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/*!
* \file
* \brief Implementation of Chebyshev series evaluation function
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* Copyright (C) 1995-2010 (see AUTHORS file for a list of contributors)
*
* This file is part of IT++ - a C++ library of mathematical, signal
* processing, speech processing, and communications classes and functions.
*
* IT++ is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* IT++ is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along
* with IT++. If not, see <http://www.gnu.org/licenses/>.
*
* -------------------------------------------------------------------------
*
* This is slightly modified routine from the Cephes library:
* http://www.netlib.org/cephes/
*/
#include <itpp/base/bessel/bessel_internal.h>
/*
* Evaluate Chebyshev series
*
* int N;
* double x, y, coef[N], chebevl();
*
* y = chbevl( x, coef, N );
*
* DESCRIPTION:
*
* Evaluates the series
*
* N-1
* - '
* y = > coef[i] T (x/2)
* - i
* i=0
*
* of Chebyshev polynomials Ti at argument x/2.
*
* Coefficients are stored in reverse order, i.e. the zero
* order term is last in the array. Note N is the number of
* coefficients, not the order.
*
* If coefficients are for the interval a to b, x must
* have been transformed to x -> 2(2x - b - a)/(b-a) before
* entering the routine. This maps x from (a, b) to (-1, 1),
* over which the Chebyshev polynomials are defined.
*
* If the coefficients are for the inverted interval, in
* which (a, b) is mapped to (1/b, 1/a), the transformation
* required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
* this becomes x -> 4a/x - 1.
*
* SPEED:
*
* Taking advantage of the recurrence properties of the
* Chebyshev polynomials, the routine requires one more
* addition per loop than evaluating a nested polynomial of
* the same degree.
*/
/*
Cephes Math Library Release 2.0: April, 1987
Copyright 1985, 1987 by Stephen L. Moshier
*/
double chbevl(double x, double array[], int n)
{
double b0, b1, b2, *p;
int i;
p = array;
b0 = *p++;
b1 = 0.0;
i = n - 1;
do {
b2 = b1;
b1 = b0;
b0 = x * b1 - b2 + *p++;
}
while (--i);
return(0.5*(b0 - b2));
}
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