entropy.js (1775B)
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 digamma = require( '@stdlib/math/base/special/digamma' ); 24 var betaln = require( '@stdlib/math/base/special/betaln' ); 25 26 27 // MAIN // 28 29 /** 30 * Returns the differential entropy of a beta distribution. 31 * 32 * @param {PositiveNumber} alpha - first shape parameter 33 * @param {PositiveNumber} beta - second shape parameter 34 * @returns {NonPositiveNumber} differential entropy 35 * 36 * @example 37 * var v = entropy( 1.0, 1.0 ); 38 * // returns 0.0 39 * 40 * @example 41 * var v = entropy( 4.0, 12.0 ); 42 * // returns ~-0.869 43 * 44 * @example 45 * var v = entropy( 8.0, 2.0 ); 46 * // returns ~-0.795 47 * 48 * @example 49 * var v = entropy( 1.0, -0.1 ); 50 * // returns NaN 51 * 52 * @example 53 * var v = entropy( -0.1, 1.0 ); 54 * // returns NaN 55 * 56 * @example 57 * var v = entropy( 2.0, NaN ); 58 * // returns NaN 59 * 60 * @example 61 * var v = entropy( NaN, 2.0 ); 62 * // returns NaN 63 */ 64 function entropy( alpha, beta ) { 65 var out; 66 if ( alpha <= 0.0 || beta <= 0.0 ) { 67 return NaN; 68 } 69 out = betaln( alpha, beta ); 70 out -= ( alpha-1.0 ) * digamma( alpha ); 71 out -= ( beta-1.0 ) * digamma( beta ); 72 out += ( alpha+beta-2.0 ) * digamma( alpha+beta ); 73 return out; 74 } 75 76 77 // EXPORTS // 78 79 module.exports = entropy;