diff options
Diffstat (limited to 'gsl-1.9/interpolation')
| -rw-r--r-- | gsl-1.9/interpolation/ChangeLog | 98 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/Makefile.am | 18 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/Makefile.in | 549 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/TODO | 10 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/accel.c | 82 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/akima.c | 389 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/bsearch.c | 47 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/bsearch.h | 80 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/cspline.c | 475 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/gsl_interp.h | 202 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/gsl_spline.h | 101 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/integ_eval.h | 36 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/interp.c | 244 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/linear.c | 198 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/poly.c | 173 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/spline.c | 193 | ||||
| -rw-r--r-- | gsl-1.9/interpolation/test.c | 949 |
17 files changed, 3844 insertions, 0 deletions
diff --git a/gsl-1.9/interpolation/ChangeLog b/gsl-1.9/interpolation/ChangeLog new file mode 100644 index 0000000..ce3a5dd --- /dev/null +++ b/gsl-1.9/interpolation/ChangeLog @@ -0,0 +1,98 @@ +2005-12-24 Brian Gough <bjg@network-theory.co.uk> + + * cspline.c (cspline_init_periodic): fix invalid memory access of + xa[3] for sys_size=2 + +2005-12-22 Brian Gough <bjg@network-theory.co.uk> + + * test.c (test_cspline2): added extra test of cspline + (test_cspline3): added extra test of cspline + +2004-11-28 Brian Gough <bjg@network-theory.co.uk> + + * cspline.c (cspline_init): support case of degenerate x[i] values + (cspline_init_periodic): support case of degenerate x[i] values + + * integ_eval.h (integ_eval): improve numerical stability of + integration formula + +2004-03-15 Brian Gough <bjg@network-theory.co.uk> + + * cspline.c (cspline_init): handle the case N=1 specially + +2003-07-24 Brian Gough <bjg@network-theory.co.uk> + + * gsl_interp.h: removed duplicate declaration of + gsl_interp_accel_find + +Sat Apr 27 20:57:22 2002 Brian Gough <bjg@network-theory.co.uk> + + * cspline.c (cspline_init_periodic): handle boundary effects + correctly + +Sun Dec 2 22:48:23 2001 Brian Gough <bjg@network-theory.co.uk> + + * poly.c: added polynomial interpolation based on divided + differences from Dan, Ho-Jin. + +Tue Jul 3 12:10:53 2001 Brian Gough <bjg@network-theory.co.uk> + + * interp.c (DISCARD_STATUS): discard error status values using a + macro for configurability + +Sun Jul 1 21:41:27 2001 Brian Gough <bjg@network-theory.co.uk> + + * cspline.c: added const to state in appropriate places + +Tue Jun 26 11:57:55 2001 Brian Gough <bjg@network-theory.co.uk> + + * spline.c: added missing #include <string.h> for memcpy + +Mon Jun 25 19:58:45 2001 Brian Gough <bjg@network-theory.co.uk> + + * standardized to gsl conventions, added high-level 'spline' + interface + +Mon Apr 30 13:29:34 2001 Brian Gough <bjg@network-theory.co.uk> + + * renamed gsl_interp_obj to gsl_interp + +Mon Apr 23 10:29:51 2001 Brian Gough <bjg@network-theory.co.uk> + + * unified error handling conventions to _e for error handling + functions and no suffix for plain functions, so _impl functions + are no longer needed. + + * removed tests for EFAULT, since EFAULT should only apply to + invalid non-null pointers. + + +Tue Apr 11 19:56:25 2000 Brian Gough <bjg@network-theory.co.uk> + + * cspline.c (cspline_calc_periodic): changed occurrence of gsl_la + name to new gsl_linalg prefix, gsl_linalg_solve_symm_cyc_tridiag + (cspline_calc_natural): ditto + +Mon Aug 30 11:31:00 1999 Brian Gough <bjg@network-theory.co.uk> + + * bsearch.c: made gsl_interp_bsearch (formerly interp_bsearch) an + exported function, since it is needed by the inline version of + gsl_interp_accel_find in gsl_interp.h + +Tue Nov 17 16:52:00 1998 Brian Gough <bjg@vvv.lanl.gov> + + * added #include <config.h> to all top-level source files + + * renamed test_interp.c to test.c + + * test_interp.c: got rid of unused function alloc_xy_table + +Fri Nov 13 16:50:05 1998 Brian Gough <bjg@vvv.lanl.gov> + + * clean up for make strict, use size_t instead of unsigned int + +1998-11-06 <bjg@ancho.lanl.gov> + + * added const to several declarations where needed. + + diff --git a/gsl-1.9/interpolation/Makefile.am b/gsl-1.9/interpolation/Makefile.am new file mode 100644 index 0000000..8889430 --- /dev/null +++ b/gsl-1.9/interpolation/Makefile.am @@ -0,0 +1,18 @@ +noinst_LTLIBRARIES = libgslinterpolation.la + +check_PROGRAMS = test + +pkginclude_HEADERS = gsl_interp.h gsl_spline.h + +libgslinterpolation_la_SOURCES = accel.c akima.c bsearch.c cspline.c interp.c linear.c integ_eval.h spline.c poly.c + +noinst_HEADERS = bsearch.h + +INCLUDES= -I$(top_builddir) + +TESTS = $(check_PROGRAMS) + +test_LDADD = libgslinterpolation.la ../poly/libgslpoly.la ../linalg/libgsllinalg.la ../permutation/libgslpermutation.la ../blas/libgslblas.la ../matrix/libgslmatrix.la ../vector/libgslvector.la ../block/libgslblock.la ../complex/libgslcomplex.la ../cblas/libgslcblas.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la + +test_SOURCES = test.c + diff --git a/gsl-1.9/interpolation/Makefile.in b/gsl-1.9/interpolation/Makefile.in new file mode 100644 index 0000000..b580609 --- /dev/null +++ b/gsl-1.9/interpolation/Makefile.in @@ -0,0 +1,549 @@ +# 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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[DOCUMENTATION] From: Conrad Curry <cwcurry@orca.st.usm.edu> + + I would suggest adding more about cspline and Akima similiar to what + is given for 'polynomial', particularly under what conditions one + would be prefered over the other. + +3. add akima splines without the Wodicka modification, so that the spline +is a smooth curve without corners. diff --git a/gsl-1.9/interpolation/accel.c b/gsl-1.9/interpolation/accel.c new file mode 100644 index 0000000..72d9345 --- /dev/null +++ b/gsl-1.9/interpolation/accel.c @@ -0,0 +1,82 @@ +/* interpolation/accel.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. + */ + +/* Author: G. Jungman + */ +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_interp.h> + +gsl_interp_accel * +gsl_interp_accel_alloc (void) +{ + gsl_interp_accel *a = (gsl_interp_accel *) malloc (sizeof (gsl_interp_accel)); + if (a == 0) + { + GSL_ERROR_NULL("could not allocate space for gsl_interp_accel", GSL_ENOMEM); + } + + a->cache = 0; + a->hit_count = 0; + a->miss_count = 0; + + return a; +} + +int +gsl_interp_accel_reset (gsl_interp_accel * a) +{ + a->cache = 0; + a->hit_count = 0; + a->miss_count = 0; + + return GSL_SUCCESS; +} + +#ifndef HIDE_INLINE_STATIC +size_t +gsl_interp_accel_find (gsl_interp_accel * a, const double xa[], size_t len, double x) +{ + size_t x_index = a->cache; + + if (x < xa[x_index]) + { + a->miss_count++; + a->cache = gsl_interp_bsearch (xa, x, 0, x_index); + } + else if (x > xa[x_index + 1]) + { + a->miss_count++; + a->cache = gsl_interp_bsearch (xa, x, x_index, len - 1); + } + else + { + a->hit_count++; + } + + return a->cache; +} +#endif + +void +gsl_interp_accel_free (gsl_interp_accel * a) +{ + free (a); +} diff --git a/gsl-1.9/interpolation/akima.c b/gsl-1.9/interpolation/akima.c new file mode 100644 index 0000000..452432f --- /dev/null +++ b/gsl-1.9/interpolation/akima.c @@ -0,0 +1,389 @@ +/* interpolation/akima.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. + */ + +/* Author: G. Jungman + */ +#include <config.h> +#include <stdlib.h> +#include <math.h> +#include <gsl/gsl_errno.h> +#include "integ_eval.h" +#include <gsl/gsl_interp.h> + +typedef struct +{ + double * b; + double * c; + double * d; + double * _m; +} akima_state_t; + + +/* common creation */ +static void * +akima_alloc (size_t size) +{ + akima_state_t *state = (akima_state_t *) malloc (sizeof (akima_state_t)); + + if (state == NULL) + { + GSL_ERROR_NULL("failed to allocate space for state", GSL_ENOMEM); + } + + state->b = (double *) malloc (size * sizeof (double)); + + if (state->b == NULL) + { + free (state); + GSL_ERROR_NULL("failed to allocate space for b", GSL_ENOMEM); + } + + state->c = (double *) malloc (size * sizeof (double)); + + if (state->c == NULL) + { + free (state->b); + free (state); + GSL_ERROR_NULL("failed to allocate space for c", GSL_ENOMEM); + } + + state->d = (double *) malloc (size * sizeof (double)); + + if (state->d == NULL) + { + free (state->c); + free (state->b); + free (state); + GSL_ERROR_NULL("failed to allocate space for d", GSL_ENOMEM); + } + + state->_m = (double *) malloc ((size + 4) * sizeof (double)); + + if (state->_m == NULL) + { + free (state->d); + free (state->c); + free (state->b); + free (state); + GSL_ERROR_NULL("failed to allocate space for _m", GSL_ENOMEM); + } + + return state; +} + + +/* common calculation */ +static void +akima_calc (const double x_array[], double b[], double c[], double d[], size_t size, double m[]) +{ + size_t i; + + for (i = 0; i < (size - 1); i++) + { + const double NE = fabs (m[i + 1] - m[i]) + fabs (m[i - 1] - m[i - 2]); + if (NE == 0.0) + { + b[i] = m[i]; + c[i] = 0.0; + d[i] = 0.0; + } + else + { + const double h_i = x_array[i + 1] - x_array[i]; + const double NE_next = fabs (m[i + 2] - m[i + 1]) + fabs (m[i] - m[i - 1]); + const double alpha_i = fabs (m[i - 1] - m[i - 2]) / NE; + double alpha_ip1; + double tL_ip1; + if (NE_next == 0.0) + { + tL_ip1 = m[i]; + } + else + { + alpha_ip1 = fabs (m[i] - m[i - 1]) / NE_next; + tL_ip1 = (1.0 - alpha_ip1) * m[i] + alpha_ip1 * m[i + 1]; + } + b[i] = (1.0 - alpha_i) * m[i - 1] + alpha_i * m[i]; + c[i] = (3.0 * m[i] - 2.0 * b[i] - tL_ip1) / h_i; + d[i] = (b[i] + tL_ip1 - 2.0 * m[i]) / (h_i * h_i); + } + } +} + + +static int +akima_init (void * vstate, const double x_array[], const double y_array[], + size_t size) +{ + akima_state_t *state = (akima_state_t *) vstate; + + double * m = state->_m + 2; /* offset so we can address the -1,-2 + components */ + + size_t i; + for (i = 0; i <= size - 2; i++) + { + m[i] = (y_array[i + 1] - y_array[i]) / (x_array[i + 1] - x_array[i]); + } + + /* non-periodic boundary conditions */ + m[-2] = 3.0 * m[0] - 2.0 * m[1]; + m[-1] = 2.0 * m[0] - m[1]; + m[size - 1] = 2.0 * m[size - 2] - m[size - 3]; + m[size] = 3.0 * m[size - 2] - 2.0 * m[size - 3]; + + akima_calc (x_array, state->b, state->c, state->d, size, m); + + return GSL_SUCCESS; +} + + +static int +akima_init_periodic (void * vstate, + const double x_array[], + const double y_array[], + size_t size) +{ + akima_state_t *state = (akima_state_t *) vstate; + + double * m = state->_m + 2; /* offset so we can address the -1,-2 + components */ + + size_t i; + for (i = 0; i <= size - 2; i++) + { + m[i] = (y_array[i + 1] - y_array[i]) / (x_array[i + 1] - x_array[i]); + } + + /* periodic boundary conditions */ + m[-2] = m[size - 1 - 2]; + m[-1] = m[size - 1 - 1]; + m[size - 1] = m[0]; + m[size] = m[1]; + + akima_calc (x_array, state->b, state->c, state->d, size, m); + + return GSL_SUCCESS; +} + +static void +akima_free (void * vstate) +{ + akima_state_t *state = (akima_state_t *) vstate; + + free (state->b); + free (state->c); + free (state->d); + free (state->_m); + free (state); +} + + +static +int +akima_eval (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double *y) +{ + const akima_state_t *state = (const akima_state_t *) vstate; + + size_t index; + + if (a != 0) + { + index = gsl_interp_accel_find (a, x_array, size, x); + } + else + { + index = gsl_interp_bsearch (x_array, x, 0, size - 1); + } + + /* evaluate */ + { + const double x_lo = x_array[index]; + const double delx = x - x_lo; + const double b = state->b[index]; + const double c = state->c[index]; + const double d = state->d[index]; + *y = y_array[index] + delx * (b + delx * (c + d * delx)); + return GSL_SUCCESS; + } +} + + +static int +akima_eval_deriv (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double *dydx) +{ + const akima_state_t *state = (const akima_state_t *) vstate; + + size_t index; + + DISCARD_POINTER(y_array); /* prevent warning about unused parameter */ + + if (a != 0) + { + index = gsl_interp_accel_find (a, x_array, size, x); + } + else + { + index = gsl_interp_bsearch (x_array, x, 0, size - 1); + } + + /* evaluate */ + { + double x_lo = x_array[index]; + double delx = x - x_lo; + double b = state->b[index]; + double c = state->c[index]; + double d = state->d[index]; + *dydx = b + delx * (2.0 * c + 3.0 * d * delx); + return GSL_SUCCESS; + } +} + + +static +int +akima_eval_deriv2 (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double *y_pp) +{ + const akima_state_t *state = (const akima_state_t *) vstate; + + size_t index; + + DISCARD_POINTER(y_array); /* prevent warning about unused parameter */ + + if (a != 0) + { + index = gsl_interp_accel_find (a, x_array, size, x); + } + else + { + index = gsl_interp_bsearch (x_array, x, 0, size - 1); + } + + /* evaluate */ + { + const double x_lo = x_array[index]; + const double delx = x - x_lo; + const double c = state->c[index]; + const double d = state->d[index]; + *y_pp = 2.0 * c + 6.0 * d * delx; + return GSL_SUCCESS; + } +} + + +static +int +akima_eval_integ (const void * vstate, + const double x_array[], const double y_array[], size_t size, + gsl_interp_accel * acc, + double a, double b, + double * result) +{ + const akima_state_t *state = (const akima_state_t *) vstate; + + size_t i, index_a, index_b; + + if (acc != 0) + { + index_a = gsl_interp_accel_find (acc, x_array, size, a); + index_b = gsl_interp_accel_find (acc, x_array, size, b); + } + else + { + index_a = gsl_interp_bsearch (x_array, a, 0, size - 1); + index_b = gsl_interp_bsearch (x_array, b, 0, size - 1); + } + + *result = 0.0; + + /* interior intervals */ + + for(i=index_a; i<=index_b; i++) { + const double x_hi = x_array[i + 1]; + const double x_lo = x_array[i]; + const double y_lo = y_array[i]; + const double dx = x_hi - x_lo; + if(dx != 0.0) { + + if (i == index_a || i == index_b) + { + double x1 = (i == index_a) ? a : x_lo; + double x2 = (i == index_b) ? b : x_hi; + *result += integ_eval (y_lo, state->b[i], state->c[i], state->d[i], + x_lo, x1, x2); + } + else + { + *result += dx * (y_lo + + dx*(0.5*state->b[i] + + dx*(state->c[i]/3.0 + + 0.25*state->d[i]*dx))); + } + } + else { + *result = 0.0; + return GSL_FAILURE; + } + } + + return GSL_SUCCESS; +} + + +static const gsl_interp_type akima_type = +{ + "akima", + 5, + &akima_alloc, + &akima_init, + &akima_eval, + &akima_eval_deriv, + &akima_eval_deriv2, + &akima_eval_integ, + &akima_free +}; + +const gsl_interp_type * gsl_interp_akima = &akima_type; + +static const gsl_interp_type akima_periodic_type = +{ + "akima-periodic", + 5, + &akima_alloc, + &akima_init_periodic, + &akima_eval, + &akima_eval_deriv, + &akima_eval_deriv2, + &akima_eval_integ, + &akima_free +}; + +const gsl_interp_type * gsl_interp_akima_periodic = &akima_periodic_type; diff --git a/gsl-1.9/interpolation/bsearch.c b/gsl-1.9/interpolation/bsearch.c new file mode 100644 index 0000000..81692db --- /dev/null +++ b/gsl-1.9/interpolation/bsearch.c @@ -0,0 +1,47 @@ +/* interpolation/bsearch.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. + */ + +/* Author: G. Jungman + */ +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_interp.h> + +#ifndef HIDE_INLINE_STATIC +size_t +gsl_interp_bsearch ( + const double x_array[], double x, + size_t index_lo, + size_t index_hi + ) +{ + size_t ilo = index_lo; + size_t ihi = index_hi; + while (ihi > ilo + 1) + { + size_t i = (ihi + ilo) / 2; + if (x_array[i] > x) + ihi = i; + else + ilo = i; + } + + return ilo; +} +#endif diff --git a/gsl-1.9/interpolation/bsearch.h b/gsl-1.9/interpolation/bsearch.h new file mode 100644 index 0000000..0379d81 --- /dev/null +++ b/gsl-1.9/interpolation/bsearch.h @@ -0,0 +1,80 @@ +/* interpolation/bsearch.h + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 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. + */ + +/* Author: G. Jungman + */ +#ifndef __GSL_INTERP_BSEARCH_H__ +#define __GSL_INTERP_BSEARCH_H__ + + +/* Perform a binary search of an array of values. + * + * The parameters index_lo and index_hi provide an initial bracket, + * and it is assumed that index_lo < index_hi. The resulting index + * is guaranteed to be strictly less than index_hi and greater than + * or equal to index_lo, so that the implicit bracket [index, index+1] + * always corresponds to a region within the implicit value range of + * the value array. + * + * Note that this means the relationship of 'x' to x_array[index] + * and x_array[index+1] depends on the result region, i.e. the + * behaviour at the boundaries may not correspond to what you + * expect. We have the following complete specification of the + * behaviour. + * Suppose the input is x_array[] = { x0, x1, ..., xN } + * if ( x == x0 ) then index == 0 + * if ( x > x0 && x <= x1 ) then index == 0, and sim. for other interior pts + * if ( x == xN ) then index == N-1 + * if ( x > xN ) then index == N-1 + * if ( x < x0 ) then index == 0 + */ +size_t +gsl_interp_bsearch( + const double x_array[], double x, + size_t index_lo, + size_t index_hi + ); + + +#ifdef HAVE_INLINE +extern +inline +size_t +gsl_interp_bsearch( + const double x_array[], double x, + size_t index_lo, + size_t index_hi + ) +{ + size_t ilo = index_lo; + size_t ihi = index_hi; + while(ihi > ilo + 1) { + size_t i = (ihi + ilo)/2; + if(x_array[i] > x) + ihi = i; + else + ilo = i; + } + + return ilo; +} +#endif /* HAVE_INLINE */ + + +#endif /* __GSL_INTERP_BSEARCH_H__ */ diff --git a/gsl-1.9/interpolation/cspline.c b/gsl-1.9/interpolation/cspline.c new file mode 100644 index 0000000..6207b16 --- /dev/null +++ b/gsl-1.9/interpolation/cspline.c @@ -0,0 +1,475 @@ +/* interpolation/cspline.