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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.
*
*
* ## Notice
*
* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_58_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* Copyright John Maddock 2006-7, 2013-14.
* Copyright Paul A. Bristow 2007, 2013-14.
* Copyright Nikhar Agrawal 2013-14.
* Copyright Christopher Kormanyos 2013-14.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var gammaln = require( '@stdlib/math/base/special/gammaln' );
var exp = require( '@stdlib/math/base/special/exp' );
var ln = require( '@stdlib/math/base/special/ln' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var FLOAT64_MAX = require( '@stdlib/constants/float64/max' );
var regularisedGammaPrefix = require( './regularised_gamma_prefix.js' );
// MAIN //
/**
* Calculates the partial derivative with respect to x of the incomplete gamma function.
*
* @private
* @param {PositiveNumber} a - function parameter
* @param {NonNegativeNumber} x - function parameter
* @returns {number} function value
*/
function gammaPDerivative( a, x ) {
var f1;
if ( a <= 0.0 ) {
return NaN;
}
if ( x < 0.0 ) {
return NaN;
}
if ( x === 0.0 ) {
if ( a > 1.0 ) {
return 0.0;
}
return ( a === 1.0 ) ? 1.0 : PINF;
}
f1 = regularisedGammaPrefix( a, x );
if ( x < 1.0 && ( FLOAT64_MAX * x < f1 ) ) {
return PINF;
}
if ( f1 === 0.0 ) {
// Underflow in calculation, use logs instead:
f1 = (a * ln( x )) - x - gammaln( a ) - ln( x );
f1 = exp( f1 );
} else {
f1 /= x;
}
return f1;
}
// EXPORTS //
module.exports = gammaPDerivative;
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