time-to-botec

Benchmark sampling in different programming languages
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logpdf.js (2791B)

      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 'use strict';
     20 
     21 // MODULES //
     22 
     23 var betaln = require( '@stdlib/math/base/special/betaln' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 var log1p = require( '@stdlib/math/base/special/log1p' );
     26 var ln = require( '@stdlib/math/base/special/ln' );
     27 var PINF = require( '@stdlib/constants/float64/pinf' );
     28 var NINF = require( '@stdlib/constants/float64/ninf' );
     29 
     30 
     31 // MAIN //
     32 
     33 /**
     34 * Evaluates the natural logarithm of the probability density function (logPDF) for a beta distribution with first shape parameter `alpha` and second shape parameter `beta` at a value `x`.
     35 *
     36 * @param {number} x - input value
     37 * @param {PositiveNumber} alpha - first shape parameter
     38 * @param {PositiveNumber} beta - second shape parameter
     39 * @returns {number} evaluated logPDF
     40 *
     41 * @example
     42 * var y = logpdf( 0.5, 1.0, 1.0 );
     43 * // returns 0.0
     44 *
     45 * @example
     46 * var y = logpdf( 0.5, 2.0, 4.0 );
     47 * // returns ~0.223
     48 *
     49 * @example
     50 * var y = logpdf( 0.2, 2.0, 2.0 );
     51 * // returns ~-0.041
     52 *
     53 * @example
     54 * var y = logpdf( 0.8, 4.0, 4.0 );
     55 * // returns ~-0.556
     56 *
     57 * @example
     58 * var y = logpdf( -0.5, 4.0, 2.0 );
     59 * // returns -Infinity
     60 *
     61 * @example
     62 * var y = logpdf( 1.5, 4.0, 2.0 );
     63 * // returns -Infinity
     64 *
     65 * @example
     66 * var y = logpdf( 0.5, -1.0, 0.5 );
     67 * // returns NaN
     68 *
     69 * @example
     70 * var y = logpdf( 0.5, 0.5, -1.0 );
     71 * // returns NaN
     72 *
     73 * @example
     74 * var y = logpdf( NaN, 1.0, 1.0 );
     75 * // returns NaN
     76 *
     77 * @example
     78 * var y = logpdf( 0.5, NaN, 1.0 );
     79 * // returns NaN
     80 *
     81 * @example
     82 * var y = logpdf( 0.5, 1.0, NaN );
     83 * // returns NaN
     84 */
     85 function logpdf( x, alpha, beta ) {
     86 	var out;
     87 	if (
     88 		isnan( x ) ||
     89 		isnan( alpha ) ||
     90 		isnan( beta ) ||
     91 		alpha <= 0.0 ||
     92 		beta <= 0.0
     93 	) {
     94 		return NaN;
     95 	}
     96 	if ( x < 0.0 || x > 1.0 ) {
     97 		// Support of the Beta distribution: [0,1]
     98 		return NINF;
     99 	}
    100 	if ( x === 0.0 ) {
    101 		if ( alpha < 1.0 ) {
    102 			return PINF;
    103 		}
    104 		if ( alpha > 1.0 ) {
    105 			return NINF;
    106 		}
    107 		return ln( beta );
    108 	}
    109 	if ( x === 1.0 ) {
    110 		if ( beta < 1.0 ) {
    111 			return PINF;
    112 		}
    113 		if ( beta > 1.0 ) {
    114 			return NINF;
    115 		}
    116 		return ln( alpha );
    117 	}
    118 	out = ( alpha-1.0 ) * ln( x );
    119 	out += ( beta-1.0 ) * log1p( -x );
    120 	out -= betaln( alpha, beta );
    121 	return out;
    122 }
    123 
    124 
    125 // EXPORTS //
    126 
    127 module.exports = logpdf;