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004 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. + */ + +/* Author: G. Jungman + */ +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_linalg.h> +#include <gsl/gsl_vector.h> +#include "integ_eval.h" +#include <gsl/gsl_interp.h> + +typedef struct +{ + double * c; + double * g; + double * diag; + double * offdiag; +} cspline_state_t; + + +/* common initialization */ +static void * +cspline_alloc (size_t size) +{ + cspline_state_t * state = (cspline_state_t *) malloc (sizeof (cspline_state_t)); + + if (state == NULL) + { + GSL_ERROR_NULL("failed to allocate space for state", GSL_ENOMEM); + } + + state->c = (double *) malloc (size * sizeof (double)); + + if (state->c == NULL) + { + free (state); + GSL_ERROR_NULL("failed to allocate space for c", GSL_ENOMEM); + } + + state->g = (double *) malloc (size * sizeof (double)); + + if (state->g == NULL) + { + free (state->c); + free (state); + GSL_ERROR_NULL("failed to allocate space for g", GSL_ENOMEM); + } + + state->diag = (double *) malloc (size * sizeof (double)); + + if (state->diag == NULL) + { + free (state->g); + free (state->c); + free (state); + GSL_ERROR_NULL("failed to allocate space for diag", GSL_ENOMEM); + } + + state->offdiag = (double *) malloc (size * sizeof (double)); + + if (state->offdiag == NULL) + { + free (state->diag); + free (state->g); + free (state->c); + free (state); + GSL_ERROR_NULL("failed to allocate space for offdiag", GSL_ENOMEM); + } + + return state; +} + + +/* natural spline calculation + * see [Engeln-Mullges + Uhlig, p. 254] + */ +static int +cspline_init (void * vstate, const double xa[], const double ya[], + size_t size) +{ + cspline_state_t *state = (cspline_state_t *) vstate; + + size_t i; + size_t num_points = size; + size_t max_index = num_points - 1; /* Engeln-Mullges + Uhlig "n" */ + size_t sys_size = max_index - 1; /* linear system is sys_size x sys_size */ + + state->c[0] = 0.0; + state->c[max_index] = 0.0; + + for (i = 0; i < sys_size; i++) + { + const double h_i = xa[i + 1] - xa[i]; + const double h_ip1 = xa[i + 2] - xa[i + 1]; + const double ydiff_i = ya[i + 1] - ya[i]; + const double ydiff_ip1 = ya[i + 2] - ya[i + 1]; + const double g_i = (h_i != 0.0) ? 1.0 / h_i : 0.0; + const double g_ip1 = (h_ip1 != 0.0) ? 1.0 / h_ip1 : 0.0; + state->offdiag[i] = h_ip1; + state->diag[i] = 2.0 * (h_ip1 + h_i); + state->g[i] = 3.0 * (ydiff_ip1 * g_ip1 - ydiff_i * g_i); + } + + if (sys_size == 1) + { + state->c[1] = state->g[0] / state->diag[0]; + return GSL_SUCCESS; + } + else + { + gsl_vector_view g_vec = gsl_vector_view_array(state->g, sys_size); + gsl_vector_view diag_vec = gsl_vector_view_array(state->diag, sys_size); + gsl_vector_view offdiag_vec = gsl_vector_view_array(state->offdiag, sys_size - 1); + gsl_vector_view solution_vec = gsl_vector_view_array ((state->c) + 1, sys_size); + + int status = gsl_linalg_solve_symm_tridiag(&diag_vec.vector, + &offdiag_vec.vector, + &g_vec.vector, + &solution_vec.vector); + return status; + } +} + + +/* periodic spline calculation + * see [Engeln-Mullges + Uhlig, p. 256] + */ +static int +cspline_init_periodic (void * vstate, const double xa[], const double ya[], + size_t size) +{ + cspline_state_t *state = (cspline_state_t *) vstate; + + size_t i; + size_t num_points = size; + size_t max_index = num_points - 1; /* Engeln-Mullges + Uhlig "n" */ + size_t sys_size = max_index; /* linear system is sys_size x sys_size */ + + if (sys_size == 2) { + /* solve 2x2 system */ + + const double h0 = xa[1] - xa[0]; + const double h1 = xa[2] - xa[1]; + + const double A = 2.0*(h0 + h1); + const double B = h0 + h1; + double g[2]; + double det; + + g[0] = 3.0 * ((ya[2] - ya[1]) / h1 - (ya[1] - ya[0]) / h0); + g[1] = 3.0 * ((ya[1] - ya[2]) / h0 - (ya[2] - ya[1]) / h1); + + det = 3.0 * (h0 + h1) * (h0 + h1); + state->c[1] = ( A * g[0] - B * g[1])/det; + state->c[2] = (-B * g[0] + A * g[1])/det; + state->c[0] = state->c[2]; + + return GSL_SUCCESS; + } else { + + for (i = 0; i < sys_size-1; i++) { + const double h_i = xa[i + 1] - xa[i]; + const double h_ip1 = xa[i + 2] - xa[i + 1]; + const double ydiff_i = ya[i + 1] - ya[i]; + const double ydiff_ip1 = ya[i + 2] - ya[i + 1]; + const double g_i = (h_i != 0.0) ? 1.0 / h_i : 0.0; + const double g_ip1 = (h_ip1 != 0.0) ? 1.0 / h_ip1 : 0.0; + state->offdiag[i] = h_ip1; + state->diag[i] = 2.0 * (h_ip1 + h_i); + state->g[i] = 3.0 * (ydiff_ip1 * g_ip1 - ydiff_i * g_i); + } + + i = sys_size - 1; + + { + const double h_i = xa[i + 1] - xa[i]; + const double h_ip1 = xa[1] - xa[0]; + const double ydiff_i = ya[i + 1] - ya[i]; + const double ydiff_ip1 = ya[1] - ya[0]; + const double g_i = (h_i != 0.0) ? 1.0 / h_i : 0.0; + const double g_ip1 = (h_ip1 != 0.0) ? 1.0 / h_ip1 : 0.0; + state->offdiag[i] = h_ip1; + state->diag[i] = 2.0 * (h_ip1 + h_i); + state->g[i] = 3.0 * (ydiff_ip1 * g_ip1 - ydiff_i * g_i); + } + + { + gsl_vector_view g_vec = gsl_vector_view_array(state->g, sys_size); + gsl_vector_view diag_vec = gsl_vector_view_array(state->diag, sys_size); + gsl_vector_view offdiag_vec = gsl_vector_view_array(state->offdiag, sys_size); + gsl_vector_view solution_vec = gsl_vector_view_array ((state->c) + 1, sys_size); + + int status = gsl_linalg_solve_symm_cyc_tridiag(&diag_vec.vector, + &offdiag_vec.vector, + &g_vec.vector, + &solution_vec.vector); + state->c[0] = state->c[max_index]; + + return status; + } + } +} + + +static +void +cspline_free (void * vstate) +{ + cspline_state_t *state = (cspline_state_t *) vstate; + + free (state->c); + free (state->g); + free (state->diag); + free (state->offdiag); + free (state); +} + +/* function for common coefficient determination + */ +static inline void +coeff_calc (const double c_array[], double dy, double dx, size_t index, + double * b, double * c, double * d) +{ + const double c_i = c_array[index]; + const double c_ip1 = c_array[index + 1]; + *b = (dy / dx) - dx * (c_ip1 + 2.0 * c_i) / 3.0; + *c = c_i; + *d = (c_ip1 - c_i) / (3.0 * dx); +} + + +static +int +cspline_eval (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double *y) +{ + const cspline_state_t *state = (const cspline_state_t *) vstate; + + double x_lo, x_hi; + double dx; + size_t index; + + if (a != 0) + { + index = gsl_interp_accel_find (a, x_array, size, x); + } + else + { + index = gsl_interp_bsearch (x_array, x, 0, size - 1); + } + + /* evaluate */ + x_hi = x_array[index + 1]; + x_lo = x_array[index]; + dx = x_hi - x_lo; + if (dx > 0.0) + { + const double y_lo = y_array[index]; + const double y_hi = y_array[index + 1]; + const double dy = y_hi - y_lo; + double delx = x - x_lo; + double b_i, c_i, d_i; + coeff_calc(state->c, dy, dx, index, &b_i, &c_i, &d_i); + *y = y_lo + delx * (b_i + delx * (c_i + delx * d_i)); + return GSL_SUCCESS; + } + else + { + *y = 0.0; + return GSL_EINVAL; + } +} + + +static +int +cspline_eval_deriv (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double *dydx) +{ + const cspline_state_t *state = (const cspline_state_t *) vstate; + + double x_lo, x_hi; + double dx; + size_t index; + + if (a != 0) + { + index = gsl_interp_accel_find (a, x_array, size, x); + } + else + { + index = gsl_interp_bsearch (x_array, x, 0, size - 1); + } + + /* evaluate */ + x_hi = x_array[index + 1]; + x_lo = x_array[index]; + dx = x_hi - x_lo; + if (dx > 0.0) + { + const double y_lo = y_array[index]; + const double y_hi = y_array[index + 1]; + const double dy = y_hi - y_lo; + double delx = x - x_lo; + double b_i, c_i, d_i; + coeff_calc(state->c, dy, dx, index, &b_i, &c_i, &d_i); + *dydx = b_i + delx * (2.0 * c_i + 3.0 * d_i * delx); + return GSL_SUCCESS; + } + else + { + *dydx = 0.0; + return GSL_FAILURE; + } +} + + +static +int +cspline_eval_deriv2 (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double * y_pp) +{ + const cspline_state_t *state = (const cspline_state_t *) vstate; + + double x_lo, x_hi; + double dx; + size_t index; + + if (a != 0) + { + index = gsl_interp_accel_find (a, x_array, size, x); + } + else + { + index = gsl_interp_bsearch (x_array, x, 0, size - 1); + } + + /* evaluate */ + x_hi = x_array[index + 1]; + x_lo = x_array[index]; + dx = x_hi - x_lo; + if (dx > 0.0) + { + const double y_lo = y_array[index]; + const double y_hi = y_array[index + 1]; + const double dy = y_hi - y_lo; + double delx = x - x_lo; + double b_i, c_i, d_i; + coeff_calc(state->c, dy, dx, index, &b_i, &c_i, &d_i); + *y_pp = 2.0 * c_i + 6.0 * d_i * delx; + return GSL_SUCCESS; + } + else + { + *y_pp = 0.0; + return GSL_FAILURE; + } +} + + +static +int +cspline_eval_integ (const void * vstate, + const double x_array[], const double y_array[], size_t size, + gsl_interp_accel * acc, + double a, double b, + double * result) +{ + const cspline_state_t *state = (const cspline_state_t *) vstate; + + size_t i, index_a, index_b; + + if (acc != 0) + { + index_a = gsl_interp_accel_find (acc, x_array, size, a); + index_b = gsl_interp_accel_find (acc, x_array, size, b); + } + else + { + index_a = gsl_interp_bsearch (x_array, a, 0, size - 1); + index_b = gsl_interp_bsearch (x_array, b, 0, size - 1); + } + + *result = 0.0; + + /* interior intervals */ + for(i=index_a; i<=index_b; i++) { + const double x_hi = x_array[i + 1]; + const double x_lo = x_array[i]; + const double y_lo = y_array[i]; + const double y_hi = y_array[i + 1]; + const double dx = x_hi - x_lo; + const double dy = y_hi - y_lo; + if(dx != 0.0) { + double b_i, c_i, d_i; + coeff_calc(state->c, dy, dx, i, &b_i, &c_i, &d_i); + + if (i == index_a || i == index_b) + { + double x1 = (i == index_a) ? a : x_lo; + double x2 = (i == index_b) ? b : x_hi; + *result += integ_eval(y_lo, b_i, c_i, d_i, x_lo, x1, x2); + } + else + { + *result += dx * (y_lo + dx*(0.5*b_i + dx*(c_i/3.0 + 0.25*d_i*dx))); + } + } + else { + *result = 0.0; + return GSL_FAILURE; + } + } + + return GSL_SUCCESS; +} + +static const gsl_interp_type cspline_type = +{ + "cspline", + 3, + &cspline_alloc, + &cspline_init, + &cspline_eval, + &cspline_eval_deriv, + &cspline_eval_deriv2, + &cspline_eval_integ, + &cspline_free +}; + +const gsl_interp_type * gsl_interp_cspline = &cspline_type; + +static const gsl_interp_type cspline_periodic_type = +{ + "cspline-periodic", + 2, + &cspline_alloc, + &cspline_init_periodic, + &cspline_eval, + &cspline_eval_deriv, + &cspline_eval_deriv2, + &cspline_eval_integ, + &cspline_free +}; + +const gsl_interp_type * gsl_interp_cspline_periodic = &cspline_periodic_type; + + diff --git a/gsl-1.9/interpolation/gsl_interp.h b/gsl-1.9/interpolation/gsl_interp.h new file mode 100644 index 0000000..d4757ca --- /dev/null +++ b/gsl-1.9/interpolation/gsl_interp.h @@ -0,0 +1,202 @@ +/* interpolation/gsl_interp.h + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 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. + */ + +/* Author: G. Jungman + */ +#ifndef __GSL_INTERP_H__ +#define __GSL_INTERP_H__ +#include <stdlib.h> +#include <gsl/gsl_types.