diff options
Diffstat (limited to 'gsl-1.9/bspline')
| -rw-r--r-- | gsl-1.9/bspline/ChangeLog | 7 | ||||
| -rw-r--r-- | gsl-1.9/bspline/Makefile.am | 15 | ||||
| -rw-r--r-- | gsl-1.9/bspline/Makefile.in | 547 | ||||
| -rw-r--r-- | gsl-1.9/bspline/TODO | 9 | ||||
| -rw-r--r-- | gsl-1.9/bspline/bspline.c | 497 | ||||
| -rw-r--r-- | gsl-1.9/bspline/gsl_bspline.h | 75 | ||||
| -rw-r--r-- | gsl-1.9/bspline/test.c | 112 |
7 files changed, 1262 insertions, 0 deletions
diff --git a/gsl-1.9/bspline/ChangeLog b/gsl-1.9/bspline/ChangeLog new file mode 100644 index 0000000..19ddc1c --- /dev/null +++ b/gsl-1.9/bspline/ChangeLog @@ -0,0 +1,7 @@ +2006-11-02 Brian Gough <bjg@network-theory.co.uk> + + * added test program + + * initial checkin from P.Alken + + diff --git a/gsl-1.9/bspline/Makefile.am b/gsl-1.9/bspline/Makefile.am new file mode 100644 index 0000000..6dc3772 --- /dev/null +++ b/gsl-1.9/bspline/Makefile.am @@ -0,0 +1,15 @@ +noinst_LTLIBRARIES = libgslbspline.la + +pkginclude_HEADERS = gsl_bspline.h + +INCLUDES= -I$(top_builddir) + +libgslbspline_la_SOURCES = bspline.c + +check_PROGRAMS = test + +TESTS = $(check_PROGRAMS) + +test_LDADD = libgslbspline.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/bspline/Makefile.in b/gsl-1.9/bspline/Makefile.in new file mode 100644 index 0000000..ac743dc --- /dev/null +++ b/gsl-1.9/bspline/Makefile.in @@ -0,0 +1,547 @@ +# 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 <gsl/gsl_errno.h> +#include <gsl/gsl_bspline.h> + +/* + * This module contains routines related to calculating B-splines. + * The algorithms used are described in + * + * [1] Carl de Boor, "A Practical Guide to Splines", Springer + * Verlag, 1978. + */ + +static int bspline_eval_all(const double x, gsl_vector *B, size_t *idx, + gsl_bspline_workspace *w); + +static inline size_t bspline_find_interval(const double x, int *flag, + gsl_bspline_workspace *w); + +/* +gsl_bspline_alloc() + Allocate space for a bspline workspace. The size of the +workspace is O(5k + nbreak) + +Inputs: k - spline order (cubic = 4) + nbreak - number of breakpoints + +Return: pointer to workspace +*/ + +gsl_bspline_workspace * +gsl_bspline_alloc(const size_t k, const size_t nbreak) +{ + if (k == 0) + { + GSL_ERROR_NULL("k must be at least 1", GSL_EINVAL); + } + else if (nbreak < 2) + { + GSL_ERROR_NULL("nbreak must be at least 2", GSL_EINVAL); + } + else + { + gsl_bspline_workspace *w; + + w = (gsl_bspline_workspace *) + calloc(1, sizeof(gsl_bspline_workspace)); + if (w == 0) + { + GSL_ERROR_NULL("failed to allocate space for workspace", GSL_ENOMEM); + } + + w->k = k; + w->km1 = k - 1; + w->nbreak = nbreak; + w->l = nbreak - 1; + w->n = w->l + k - 1; + + w->knots = gsl_vector_alloc(w->n + k); + if (w->knots == 0) + { + gsl_bspline_free(w); + GSL_ERROR_NULL("failed to allocate space for knots vector", GSL_ENOMEM); + } + + w->deltal = gsl_vector_alloc(k); + w->deltar = gsl_vector_alloc(k); + if (!w->deltal || !w->deltar) + { + gsl_bspline_free(w); + GSL_ERROR_NULL("failed to allocate space for delta vectors", GSL_ENOMEM); + } + + w->B = gsl_vector_alloc(k); + if (w->B == 0) + { + gsl_bspline_free(w); + GSL_ERROR_NULL("failed to allocate space for temporary spline vector", GSL_ENOMEM); + } + + return (w); + } +} /* gsl_bspline_alloc() */ + +/* Return number of coefficients */ +size_t +gsl_bspline_ncoeffs (gsl_bspline_workspace * w) +{ + return w->n; +} + +/* Return order */ +size_t +gsl_bspline_order (gsl_bspline_workspace * w) +{ + return w->k; +} + +/* Return number of breakpoints */ +size_t +gsl_bspline_nbreak (gsl_bspline_workspace * w) +{ + return w->nbreak; +} + +double +gsl_bspline_breakpoint (size_t i, gsl_bspline_workspace * w) +{ + size_t j = i + w->k - 1; + return gsl_vector_get(w->knots, j); +} + +/* +gsl_bspline_free() + Free a bspline workspace + +Inputs: w - workspace to free + +Return: none +*/ + +void +gsl_bspline_free(gsl_bspline_workspace *w) +{ + if (!w) + return; + + if (w->knots) + gsl_vector_free(w->knots); + + if (w->deltal) + gsl_vector_free(w->deltal); + + if (w->deltar) + gsl_vector_free(w->deltar); + + if (w->B) + gsl_vector_free(w->B); + + free(w); +} /* gsl_bspline_free() */ + +/* +gsl_bspline_knots() + Compute the knots from the given breakpoints: + +knots(1:k) = breakpts(1) +knots(k+1:k+l-1) = breakpts(i), i = 2 .. l +knots(n+1:n+k) = breakpts(l + 1) + +where l is the number of polynomial pieces (l = nbreak - 1) and +n = k + l - 1 +(using matlab syntax for the arrays) + +The repeated knots at the beginning and end of the interval +correspond to the continuity condition there. See pg. 119 +of [1]. + +Inputs: breakpts - breakpoints + w - bspline workspace + +Return: success or error +*/ + +int +gsl_bspline_knots(const gsl_vector *breakpts, gsl_bspline_workspace *w) +{ + if (breakpts->size != w->nbreak) + { + GSL_ERROR("breakpts vector has wrong size", GSL_EBADLEN); + } + else + { + size_t i; /* looping */ + + for (i = 0; i < w->k; ++i) + gsl_vector_set(w->knots, i, gsl_vector_get(breakpts, 0)); + + for (i = 1; i < w->l; ++i) + { + gsl_vector_set(w->knots, w->k - 1 + i, + gsl_vector_get(breakpts, i)); + } + + for (i = w->n; i < w->n + w->k; ++i) + gsl_vector_set(w->knots, i, gsl_vector_get(breakpts, w->l)); + + return GSL_SUCCESS; + } +} /* gsl_bspline_knots() */ + +/* +gsl_bspline_knots_uniform() + Construct uniformly spaced knots on the interval [a,b] using +the previously specified number of breakpoints. 'a' is the position +of the first breakpoint and 'b' is the position of the last +breakpoint. + +Inputs: a - left side of interval + b - right side of interval + w - bspline workspace + +Return: success or error + +Notes: 1) w->knots is modified to contain the uniformly spaced + knots + + 2) The knots vector is set up as follows (using octave syntax): + + knots(1:k) = a + knots(k+1:k+l-1) = a + i*delta, i = 1 .. l - 1 + knots(n+1:n+k) = b +*/ + +int +gsl_bspline_knots_uniform(const double a, const double b, + gsl_bspline_workspace *w) +{ + size_t i; /* looping */ + double delta; /* interval spacing */ + double x; + + delta = (b - a) / (double) w->l; + + for (i = 0; i < w->k; ++i) + gsl_vector_set(w->knots, i, a); + + x = a + delta; + for (i = 0; i < w->l - 1; ++i) + { + gsl_vector_set(w->knots, w->k + i, x); + x += delta; + } + + for (i = w->n; i < w->n + w->k; ++i) + gsl_vector_set(w->knots, i, b); + + return GSL_SUCCESS; +} /* gsl_bspline_knots_uniform() */ + +/* +gsl_bspline_eval() + Evaluate the basis functions B_i(x) for all i. This is +basically a wrapper function for bspline_eval_all() +which formats the output in a nice way. + +Inputs: x - point for evaluation + B - (output) where to store B_i(x) values + the length of this vector is + n = nbreak + k - 2 = l + k - 1 = w->n + w - bspline workspace + +Return: success or error + +Notes: The w->knots vector must be initialized prior to calling + this function (see gsl_bspline_knots()) +*/ + +int +gsl_bspline_eval(const double x, gsl_vector *B, + gsl_bspline_workspace *w) +{ + if (B->size != w->n) + { + GSL_ERROR("B vector length does not match n", GSL_EBADLEN); + } + else + { + size_t i; /* looping */ + size_t idx = 0; + size_t start; /* first non-zero spline */ + + /* find all non-zero B_i(x) values */ + bspline_eval_all(x, w->B, &idx, w); + + /* store values in appropriate part of given vector */ + + start = idx - w->k + 1; + for (i = 0; i < start; ++i) + gsl_vector_set(B, i, 0.0); + + for (i = start; i <= idx; ++i) + gsl_vector_set(B, i, gsl_vector_get(w->B, i - start)); + + for (i = idx + 1; i < w->n; ++i) + gsl_vector_set(B, i, 0.0); + + return GSL_SUCCESS; + } +} /* gsl_bspline_eval() */ + +/**************************************** + * INTERNAL ROUTINES * + ****************************************/ + +/* +bspline_eval_all() + Evaluate all non-zero B-splines B_i(x) using algorithm (8) +of chapter X of [1] + +The idea is something like this. Given x \in [t_i, t_{i+1}] +with t_i < t_{i+1} and the t_i are knots, the values of the +B-splines not automatically zero fit into a triangular +array as follows: + 0 + 0 +0 B_{i-2,3} + B_{i-1,2} +B_{i,1} B_{i-1,3} ... + B_{i,2} +0 B_{i,3} + 0 + 0 + +where B_{i,k} is the ith B-spline of order k. The boundary 0s +indicate that those B-splines not in the table vanish at x. + +To compute the non-zero B-splines of a given order k, we use +Eqs. (4) and (5) of chapter X of [1]: + +(4) B_{i,1}(x) = { 1, t_i <= x < t_{i+1} + 0, else } + +(5) B_{i,k}(x) = (x - t_i) + ----------------- B_{i,k-1}(x) + (t_{i+k-1} - t_i) + + t_{i+k} - x + + ----------------- B_{i+1,k-1}(x) + t_{i+k} - t_{i+1} + +So (4) gives us the first column of the table and we can use +the recurrence relation (5) to get the rest of the columns. + +Inputs: x - point at which to evaluate splines + B - (output) where to store B-spline values (length k) + idx - (output) B-spline function index of last output + value (B_{idx}(x) is stored in the last slot of 'B') + w - bspline workspace + +Return: success or error + +Notes: 1) the w->knots vector must be initialized before calling + this function + + 2) On output, B contains: + + B = [B_{i-k+1,k}, B_{i-k+2,k}, ..., B_{i-1,k}, B_{i,k}] + + where 'i' is stored in 'idx' on output + + 3) based on PPPACK bsplvb +*/ + +static int +bspline_eval_all(const double x, gsl_vector *B, size_t *idx, + gsl_bspline_workspace *w) +{ + if (B->size != w->k) + { + GSL_ERROR("B vector not of length k", GSL_EBADLEN); + } + else + { + size_t i; /* spline index */ + size_t j; /* looping */ + size_t ii; /* looping */ + int flag = 0; /* error flag */ + double saved; + double term; + + i = bspline_find_interval(x, &flag, w); + + if (flag == -1) + { + GSL_ERROR("x outside of knot interval", GSL_EINVAL); + } + else if (flag == 1) + { + if (x <= gsl_vector_get(w->knots, i) + GSL_DBL_EPSILON) + { + --i; + } + else + { + GSL_ERROR("x outside of knot interval", GSL_EINVAL); + } + } + + *idx = i; + + gsl_vector_set(B, 0, 1.0); + + for (j = 0; j < w->k - 1; ++j) + { + gsl_vector_set(w->deltar, j, + gsl_vector_get(w->knots, i + j + 1) - x); + gsl_vector_set(w->deltal, j, + x - gsl_vector_get(w->knots, i - j)); + + saved = 0.0; + + for (ii = 0; ii <= j; ++ii) + { + term = gsl_vector_get(B, ii) / + (gsl_vector_get(w->deltar, ii) + + gsl_vector_get(w->deltal, j - ii)); + + gsl_vector_set(B, ii, + saved + + gsl_vector_get(w->deltar, ii) * term); + + saved = gsl_vector_get(w->deltal, j - ii) * term; + } + + gsl_vector_set(B, j + 1, saved); + } + + return GSL_SUCCESS; + } +} /* bspline_eval_all() */ + +/* +bspline_find_interval() + Find knot interval such that + + t_i <= x < t_{i + 1} + +where the t_i are knot values. + +Inputs: x - x value + flag - (output) error flag + w - bspline workspace + +Return: i (index in w->knots corresponding to left limit of interval) + +Notes: The error conditions are reported as follows: + +Condition Return value Flag +--------- ------------ ---- +x < t_0 0 -1 +t_i <= x < t_{i+1} i 0 +t_{n+k-1} <= x l+k-1 +1 +*/ + +static inline size_t +bspline_find_interval(const double x, int *flag, + gsl_bspline_workspace *w) +{ + size_t i; + + if (x < gsl_vector_get(w->knots, 0)) + { + *flag = -1; + return 0; + } + + /* find i such that t_i <= x < t_{i+1} */ + for (i = w->k - 1; i < w->k + w->l - 1; ++i) + { + const double ti = gsl_vector_get(w->knots, i); + const double tip1 = gsl_vector_get(w->knots, i + 1); + + if (tip1 < ti) + { + GSL_ERROR("knots vector is not increasing", GSL_EINVAL); + } + + if (ti <= x && x < tip1) + break; + } + + if (i == w->k + w->l - 1) + *flag = 1; + else + *flag = 0; + + return i; +} /* bspline_find_interval() */ diff --git a/gsl-1.9/bspline/gsl_bspline.h b/gsl-1.9/bspline/gsl_bspline.h new file mode 100644 index 0000000..26794ec --- /dev/null +++ b/gsl-1.9/bspline/gsl_bspline.h @@ -0,0 +1,75 @@ +/* bspline/gsl_bspline.h + * + * Copyright (C) 2006 Patrick Alken + * + * 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_BSPLINE_H__ +#define __GSL_BSPLINE_H__ + +#include <stdlib.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_vector.