time-to-botec

Benchmark sampling in different programming languages
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lower_gamma_series.js (2204B)

      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 * ## Notice
     20 *
     21 * The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_61_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript.
     22 *
     23 * ```text
     24 * Copyright John Maddock 2006-7, 2013-14.
     25 * Copyright Paul A. Bristow 2007, 2013-14.
     26 * Copyright Nikhar Agrawal 2013-14.
     27 * Copyright Christopher Kormanyos 2013-14.
     28 *
     29 * Use, modification and distribution are subject to the
     30 * Boost Software License, Version 1.0. (See accompanying file
     31 * LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
     32 * ```
     33 */
     34 
     35 'use strict';
     36 
     37 // MODULES //
     38 
     39 var sumSeries = require( './../../../../base/tools/sum-series' );
     40 var lowerIncompleteGammaSeries = require( './lower_incomplete_gamma_series.js' );
     41 
     42 
     43 // VARIABLES //
     44 
     45 var opts = {
     46 	'maxIter': 1000
     47 };
     48 
     49 
     50 // MAIN //
     51 
     52 /**
     53 * Sums elements of the series expansion of the lower incomplete gamma function.
     54 *
     55 * ## Method
     56 *
     57 * -   Multiply result by `(z^a)*(e^-z) / a` to get the full lower incomplete integral.
     58 * -   Divide by `tgamma(a)` to get the normalized value.
     59 *
     60 * @private
     61 * @param {number} a - function parameter
     62 * @param {number} z - function parameter
     63 * @param {number} initialValue - initial value of the resulting sum
     64 * @returns {number} sum of terms of lower gamma series
     65 */
     66 function lowerGammaSeries( a, z, initialValue ) {
     67 	var result;
     68 	var s;
     69 
     70 	initialValue = initialValue || 0.0;
     71 	s = lowerIncompleteGammaSeries( a, z );
     72 	opts.initialValue = initialValue;
     73 	result = sumSeries( s, opts );
     74 	return result;
     75 }
     76 
     77 
     78 // EXPORTS //
     79 
     80 module.exports = lowerGammaSeries;