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 + +/* evaluation accelerator */ +typedef struct { + size_t cache; /* cache of index */ + size_t miss_count; /* keep statistics */ + size_t hit_count; +} +gsl_interp_accel; + + +/* interpolation object type */ +typedef struct { + const char * name; + unsigned int min_size; + void * (*alloc) (size_t size); + int (*init) (void *, const double xa[], const double ya[], size_t size); + int (*eval) (const void *, const double xa[], const double ya[], size_t size, double x, gsl_interp_accel *, double * y); + int (*eval_deriv) (const void *, const double xa[], const double ya[], size_t size, double x, gsl_interp_accel *, double * y_p); + int (*eval_deriv2) (const void *, const double xa[], const double ya[], size_t size, double x, gsl_interp_accel *, double * y_pp); + int (*eval_integ) (const void *, const double xa[], const double ya[], size_t size, gsl_interp_accel *, double a, double b, double * result); + void (*free) (void *); + +} gsl_interp_type; + + +/* general interpolation object */ +typedef struct { + const gsl_interp_type * type; + double xmin; + double xmax; + size_t size; + void * state; +} gsl_interp; + + +/* available types */ +GSL_VAR const gsl_interp_type * gsl_interp_linear; +GSL_VAR const gsl_interp_type * gsl_interp_polynomial; +GSL_VAR const gsl_interp_type * gsl_interp_cspline; +GSL_VAR const gsl_interp_type * gsl_interp_cspline_periodic; +GSL_VAR const gsl_interp_type * gsl_interp_akima; +GSL_VAR const gsl_interp_type * gsl_interp_akima_periodic; + +gsl_interp_accel * +gsl_interp_accel_alloc(void); + +size_t +gsl_interp_accel_find(gsl_interp_accel * a, const double x_array[], size_t size, double x); + +int +gsl_interp_accel_reset (gsl_interp_accel * a); + +void +gsl_interp_accel_free(gsl_interp_accel * a); + +gsl_interp * +gsl_interp_alloc(const gsl_interp_type * T, size_t n); + +int +gsl_interp_init(gsl_interp * obj, const double xa[], const double ya[], size_t size); + +const char * gsl_interp_name(const gsl_interp * interp); +unsigned int gsl_interp_min_size(const gsl_interp * interp); + + +int +gsl_interp_eval_e(const gsl_interp * obj, + const double xa[], const double ya[], double x, + gsl_interp_accel * a, double * y); + +double +gsl_interp_eval(const gsl_interp * obj, + const double xa[], const double ya[], double x, + gsl_interp_accel * a); + +int +gsl_interp_eval_deriv_e(const gsl_interp * obj, + const double xa[], const double ya[], double x, + gsl_interp_accel * a, + double * d); + +double +gsl_interp_eval_deriv(const gsl_interp * obj, + const double xa[], const double ya[], double x, + gsl_interp_accel * a); + +int +gsl_interp_eval_deriv2_e(const gsl_interp * obj, + const double xa[], const double ya[], double x, + gsl_interp_accel * a, + double * d2); + +double +gsl_interp_eval_deriv2(const gsl_interp * obj, + const double xa[], const double ya[], double x, + gsl_interp_accel * a); + +int +gsl_interp_eval_integ_e(const gsl_interp * obj, + const double xa[], const double ya[], + double a, double b, + gsl_interp_accel * acc, + double * result); + +double +gsl_interp_eval_integ(const gsl_interp * obj, + const double xa[], const double ya[], + double a, double b, + gsl_interp_accel * acc); + +void +gsl_interp_free(gsl_interp * interp); + +size_t gsl_interp_bsearch(const double x_array[], double x, + size_t index_lo, size_t index_hi); + +#ifdef HAVE_INLINE +extern inline size_t +gsl_interp_bsearch(const double x_array[], double x, + size_t index_lo, size_t index_hi); + +extern inline size_t +gsl_interp_bsearch(const double x_array[], double x, + size_t index_lo, size_t index_hi) +{ + size_t ilo = index_lo; + size_t ihi = index_hi; + while(ihi > ilo + 1) { + size_t i = (ihi + ilo)/2; + if(x_array[i] > x) + ihi = i; + else + ilo = i; + } + + return ilo; +} +#endif + +#ifdef HAVE_INLINE +extern inline size_t +gsl_interp_accel_find(gsl_interp_accel * a, const double xa[], size_t len, double x) +{ + size_t x_index = a->cache; + + if(x < xa[x_index]) { + a->miss_count++; + a->cache = gsl_interp_bsearch(xa, x, 0, x_index); + } + else if(x > xa[x_index + 1]) { + a->miss_count++; + a->cache = gsl_interp_bsearch(xa, x, x_index, len-1); + } + else { + a->hit_count++; + } + + return a->cache; +} +#endif /* HAVE_INLINE */ + + +__END_DECLS + +#endif /* __GSL_INTERP_H__ */ diff --git a/gsl-1.9/interpolation/gsl_spline.h b/gsl-1.9/interpolation/gsl_spline.h new file mode 100644 index 0000000..7eb40e9 --- /dev/null +++ b/gsl-1.9/interpolation/gsl_spline.h @@ -0,0 +1,101 @@ +/* interpolation/gsl_spline.h + * + * Copyright (C) 2001 Brian Gough + * + * 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_SPLINE_H__ +#define __GSL_SPLINE_H__ +#include <stdlib.h> +#include <gsl/gsl_interp.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 + + +/* general interpolation object */ +typedef struct { + gsl_interp * interp; + double * x; + double * y; + size_t size; +} gsl_spline; + +gsl_spline * +gsl_spline_alloc(const gsl_interp_type * T, size_t size); + +int +gsl_spline_init(gsl_spline * spline, const double xa[], const double ya[], size_t size); + +const char * gsl_spline_name(const gsl_spline * spline); +unsigned int gsl_spline_min_size(const gsl_spline * spline); + + +int +gsl_spline_eval_e(const gsl_spline * spline, double x, + gsl_interp_accel * a, double * y); + +double +gsl_spline_eval(const gsl_spline * spline, double x, gsl_interp_accel * a); + +int +gsl_spline_eval_deriv_e(const gsl_spline * spline, + double x, + gsl_interp_accel * a, + double * y); + +double +gsl_spline_eval_deriv(const gsl_spline * spline, + double x, + gsl_interp_accel * a); + +int +gsl_spline_eval_deriv2_e(const gsl_spline * spline, + double x, + gsl_interp_accel * a, + double * y); + +double +gsl_spline_eval_deriv2(const gsl_spline * spline, + double x, + gsl_interp_accel * a); + +int +gsl_spline_eval_integ_e(const gsl_spline * spline, + double a, double b, + gsl_interp_accel * acc, + double * y); + +double +gsl_spline_eval_integ(const gsl_spline * spline, + double a, double b, + gsl_interp_accel * acc); + +void +gsl_spline_free(gsl_spline * spline); + +__END_DECLS + +#endif /* __GSL_INTERP_H__ */ diff --git a/gsl-1.9/interpolation/integ_eval.h b/gsl-1.9/interpolation/integ_eval.h new file mode 100644 index 0000000..4cc21f0 --- /dev/null +++ b/gsl-1.9/interpolation/integ_eval.h @@ -0,0 +1,36 @@ +/* interpolation/integ_eval_macro.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. + */ + +/* function for doing the spline integral evaluation + which is common to both the cspline and akima methods + */ + +static inline double +integ_eval (double ai, double bi, double ci, double di, double xi, double a, + double b) +{ + const double r1 = a - xi; + const double r2 = b - xi; + const double r12 = r1 + r2; + const double bterm = 0.5 * bi * r12; + const double cterm = (1.0 / 3.0) * ci * (r1 * r1 + r2 * r2 + r1 * r2); + const double dterm = 0.25 * di * r12 * (r1 * r1 + r2 * r2); + + return (b - a) * (ai + bterm + cterm + dterm); +} diff --git a/gsl-1.9/interpolation/interp.c b/gsl-1.9/interpolation/interp.c new file mode 100644 index 0000000..0361730 --- /dev/null +++ b/gsl-1.9/interpolation/interp.c @@ -0,0 +1,244 @@ +/* interpolation/interp.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. + */ + +/* Author: G. Jungman + */ +#include <config.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_interp.h> + +#define DISCARD_STATUS(s) if ((s) != GSL_SUCCESS) { GSL_ERROR_VAL("interpolation error", (s), GSL_NAN); } + +gsl_interp * +gsl_interp_alloc (const gsl_interp_type * T, size_t size) +{ + gsl_interp * interp; + + if (size < T->min_size) + { + GSL_ERROR_NULL ("insufficient number of points for interpolation type", + GSL_EINVAL); + } + + interp = (gsl_interp *) malloc (sizeof(gsl_interp)); + + if (interp == NULL) + { + GSL_ERROR_NULL ("failed to allocate space for interp struct", + GSL_ENOMEM); + } + + interp->type = T; + interp->size = size; + + if (interp->type->alloc == NULL) + { + interp->state = NULL; + return interp; + } + + interp->state = interp->type->alloc(size); + + if (interp->state == NULL) + { + free (interp); + GSL_ERROR_NULL ("failed to allocate space for interp state", GSL_ENOMEM); + }; + + return interp; +} + +int +gsl_interp_init (gsl_interp * interp, const double x_array[], const double y_array[], size_t size) +{ + if (size != interp->size) + { + GSL_ERROR ("data must match size of interpolation object", GSL_EINVAL); + } + + interp->xmin = x_array[0]; + interp->xmax = x_array[size - 1]; + + { + int status = interp->type->init(interp->state, x_array, y_array, size); + return status; + } +} + +const char * +gsl_interp_name(const gsl_interp * interp) +{ + return interp->type->name; +} + +unsigned int +gsl_interp_min_size(const gsl_interp * interp) +{ + return interp->type->min_size; +} + +void +gsl_interp_free (gsl_interp * interp) +{ + if (interp->type->free) + interp->type->free (interp->state); + free (interp); +} + + + +int +gsl_interp_eval_e (const gsl_interp * interp, + const double xa[], const double ya[], double x, + gsl_interp_accel * a, double *y) +{ + if (x < interp->xmin) + { + *y = ya[0]; + return GSL_EDOM; + } + else if (x > interp->xmax) + { + *y = ya[interp->size - 1]; + return GSL_EDOM; + } + + return interp->type->eval (interp->state, xa, ya, interp->size, x, a, y); +} + +double +gsl_interp_eval (const gsl_interp * interp, + const double xa[], const double ya[], double x, + gsl_interp_accel * a) +{ + double y; + int status = interp->type->eval (interp->state, xa, ya, interp->size, x, a, &y); + + DISCARD_STATUS(status); + + return y; +} + + +int +gsl_interp_eval_deriv_e (const gsl_interp * interp, + const double xa[], const double ya[], double x, + gsl_interp_accel * a, + double *dydx) +{ + if (x < interp->xmin) + { + *dydx = 0.0; + return GSL_EDOM; + } + else if (x > interp->xmax) + { + *dydx = 0.0; + return GSL_EDOM; + } + + return interp->type->eval_deriv (interp->state, xa, ya, interp->size, x, a, dydx); +} + +double +gsl_interp_eval_deriv (const gsl_interp * interp, + const double xa[], const double ya[], double x, + gsl_interp_accel * a) +{ + double dydx; + int status = interp->type->eval_deriv (interp->state, xa, ya, interp->size, x, a, &dydx); + + DISCARD_STATUS(status); + + return dydx; +} + + +int +gsl_interp_eval_deriv2_e (const gsl_interp * interp, + const double xa[], const double ya[], double x, + gsl_interp_accel * a, + double * d2) +{ + if (x < interp->xmin) + { + *d2 = 0.0; + return GSL_EDOM; + } + else if (x > interp->xmax) + { + *d2 = 0.0; + return GSL_EDOM; + } + + return interp->type->eval_deriv2 (interp->state, xa, ya, interp->size, x, a, d2); +} + +double +gsl_interp_eval_deriv2 (const gsl_interp * interp, + const double xa[], const double ya[], double x, + gsl_interp_accel * a) +{ + double d2; + int status = interp->type->eval_deriv2 (interp->state, xa, ya, interp->size, x, a, &d2); + + DISCARD_STATUS(status); + + return d2; +} + + +int +gsl_interp_eval_integ_e (const gsl_interp * interp, + const double xa[], const double ya[], + double a, double b, + gsl_interp_accel * acc, + double * result) +{ + if (a > b || a < interp->xmin || b > interp->xmax) + { + *result = 0.0; + return GSL_EDOM; + } + else if(a == b) + { + *result = 0.0; + return GSL_SUCCESS; + } + + return interp->type->eval_integ (interp->state, xa, ya, interp->size, acc, a, b, result); +} + + +double +gsl_interp_eval_integ (const gsl_interp * interp, + const double xa[], const double ya[], + double a, double b, + gsl_interp_accel * acc) +{ + double result; + int status = interp->type->eval_integ (interp->state, xa, ya, interp->size, acc, a, b, &result); + + DISCARD_STATUS(status); + + return result; +} + + diff --git a/gsl-1.9/interpolation/linear.c b/gsl-1.9/interpolation/linear.c new file mode 100644 index 0000000..aa9ec00 --- /dev/null +++ b/gsl-1.9/interpolation/linear.c @@ -0,0 +1,198 @@ +/* interpolation/linear.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. + */ + +/* Author: G. Jungman + */ +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_interp.h> + +static int +linear_init (void * vstate, + const double x_array[], + const double y_array[], + size_t size) +{ + return GSL_SUCCESS; +} + +static +int +linear_eval (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double *y) +{ + double x_lo, x_hi; + double y_lo, y_hi; + double dx; + size_t index; + + if (a != 0) + { + index = gsl_interp_accel_find (a, x_array, size, x); + } + else + { + index = gsl_interp_bsearch (x_array, x, 0, size - 1); + } + + /* evaluate */ + x_lo = x_array[index]; + x_hi = x_array[index + 1]; + y_lo = y_array[index]; + y_hi = y_array[index + 1]; + dx = x_hi - x_lo; + if (dx > 0.0) + { + *y = y_lo + (x - x_lo) / dx * (y_hi - y_lo); + return GSL_SUCCESS; + } + else + { + *y = 0.0; + return GSL_EINVAL; + } +} + + +static +int +linear_eval_deriv (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double *dydx) +{ + double x_lo, x_hi; + double y_lo, y_hi; + double dx; + double dy; + size_t index; + + if (a != 0) + { + index = gsl_interp_accel_find (a, x_array, size, x); + } + else + { + index = gsl_interp_bsearch (x_array, x, 0, size - 1); + } + + /* evaluate */ + x_lo = x_array[index]; + x_hi = x_array[index + 1]; + y_lo = y_array[index]; + y_hi = y_array[index + 1]; + dx = x_hi - x_lo; + dy = y_hi - y_lo; + if (dx > 0.0) + { + *dydx = dy / dx;; + return GSL_SUCCESS; + } + else + { + *dydx = 0.0; + return GSL_EINVAL; + } +} + + +static +int +linear_eval_deriv2 (const void * vstate, + const double x_array[], const double y_array[], size_t size, + double x, + gsl_interp_accel * a, + double *y_pp) +{ + *y_pp = 0.0; + + return GSL_SUCCESS; +} + + +static +int +linear_eval_integ (const void * vstate, + const double x_array[], const double y_array[], size_t size, + gsl_interp_accel * acc, + double a, double b, + double * result) +{ + size_t i, index_a, index_b; + + if (acc != 0) + { + index_a = gsl_interp_accel_find (acc, x_array, size, a); + index_b = gsl_interp_accel_find (acc, x_array, size, b); + } + else + { + index_a = gsl_interp_bsearch (x_array, a, 0, size - 1); + index_b = gsl_interp_bsearch (x_array, b, 0, size - 1); + } + + /* endpoints span more than one interval */ + + *result = 0.0; + + /* interior intervals */ + for(i=index_a; i<=index_b; i++) { + const double x_hi = x_array[i + 1]; + const double x_lo = x_array[i]; + const double y_lo = y_array[i]; + const double y_hi = y_array[i + 1]; + const double dx = x_hi - x_lo; + + if(dx != 0.0) { + if (i == index_a || i == index_b) + { + double x1 = (i == index_a) ? a : x_lo; + double x2 = (i == index_b) ? b : x_hi; + const double D = (y_hi-y_lo)/dx; + *result += (x2-x1) * (y_lo + 0.5*D*((x2-x_lo)+(x1-x_lo))); + } + else + { + *result += 0.5 * dx * (y_lo + y_hi); + } + } + } + + return GSL_SUCCESS; +} + +static const gsl_interp_type linear_type = +{ + "linear", + 2, + NULL, /* alloc, not applicable */ + &linear_init, + &linear_eval, + &linear_eval_deriv, + &linear_eval_deriv2, + &linear_eval_integ, + NULL, /* free, not applicable */ +}; + +const gsl_interp_type * gsl_interp_linear = &linear_type; diff --git a/gsl-1.9/interpolation/poly.c b/gsl-1.9/interpolation/poly.c new file mode 100644 index 0000000..a0cd68a --- /dev/null +++ b/gsl-1.9/interpolation/poly.c @@ -0,0 +1,173 @@ +/* interpolation/interp_poly.c + * + * Copyright (C) 2001 DAN, HO-JIN + * + * 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 <math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_poly.h> +#include <gsl/gsl_interp.h> + +typedef struct +{ + double *d; + double *coeff; + double *work; +} +polynomial_state_t; + +static void * +polynomial_alloc (size_t size) +{ + polynomial_state_t *state = + (polynomial_state_t *) malloc (sizeof (polynomial_state_t)); + + if (state == 0) + { + GSL_ERROR_NULL ("failed to allocate space for polynomial state", + GSL_ENOMEM); + } + + state->d = (double *) malloc (sizeof (double) * size); + + if (state->d == 0) + { + free (state); + GSL_ERROR_NULL ("failed to allocate space for d", GSL_ENOMEM); + } + + state->coeff = (double *) malloc (sizeof (double) * size); + + if (state->coeff == 0) + { + free (state->d); + free (state); + GSL_ERROR_NULL ("failed to allocate space for d", GSL_ENOMEM); + } + + state->work = (double *) malloc (sizeof (double) * size); + + if (state->work == 0) + { + free (state->coeff); + free (state->d); + free (state); + GSL_ERROR_NULL ("failed to allocate space for d", GSL_ENOMEM); + } + + return state; +} + +static int +polynomial_init (void *vstate, + const double xa[], const double ya[], size_t size) +{ + polynomial_state_t *state = (polynomial_state_t *) vstate; + + int status = gsl_poly_dd_init (state->d, xa, ya, size); + + return status; +} + +static int +polynomial_eval (const void *vstate, + const double xa[], const double ya[], size_t size, double x, + gsl_interp_accel * acc, double *y) +{ + const polynomial_state_t *state = (const polynomial_state_t *) vstate; + + *y = gsl_poly_dd_eval (state->d, xa, size, x); + + return GSL_SUCCESS; +} + + +static int +polynomial_deriv (const void *vstate, + const double xa[], const double ya[], size_t size, double x, + gsl_interp_accel * acc, double *y) +{ + const polynomial_state_t *state = (const polynomial_state_t *) vstate; + + gsl_poly_dd_taylor (state->coeff, x, state->d, xa, size, state->work); + + *y = state->coeff[1]; + + return GSL_SUCCESS; +} + +static int +polynomial_deriv2 (const void *vstate, + const double xa[], const double ya[], size_t size, + double x, gsl_interp_accel * acc, double *y) +{ + const polynomial_state_t *state = (const polynomial_state_t *) vstate; + + gsl_poly_dd_taylor (state->coeff, x, state->d, xa, size, state->work); + + *y = 2.0 * state->coeff[2]; + + return GSL_SUCCESS; +} + +static int +polynomial_integ (const void *vstate, const double xa[], const double ya[], + size_t size, gsl_interp_accel * acc, double a, double b, + double *result) +{ + const polynomial_state_t *state = (const polynomial_state_t *) vstate; + size_t i; + double sum; + + gsl_poly_dd_taylor (state->coeff, 0.0, state->d, xa, size, state->work); + + sum = state->coeff[0] * (b - a); + + for (i = 1; i < size; i++) + { + sum += state->coeff[i] * (pow (b, i + 1) - pow (a, i + 1)) / (i + 1.0); + } + + *result = sum; + + return GSL_SUCCESS; +} + +static void +polynomial_free (void *vstate) +{ + polynomial_state_t *state = (polynomial_state_t *) vstate; + free (state->d); + free (state->coeff); + free (state->work); + free (state); +} + +static const gsl_interp_type polynomial_type = { + "polynomial", + 3, + &polynomial_alloc, + &polynomial_init, + &polynomial_eval, + &polynomial_deriv, + &polynomial_deriv2, + &polynomial_integ, + &polynomial_free, +}; + +const gsl_interp_type *gsl_interp_polynomial = &polynomial_type; diff --git a/gsl-1.9/interpolation/spline.c b/gsl-1.9/interpolation/spline.c new file mode 100644 index 0000000..d5b5a0f --- /dev/null +++ b/gsl-1.9/interpolation/spline.c @@ -0,0 +1,193 @@ +/* interpolation/spline.c + * + * Copyright (C) 2001 Brian Gough + * + * 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 <string.