time-to-botec

Benchmark sampling in different programming languages
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entropy.js (1911B)

      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 isPositiveInteger = require( '@stdlib/math/base/assert/is-positive-integer' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 var digamma = require( '@stdlib/math/base/special/digamma' );
     26 var gamma = require( '@stdlib/math/base/special/gamma' );
     27 var ln = require( '@stdlib/math/base/special/ln' );
     28 
     29 
     30 // MAIN //
     31 
     32 /**
     33 * Returns the differential entropy of an Erlang distribution.
     34 *
     35 * @param {PositiveInteger} k - shape parameter
     36 * @param {PositiveNumber} lambda - rate parameter
     37 * @returns {number} differential entropy
     38 *
     39 * @example
     40 * var v = entropy( 1, 1.0 );
     41 * // returns 1.0
     42 *
     43 * @example
     44 * var v = entropy( 4, 12.0 );
     45 * // returns ~-0.462
     46 *
     47 * @example
     48 * var v = entropy( 8, 2.0 );
     49 * // returns ~1.723
     50 *
     51 * @example
     52 * var v = entropy( 1.5, 2.0 );
     53 * // returns NaN
     54 *
     55 * @example
     56 * var v = entropy( 1, -0.1 );
     57 * // returns NaN
     58 *
     59 * @example
     60 * var v = entropy( -0.1, 1.0 );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var v = entropy( 2, NaN );
     65 * // returns NaN
     66 *
     67 * @example
     68 * var v = entropy( NaN, 2.0 );
     69 * // returns NaN
     70 */
     71 function entropy( k, lambda ) {
     72 	if (
     73 		!isPositiveInteger( k ) ||
     74 		isnan( lambda ) ||
     75 		lambda <= 0.0
     76 	) {
     77 		return NaN;
     78 	}
     79 	return ( ( 1-k ) * digamma( k ) ) + ln( gamma( k ) / lambda ) + k;
     80 }
     81 
     82 
     83 // EXPORTS //
     84 
     85 module.exports = entropy;