diff options
Diffstat (limited to 'gsl-1.9/cheb')
| -rw-r--r-- | gsl-1.9/cheb/ChangeLog | 54 | ||||
| -rw-r--r-- | gsl-1.9/cheb/Makefile.am | 17 | ||||
| -rw-r--r-- | gsl-1.9/cheb/Makefile.in | 543 | ||||
| -rw-r--r-- | gsl-1.9/cheb/deriv.c | 63 | ||||
| -rw-r--r-- | gsl-1.9/cheb/eval.c | 206 | ||||
| -rw-r--r-- | gsl-1.9/cheb/gsl_chebyshev.h | 129 | ||||
| -rw-r--r-- | gsl-1.9/cheb/init.c | 101 | ||||
| -rw-r--r-- | gsl-1.9/cheb/integ.c | 65 | ||||
| -rw-r--r-- | gsl-1.9/cheb/test.c | 208 |
9 files changed, 1386 insertions, 0 deletions
diff --git a/gsl-1.9/cheb/ChangeLog b/gsl-1.9/cheb/ChangeLog new file mode 100644 index 0000000..7465d7e --- /dev/null +++ b/gsl-1.9/cheb/ChangeLog @@ -0,0 +1,54 @@ +2007-01-29 Brian Gough <bjg@network-theory.co.uk> + + * eval.c (gsl_cheb_eval_mode_e): compute error consistently with + other routines + +2004-12-29 Brian Gough <bjg@network-theory.co.uk> + + * gsl_chebyshev.h: added const to declaration of + gsl_cheb_eval_mode to match definition + +2004-12-24 Brian Gough <bjg@network-theory.co.uk> + + * eval.c (gsl_cheb_eval_n_err): use eval_order instead of + cs->order for error estimate + +2004-12-23 Brian Gough <bjg@network-theory.co.uk> + + * eval.c (gsl_cheb_eval_mode): added missing function + +2004-08-27 Brian Gough <bjg@network-theory.co.uk> + + * test.c (main): make the hard-coded tolerances a variable, ftol + +2003-06-09 Brian Gough <bjg@network-theory.co.uk> + + * test.c (main): added some tests for the coefficients + +2003-02-09 Brian Gough <bjg@network-theory.co.uk> + + * gsl_chebyshev.h: added missing #include for gsl_math (to declare + gsl_function) fixes Debian Bug#179665 + +Fri May 24 19:23:47 2002 Brian Gough <bjg@network-theory.co.uk> + + * init.c (gsl_cheb_free): added missing free() for cs->f + +Fri Aug 24 19:18:23 2001 Brian Gough <bjg@network-theory.co.uk> + + * test.c (main): renamed fsin to f_sin to avoid conflicts with + irix math libs. + +Sun May 6 09:49:28 2001 Brian Gough <bjg@network-theory.co.uk> + + * eval.c (gsl_cheb_eval_err): take roundoff into account when + computing evaluation error (important when result is near zero). + (gsl_cheb_eval_n_err): ditto + +Tue Apr 24 17:08:29 2001 Brian Gough <bjg@network-theory.co.uk> + + * made deriv/integ functions thread safe + + * split out from specfunc directory + + diff --git a/gsl-1.9/cheb/Makefile.am b/gsl-1.9/cheb/Makefile.am new file mode 100644 index 0000000..cf28e27 --- /dev/null +++ b/gsl-1.9/cheb/Makefile.am @@ -0,0 +1,17 @@ +noinst_LTLIBRARIES = libgslcheb.la + +pkginclude_HEADERS = gsl_chebyshev.h + +INCLUDES= -I$(top_builddir) + +libgslcheb_la_SOURCES = deriv.c eval.c init.c integ.c + +TESTS = $(check_PROGRAMS) + +check_PROGRAMS = test + +test_LDADD = libgslcheb.la ../ieee-utils/libgslieeeutils.la ../test/libgsltest.la ../sys/libgslsys.la ../err/libgslerr.la ../utils/libutils.la + +test_SOURCES = test.c + + diff --git a/gsl-1.9/cheb/Makefile.in b/gsl-1.9/cheb/Makefile.in new file mode 100644 index 0000000..b2a8bda --- /dev/null +++ b/gsl-1.9/cheb/Makefile.in @@ -0,0 +1,543 @@ +# Makefile.in generated by automake 1.9.6 from Makefile.am. +# @configure_input@ + +# Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, +# 2003, 2004, 2005 Free Software Foundation, Inc. +# This Makefile.in is free software; 