time-to-botec

Benchmark sampling in different programming languages
Log | Files | Refs | README

entropy.js (2299B)

      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 sumSeries = require( '@stdlib/math/base/tools/sum-series' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 var factorialln = require( '@stdlib/math/base/special/factorialln' );
     26 var factorial = require( '@stdlib/math/base/special/factorial' );
     27 var exp = require( '@stdlib/math/base/special/exp' );
     28 var ln = require( '@stdlib/math/base/special/ln' );
     29 
     30 
     31 // FUNCTIONS //
     32 
     33 /**
     34 * Returns a function to retrieve elements of the series \\( \sum_{k=0}^{\infty} \frac{ \lambda^k \log(k!) }{ k! } \\).
     35 *
     36 * @private
     37 * @param {NonNegativeNumber} lambda - mean parameter
     38 * @returns {Function} function to retrieve series elements
     39 */
     40 function seriesClosure( lambda ) {
     41 	var lk;
     42 	var k;
     43 	k = 1;
     44 	lk = lambda;
     45 	return seriesElement;
     46 
     47 	/**
     48 	* Returns the current series element.
     49 	*
     50 	* @private
     51 	* @returns {number} series element
     52 	*/
     53 	function seriesElement() {
     54 		k += 1;
     55 		lk *= lambda;
     56 		return lk * factorialln( k ) / factorial( k );
     57 	}
     58 }
     59 
     60 
     61 // MAIN //
     62 
     63 /**
     64 * Returns the entropy of a Poisson distribution.
     65 *
     66 * @param {NonNegativeNumber} lambda - mean parameter
     67 * @returns {PositiveNumber} entropy
     68 *
     69 * @example
     70 * var v = entropy( 9.0 );
     71 * // returns ~2.508
     72 *
     73 * @example
     74 * var v = entropy( 1.0 );
     75 * // returns ~1.305
     76 *
     77 * @example
     78 * var v = entropy( -0.2 );
     79 * // returns NaN
     80 *
     81 * @example
     82 * var v = entropy( NaN );
     83 * // returns NaN
     84 */
     85 function entropy( lambda ) {
     86 	var gen;
     87 	var out;
     88 	if ( isnan( lambda ) || lambda < 0.0 ) {
     89 		return NaN;
     90 	}
     91 	if ( lambda === 0.0 ) {
     92 		return 0.0;
     93 	}
     94 	gen = seriesClosure( lambda );
     95 	out = lambda * ( 1.0-ln(lambda) );
     96 	out += exp( -lambda ) * sumSeries( gen );
     97 	return out;
     98 }
     99 
    100 
    101 // EXPORTS //
    102 
    103 module.exports = entropy;