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/* cheb/eval.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
*
* 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, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_chebyshev.h>
/* For efficiency there are separate implementations of each of these
functions */
double
gsl_cheb_eval (const gsl_cheb_series * cs, const double x)
{
size_t i;
double d1 = 0.0;
double d2 = 0.0;
double y = (2.0 * x - cs->a - cs->b) / (cs->b - cs->a);
double y2 = 2.0 * y;
for (i = cs->order; i >= 1; i--)
{
double temp = d1;
d1 = y2 * d1 - d2 + cs->c[i];
d2 = temp;
}
return y * d1 - d2 + 0.5 * cs->c[0];
}
double
gsl_cheb_eval_n (const gsl_cheb_series * cs, const size_t n, const double x)
{
size_t i;
double d1 = 0.0;
double d2 = 0.0;
size_t eval_order = GSL_MIN (n, cs->order);
double y = (2.0 * x - cs->a - cs->b) / (cs->b - cs->a);
double y2 = 2.0 * y;
for (i = eval_order; i >= 1; i--)
{
double temp = d1;
d1 = y2 * d1 - d2 + cs->c[i];
d2 = temp;
}
return y * d1 - d2 + 0.5 * cs->c[0];
}
int
gsl_cheb_eval_err (const gsl_cheb_series * cs, const double x,
double *result, double *abserr)
{
size_t i;
double d1 = 0.0;
double d2 = 0.0;
double y = (2. * x - cs->a - cs->b) / (cs->b - cs->a);
double y2 = 2.0 * y;
double absc = 0.0;
for (i = cs->order; i >= 1; i--)
{
double temp = d1;
d1 = y2 * d1 - d2 + cs->c[i];
d2 = temp;
}
*result = y * d1 - d2 + 0.5 * cs->c[0];
/* Estimate cumulative numerical error */
for (i = 0; i <= cs->order; i++)
{
absc += fabs(cs->c[i]);
}
/* Combine truncation error and numerical error */
*abserr = fabs (cs->c[cs->order]) + absc * GSL_DBL_EPSILON;
return GSL_SUCCESS;
}
int
gsl_cheb_eval_n_err (const gsl_cheb_series * cs,
const size_t n, const double x,
double *result, double *abserr)
{
size_t i;
double d1 = 0.0;
double d2 = 0.0;
double y = (2. * x - cs->a - cs->b) / (cs->b - cs->a);
double y2 = 2.0 * y;
double absc = 0.0;
size_t eval_order = GSL_MIN (n, cs->order);
for (i = eval_order; i >= 1; i--)
{
double temp = d1;
d1 = y2 * d1 - d2 + cs->c[i];
d2 = temp;
}
*result = y * d1 - d2 + 0.5 * cs->c[0];
/* Estimate cumulative numerical error */
for (i = 0; i <= eval_order; i++)
{
absc += fabs(cs->c[i]);
}
/* Combine truncation error and numerical error */
*abserr = fabs (cs->c[eval_order]) + absc * GSL_DBL_EPSILON;
return GSL_SUCCESS;
}
int
gsl_cheb_eval_mode_e (const gsl_cheb_series * cs,
const double x, gsl_mode_t mode,
double *result, double *abserr)
{
size_t i;
double d1 = 0.0;
double d2 = 0.0;
double y = (2. * x - cs->a - cs->b) / (cs->b - cs->a);
double y2 = 2.0 * y;
double absc = 0.0;
size_t eval_order;
if (GSL_MODE_PREC (mode) == GSL_PREC_DOUBLE)
eval_order = cs->order;
else
eval_order = cs->order_sp;
for (i = eval_order; i >= 1; i--)
{
double temp = d1;
d1 = y2 * d1 - d2 + cs->c[i];
d2 = temp;
}
*result = y * d1 - d2 + 0.5 * cs->c[0];
/* Estimate cumulative numerical error */
for (i = 0; i <= eval_order; i++)
{
absc += fabs(cs->c[i]);
}
/* Combine truncation error and numerical error */
*abserr = fabs (cs->c[eval_order]) + absc * GSL_DBL_EPSILON;
return GSL_SUCCESS;
}
double
gsl_cheb_eval_mode (const gsl_cheb_series * cs,
const double x, gsl_mode_t mode)
{
double result, abserr;
int status = gsl_cheb_eval_mode_e (cs, x, mode, &result, &abserr);
if (status != GSL_SUCCESS)
{
GSL_ERROR_VAL("gsl_cheb_eval_mode", status, result);
};
return result;
}
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