entropy.js (1669B)
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 ln = require( '@stdlib/math/base/special/ln' ); 25 var GAMMA = require( '@stdlib/constants/float64/eulergamma' ); 26 var PI = require( '@stdlib/constants/float64/pi' ); 27 28 29 // VARIABLES // 30 31 var THREE_GAMMA = 3.0 * GAMMA; 32 33 34 // MAIN // 35 36 /** 37 * Returns the differential entropy for a Lévy distribution with location `mu` and scale `s`. 38 * 39 * @param {number} mu - location parameter 40 * @param {PositiveNumber} c - scale parameter 41 * @returns {number} entropy 42 * 43 * @example 44 * var y = entropy( 0.0, 1.0 ); 45 * // returns ~3.324 46 * 47 * @example 48 * var y = entropy( 5.0, 2.0 ); 49 * // returns ~4.018 50 * 51 * @example 52 * var y = entropy( NaN, 1.0 ); 53 * // returns NaN 54 * 55 * @example 56 * var y = entropy( 0.0, NaN ); 57 * // returns NaN 58 * 59 * @example 60 * var y = entropy( 0.0, 0.0 ); 61 * // returns NaN 62 */ 63 function entropy( mu, c ) { 64 if ( 65 isnan( mu ) || 66 isnan( c ) || 67 c <= 0.0 68 ) { 69 return NaN; 70 } 71 return ( 1.0 + THREE_GAMMA + ln( 16.0*c*c*PI ) ) / 2.0; 72 } 73 74 75 // EXPORTS // 76 77 module.exports = entropy;