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- /* multiroots/gnewton.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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 "gsl__config.h"
- #include <stddef.h>
- #include <stdlib.h>
- #include <stdio.h>
- #include <math.h>
- #include <float.h>
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_multiroots.h"
- #include "gsl_linalg.h"
- #include "gsl_multiroots__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;
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