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_interp.h> +#include <gsl/gsl_spline.h> + +gsl_spline * +gsl_spline_alloc (const gsl_interp_type * T, size_t size) +{ + gsl_spline * spline = (gsl_spline *) malloc (sizeof(gsl_spline)); + + if (spline == NULL) + { + GSL_ERROR_NULL ("failed to allocate space for spline struct", + GSL_ENOMEM); + } + + spline->interp = gsl_interp_alloc (T, size); + + if (spline->interp == NULL) + { + free (spline); + GSL_ERROR_NULL ("failed to allocate space for interp", GSL_ENOMEM); + }; + + spline->x = (double *) malloc (size * sizeof(double)); + + if (spline->x == NULL) + { + gsl_interp_free(spline->interp); + free(spline); + GSL_ERROR_NULL ("failed to allocate space for x", GSL_ENOMEM); + } + + spline->y = (double *) malloc (size * sizeof(double)); + + if (spline->y == NULL) + { + free(spline->x); + gsl_interp_free(spline->interp); + free(spline); + GSL_ERROR_NULL ("failed to allocate space for y", GSL_ENOMEM); + } + + spline->size = size; + + return spline; +} + +int +gsl_spline_init (gsl_spline * spline, const double x_array[], const double y_array[], size_t size) +{ + if (size != spline->size) + { + GSL_ERROR ("data must match size of spline object", GSL_EINVAL); + } + + memcpy (spline->x, x_array, size * sizeof(double)); + memcpy (spline->y, y_array, size * sizeof(double)); + + { + int status = gsl_interp_init (spline->interp, x_array, y_array, size); + return status; + } +} + +const char * +gsl_spline_name(const gsl_spline * spline) +{ + return gsl_interp_name(spline->interp); +} + +unsigned int +gsl_spline_min_size(const gsl_spline * spline) +{ + return gsl_interp_min_size(spline->interp); +} + +void +gsl_spline_free (gsl_spline * spline) +{ + gsl_interp_free (spline->interp); + free (spline->x); + free (spline->y); + free (spline); +} + +int +gsl_spline_eval_e (const gsl_spline * spline, + double x, + gsl_interp_accel * a, double *y) +{ + return gsl_interp_eval_e (spline->interp, + spline->x, spline->y, + x, a, y); +} + +double +gsl_spline_eval (const gsl_spline * spline, + double x, + gsl_interp_accel * a) +{ + return gsl_interp_eval (spline->interp, + spline->x, spline->y, + x, a); +} + + +int +gsl_spline_eval_deriv_e (const gsl_spline * spline, + double x, + gsl_interp_accel * a, + double *dydx) +{ + return gsl_interp_eval_deriv_e (spline->interp, + spline->x, spline->y, + x, a, dydx); +} + +double +gsl_spline_eval_deriv (const gsl_spline * spline, + double x, + gsl_interp_accel * a) +{ + return gsl_interp_eval_deriv (spline->interp, + spline->x, spline->y, + x, a); +} + + +int +gsl_spline_eval_deriv2_e (const gsl_spline * spline, + double x, + gsl_interp_accel * a, + double * d2) +{ + return gsl_interp_eval_deriv2_e (spline->interp, + spline->x, spline->y, + x, a, d2); +} + +double +gsl_spline_eval_deriv2 (const gsl_spline * spline, + double x, + gsl_interp_accel * a) +{ + return gsl_interp_eval_deriv2 (spline->interp, + spline->x, spline->y, + x, a); +} + + +int +gsl_spline_eval_integ_e (const gsl_spline * spline, + double a, double b, + gsl_interp_accel * acc, + double * result) +{ + return gsl_interp_eval_integ_e (spline->interp, + spline->x, spline->y, + a, b, acc, result); +} + + +double +gsl_spline_eval_integ (const gsl_spline * spline, + double a, double b, + gsl_interp_accel * acc) +{ + return gsl_interp_eval_integ (spline->interp, + spline->x, spline->y, + a, b, acc); +} + diff --git a/gsl-1.9/interpolation/test.c b/gsl-1.9/interpolation/test.c new file mode 100644 index 0000000..feb01d5 --- /dev/null +++ b/gsl-1.9/interpolation/test.c @@ -0,0 +1,949 @@ +/* interpolation/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. + */ + + +/* Author: G. Jungman + */ +#include <config.h> +#include <stddef.h> +#include <stdlib.h> +#include <stdio.h> +#include <math.h> +#include <gsl/gsl_test.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_interp.h> +#include <gsl/gsl_ieee_utils.h> + +int +test_bsearch(void) +{ + double x_array[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 }; + size_t index_result; + int status = 0; + int s; + + /* check an interior point */ + index_result = gsl_interp_bsearch(x_array, 1.5, 0, 4); + s = (index_result != 1); + status += s; + gsl_test (s, "simple bsearch"); + + /* check that we get the last interval if x == last value */ + index_result = gsl_interp_bsearch(x_array, 4.0, 0, 4); + s = (index_result != 3); + status += s; + gsl_test (s, "upper endpoint bsearch"); + + /* check that we get the first interval if x == first value */ + index_result = gsl_interp_bsearch(x_array, 0.0, 0, 4); + s = (index_result != 0); + status += s; + gsl_test (s, "lower endpoint bsearch"); + + /* check that we get correct interior boundary behaviour */ + index_result = gsl_interp_bsearch(x_array, 2.0, 0, 4); + s = (index_result != 2); + status += s; + gsl_test (s, "degenerate bsearch"); + + /* check out of bounds above */ + index_result = gsl_interp_bsearch(x_array, 10.0, 0, 4); + s = (index_result != 3); + status += s; + gsl_test (s, "out of bounds bsearch +"); + + /* check out of bounds below */ + index_result = gsl_interp_bsearch(x_array, -10.0, 0, 4); + s = (index_result != 0); + status += s; + gsl_test (s, "out of bounds bsearch -"); + + return status; +} + + + +typedef double TEST_FUNC (double); +typedef struct _xy_table xy_table; + +struct _xy_table + { + double * x; + double * y; + size_t n; + }; + +xy_table make_xy_table (double x[], double y[], size_t n); + +xy_table +make_xy_table (double x[], double y[], size_t n) +{ + xy_table t; + t.x = x; + t.y = y; + t.n = n; + return t; +} + +static int +test_interp ( + const xy_table * data_table, + const gsl_interp_type * T, + xy_table * test_table, + xy_table * test_d_table, + xy_table * test_i_table + ) +{ + int status = 0, s1, s2, s3; + size_t i; + + gsl_interp_accel *a = gsl_interp_accel_alloc (); + gsl_interp *interp = gsl_interp_alloc (T, data_table->n); + + gsl_interp_init (interp, data_table->x, data_table->y, data_table->n); + + for (i = 0; i < test_table->n; i++) + { + double x = test_table->x[i]; + double y; + double deriv; + double integ; + double diff_y, diff_deriv, diff_integ; + s1 = gsl_interp_eval_e (interp, data_table->x, data_table->y, x, a, &y); + s2 = gsl_interp_eval_deriv_e (interp, data_table->x, data_table->y, x, a, &deriv); + s3 = gsl_interp_eval_integ_e (interp, data_table->x, data_table->y, test_table->x[0], x, a, &integ); + + gsl_test (s1, "gsl_interp_eval_e %s", gsl_interp_name(interp)); + gsl_test (s2, "gsl_interp_eval_deriv_e %s", gsl_interp_name(interp)); + gsl_test (s3, "gsl_interp_eval_integ_e %s", gsl_interp_name(interp)); + + gsl_test_abs (y, test_table->y[i], 1e-10, "%s %d", gsl_interp_name(interp), i); + gsl_test_abs (deriv, test_d_table->y[i], 1e-10, "%s deriv %d", gsl_interp_name(interp), i); + gsl_test_abs (integ, test_i_table->y[i], 1e-10, "%s integ %d", gsl_interp_name(interp), i); + + diff_y = y - test_table->y[i]; + diff_deriv = deriv - test_d_table->y[i]; + diff_integ = integ - test_i_table->y[i]; + if (fabs (diff_y) > 1.e-10 || fabs(diff_deriv) > 1.0e-10 || fabs(diff_integ) > 1.0e-10) { + status++; + } + } + + gsl_interp_accel_free (a); + gsl_interp_free (interp); + + return status; +} + +static int +test_linear (void) +{ + int s; + + double data_x[4] = { 0.0, 1.0, 2.0, 3.0 }; + double data_y[4] = { 0.0, 1.0, 2.0, 3.0 }; + double test_x[6] = { 0.0, 0.5, 1.0, 1.5, 2.5, 3.0 }; + double test_y[6] = { 0.0, 0.5, 1.0, 1.5, 2.5, 3.0 }; + double test_dy[6] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 }; + double test_iy[6] = { 0.0, 0.125, 0.5, 9.0/8.0, 25.0/8.0, 9.0/2.0 }; + + xy_table data_table = make_xy_table(data_x, data_y, 4); + xy_table test_table = make_xy_table(test_x, test_y, 6); + xy_table test_d_table = make_xy_table(test_x, test_dy, 6); + xy_table test_i_table = make_xy_table(test_x, test_iy, 6); + + s = test_interp (&data_table, gsl_interp_linear, &test_table, &test_d_table, &test_i_table); + gsl_test (s, "linear interpolation"); + return s; +} + +static int +test_polynomial (void) +{ + int s; + + double data_x[4] = { 0.0, 1.0, 2.0, 3.0 }; + double data_y[4] = { 0.0, 1.0, 2.0, 3.0 }; + double test_x[6] = { 0.0, 0.5, 1.0, 1.5, 2.5, 3.0 }; + double test_y[6] = { 0.0, 0.5, 1.0, 1.5, 2.5, 3.0 }; + double test_dy[6] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 }; + double test_iy[6] = { 0.0, 0.125, 0.5, 9.0/8.0, 25.0/8.0, 9.0/2.0 }; + + xy_table data_table = make_xy_table(data_x, data_y, 4); + xy_table test_table = make_xy_table(test_x, test_y, 6); + xy_table test_d_table = make_xy_table(test_x, test_dy, 6); + xy_table test_i_table = make_xy_table(test_x, test_iy, 6); + + s = test_interp (&data_table, gsl_interp_polynomial, &test_table, &test_d_table, &test_i_table); + gsl_test (s, "polynomial interpolation"); + return s; +} + + +static int +test_cspline (void) +{ + int s; + + double data_x[3] = { 0.0, 1.0, 2.0 }; + double data_y[3] = { 0.0, 1.0, 2.0 }; + double test_x[4] = { 0.0, 0.5, 1.0, 2.0 }; + double test_y[4] = { 0.0, 0.5, 1.0, 2.0 }; + double test_dy[4] = { 1.0, 1.0, 1.0, 1.0 }; + double test_iy[4] = { 0.0, 0.125, 0.5, 2.0 }; + + xy_table data_table = make_xy_table(data_x, data_y, 3); + xy_table test_table = make_xy_table(test_x, test_y, 4); + xy_table test_d_table = make_xy_table(test_x, test_dy, 4); + xy_table test_i_table = make_xy_table(test_x, test_iy, 4); + + s = test_interp (&data_table, gsl_interp_cspline, &test_table, &test_d_table, &test_i_table); + gsl_test (s, "cspline interpolation"); + return s; +} + +static int +test_cspline2 (void) +{ + /* Test taken from Young & Gregory, A Survey of Numerical + Mathematics, Vol 1 Chapter 6.8 */ + + int s; + + double data_x[6] = { 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 }; + + double data_y[6] = { 1.0, + 0.961538461538461, 0.862068965517241, + 0.735294117647059, 0.609756097560976, + 0.500000000000000 } ; + + double test_x[50] = { + 0.00, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, + 0.20, 0.22, 0.24, 0.26, 0.28, 0.30, 0.32, 0.34, 0.36, 0.38, + 0.40, 0.42, 0.44, 0.46, 0.48, 0.50, 0.52, 0.54, 0.56, 0.58, + 0.60, 0.62, 0.64, 0.66, 0.68, 0.70, 0.72, 0.74, 0.76, 0.78, + 0.80, 0.82, 0.84, 0.86, 0.88, 0.90, 0.92, 0.94, 0.96, 0.98 }; + + double test_y[50] = { + 1.000000000000000, 0.997583282975581, 0.995079933416512, + 0.992403318788142, 0.989466806555819, 0.986183764184894, + 0.982467559140716, 0.978231558888635, 0.973389130893999, + 0.967853642622158, 0.961538461538461, 0.954382579685350, + 0.946427487413627, 0.937740299651188, 0.928388131325928, + 0.918438097365742, 0.907957312698524, 0.897012892252170, + 0.885671950954575, 0.874001603733634, 0.862068965517241, + 0.849933363488199, 0.837622973848936, 0.825158185056786, + 0.812559385569085, 0.799846963843167, 0.787041308336369, + 0.774162807506023, 0.761231849809467, 0.748268823704033, + 0.735294117647059, 0.722328486073082, 0.709394147325463, + 0.696513685724764, 0.683709685591549, 0.671004731246381, + 0.658421407009825, 0.645982297202442, 0.633709986144797, + 0.621627058157454, 0.609756097560976, 0.598112015427308, + 0.586679029833925, 0.575433685609685, 0.564352527583445, + 0.553412100584061, 0.542588949440392, 0.531859618981294, + 0.521200654035625, 0.510588599432241}; + + double test_dy[50] = { + -0.120113913432180, -0.122279726798445, -0.128777166897241, + -0.139606233728568, -0.154766927292426, -0.174259247588814, + -0.198083194617734, -0.226238768379184, -0.258725968873165, + -0.295544796099676, -0.336695250058719, -0.378333644186652, + -0.416616291919835, -0.451543193258270, -0.483114348201955, + -0.511329756750890, -0.536189418905076, -0.557693334664512, + -0.575841504029200, -0.590633926999137, -0.602070603574326, + -0.611319695518765, -0.619549364596455, -0.626759610807396, + -0.632950434151589, -0.638121834629033, -0.642273812239728, + -0.645406366983674, -0.647519498860871, -0.648613207871319, + -0.648687494015019, -0.647687460711257, -0.645558211379322, + -0.642299746019212, -0.637912064630930, -0.632395167214473, + -0.625749053769843, -0.617973724297039, -0.609069178796061, + -0.599035417266910, -0.587872439709585, -0.576731233416743, + -0.566762785681043, -0.557967096502484, -0.550344165881066, + -0.543893993816790, -0.538616580309654, -0.534511925359660, + -0.531580028966807, -0.529820891131095}; + + double test_iy[50] = { + 0.000000000000000, 0.019975905023535, 0.039902753768792, + 0.059777947259733, 0.079597153869625, 0.099354309321042, + 0.119041616685866, 0.138649546385285, 0.158166836189794, + 0.177580491219196, 0.196875783942601, 0.216036382301310, + 0.235045759060558, 0.253888601161251, 0.272550937842853, + 0.291020140643388, 0.309284923399436, 0.327335342246135, + 0.345162795617181, 0.362760024244829, 0.380121111159890, + 0.397241442753010, 0.414117280448683, 0.430745332379281, + 0.447122714446318, 0.463246950320456, 0.479115971441505, + 0.494728117018421, 0.510082134029305, 0.525177177221407, + 0.540012809111123, 0.554589001813881, 0.568906157172889, + 0.582965126887879, 0.596767214344995, 0.610314174616794, + 0.623608214462242, 0.636651992326715, 0.649448618342004, + 0.662001654326309, 0.674315113784241, 0.686393423540581, + 0.698241001711602, 0.709861835676399, 0.721259443710643, + 0.732436874986582, 0.743396709573044, 0.754141058435429, + 0.764671563435718, 0.774989397332469 }; + + xy_table data_table = make_xy_table(data_x, data_y, 6); + xy_table test_table = make_xy_table(test_x, test_y, 50); + xy_table test_d_table = make_xy_table(test_x, test_dy, 50); + xy_table test_i_table = make_xy_table(test_x, test_iy, 50); + + s = test_interp (&data_table, gsl_interp_cspline, &test_table, &test_d_table, &test_i_table); + gsl_test (s, "cspline 1/(1+x^2) interpolation"); + return s; +} + +static int +test_cspline3 (void) +{ + /* This data has been chosen to be random (uneven spacing in x and y) + and the exact cubic spine solution computed using Octave */ + + int s; + + double data_x[7] = { + -1.2139767065644265, + -0.792590494453907, + -0.250954683125019, + 0.665867809951305, + 0.735655088722706, + 0.827622053027153, + 1.426592227816582 + }; + + double data_y[7] = { + -0.00453877449035645, + 0.49763182550668716, + 0.17805472016334534, + 0.40514493733644485, + -0.21595209836959839, + 0.47405586764216423, + 0.46561462432146072 + } ; + + double test_x[19] = { + -1.2139767065644265, + -1.0735146358609200, + -0.9330525651574135, + -0.7925904944539071, + -0.6120452240109444, + -0.4314999535679818, + -0.2509546831250191, + 0.0546528145670890, + 0.3602603122591972, + 0.6658678099513053, + 0.6891302362084388, + 0.7123926624655723, + 0.7356550887227058, + 0.7663107434908548, + 0.7969663982590039, + 0.8276220530271530, + 1.0272787779569625, + 1.2269355028867721, + 1.4265922278165817, + }; + + double test_y[19] = { + -0.00453877449035645, + 0.25816917628390590, + 0.44938881397673230, + 0.49763182550668716, + 0.31389980410075147, + 0.09948951681196887, + 0.17805472016334534, + 1.27633142487980233, + 2.04936553432792001, + 0.40514493733644485, + 0.13322324792901385, + -0.09656315924697809, + -0.21595209836959839, + -0.13551147728045118, + 0.13466779030061801, + 0.47405586764216423, + 1.68064089899304370, + 1.43594739539458649, + 0.46561462432146072 + }; + + double test_dy[19] = { + 1.955137555965937, + 1.700662049790549, + 0.937235531264386, + -0.335141999612553, + -1.401385073563169, + -0.674982149482761, + 1.844066772628670, + 4.202528085784793, + -0.284432022227558, + -11.616813551408383, + -11.272731243226174, + -7.994209291156876, + -1.781247695200491, + 6.373970868827501, + 10.597456848997197, + 10.889210245308570, + 1.803124267866902, + -3.648527318598099, + -5.465744514086432, + }; + + double test_iy[19] = { + 0.000000000000000, + 0.018231117234914, + 0.069178822023139, + 0.137781019634897, + 0.213936442847744, + 0.249280997744777, + 0.267492946016120, + 0.471372708120518, + 1.014473660088477, + 1.477731933018837, + 1.483978291717981, + 1.484256847945450, + 1.480341742628893, + 1.474315901028282, + 1.473972210647307, + 1.483279773396950, + 1.728562698140330, + 2.057796448999396, + 2.253662886537457, + }; + + xy_table data_table = make_xy_table(data_x, data_y, 7); + xy_table test_table = make_xy_table(test_x, test_y, 19); + xy_table test_d_table = make_xy_table(test_x, test_dy, 19); + xy_table test_i_table = make_xy_table(test_x, test_iy, 19); + + s = test_interp (&data_table, gsl_interp_cspline, &test_table, &test_d_table, &test_i_table); + gsl_test (s, "cspline arbitrary data interpolation"); + return s; +} + +static int +test_csplinep (void) +{ + /* This data has been chosen to be random (uneven spacing in x and y) + and the exact cubic spine solution computed using Octave */ + + int s; + + double data_x[11] = { + 0.000000000000000, + 0.130153674349869, + 0.164545962312740, + 0.227375461261537, + 0.256465324353657, + 0.372545206874658, + 0.520820016781720, + 0.647654717733075, + 0.753429306654340, + 0.900873984827658, + 1.000000000000000, + }; + + double data_y[11] = { + 0.000000000000000, + 0.729629261832041, + 0.859286331568207, + 0.989913099419008, + 0.999175006262120, + 0.717928599519215, + -0.130443237213363, + -0.800267961158980, + -0.999767873040527, + -0.583333769240853, + -0.000000000000000, + } ; + + double test_x[31] = { + 0.000000000000000, + 0.043384558116623, + 0.086769116233246, + 0.130153674349869, + 0.141617770337492, + 0.153081866325116, + 0.164545962312740, + 0.185489128629005, + 0.206432294945271, + 0.227375461261537, + 0.237072082292243, + 0.246768703322951, + 0.256465324353657, + 0.295158618527324, + 0.333851912700991, + 0.372545206874658, + 0.421970143510346, + 0.471395080146033, + 0.520820016781720, + 0.563098250432172, + 0.605376484082623, + 0.647654717733075, + 0.682912914040164, + 0.718171110347252, + 0.753429306654340, + 0.802577532712113, + 0.851725758769885, + 0.900873984827658, + 0.933915989885105, + 0.966957994942553, + 1.000000000000000 + }; + + double test_y[31] = { + 0.000000000000000, + 0.268657574670719, + 0.517940878523929, + 0.729629261832041, + 0.777012551497867, + 0.820298314554859, + 0.859286331568207, + 0.918833991960315, + 0.962624749226346, + 0.989913099419008, + 0.996756196601349, + 0.999858105635752, + 