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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_61_0/boost/math/special_functions/beta.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* (C) Copyright John Maddock 2006.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var continuedFraction = require( '@stdlib/math/base/tools/continued-fraction' );
var ibetaPowerTerms = require( './ibeta_power_terms.js' );
// VARIABLES //
var OPTS = {
'keep': true,
'maxIter': 1000
};
// FUNCTIONS //
/**
* Continued fraction for the incomplete beta.
*
* @private
* @param {NonNegativeNumber} a - function parameter
* @param {NonNegativeNumber} b - function parameter
* @param {Probability} x - function parameter
* @param {Probability} y - probability equal to `1-x`
* @returns {Function} series function
*/
function ibetaFraction2t( a, b, x, y ) {
var m = 0;
return next;
/**
* Calculate the numerator and denominator of the next term of the series.
*
* @private
* @returns {Array} series expansion terms
*/
function next() {
var denom;
var aN;
var bN;
aN = (a + m - 1) * (a + b + m - 1) * m * (b - m) * x * x;
denom = a + ( 2.0*m ) - 1.0;
aN /= denom * denom;
bN = m;
bN += (m * (b - m) * x) / ( a + ( 2.0*m ) - 1.0 );
bN += ( (a+m) * ( (a*y) - (b*x) + 1.0 + ( m*(2.0-x) ) ) ) / ( a + (2.0*m) + 1.0 ); // eslint-disable-line max-len
m += 1;
return [ aN, bN ];
}
}
// MAIN //
/**
* Evaluates the incomplete beta via the continued fraction representation.
*
* @private
* @param {NonNegativeNumber} a - function parameter
* @param {NonNegativeNumber} b - function parameter
* @param {Probability} x - function parameter
* @param {Probability} y - probability equal to `1-x`
* @param {boolean} normalized - boolean indicating whether to evaluate the power terms of the regularized or non-regularized incomplete beta function
* @param {(Array|TypedArray|Object)} out - output array holding the derivative as the second element
* @returns {number} incomplete beta value
*/
function ibetaFraction2( a, b, x, y, normalized, out ) {
var result;
var fract;
var f;
result = ibetaPowerTerms( a, b, x, y, normalized );
if ( out ) {
out[ 1 ] = result;
}
if ( result === 0.0 ) {
return result;
}
f = ibetaFraction2t( a, b, x, y );
fract = continuedFraction( f, OPTS );
return result / fract;
}
// EXPORTS //
module.exports = ibetaFraction2;
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