) { + var collectorMax; + var collector; + var sum; + var k; + + sum = 1; + collector = 1; + collectorMax = 1; + + if ( !( abs( b ) < 1e5 ) ) { + return NaN; + } + + for ( k = 1; k <= -b; k++ ) { + collector *= ( a + k - 1) * (x / k); + collectorMax = max( abs( collector ), collectorMax ); + sum += collector; + } + + if ( 1e-16 * (1 + ( collectorMax / abs( sum ) ) ) > 1e-7 ) { + return NaN; + } + + return sum; +} + + +// EXPORTS // + +module.exports = hyp2f1; diff --git a/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/support.js b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/support.js new file mode 100644 index 000000000000..8566c8ca3e35 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/support.js @@ -0,0 +1,412 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 abs = require( '@stdlib/math/base/special/abs' ); +var round = require( '@stdlib/math/base/special/round' ); +var PINF = require( '@stdlib/constants/math/float64-pinf' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var floor = require( '@stdlib/math/base/special/floor' ); +var gammaln = require( '@stdlib/math/base/special/gammaln' ); +var exp = require( '@stdlib/math/base/special/exp' ); +var gamma = require( '@stdlib/math/base/special/gamma' ); +var log = require( '@stdlib/math/base/special/log' ); +var digamma = require( '@stdlib/math/base/special/digamma' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var isNegInt = require( '@stdlib/math/base/assert/is-negative-integer' ); + + +// VARIABLES // + +var EPS = 1.0e-13; +var MAX_ITERATIONS = 10000; +var MACHEP = 1.0e-12; +var ETHRESH = 1.0e-12; + +/** +* Evaluates the 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 {Object} loss - loss +* @returns {number} function value +* +*/ +function hys2f1( a, b, c, x, loss ) { + var intflag; + var umax; + var ib; + var u; + var s; + var m; + var k; + var h; + var g; + var f; + var i; + + ib = 0; + intflag = 0; + + if ( abs( b ) > abs( a ) ) { + f = b; + b = a; + a = f; + } + + ib = round( b ); + + if ( abs( b - ib ) < EPS && ib <= 0 && abs( b ) < abs( a ) ) { + f = b; + b = a; + a = f; + intflag = 1; + } + + // eslint-disable-next-line max-len + if ( ( abs( a ) > ( abs( c ) + 1 ) || intflag === 1 ) && abs( c-a ) > 2 && abs( a ) > 2 ) { + return hyp2f1ra( a, b, c, x, loss ); + } + + i = 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.v = 1.0; + return PINF; + } + m = k + 1.0; + u *= ( ( f + k ) * ( g + k ) * x / ( ( h + k ) * m ) ); + s += u; + k = abs( u ); + if ( k > umax ) { + umax = k; + } + i += 1; + if ( i > MAX_ITERATIONS ) { + loss.v = 1.0; + return s; + } + } while ( s === 0 || abs( u / s ) > MACHEP ); + + loss.v = ( ( MACHEP * umax ) / abs( s ) ) + ( MACHEP * i ); + + return s; +} + +/** +* Evaluates the 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 {Object} loss - loss +* @returns {number} function value +* +*/ +function hyp2f1ra( a, b, c, x, loss ) { + var err; + var da; + var f0; + var f1; + var f2; + var n; + var t; + + err = { + 'v': 0.0 + }; + + if ( (c < 0 && a <= c) || ( c >= 0 && a >= c ) ) { + da = round( a - c ); + } else { + da = round( a ); + } + t = a - da; + + loss.v = 0.0; + + // Assert: assert ( da != 0 ) + if ( abs( da ) > MAX_ITERATIONS ) { + // Give up, too expensive to compute + loss.v = 1.0; + return NaN; + } + + if ( da < 0 ) { + // Recurse down + f2 = 0.0; + f1 = hys2f1( t, b, c, x, err ); + loss.v += err.v; + f0 = hys2f1( t-1.0, b, c, x, err ); + loss.v += err.v; + t -= 1.0; + for (n = 1; n < -da; n++ ) { + f2 = f1; + f1 = f0; + f0 = -(((2.0*t)-c-(t*x)+(b*x))/(c-t)*f1) - (t*(x-1)/(c-t)*f2); + t -= 1.0; + } + } else { + // Recurse up + f2 = 0.0; + f1 = hys2f1( t, b, c, x, err ); + loss.v += err.v; + f0 = hys2f1( t + 1, b, c, x, err ); + loss.v += err.v; + t += 1.0; + for ( n = 1; n < da; n++ ) { + f2 = f1; + f1 = f0; + f0 = -(((((2*t)-c-(t*x)+(b*x))*f1)+(c-t))*f2)/(t*(x-1.0)); + t += 1.0; + } + } + return f0; +} + +/** +* Evaluates the 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 {Object} loss - loss +* @returns {number} function value +* +*/ +function hyt2f1( a, b, c, x, loss ) { + var negIntA; + var negIntB; + var sign; + var err1; + var aid; + var err; + var d1; + var d2; + var ax; + var id; + var y1; + var p; + var q; + var r; + var s; + var t; + var y; + var w; + var d; + var e; + var i; + + y1 = 0.0; + negIntA = isNegInt( a ); + negIntB = isNegInt( b ); + err = { + 'v': 0.0 + }; + err1 = { + 'v': 0.0 + }; + s = 1.0 - x; + + if ( x < -0.5 && !( negIntA || negIntB ) ) { + if ( b > a ) { + y = pow( s, -a ) * hys2f1( a, c - b, c, -x / s, err ); + } + y = pow( s, -b ) * hys2f1( c - a, b, c, -x / s, err ); + + // CEPHES: goto done + loss.v = err.v; + return y; + } + + d = c - a - b; + id = round( d ); + + if ( x > 0.9 && !( negIntA || negIntB) ) { + if ( abs( d - id ) > EPS ) { + y = hys2f1( a, b, c, x, err ); + if ( err < ETHRESH ) { // CEPHES: goto done + loss.v = err.v; + return y; + } + q = hys2f1( a, b, 1.0-d, s, err); + sign = 1; + w = gammaln( d ); + sign *= logGammaSgn( d ); + w -= gammaln( c - a ); + sign *= logGammaSgn( c - a ); + w -= gammaln( c - b ); + sign *= logGammaSgn( c - b ); + q *= sign * exp( w ); + r = pow( s, d ) * hys2f1( c-a, c-b, d+1.0, s, err1); + sign = 1; + w = gammaln( -d ); + sign *= logGammaSgn( -d ); + w -= gammaln( a ); + sign *= logGammaSgn( a ); + w -= gammaln( b ); + sign *= logGammaSgn( b ); + r *= sign * exp( w ); + y = q + r; + + q = abs( q ); + r = abs( r ); + if ( q > r ) { + r = q; + } + err.v += err1.v + ( ( MACHEP * r ) / y ); + y *= gamma( c ); + + // CEPHES: goto done + loss.v = err.v; + return y; + } + + if ( id >= 0.0 ) { + e = d; + d1 = d; + d2 = 0.0; + aid = id; + } else { + e = -d; + d1 = 0.0; + d2 = d; + aid = -id; + } + ax = log( s ); + + 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 { + 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.v = 1.0; + return NaN; + } + } while ( y === 0 || abs( q/y ) > EPS ); + + if ( id === 0.0 ) { + y *= gamma( c ) / ( gamma( a ) * gamma( b ) ); + + // CEPHES: goto psidon + loss.v = err.v; + return y; + } + + y1 = 1.0; + + if ( aid === 1 ) { + p = gamma(c); + y1 *= gamma(e) * p / (gamma(a + d1) * gamma(b + d1)); + y *= p / (gamma(a + d2) * gamma(b + d2)); + if ((aid & 1) !== 0) { + y = -y; + } + + q = pow(s, id); /* s to the id power */ + if (id > 0.0) { + y *= q; + } else { + y1 *= q; + } + y += y1; + } + + 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; + } + } + + y = hys2f1(a, b, c, x, err); + loss.v = err.v; + return y; +} + +/** +* Evaluates the sign of log of gamma function. +* +* @private +* @param {number} x - input value +* @returns {number} function value +* +*/ +function logGammaSgn( x ) { + var fx; + if ( isnan( x ) ) { + return x; + } + if ( x > 0 ) { + return 1.0; + } + + fx = floor( x ); + if ( x - fx === 0.0 ) { + return 0.0; + } + + if ( fx % 2 === 0 ) { + return -1.0; + } + + return 1.0; +} + +module.exports = { + 'hyt2f1': hyt2f1, + 'hys2f1': hys2f1 +}; 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..ee8297c25053 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/package.json @@ -0,0 +1,61 @@ +{ + "name": "@stdlib/math/base/special/hyp2f1", + "version": "0.0.0", + "description": "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" + }, + "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", + "math.hyp2f1", + "hyp2f1", + "gaussian", + "hypergeometric" + ], + "__stdlib__": {} +} 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..6a5a9cff0a49 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/basic.json @@ -0,0 +1 @@ +{"a": [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 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225580325.26596233, 323872622.84062797, 476015763.9653681, 718530668.1253507, 1118306232.5845838, 1803407430.2838802, 3031976194.38876, 5356786152.304961, 10050025303.874605, 20307486440.515915, 45079143775.12229, 113165687504.68109, 336020133999.99817]} \ No newline at end of file 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..843f1b88d4c6 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/fixtures/python/runner.py @@ -0,0 +1,104 @@ +#!/usr/bin/env python +# +# @license Apache-2.0 +# +# Copyright (c) 2018 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 + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + + +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> x = linspace(-1000, 1000, 2001) + python> gen(x, './data.json') + ``` + """ + y = hyp2f1(a, b, c, x) + data = { + "a": a.tolist(), + "b": b.tolist(), + "c": c.tolist(), + "x": x.tolist(), + "expected": y.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") as outfile: + json.dump(data, outfile) + + +def main(): + + """Generate fixture data.""" + # Basic values: + n = 1000 + a = np.ones(n) + b = np.ones(n) + c = np.ones(n) + x = np.linspace(-1.0, 0.99, n) + gen(a, b, c, x, "basic1.json") + + # Basic values: + n = 1000 + a = 2*np.ones(n) + b = np.ones(n ) + c = np.ones(n) + x = np.linspace(-1.0, 0.99, n) + gen(a, b, c, x, "basic2.json") + + # Basic values: + n = 1000 + a = np.ones(n) + b = 2*np.ones(n) + c = np.ones(n) + x = np.linspace(-1.0, 0.99, n) + gen(a, b, c, x, "basic3.json") + + # Basic values: + n = 1000 + a = 2*np.ones(n) + b = 7*np.ones(n) + c = 3*np.ones(n) + x = np.linspace(-1.0, 0.99, n) + gen(a, b, c, x, "basic4.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..1f76872fbe99 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/hyp2f1/test/test.js @@ -0,0 +1,147 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 EPS = require( '@stdlib/constants/math/float64-eps' ); +var hyp2f1 = require( './../lib' ); + + +// FIXTURES // + +var basic1 = require( './fixtures/python/basic1.json' ); +var basic2 = require( './fixtures/python/basic2.json' ); +var basic3 = require( './fixtures/python/basic3.json' ); +var basic4 = require( './fixtures/python/basic4.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 accurately computes the function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = basic1.a; + b = basic1.b; + c = basic1.c; + x = basic1.x; + expected = basic1.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = basic2.a; + b = basic2.b; + c = basic2.c; + x = basic2.x; + expected = basic2.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = basic3.a; + b = basic3.b; + c = basic3.c; + x = basic3.x; + expected = basic3.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes the function', function test( t ) { + var expected; + var delta; + var tol; + var a; + var b; + var c; + var x; + var v; + var i; + + a = basic4.a; + b = basic4.b; + c = basic4.c; + x = basic4.x; + expected = basic4.expected; + + for ( i = 0; i < x.length; i++ ) { + v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +});