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Diffstat (limited to 'gsl-1.9/multiroots/gnewton.c')
-rw-r--r-- | gsl-1.9/multiroots/gnewton.c | 226 |
1 files changed, 226 insertions, 0 deletions
diff --git a/gsl-1.9/multiroots/gnewton.c b/gsl-1.9/multiroots/gnewton.c new file mode 100644 index 0000000..13ade76 --- /dev/null +++ b/gsl-1.9/multiroots/gnewton.c @@ -0,0 +1,226 @@ +/* multiroots/gnewton.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 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 <stddef.h> +#include <stdlib.h> +#include <stdio.h> +#include <math.h> +#include <float.h> + +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_multiroots.h> +#include <gsl/gsl_linalg.h> + +#include "enorm.c" + +/* Simple globally convergent Newton method (rejects uphill steps) */ + +typedef struct + { + double phi; + gsl_vector * x_trial; + gsl_vector * d; + gsl_matrix * lu; + gsl_permutation * permutation; + } +gnewton_state_t; + +static int gnewton_alloc (void * vstate, size_t n); +static int gnewton_set (void * vstate, gsl_multiroot_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx); +static int gnewton_iterate (void * vstate, gsl_multiroot_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx); +static void gnewton_free (void * vstate); + +static int +gnewton_alloc (void * vstate, size_t n) +{ + gnewton_state_t * state = (gnewton_state_t *) vstate; + gsl_vector * d, * x_trial ; + gsl_permutation * p; + gsl_matrix * m; + + m = gsl_matrix_calloc (n,n); + + if (m == 0) + { + GSL_ERROR ("failed to allocate space for lu", GSL_ENOMEM); + } + + state->lu = m ; + + p = gsl_permutation_calloc (n); + + if (p == 0) + { + gsl_matrix_free(m); + + GSL_ERROR ("failed to allocate space for permutation", GSL_ENOMEM); + } + + state->permutation = p ; + + d = gsl_vector_calloc (n); + + if (d == 0) + { + gsl_permutation_free(p); + gsl_matrix_free(m); + + GSL_ERROR ("failed to allocate space for d", GSL_ENOMEM); + } + + state->d = d; + + x_trial = gsl_vector_calloc (n); + + if (x_trial == 0) + { + gsl_vector_free(d); + gsl_permutation_free(p); + gsl_matrix_free(m); + + GSL_ERROR ("failed to allocate space for x_trial", GSL_ENOMEM); + } + + state->x_trial = x_trial; + + return GSL_SUCCESS; +} + + +static int +gnewton_set (void * vstate, gsl_multiroot_function_fdf * FDF, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx) +{ + gnewton_state_t * state = (gnewton_state_t *) vstate; + size_t i, n = FDF->n ; + + GSL_MULTIROOT_FN_EVAL_F_DF (FDF, x, f, J); + + for (i = 0; i < n; i++) + { + gsl_vector_set (dx, i, 0.0); + } + + state->phi = enorm(f); + + return GSL_SUCCESS; +} + +static int +gnewton_iterate (void * vstate, gsl_multiroot_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx) +{ + gnewton_state_t * state = (gnewton_state_t *) vstate; + + int signum ; + double t, phi0, phi1; + + size_t i; + + size_t n = fdf->n ; + + gsl_matrix_memcpy (state->lu, J); + + gsl_linalg_LU_decomp (state->lu, state->permutation, &signum); + + gsl_linalg_LU_solve (state->lu, state->permutation, f, state->d); + + t = 1; + + phi0 = state->phi; + +new_step: + + for (i = 0; i < n; i++) + { + double di = gsl_vector_get (state->d, i); + double xi = gsl_vector_get (x, i); + gsl_vector_set (state->x_trial, i, xi - t*di); + } + + { + int status = GSL_MULTIROOT_FN_EVAL_F (fdf, state->x_trial, f); + + if (status != GSL_SUCCESS) + { + return GSL_EBADFUNC; + } + } + + phi1 = enorm (f); + + if (phi1 > phi0 && t > GSL_DBL_EPSILON) + { + /* full step goes uphill, take a reduced step instead */ + + double theta = phi1 / phi0; + double u = (sqrt(1.0 + 6.0 * theta) - 1.0) / (3.0 * theta); + + t *= u ; + + goto new_step; + } + + /* copy x_trial into x */ + + gsl_vector_memcpy (x, state->x_trial); + + for (i = 0; i < n; i++) + { + double di = gsl_vector_get (state->d, i); + gsl_vector_set (dx, i, -t*di); + } + + { + int status = GSL_MULTIROOT_FN_EVAL_DF (fdf, x, J); + + if (status != GSL_SUCCESS) + { + return GSL_EBADFUNC; + } + } + + state->phi = phi1; + + return GSL_SUCCESS; +} + + +static void +gnewton_free (void * vstate) +{ + gnewton_state_t * state = (gnewton_state_t *) vstate; + + gsl_vector_free(state->d); + gsl_vector_free(state->x_trial); + gsl_matrix_free(state->lu); + gsl_permutation_free(state->permutation); +} + + +static const gsl_multiroot_fdfsolver_type gnewton_type = +{"gnewton", /* name */ + sizeof (gnewton_state_t), + &gnewton_alloc, + &gnewton_set, + &gnewton_iterate, + &gnewton_free}; + +const gsl_multiroot_fdfsolver_type * gsl_multiroot_fdfsolver_gnewton = &gnewton_type; |