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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. + */ + +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_chebyshev.h> + +int gsl_cheb_calc_deriv(gsl_cheb_series * deriv, const gsl_cheb_series * f) +{ + const size_t n = f->order + 1; + const double con = 2.0 / (f->b - f->a); + size_t i; + + if(deriv->order != f->order) + { + GSL_ERROR ("order of chebyshev series must be equal", GSL_ENOMEM); + } + + /* set the other parameters in the chebyshev struct */ + + deriv->a = f->a; + deriv->b = f->b; + +#ifdef ERR + deriv->err = n * n * f->c[n-1]; /* error in derivative is n^2 c_n */ +#endif + + /* FIXME: should probably set deriv->f[] as well */ + + deriv->c[n-1] = 0.0; + + if(n > 1) { + deriv->c[n-2] = 2.0 *(n-1.0) * f->c[n-1]; + + for(i = n-3; i>0; i--) + deriv->c[i] = deriv->c[i+2] + 2.0 *(i+1.0) * f->c[i+1]; + + deriv->c[0] = deriv->c[2] + 2.0 * f->c[1]; + + for(i = 0 ; i<n ; i++) + deriv->c[i] *= con; + } + + return GSL_SUCCESS; +} diff --git a/gsl-1.9/cheb/eval.c b/gsl-1.9/cheb/eval.c new file mode 100644 index 0000000..9d5acda --- /dev/null +++ b/gsl-1.9/cheb/eval.c @@ -0,0 +1,206 @@ +/* cheb/eval.c + * + * 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. + */ + +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_chebyshev.h> + +/* For efficiency there are separate implementations of each of these + functions */ + +double +gsl_cheb_eval (const gsl_cheb_series * cs, const double x) +{ + size_t i; + double d1 = 0.0; + double d2 = 0.0; + + double y = (2.0 * x - cs->a - cs->b) / (cs->b - cs->a); + double y2 = 2.0 * y; + + for (i = cs->order; i >= 1; i--) + { + double temp = d1; + d1 = y2 * d1 - d2 + cs->c[i]; + d2 = temp; + } + + return y * d1 - d2 + 0.5 * cs->c[0]; +} + +double +gsl_cheb_eval_n (const gsl_cheb_series * cs, const size_t n, const double x) +{ + size_t i; + double d1 = 0.0; + double d2 = 0.0; + + size_t eval_order = GSL_MIN (n, cs->order); + + double y = (2.0 * x - cs->a - cs->b) / (cs->b - cs->a); + double y2 = 2.0 * y; + + for (i = eval_order; i >= 1; i--) + { + double temp = d1; + d1 = y2 * d1 - d2 + cs->c[i]; + d2 = temp; + } + + return y * d1 - d2 + 0.5 * cs->c[0]; +} + + +int +gsl_cheb_eval_err (const gsl_cheb_series * cs, const double x, + double *result, double *abserr) +{ + size_t i; + double d1 = 0.0; + double d2 = 0.0; + + double y = (2. * x - cs->a - cs->b) / (cs->b - cs->a); + double y2 = 2.0 * y; + + double absc = 0.0; + + for (i = cs->order; i >= 1; i--) + { + double temp = d1; + d1 = y2 * d1 - d2 + cs->c[i]; + d2 = temp; + } + + *result = y * d1 - d2 + 0.5 * cs->c[0]; + + /* Estimate cumulative numerical error */ + + for (i = 0; i <= cs->order; i++) + { + absc += fabs(cs->c[i]); + } + + /* Combine truncation error and numerical error */ + + *abserr = fabs (cs->c[cs->order]) + absc * GSL_DBL_EPSILON; + + return GSL_SUCCESS; +} + +int +gsl_cheb_eval_n_err (const gsl_cheb_series * cs, + const size_t n, const double x, + double *result, double *abserr) +{ + size_t i; + double d1 = 0.0; + double d2 = 0.0; + + double y = (2. * x - cs->a - cs->b) / (cs->b - cs->a); + double y2 = 2.0 * y; + + double absc = 0.0; + + size_t eval_order = GSL_MIN (n, cs->order); + + for (i = eval_order; i >= 1; i--) + { + double temp = d1; + d1 = y2 * d1 - d2 + cs->c[i]; + d2 = temp; + } + + *result = y * d1 - d2 + 0.5 * cs->c[0]; + + /* Estimate cumulative numerical error */ + + for (i = 0; i <= eval_order; i++) + { + absc += fabs(cs->c[i]); + } + + /* Combine truncation error and numerical error */ + + *abserr = fabs (cs->c[eval_order]) + absc * GSL_DBL_EPSILON; + + return GSL_SUCCESS; +} + +int +gsl_cheb_eval_mode_e (const gsl_cheb_series * cs, + const double x, gsl_mode_t mode, + double *result, double *abserr) +{ + size_t i; + double d1 = 0.0; + double d2 = 0.0; + + double y = (2. * x - cs->a - cs->b) / (cs->b - cs->a); + double y2 = 2.0 * y; + + double absc = 0.0; + + size_t eval_order; + + if (GSL_MODE_PREC (mode) == GSL_PREC_DOUBLE) + eval_order = cs->order; + else + eval_order = cs->order_sp; + + for (i = eval_order; i >= 1; i--) + { + double temp = d1; + d1 = y2 * d1 - d2 + cs->c[i]; + d2 = temp; + } + + *result = y * d1 - d2 + 0.5 * cs->c[0]; + + /* Estimate cumulative numerical error */ + + for (i = 0; i <= eval_order; i++) + { + absc += fabs(cs->c[i]); + } + + /* Combine truncation error and numerical error */ + + *abserr = fabs (cs->c[eval_order]) + absc * GSL_DBL_EPSILON; + + return GSL_SUCCESS; +} + +double +gsl_cheb_eval_mode (const gsl_cheb_series * cs, + const double x, gsl_mode_t mode) +{ + double result, abserr; + int status = gsl_cheb_eval_mode_e (cs, x, mode, &result, &abserr); + + if (status != GSL_SUCCESS) + { + GSL_ERROR_VAL("gsl_cheb_eval_mode", status, result); + }; + + return result; +} + + diff --git a/gsl-1.9/cheb/gsl_chebyshev.h b/gsl-1.9/cheb/gsl_chebyshev.h new file mode 100644 index 0000000..2557908 --- /dev/null +++ b/gsl-1.9/cheb/gsl_chebyshev.h @@ -0,0 +1,129 @@ +/* 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__ */ diff --git a/gsl-1.9/cheb/init.c b/gsl-1.9/cheb/init.c new file mode 100644 index 0000000..9b42021 --- /dev/null +++ b/gsl-1.9/cheb/init.c @@ -0,0 +1,101 @@ +/* cheb/init.c + * + * 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. + */ + +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_chebyshev.h> + +/*-*-*-*-*-*-*-*-*-*-*-* Allocators *-*-*-*-*-*-*-*-*-*-*-*/ + +gsl_cheb_series * +gsl_cheb_alloc(const size_t order) +{ + gsl_cheb_series * cs = (gsl_cheb_series *) malloc(sizeof(gsl_cheb_series)); + + if(cs == 0) { + GSL_ERROR_VAL("failed to allocate gsl_cheb_series struct", GSL_ENOMEM, 0); + } + + cs->order = order; + cs->order_sp = order; + + cs->c = (double *) malloc((order+1) * sizeof(double)); + + if(cs->c == 0) { + GSL_ERROR_VAL("failed to allocate cheb coefficients", GSL_ENOMEM, 0); + } + + cs->f = (double *) malloc((order+1) * sizeof(double)); + + if(cs->f == 0) { + GSL_ERROR_VAL("failed to allocate cheb function space", GSL_ENOMEM, 0); + } + + return cs; +} + + +void gsl_cheb_free(gsl_cheb_series * cs) +{ + free(cs->f); + free(cs->c); + free(cs); +} + +/*-*-*-*-*-*-*-*-*-*-*-* Initializer *-*-*-*-*-*-*-*-*-*-*-*/ + +int gsl_cheb_init(gsl_cheb_series * cs, const gsl_function *func, + const double a, const double b) +{ + size_t k, j; + + if(a >= b) { + GSL_ERROR_VAL("null function interval [a,b]", GSL_EDOM, 0); + } + cs->a = a; + cs->b = b; + /* cs->err = 0.0; */ + + { + double bma = 0.5 * (cs->b - cs->a); + double bpa = 0.5 * (cs->b + cs->a); + double fac = 2.0/(cs->order +1.0); + + for(k = 0; k<=cs->order; k++) { + double y = cos(M_PI * (k+0.5)/(cs->order+1)); + cs->f[k] = GSL_FN_EVAL(func, (y*bma + bpa)); + } + + for(j = 0; j<=cs->order; j++) { + double sum = 0.0; + for(k = 0; k<=cs->order; k++) + sum += cs->f[k]*cos(M_PI * j*(k+0.5)/(cs->order+1)); + cs->c[j] = fac * sum; + } + + } + return GSL_SUCCESS; +} + + + + + diff --git a/gsl-1.9/cheb/integ.c b/gsl-1.9/cheb/integ.c new file mode 100644 index 0000000..0f49dd9 --- /dev/null +++ b/gsl-1.9/cheb/integ.c @@ -0,0 +1,65 @@ +/* cheb/integ.c + * + * 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. + */ + +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_chebyshev.h> + +int gsl_cheb_calc_integ(gsl_cheb_series * integ, const gsl_cheb_series * f) +{ + const size_t n = f->order + 1; + const double con = 0.25 * (f->b - f->a); + + if(integ->order != f->order) + { + GSL_ERROR ("order of chebyshev series must be equal", GSL_ENOMEM); + } + + /* set the other parameters in the chebyshev struct */ + + integ->a = f->a; + integ->b = f->b; + + /* FIXME: should probably set integ->f[] as well */ + + if(n == 1) { + integ->c[0] = 0.; + } + else if(n == 2) { + integ->c[1] = con * f->c[0]; + integ->c[0] = 2.0 * integ->c[1]; + } + else { + double sum = 0.0; + double fac = 1.0; + size_t i; + for(i=1; i<=n-2; i++) { + integ->c[i] = con * (f->c[i-1] - f->c[i+1])/((double)i); + sum += fac * integ->c[i]; + fac = -fac; + } + integ->c[n-1] = con * f->c[n-2]/(n-1.0); + sum += fac * integ->c[n-1]; + integ->c[0] = 2.0 * sum; + } + + return GSL_SUCCESS; +} diff --git a/gsl-1.9/cheb/test.c b/gsl-1.9/cheb/test.c new file mode 100644 index 0000000..7c27d84 --- /dev/null +++ b/gsl-1.9/cheb/test.c @@ -0,0 +1,208 @@ +/* cheb/test.c + * + * 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. + */ + +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_test.h> +#include <gsl/gsl_ieee_utils.h> +#include <gsl/gsl_chebyshev.h> + +double f_T0 (double x, void * p) { + p = 0; + return 1.0; +} + +double f_T1 (double x, void * p) { + p = 0; + return x; +} + +double f_T2 (double x, void * p) { + p = 0; + return 2*x*x - 1; +} + +double f_sin (double x, void * p) { + p = 0; + return sin(x); +} + +int +main(void) +{ + double tol = 100.0 * GSL_DBL_EPSILON; + double ftol = 20.0; + double x; + size_t i; + + gsl_cheb_series * cs = gsl_cheb_alloc(40); + gsl_cheb_series * csd = gsl_cheb_alloc(40); + gsl_cheb_series * csi = gsl_cheb_alloc(40); + + gsl_function F_sin, F_T0, F_T1, F_T2; + + F_sin.function = f_sin; + F_sin.params = 0; + + F_T0.function = f_T0; + F_T0.params = 0; + + F_T1.function = f_T1; + F_T1.params = 0; + + F_T2.function = f_T2; + F_T2.params = 0; + + gsl_ieee_env_setup(); + + gsl_cheb_init(cs, &F_T0, -1.0, 1.0); + + for (i = 0; i<cs->order; i++) + { + double c_exp = (i == 0) ? 2.0 : 0.0; + gsl_test_abs (cs->c[i], c_exp, tol, "c[%d] for T_0(x)", i); + } + + gsl_cheb_init(cs, &F_T1, -1.0, 1.0); + + for (i = 0; i<cs->order; i++) + { + double c_exp = (i == 1) ? 1.0 : 0.0; + gsl_test_abs (cs->c[i], c_exp, tol, "c[%d] for T_1(x)", i); + } + + gsl_cheb_init(cs, &F_T2, -1.0, 1.0); + + for (i = 0; i<cs->order; i++) + { + double c_exp = (i == 2) ? 