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 + +typedef struct +{ + size_t k; /* spline order */ + size_t km1; /* k - 1 (polynomial order) */ + size_t l; /* number of polynomial pieces on interval */ + size_t nbreak; /* number of breakpoints (l + 1) */ + size_t n; /* number of bspline basis functions (l + k - 1) */ + + gsl_vector *knots; /* knots vector */ + gsl_vector *deltal; /* left delta */ + gsl_vector *deltar; /* right delta */ + gsl_vector *B; /* temporary spline results */ +} gsl_bspline_workspace; + +gsl_bspline_workspace * +gsl_bspline_alloc(const size_t k, const size_t nbreak); + +void gsl_bspline_free(gsl_bspline_workspace *w); + +size_t gsl_bspline_ncoeffs (gsl_bspline_workspace * w); +size_t gsl_bspline_order (gsl_bspline_workspace * w); +size_t gsl_bspline_nbreak (gsl_bspline_workspace * w); +double gsl_bspline_breakpoint (size_t i, gsl_bspline_workspace * w); + +int +gsl_bspline_knots(const gsl_vector *breakpts, gsl_bspline_workspace *w); + +int gsl_bspline_knots_uniform(const double a, const double b, + gsl_bspline_workspace *w); + +int +gsl_bspline_eval(const double x, gsl_vector *B, + gsl_bspline_workspace *w); + +__END_DECLS + +#endif /* __GSL_BSPLINE_H__ */ diff --git a/gsl-1.9/bspline/test.c b/gsl-1.9/bspline/test.c new file mode 100644 index 0000000..e05dde0 --- /dev/null +++ b/gsl-1.9/bspline/test.c @@ -0,0 +1,112 @@ +/* bspline/test.c + * + * Copyright (C) 2006 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 <gsl/gsl_test.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_bspline.h> +#include <gsl/gsl_ieee_utils.h> + +void +test_bspline (gsl_bspline_workspace * bw) +{ + gsl_vector *B; + size_t i, j; + size_t n = 100; + size_t ncoeffs = gsl_bspline_ncoeffs (bw); + size_t order = gsl_bspline_order (bw); + size_t nbreak = gsl_bspline_nbreak (bw); + double a = gsl_bspline_breakpoint (0, bw); + double b = gsl_bspline_breakpoint (nbreak - 1, bw); + + B = gsl_vector_alloc (ncoeffs); + + for (i = 0; i < n; i++) + { + double xi = a + (b - a) * (i / (n - 1.0)); + double sum = 0; + gsl_bspline_eval (xi, B, bw); + + for (j = 0; j < ncoeffs; j++) + { + double Bj = gsl_vector_get (B, j); + int s = (Bj < 0 || Bj > 1); + gsl_test (s, + "basis-spline coefficient %u is in range [0,1] for x=%g", + j, xi); + sum += Bj; + } + + gsl_test_rel (sum, 1.0, order * GSL_DBL_EPSILON, + "basis-spline order %u is normalized for x=%g", order, + xi); + } + + gsl_vector_free (B); +} + + + +int +main (int argc, char **argv) +{ + int status = 0; + size_t order, breakpoints, i; + + gsl_ieee_env_setup (); + + argc = 0; /* prevent warnings about unused parameters */ + argv = 0; + + for (order = 1; order < 10; order++) + { + for (breakpoints = 2; breakpoints < 100; breakpoints++) + { + double a = -1.23 * order, b = 45.6 * order; + gsl_bspline_workspace *bw = gsl_bspline_alloc (order, breakpoints); + gsl_bspline_knots_uniform (a, b, bw); + test_bspline (bw); + gsl_bspline_free (bw); + } + } + + + for (order = 1; order < 10; order++) + { + for (breakpoints = 2; breakpoints < 100; breakpoints++) + { + double a = -1.23 * order, b = 45.6 * order; + gsl_bspline_workspace *bw = gsl_bspline_alloc (order, breakpoints); + gsl_vector *k = gsl_vector_alloc (breakpoints); + for (i = 0; i < breakpoints; i++) + { + double f, x; + f = sqrt (i / (breakpoints - 1.0)); + x = (1 - f) * a + f * b; + gsl_vector_set (k, i, x); + }; + gsl_bspline_knots (k, bw); + test_bspline (bw); + gsl_vector_free (k); + gsl_bspline_free (bw); + } + } + + exit (gsl_test_summary ()); +} |