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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_60_0/boost/math/tools/rational.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 abs = require( '@stdlib/math/base/special/abs' );
// MAIN //
/**
* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)) using double-precision floating-point arithmetic.
*
* ## Notes
*
* - Coefficients should be sorted in ascending degree.
* - The implementation uses [Horner's rule][horners-method] for efficient computation.
*
* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
*
* @param {NumericArray} P - numerator polynomial coefficients sorted in ascending degree
* @param {NumericArray} Q - denominator polynomial coefficients sorted in ascending degree
* @param {number} x - value at which to evaluate the rational function
* @returns {number} evaluated rational function
*
* @example
* var P = [ -6.0, -5.0 ];
* var Q = [ 3.0, 0.5 ];
*
* var v = evalrational( P, Q, 6.0 ); // => ( -6*6^0 - 5*6^1 ) / ( 3*6^0 + 0.5*6^1 ) = (-6-30)/(3+3)
* // returns -6.0
*
* @example
* // 2x^3 + 4x^2 - 5x^1 - 6x^0 => degree 4
* var P = [ -6.0, -5.0, 4.0, 2.0 ];
*
* // 0.5x^1 + 3x^0 => degree 2
* var Q = [ 3.0, 0.5, 0.0, 0.0 ]; // zero-padded
*
* var v = evalrational( P, Q, 6.0 ); // => ( -6*6^0 - 5*6^1 + 4*6^2 + 2*6^3 ) / ( 3*6^0 + 0.5*6^1 + 0*6^2 + 0*6^3 ) = (-6-30+144+432)/(3+3)
* // returns 90.0
*/
function evalrational( P, Q, x ) {
var len;
var s1;
var s2;
var i;
len = P.length;
if ( len === 0 ) {
return NaN;
}
if ( len !== Q.length ) {
return NaN;
}
if ( x === 0.0 || len === 1 ) {
return P[ 0 ] / Q[ 0 ];
}
// Use Horner's method...
if ( abs( x ) <= 1.0 ) {
s1 = P[ len-1 ];
s2 = Q[ len-1 ];
for ( i = len-2; i >= 0; --i ) {
s1 *= x;
s2 *= x;
s1 += P[ i ];
s2 += Q[ i ];
}
} else {
x = 1.0 / x; // use inverse to avoid overflow
s1 = P[ 0 ];
s2 = Q[ 0 ];
for ( i = 1; i < len; ++i ) {
s1 *= x;
s2 *= x;
s1 += P[ i ];
s2 += Q[ i ];
}
}
return s1 / s2;
}
// EXPORTS //
module.exports = evalrational;
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