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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 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_math.h"
- #include "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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