src/nmath/chebyshev.c

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *
 *  This program 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 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program 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 this program; if not, a copy is available at
 *  https://www.R-project.org/Licenses/
 *
 *  SYNOPSIS
 *
 *    int chebyshev_init(double *dos, int nos, double eta)
 *    double chebyshev_eval(double x, double *a, int n)
 *
 *  DESCRIPTION
 *
 *    "chebyshev_init" determines the number of terms for the
 *    double precision orthogonal series "dos" needed to insure
 *    the error is no larger than "eta".  Ordinarily eta will be
 *    chosen to be one-tenth machine precision.
 *
 *    "chebyshev_eval" evaluates the n-term Chebyshev series
 *    "a" at "x".
 *
 *  NOTES
 *
 *    These routines are translations into C of Fortran routines
 *    by W. Fullerton of Los Alamos Scientific Laboratory.
 *
 *    Based on the Fortran routine dcsevl by W. Fullerton.
 *    Adapted from R. Broucke, Algorithm 446, CACM., 16, 254 (1973).
 */

#include "nmath.h"

/* NaNs propagated correctly */


int attribute_hidden chebyshev_init(double *dos, int nos, double eta)
{
    int i, ii;
    double err;

    if (nos < 1)
	return 0;

    err = 0.0;
    i = 0;			/* just to avoid compiler warnings */
    for (ii=1; ii<=nos; ii++) {
	i = nos - ii;
	err += fabs(dos[i]);
	if (err > eta) {
	    return i;
	}
    }
    return i;
}


double attribute_hidden chebyshev_eval(double x, const double *a, const int n)
{
    double b0, b1, b2, twox;
    int i;

    if (n < 1 || n > 1000) ML_ERR_return_NAN;

    if (x < -1.1 || x > 1.1) ML_ERR_return_NAN;

    twox = x * 2;
    b2 = b1 = 0;
    b0 = 0;
    for (i = 1; i <= n; i++) {
	b2 = b1;
	b1 = b0;
	b0 = twox * b1 - b2 + a[n - i];
    }
    return (b0 - b2) * 0.5;
}