entropy.js (1487B)
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 isnan = require( '@stdlib/math/base/assert/is-nan' ); 24 var digamma = require( '@stdlib/math/base/special/digamma' ); 25 var gamma = require( '@stdlib/math/base/special/gamma' ); 26 var ln = require( '@stdlib/math/base/special/ln' ); 27 28 29 // MAIN // 30 31 /** 32 * Returns the differential entropy of a chi-squared distribution. 33 * 34 * @param {PositiveNumber} k - degrees of freedom 35 * @returns {number} entropy 36 * 37 * @example 38 * var v = entropy( 9.0 ); 39 * // returns ~2.786 40 * 41 * @example 42 * var v = entropy( 1.0 ); 43 * // returns ~0.784 44 * 45 * @example 46 * var v = entropy( -0.2 ); 47 * // returns NaN 48 * 49 * @example 50 * var v = entropy( NaN ); 51 * // returns NaN 52 */ 53 function entropy( k ) { 54 var kh; 55 if ( isnan( k ) || k <= 0.0 ) { 56 return NaN; 57 } 58 kh = k / 2.0; 59 return kh + ln( 2.0*gamma( kh ) ) + ( ( 1.0-kh ) * digamma( kh ) ); 60 } 61 62 63 // EXPORTS // 64 65 module.exports = entropy;