entropy.js (1615B)
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 sqrt = require( '@stdlib/math/base/special/sqrt' ); 26 var beta = require( '@stdlib/math/base/special/beta' ); 27 var ln = require( '@stdlib/math/base/special/ln' ); 28 29 30 // MAIN // 31 32 /** 33 * Returns the differential entropy of a Student's t distribution. 34 * 35 * @param {PositiveNumber} v - degrees of freedom 36 * @returns {number} entropy 37 * 38 * @example 39 * var v = entropy( 9.0 ); 40 * // returns ~1.533 41 * 42 * @example 43 * var v = entropy( 2.0 ); 44 * // returns ~1.96 45 * 46 * @example 47 * var v = entropy( -0.2 ); 48 * // returns NaN 49 * 50 * @example 51 * var v = entropy( NaN ); 52 * // returns NaN 53 */ 54 function entropy( v ) { 55 var out; 56 var vh; 57 if ( isnan( v ) || v <= 0.0 ) { 58 return NaN; 59 } 60 vh = v / 2.0; 61 out = ( v + 1.0 ) / 2.0; 62 out *= digamma( ( 1.0+v ) / 2.0 ) - digamma( vh ); 63 out += ln( sqrt( v ) * beta( vh, 0.5 ) ); 64 return out; 65 } 66 67 68 // EXPORTS // 69 70 module.exports = entropy;