time-to-botec

Benchmark sampling in different programming languages
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betaln.js (2982B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2018 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 *
     18 *
     19 * ## Notice
     20 *
     21 * The code is adapted from the Fortran routine from the FNLIB library of the [SLATEC Common Mathematical Library]{@link http://www.netlib.no/netlib/slatec/fnlib/albeta.f}.
     22 *
     23 * The original code was developed by W. Fullerton of Los Alamos Scientific Laboratory, a governmental institution, and is therefore public domain.
     24 */
     25 
     26 'use strict';
     27 
     28 // MODULES //
     29 
     30 var gammaln = require( './../../../../base/special/gammaln' );
     31 var log1p = require( './../../../../base/special/log1p' );
     32 var gamma = require( './../../../../base/special/gamma' );
     33 var max = require( './../../../../base/special/max' );
     34 var min = require( './../../../../base/special/min' );
     35 var ln = require( './../../../../base/special/ln' );
     36 var LN_SQRT_TWO_PI = require( '@stdlib/constants/float64/ln-sqrt-two-pi' );
     37 var NINF = require( '@stdlib/constants/float64/ninf' );
     38 var PINF = require( '@stdlib/constants/float64/pinf' );
     39 var correction = require( './gamma_correction.js' );
     40 
     41 
     42 // MAIN //
     43 
     44 /**
     45 * Evaluate the natural logarithm of the beta function.
     46 *
     47 * @param {NonNegativeNumber} a - first input value
     48 * @param {NonNegativeNumber} b - second input value
     49 * @returns {number} natural logarithm of beta function
     50 *
     51 * @example
     52 * var v = betaln( 0.0, 0.0 );
     53 * // returns Infinity
     54 *
     55 * @example
     56 * var v = betaln( 1.0, 1.0 );
     57 * // returns 0.0
     58 *
     59 * @example
     60 * var v = betaln( -1.0, 2.0 );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var v = betaln( 5.0, 0.2 );
     65 * // returns ~1.218
     66 *
     67 * @example
     68 * var v = betaln( 4.0, 1.0 );
     69 * // returns ~-1.386
     70 *
     71 * @example
     72 * var v = betaln( NaN, 2.0 );
     73 * // returns NaN
     74 */
     75 function betaln( a, b ) {
     76 	var corr;
     77 	var p;
     78 	var q;
     79 
     80 	p = min( a, b );
     81 	q = max( a, b );
     82 
     83 	if ( p < 0.0 ) {
     84 		return NaN;
     85 	}
     86 	if ( p === 0.0 ) {
     87 		return PINF;
     88 	}
     89 	if ( q === PINF ) {
     90 		return NINF;
     91 	}
     92 	// Case: p and q are big
     93 	if ( p >= 10.0 ) {
     94 		corr = correction( p ) + correction( q ) - correction( p+q );
     95 		return ( -0.5*ln( q ) ) + LN_SQRT_TWO_PI + corr + ( (p-0.5) * ln( p/(p+q) ) ) + ( q*log1p( -p/(p+q) ) ); // eslint-disable-line max-len
     96 	}
     97 	// Case: p is small, but q is big
     98 	if ( q >= 10.0 ) {
     99 		corr = correction( q ) - correction( p+q );
    100 		return gammaln( p ) + corr + p - (p*ln( p+q )) + ( (q-0.5)*log1p( -p/(p+q) ) ); // eslint-disable-line max-len
    101 	}
    102 	// Case: p and q are small
    103 	return ln( gamma( p ) * ( gamma( q ) / gamma( p+q ) ) );
    104 }
    105 
    106 
    107 // EXPORTS //
    108 
    109 module.exports = betaln;