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/* 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 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.
*/
#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);
/* 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__ */
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