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* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
/*
* Translated from the Fortran module by
* ----------------------------------------------------------------------
* Authors:
* Amparo Gil (U. Cantabria, Santander, Spain)
* e-mail: amparo.gil@unican.es
* Javier Segura (U. Cantabria, Santander, Spain)
* e-mail: javier.segura@unican.es
* Nico M. Temme (CWI, Amsterdam, The Netherlands)
* e-mail: nico.temme@cwi.nl
* ---------------------------------------------------------------------
*/
// MODULES //
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var FLOAT32_SMALLEST = require( '@stdlib/constants/float32/smallest-normal' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var compute = require( './compute.js' );
// MAIN //
/**
* Inverts the lower gamma function; i.e., computes `xr` such that `P(a,xr) = p`.
*
* ## Method
*
* The present code uses different methods of computation depending on the values of the input values: Taylor, asymptotic expansions and high-order Newton methods.
*
* ## Notes
*
* - The claimed accuracy obtained using this inversion routine is near `1e-12`.
*
* ## References
*
* - 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
* - 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
*
* @param {Probability} p - probability value
* @param {number} a - scale parameter
* @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`.
* @returns {number} function value of the inverse
*/
function gammaincinv( p, a, upper ) {
if ( isnan( p ) || isnan( a ) ) {
return NaN;
}
if ( a < FLOAT32_SMALLEST ) {
return NaN;
}
if ( p > 1.0 || p < 0.0 ) {
return NaN;
}
// Case: invert upper gamma function
if ( upper === true ) {
if ( p === 0.0 ) {
return PINF;
}
if ( p === 1.0 ) {
return 0.0;
}
return compute( a, 1.0-p, p );
}
// Default: invert lower gamma function
if ( p === 0.0 ) {
return 0.0;
}
if ( p === 1.0 ) {
return PINF;
}
return compute( a, p, 1.0-p );
}
// EXPORTS //
module.exports = gammaincinv;
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