entropy.js (1722B)
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 gammaln = require( '@stdlib/math/base/special/gammaln' ); 25 var ln = require( '@stdlib/math/base/special/ln' ); 26 27 28 // MAIN // 29 30 /** 31 * Returns the differential entropy of a gamma distribution. 32 * 33 * @param {PositiveNumber} alpha - shape parameter 34 * @param {PositiveNumber} beta - rate parameter 35 * @returns {number} entropy 36 * 37 * @example 38 * var v = entropy( 1.0, 1.0 ); 39 * // returns 1.0 40 * 41 * @example 42 * var v = entropy( 4.0, 12.0 ); 43 * // returns ~-0.462 44 * 45 * @example 46 * var v = entropy( 8.0, 2.0 ); 47 * // returns ~1.723 48 * 49 * @example 50 * var v = entropy( 1.0, -0.1 ); 51 * // returns NaN 52 * 53 * @example 54 * var v = entropy( -0.1, 1.0 ); 55 * // returns NaN 56 * 57 * @example 58 * var v = entropy( 2.0, NaN ); 59 * // returns NaN 60 * 61 * @example 62 * var v = entropy( NaN, 2.0 ); 63 * // returns NaN 64 */ 65 function entropy( alpha, beta ) { 66 var out; 67 if ( alpha <= 0.0 || beta <= 0.0 ) { 68 return NaN; 69 } 70 out = alpha - ln( beta ); 71 out += gammaln( alpha ); 72 out += ( 1.0-alpha ) * digamma( alpha ); 73 return out; 74 } 75 76 77 // EXPORTS // 78 79 module.exports = entropy;