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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__ */