1.0 : 0.0; + gsl_test_abs (cs->c[i], c_exp, tol, "c[%d] for T_2(x)", i); + } + + gsl_cheb_init(cs, &F_sin, -M_PI, M_PI); + + gsl_test_abs (cs->c[0], 0.0, tol, "c[0] for F_sin(x)"); + gsl_test_abs (cs->c[1], 5.69230686359506e-01, tol, "c[1] for F_sin(x)"); + gsl_test_abs (cs->c[2], 0.0, tol, "c[2] for F_sin(x)"); + gsl_test_abs (cs->c[3], -6.66916672405979e-01, tol, "c[3] for F_sin(x)"); + gsl_test_abs (cs->c[4], 0.0, tol, "c[4] for F_sin(x)"); + gsl_test_abs (cs->c[5], 1.04282368734237e-01, tol, "c[5] for F_sin(x)"); + + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r = gsl_cheb_eval(cs, x); + gsl_test_abs(r, sin(x), tol, "gsl_cheb_eval, sin(%.3g)", x); + } + + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r, e; + gsl_cheb_eval_err(cs, x, &r, &e); + gsl_test_abs(r, sin(x), tol, "gsl_cheb_eval_err, sin(%.3g)", x); + gsl_test_factor(fabs(r-sin(x)) + GSL_DBL_EPSILON, e, ftol, + "gsl_cheb_eval_err, error sin(%.3g)", x); + } + + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r = gsl_cheb_eval_n(cs, 25, x); + gsl_test_abs(r, sin(x), tol, "gsl_cheb_eval_n, sin(%.3g)", x); + } + + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r, e; + gsl_cheb_eval_n_err(cs, 25, x, &r, &e); + gsl_test_abs(r, sin(x), 100.0 * tol, "gsl_cheb_eval_n_err, deriv sin(%.3g)", x); + gsl_test_factor(fabs(r-sin(x)) + GSL_DBL_EPSILON, e, ftol, + "gsl_cheb_eval_n_err, error sin(%.3g)", x); + } + + /* Test derivative */ + + gsl_cheb_calc_deriv(csd, cs); + + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r = gsl_cheb_eval(csd, x); + gsl_test_abs(r, cos(x), 1600 * tol, "gsl_cheb_eval, deriv sin(%.3g)", x); + } + +#ifdef TEST_DERIVATIVE_ERR + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r, e; + gsl_cheb_eval_err(csd, x, &r, &e); + gsl_test_abs(r, cos(x), tol, "gsl_cheb_eval_err, deriv sin(%.3g)", x); + gsl_test_factor(fabs(r-cos(x)) + GSL_DBL_EPSILON, e, ftol, + "gsl_cheb_eval_err, deriv error sin(%.3g)", x); + } +#endif + + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r = gsl_cheb_eval_n(csd, 25, x); + gsl_test_abs(r, cos(x), 1600 * tol, "gsl_cheb_eval_n, deriv sin(%.3g)", x); + } + +#ifdef TEST_DERIVATIVE_ERR + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r, e; + gsl_cheb_eval_n_err(csd, 25, x, &r, &e); + gsl_test_abs(r, cos(x), 100.0 * tol, "gsl_cheb_eval_n_err, deriv sin(%.3g)", x); + gsl_test_factor(fabs(r-cos(x)) + GSL_DBL_EPSILON, e, ftol, + "gsl_cheb_eval_n_err, deriv error sin(%.3g)", x); + } +#endif + + /* Test integral */ + + gsl_cheb_calc_integ(csi, cs); + + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r = gsl_cheb_eval(csi, x); + gsl_test_abs(r, -(1+cos(x)), tol, "gsl_cheb_eval, integ sin(%.3g)", x); + } + +#ifdef TEST_INTEGRAL_ERR + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r, e; + gsl_cheb_eval_err(csi, x, &r, &e); + gsl_test_abs(r, -(1+cos(x)), tol, "gsl_cheb_eval_err, integ sin(%.3g)", x); + gsl_test_factor(fabs(r-(-1-cos(x))) + GSL_DBL_EPSILON, e, ftol, + "gsl_cheb_eval_err, integ error sin(%.3g)", x); + } +#endif + + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r = gsl_cheb_eval_n(csi, 25, x); + gsl_test_abs(r, -(1+cos(x)), tol, "gsl_cheb_eval_n, integ sin(%.3g)", x); + } + +#ifdef TEST_INTEGRAL_ERR + for(x=-M_PI; x<M_PI; x += M_PI/100.0) { + double r, e; + gsl_cheb_eval_n_err(csi, 25, x, &r, &e); + gsl_test_abs(r, -(1+cos(x)), 100.0 * tol, "gsl_cheb_eval_n_err, integ sin(%.3g)", x); + gsl_test_factor(fabs(r-(-1-cos(x))) + GSL_DBL_EPSILON, e, ftol, + "gsl_cheb_eval_n_err, integ error sin(%.3g)", x); + } +#endif + + gsl_cheb_free(csi); + gsl_cheb_free(csd); + gsl_cheb_free(cs); + + exit (gsl_test_summary()); +} |