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eval.c

/* 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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