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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 ibetaPowerTerms = require( './ibeta_power_terms.js' );
// MAIN //
/**
* Computes the difference between `ibeta(a,b,x)` and `ibeta(a+k,b,x)`.
*
* @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 {NonNegativeInteger} k - function input
* @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} difference between ibeta(a,b,x) and ibeta(a+k,b,x)
*/
function ibetaAStep( a, b, x, y, k, normalized, out ) {
var prefix;
var term;
var sum;
var i;
prefix = ibetaPowerTerms( a, b, x, y, normalized );
if ( out ) {
out[ 1 ] = prefix;
}
prefix /= a;
if ( prefix === 0.0 ) {
return prefix;
}
sum = 1.0;
term = 1.0;
// Series summation from 0 to k-1:
for ( i = 0; i < k-1; ++i ) {
term *= (a+b+i) * x / (a+i+1.0);
sum += term;
}
prefix *= sum;
return prefix;
}
// EXPORTS //
module.exports = ibetaAStep;
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