include/gsl/gsl_chebyshev.h

0001 /* cheb/gsl_chebyshev.h
0002  *
0003  * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
0004  *
0005  * This program is free software; you can redistribute it and/or modify
0006  * it under the terms of the GNU General Public License as published by
0007  * the Free Software Foundation; either version 3 of the License, or (at
0008  * your option) any later version.
0009  *
0010  * This program is distributed in the hope that it will be useful, but
0011  * WITHOUT ANY WARRANTY; without even the implied warranty of
0012  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0013  * General Public License for more details.
0014  *
0015  * You should have received a copy of the GNU General Public License
0016  * along with this program; if not, write to the Free Software
0017  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
0018  */
0019
0020 #ifndef __GSL_CHEBYSHEV_H__
0021 #define __GSL_CHEBYSHEV_H__
0022
0023 #include <stdlib.h>
0024 #include <gsl/gsl_math.h>
0025 #include <gsl/gsl_mode.h>
0026
0027 #undef __BEGIN_DECLS
0028 #undef __END_DECLS
0029 #ifdef __cplusplus
0030 # define __BEGIN_DECLS extern "C" {
0031 # define __END_DECLS }
0032 #else
0033 # define __BEGIN_DECLS /* empty */
0034 # define __END_DECLS /* empty */
0035 #endif
0036
0037 __BEGIN_DECLS
0038
0039
0040 /* data for a Chebyshev series over a given interval */
0041
0042 struct gsl_cheb_series_struct {
0043
0044   double * c;   /* coefficients                */
0045   size_t order; /* order of expansion          */
0046   double a;     /* lower interval point        */
0047   double b;     /* upper interval point        */
0048
0049   /* The following exists (mostly) for the benefit
0050    * of the implementation. It is an effective single
0051    * precision order, for use in single precision
0052    * evaluation. Users can use it if they like, but
0053    * only they know how to calculate it, since it is
0054    * specific to the approximated function. By default,
0055    * order_sp = order.
0056    * It is used explicitly only by the gsl_cheb_eval_mode
0057    * functions, which are not meant for casual use.
0058    */
0059   size_t order_sp;
0060
0061   /* Additional elements not used by specfunc */
0062
0063   double * f;   /* function evaluated at chebyschev points  */
0064 };
0065 typedef struct gsl_cheb_series_struct gsl_cheb_series;
0066
0067
0068 /* Calculate a Chebyshev series of specified order over
0069  * a specified interval, for a given function.
0070  * Return 0 on failure.
0071  */
0072 gsl_cheb_series * gsl_cheb_alloc(const size_t order);
0073
0074 /* Free a Chebyshev series previously calculated with gsl_cheb_alloc().
0075  */
0076 void gsl_cheb_free(gsl_cheb_series * cs);
0077
0078 /* Calculate a Chebyshev series using the storage provided.
0079  * Uses the interval (a,b) and the order with which it
0080  * was initially created.
0081  *
0082  */
0083 int gsl_cheb_init(gsl_cheb_series * cs, const gsl_function * func,
0084                   const double a, const double b);
0085
0086 /* Return the order, size of coefficient array and coefficient array ptr */
0087 size_t gsl_cheb_order (const gsl_cheb_series * cs);
0088 size_t gsl_cheb_size (const gsl_cheb_series * cs);
0089 double *gsl_cheb_coeffs (const gsl_cheb_series * cs);
0090
0091 /* Evaluate a Chebyshev series at a given point.
0092  * No errors can occur for a struct obtained from gsl_cheb_new().
0093  */
0094 double gsl_cheb_eval(const gsl_cheb_series * cs, const double x);
0095 int gsl_cheb_eval_err(const gsl_cheb_series * cs, const double x,
0096                       double * result, double * abserr);
0097
0098
0099 /* Evaluate a Chebyshev series at a given point, to (at most) the given order.
0100  * No errors can occur for a struct obtained from gsl_cheb_new().
0101  */
0102 double gsl_cheb_eval_n(const gsl_cheb_series * cs, const size_t order,
0103                        const double x);
0104 int gsl_cheb_eval_n_err(const gsl_cheb_series * cs, const size_t order,
0105                         const double x, double * result, double * abserr);
0106
0107
0108 /* Evaluate a Chebyshev series at a given point, using the default
0109  * order for double precision mode(s) and the single precision
0110  * order for other modes.
0111  * No errors can occur for a struct obtained from gsl_cheb_new().
0112  */
0113 double gsl_cheb_eval_mode(const gsl_cheb_series * cs, const double x, gsl_mode_t mode);
0114 int gsl_cheb_eval_mode_e(const gsl_cheb_series * cs, const double x, gsl_mode_t mode, double * result, double * abserr);
0115
0116
0117
0118 /* Compute the derivative of a Chebyshev series.
0119  */
0120 int gsl_cheb_calc_deriv(gsl_cheb_series * deriv, const gsl_cheb_series * cs);
0121
0122 /* Compute the integral of a Chebyshev series. The
0123  * integral is fixed by the condition that it equals zero at
0124  * the left end-point, ie it is precisely
0125  *       Integrate[cs(t; a,b), {t, a, x}]
0126  */
0127 int gsl_cheb_calc_integ(gsl_cheb_series * integ, const gsl_cheb_series * cs);
0128
0129
0130
0131
0132 __END_DECLS
0133
0134 #endif /* __GSL_CHEBYSHEV_H__ */