time-to-botec

Benchmark sampling in different programming languages
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gammaincinv.js (3048B)

      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 /*
     22 * Translated from the Fortran module by
     23 * ----------------------------------------------------------------------
     24 * Authors:
     25 *  Amparo Gil    (U. Cantabria, Santander, Spain)
     26 *                 e-mail: amparo.gil@unican.es
     27 *  Javier Segura (U. Cantabria, Santander, Spain)
     28 *                 e-mail: javier.segura@unican.es
     29 *  Nico M. Temme (CWI, Amsterdam, The Netherlands)
     30 *                 e-mail: nico.temme@cwi.nl
     31 * ---------------------------------------------------------------------
     32 */
     33 
     34 // MODULES //
     35 
     36 var isnan = require( './../../../../base/assert/is-nan' );
     37 var FLOAT32_SMALLEST = require( '@stdlib/constants/float32/smallest-normal' );
     38 var PINF = require( '@stdlib/constants/float64/pinf' );
     39 var compute = require( './compute.js' );
     40 
     41 
     42 // MAIN //
     43 
     44 /**
     45 * Inverts the lower gamma function; i.e., computes `xr` such that `P(a,xr) = p`.
     46 *
     47 * ## Method
     48 *
     49 * The present code uses different methods of computation depending on the values of the input values: Taylor, asymptotic expansions and high-order Newton methods.
     50 *
     51 * ## Notes
     52 *
     53 * -   The claimed accuracy obtained using this inversion routine is near `1e-12`.
     54 *
     55 * ## References
     56 *
     57 * -   A. Gil, J. Segura and N.M. Temme, GammaCHI: a package for the inversion and computation of the gamma and chi-square distribution functions (central and noncentral). Computer Physics Commun
     58 * -   A. Gil, J. Segura and N.M. Temme. Efficient and accurate algorithms for the computation and inversion of the incomplete gamma function ratios. SIAM J Sci Comput. (2012) 34(6), A2965-A2981
     59 *
     60 *
     61 * @param {Probability} p - probability value
     62 * @param {number} a - scale parameter
     63 * @param {boolean} [upper=false] - boolean indicating if the function should invert the upper tail of the incomplete gamma function instead; i.e., compute `xr` such that `Q(a,xr) = p`.
     64 * @returns {number} function value of the inverse
     65 */
     66 function gammaincinv( p, a, upper ) {
     67 	if ( isnan( p ) || isnan( a ) ) {
     68 		return NaN;
     69 	}
     70 	if ( a < FLOAT32_SMALLEST ) {
     71 		return NaN;
     72 	}
     73 	if ( p > 1.0 || p < 0.0 ) {
     74 		return NaN;
     75 	}
     76 	// Case: invert upper gamma function
     77 	if ( upper === true ) {
     78 		if ( p === 0.0 ) {
     79 			return PINF;
     80 		}
     81 		if ( p === 1.0 ) {
     82 			return 0.0;
     83 		}
     84 		return compute( a, 1.0-p, p );
     85 	}
     86 	// Default: invert lower gamma function
     87 	if ( p === 0.0 ) {
     88 		return 0.0;
     89 	}
     90 	if ( p === 1.0 ) {
     91 		return PINF;
     92 	}
     93 	return compute( a, p, 1.0-p );
     94 }
     95 
     96 
     97 // EXPORTS //
     98 
     99 module.exports = gammaincinv;