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- /* multiroots/dnewton.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"
- /* Newton method using a finite difference approximation to the jacobian.
- The derivatives are estimated using a step size of
- h_i = sqrt(DBL_EPSILON) * x_i
- */
- typedef struct
- {
- gsl_matrix * J;
- gsl_matrix * lu;
- gsl_permutation * permutation;
- }
- dnewton_state_t;
- static int dnewton_alloc (void * vstate, size_t n);
- static int dnewton_set (void * vstate, gsl_multiroot_function * function, gsl_vector * x, gsl_vector * f, gsl_vector * dx);
- static int dnewton_iterate (void * vstate, gsl_multiroot_function * function, gsl_vector * x, gsl_vector * f, gsl_vector * dx);
- static void dnewton_free (void * vstate);
- static int
- dnewton_alloc (void * vstate, size_t n)
- {
- dnewton_state_t * state = (dnewton_state_t *) vstate;
- gsl_permutation * p;
- gsl_matrix * m, * J;
- 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 ;
- J = gsl_matrix_calloc (n,n);
- if (J == 0)
- {
- gsl_permutation_free(p);
- gsl_matrix_free(m);
- GSL_ERROR ("failed to allocate space for d", GSL_ENOMEM);
- }
- state->J = J;
- return GSL_SUCCESS;
- }
- static int
- dnewton_set (void * vstate, gsl_multiroot_function * function, gsl_vector * x, gsl_vector * f, gsl_vector * dx)
- {
- dnewton_state_t * state = (dnewton_state_t *) vstate;
- size_t i, n = function->n ;
- int status;
- status = GSL_MULTIROOT_FN_EVAL (function, x, f);
- if (status)
- return status;
- status = gsl_multiroot_fdjacobian (function, x, f, GSL_SQRT_DBL_EPSILON,
- state->J);
- if (status)
- return status;
- for (i = 0; i < n; i++)
- {
- gsl_vector_set (dx, i, 0.0);
- }
- return GSL_SUCCESS;
- }
- static int
- dnewton_iterate (void * vstate, gsl_multiroot_function * function, gsl_vector * x, gsl_vector * f, gsl_vector * dx)
- {
- dnewton_state_t * state = (dnewton_state_t *) vstate;
-
- int signum ;
- size_t i;
- size_t n = function->n ;
- gsl_matrix_memcpy (state->lu, state->J);
- {
- int status = gsl_linalg_LU_decomp (state->lu, state->permutation, &signum);
- if (status)
- return status;
- }
-
- {
- int status = gsl_linalg_LU_solve (state->lu, state->permutation, f, dx);
- if (status)
- return status;
- }
- for (i = 0; i < n; i++)
- {
- double e = gsl_vector_get (dx, i);
- double y = gsl_vector_get (x, i);
- gsl_vector_set (dx, i, -e);
- gsl_vector_set (x, i, y - e);
- }
-
- {
- int status = GSL_MULTIROOT_FN_EVAL (function, x, f);
- if (status != GSL_SUCCESS)
- {
- return GSL_EBADFUNC;
- }
- }
-
- gsl_multiroot_fdjacobian (function, x, f, GSL_SQRT_DBL_EPSILON, state->J);
- return GSL_SUCCESS;
- }
- static void
- dnewton_free (void * vstate)
- {
- dnewton_state_t * state = (dnewton_state_t *) vstate;
- gsl_matrix_free(state->J);
- gsl_matrix_free(state->lu);
- gsl_permutation_free(state->permutation);
- }
- static const gsl_multiroot_fsolver_type dnewton_type =
- {"dnewton", /* name */
- sizeof (dnewton_state_t),
- &dnewton_alloc,
- &dnewton_set,
- &dnewton_iterate,
- &dnewton_free};
- const gsl_multiroot_fsolver_type * gsl_multiroot_fsolver_dnewton = &dnewton_type;
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