/* 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 3 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;

}