0.999175006262120, + 0.959248551766306, + 0.863713527741856, + 0.717928599519215, + 0.470065187871106, + 0.177694938589523, + -0.130443237213363, + -0.385093922365765, + -0.613840011545983, + -0.800267961158980, + -0.912498361131651, + -0.980219217412290, + -0.999767873040528, + -0.943635958253643, + -0.800314354800596, + -0.583333769240853, + -0.403689914131666, + -0.206151346799382, + -0.000000000000000 + }; + + double test_dy[31] = { + 6.275761975917336, + 6.039181349093287, + 5.382620652895025, + 4.306079887322550, + 3.957389777282752, + 3.591234754612763, + 3.207614819312586, + 2.473048186927024, + 1.702885029353488, + 0.897125346591982, + 0.513561009477969, + 0.125477545550710, + -0.267125045189792, + -1.773533414873785, + -3.141450982859891, + -4.370877749148106, + -5.562104227060234, + -6.171864888961167, + -6.200159734850907, + -5.781556055213110, + -4.974725570010514, + -3.779668279243120, + -2.569220222282655, + -1.254891157670244, + 0.163318914594122, + 2.074985916277011, + 3.711348850147548, + 5.072407716205733, + 5.754438923510391, + 6.155557010080926, + 6.275761975917336 + }; + + double test_iy[31] = { + 0.000000000000000, + 0.005864903144198, + 0.023030998930796, + 0.050262495763030, + 0.058902457844100, + 0.068062330564832, + 0.077693991819461, + 0.096340576055474, + 0.116070578226521, + 0.136546192283223, + 0.146181187290769, + 0.155864434185569, + 0.165559443629720, + 0.203636318965633, + 0.239075190181586, + 0.269828050745236, + 0.299428805999600, + 0.315560685785616, + 0.316734151903742, + 0.305773798930857, + 0.284537037103156, + 0.254466034797342, + 0.224146112780097, + 0.190643050847000, + 0.155590744566140, + 0.107448508851745, + 0.064263083957312, + 0.029987183298960, + 0.013618510529526, + 0.003506827320794, + 0.000090064010007, + }; + + xy_table data_table = make_xy_table(data_x, data_y, 11); + xy_table test_table = make_xy_table(test_x, test_y, 31); + xy_table test_d_table = make_xy_table(test_x, test_dy, 31); + xy_table test_i_table = make_xy_table(test_x, test_iy, 31); + + s = test_interp (&data_table, gsl_interp_cspline_periodic, &test_table, &test_d_table, &test_i_table); + gsl_test (s, "cspline periodic sine interpolation"); + return s; +} + +static int +test_csplinep2 (void) +{ + /* This data tests the periodic case n=3 */ + + int s; + + double data_x[3] = { + 0.123, + 0.423, + 1.123 + }; + + double data_y[3] = { + 0.456000000000000, + 1.407056516295154, + 0.456000000000000 + } ; + + double test_x[61] = { + 0.123000000000000, + 0.133000000000000, + 0.143000000000000, + 0.153000000000000, + 0.163000000000000, + 0.173000000000000, + 0.183000000000000, + 0.193000000000000, + 0.203000000000000, + 0.213000000000000, + 0.223000000000000, + 0.233000000000000, + 0.243000000000000, + 0.253000000000000, + 0.263000000000000, + 0.273000000000000, + 0.283000000000000, + 0.293000000000000, + 0.303000000000000, + 0.313000000000000, + 0.323000000000000, + 0.333000000000000, + 0.343000000000000, + 0.353000000000000, + 0.363000000000000, + 0.373000000000000, + 0.383000000000000, + 0.393000000000000, + 0.403000000000000, + 0.413000000000000, + 0.423000000000000, + 0.446333333333333, + 0.469666666666667, + 0.493000000000000, + 0.516333333333333, + 0.539666666666667, + 0.563000000000000, + 0.586333333333333, + 0.609666666666667, + 0.633000000000000, + 0.656333333333333, + 0.679666666666667, + 0.703000000000000, + 0.726333333333333, + 0.749666666666667, + 0.773000000000000, + 0.796333333333333, + 0.819666666666667, + 0.843000000000000, + 0.866333333333333, + 0.889666666666667, + 0.913000000000000, + 0.936333333333333, + 0.959666666666667, + 0.983000000000000, + 1.006333333333333, + 1.029666666666667, + 1.053000000000000, + 1.076333333333333, + 1.099666666666667, + 1.123000000000000 + }; + + double test_y[61] = { + 0.456000000000000, + 0.475443822110923, + 0.497423794931967, + 0.521758764840979, + 0.548267578215809, + 0.576769081434305, + 0.607082120874316, + 0.639025542913690, + 0.672418193930275, + 0.707078920301921, + 0.742826568406475, + 0.779479984621787, + 0.816858015325704, + 0.854779506896076, + 0.893063305710751, + 0.931528258147577, + 0.969993210584403, + 1.008277009399078, + 1.046198500969450, + 1.083576531673367, + 1.120229947888679, + 1.155977595993233, + 1.190638322364879, + 1.224030973381464, + 1.255974395420838, + 1.286287434860848, + 1.314788938079344, + 1.341297751454174, + 1.365632721363187, + 1.387612694184230, + 1.407056516295154, + 1.442092968697928, + 1.463321489456714, + 1.471728359403224, + 1.468299859369172, + 1.454022270186272, + 1.429881872686237, + 1.396864947700781, + 1.355957776061616, + 1.308146638600458, + 1.254417816149018, + 1.195757589539010, + 1.133152239602149, + 1.067588047170148, + 1.000051293074719, + 0.931528258147577, + 0.863005223220435, + 0.795468469125006, + 0.729904276693004, + 0.667298926756143, + 0.608638700146136, + 0.554909877694696, + 0.507098740233537, + 0.466191568594372, + 0.433174643608916, + 0.409034246108881, + 0.394756656925981, + 0.391328156891929, + 0.399735026838439, + 0.420963547597225, + 0.456000000000000 + }; + + double test_dy[61] = { + 1.8115362215145774, + 2.0742089736341924, + 2.3187663635386602, + 2.5452083912279826, + 2.7535350567021584, + 2.9437463599611897, + 3.1158423010050744, + 3.2698228798338147, + 3.4056880964474079, + 3.5234379508458549, + 3.6230724430291570, + 3.7045915729973125, + 3.7679953407503231, + 3.8132837462881874, + 3.8404567896109061, + 3.8495144707184790, + 3.8404567896109061, + 3.8132837462881874, + 3.7679953407503231, + 3.7045915729973125, + 3.6230724430291565, + 3.5234379508458549, + 3.4056880964474074, + 3.2698228798338147, + 3.1158423010050749, + 2.9437463599611897, + 2.7535350567021584, + 2.5452083912279830, + 2.3187663635386597, + 2.0742089736341924, + 1.8115362215145772, + 1.1986331332354823, + 0.6279992234583869, + 0.0996344921833026, + -0.3864610605897765, + -0.8302874348608467, + -1.2318446306299125, + -1.5911326478969707, + -1.9081514866620208, + -2.1829011469250670, + -2.4153816286861041, + -2.6055929319451341, + -2.7535350567021584, + -2.8592080029571765, + -2.9226117707101862, + -2.9437463599611893, + -2.9226117707101862, + -2.8592080029571760, + -2.7535350567021593, + -2.6055929319451354, + -2.4153816286861045, + -2.1829011469250656, + -1.9081514866620242, + -1.5911326478969716, + -1.2318446306299160, + -0.8302874348608498, + -0.3864610605897769, + 0.0996344921832995, + 0.6279992234583824, + 1.1986331332354769, + 1.8115362215145772 + }; + + double test_iy[61] = { + 0.000000000000000, + 0.004655030170954, + 0.009517330277919, + 0.014611356059886, + 0.019959751719625, + 0.025583349923681, + 0.031501171802382, + 0.037730426949832, + 0.044286513423914, + 0.051183017746288, + 0.058431714902395, + 0.066042568341453, + 0.074023729976459, + 0.082381540184189, + 0.091120527805195, + 0.100243410143811, + 0.109751092968147, + 0.119642670510092, + 0.129915425465314, + 0.140564828993259, + 0.151584540717153, + 0.162966408723997, + 0.174700469564574, + 0.186774948253444, + 0.199176258268946, + 0.211889001553197, + 0.224895968512091, + 0.238178138015305, + 0.251714677396289, + 0.265482942452275, + 0.279458477444273, + 0.312726362409309, + 0.346648754292945, + 0.380914974633193, + 0.415237358187469, + 0.449351252932597, + 0.483015020064806, + 0.516010033999735, + 0.548140682372425, + 0.579234366037328, + 0.609141499068300, + 0.637735508758604, + 0.664912835620912, + 0.690592933387298, + 0.714718269009247, + 0.737254322657649, + 0.758189587722801, + 0.777535570814405, + 0.795326791761572, + 0.811620783612819, + 0.826498092636068, + 0.840062278318649, + 0.852439913367300, + 0.863780583708163, + 0.874256888486789, + 0.884064440068133, + 0.893421864036559, + 0.902570799195836, + 0.911775897569142, + 0.921324824399059, + 0.931528258147577 + }; + + xy_table data_table = make_xy_table(data_x, data_y, 3); + xy_table test_table = make_xy_table(test_x, test_y, 61); + xy_table test_d_table = make_xy_table(test_x, test_dy, 61); + xy_table test_i_table = make_xy_table(test_x, test_iy, 61); + + s = test_interp (&data_table, gsl_interp_cspline_periodic, &test_table, &test_d_table, &test_i_table); + gsl_test (s, "cspline periodic 3pt interpolation"); + return s; +} + + + +static int +test_akima (void) +{ + int s; + + double data_x[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 }; + double data_y[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 }; + double test_x[4] = { 0.0, 0.5, 1.0, 2.0 }; + double test_y[4] = { 0.0, 0.5, 1.0, 2.0 }; + double test_dy[4] = { 1.0, 1.0, 1.0, 1.0 }; + double test_iy[4] = { 0.0, 0.125, 0.5, 2.0 }; + + xy_table data_table = make_xy_table(data_x, data_y, 5); + xy_table test_table = make_xy_table(test_x, test_y, 4); + xy_table test_d_table = make_xy_table(test_x, test_dy, 4); + xy_table test_i_table = make_xy_table(test_x, test_iy, 4); + + s = test_interp (&data_table, gsl_interp_akima, &test_table, &test_d_table, &test_i_table); + gsl_test (s, "akima interpolation"); + return s; +} + + +int +main (int argc, char **argv) +{ + int status = 0; + + gsl_ieee_env_setup (); + + argc = 0; /* prevent warnings about unused parameters */ + argv = 0; + + status += test_bsearch(); + status += test_linear(); + status += test_polynomial(); + status += test_cspline(); + status += test_cspline2(); + status += test_cspline3(); + status += test_csplinep(); + status += test_csplinep2(); + status += test_akima(); + + exit (gsl_test_summary()); +} |