/* cheb/gsl_chebyshev.h

 * 

 * 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.

 */

#ifndef __GSL_CHEBYSHEV_H__

#define __GSL_CHEBYSHEV_H__

#include <gsl/gsl_math.h>

#include <gsl/gsl_mode.h>

#undef __BEGIN_DECLS

#undef __END_DECLS

#ifdef __cplusplus

# define __BEGIN_DECLS extern "C" {

# define __END_DECLS }

#else

# define __BEGIN_DECLS /* empty */

# define __END_DECLS /* empty */

#endif

__BEGIN_DECLS

/* data for a Chebyshev series over a given interval */

struct gsl_cheb_series_struct {

  double * c;   /* coefficients                */

  size_t order; /* order of expansion          */

  double a;     /* lower interval point        */

  double b;     /* upper interval point        */

  /* The following exists (mostly) for the benefit

   * of the implementation. It is an effective single

   * precision order, for use in single precision

   * evaluation. Users can use it if they like, but

   * only they know how to calculate it, since it is

   * specific to the approximated function. By default,

   * order_sp = order.

   * It is used explicitly only by the gsl_cheb_eval_mode

   * functions, which are not meant for casual use.

   */

  size_t order_sp;

  /* Additional elements not used by specfunc */

  double * f;   /* function evaluated at chebyschev points  */

};

typedef struct gsl_cheb_series_struct gsl_cheb_series;

/* Calculate a Chebyshev series of specified order over

 * a specified interval, for a given function.

 * Return 0 on failure.

 */

gsl_cheb_series * gsl_cheb_alloc(const size_t order);

/* Free a Chebyshev series previously calculated with gsl_cheb_alloc().

 */

void gsl_cheb_free(gsl_cheb_series * cs);

/* Calculate a Chebyshev series using the storage provided.

 * Uses the interval (a,b) and the order with which it

 * was initially created.

 *

 */

int gsl_cheb_init(gsl_cheb_series * cs, const gsl_function * func,

                  const double a, const double b);

/* Return the order, size of coefficient array and coefficient array ptr */

size_t gsl_cheb_order (const gsl_cheb_series * cs);

size_t gsl_cheb_size (const gsl_cheb_series * cs);

double *gsl_cheb_coeffs (const gsl_cheb_series * cs);

/* Evaluate a Chebyshev series at a given point.

 * No errors can occur for a struct obtained from gsl_cheb_new().

 */

double gsl_cheb_eval(const gsl_cheb_series * cs, const double x);

int gsl_cheb_eval_err(const gsl_cheb_series * cs, const double x, 

                      double * result, double * abserr);

/* Evaluate a Chebyshev series at a given point, to (at most) the given order.

 * No errors can occur for a struct obtained from gsl_cheb_new().

 */

double gsl_cheb_eval_n(const gsl_cheb_series * cs, const size_t order, 

                       const double x);

int gsl_cheb_eval_n_err(const gsl_cheb_series * cs, const size_t order, 

                        const double x, double * result, double * abserr);

/* Evaluate a Chebyshev series at a given point, using the default

 * order for double precision mode(s) and the single precision

 * order for other modes.

 * No errors can occur for a struct obtained from gsl_cheb_new().

 */

double gsl_cheb_eval_mode(const gsl_cheb_series * cs, const double x, gsl_mode_t mode);

int gsl_cheb_eval_mode_e(const gsl_cheb_series * cs, const double x, gsl_mode_t mode, double * result, double * abserr);

/* Compute the derivative of a Chebyshev series.

 */

int gsl_cheb_calc_deriv(gsl_cheb_series * deriv, const gsl_cheb_series * cs);

/* Compute the integral of a Chebyshev series. The

 * integral is fixed by the condition that it equals zero at

 * the left end-point, ie it is precisely

 *       Integrate[cs(t; a,b), {t, a, x}]

 */

int gsl_cheb_calc_integ(gsl_cheb_series * integ, const gsl_cheb_series * cs);

__END_DECLS

#endif /* __GSL_CHEBYSHEV_H__ */