| /* multiroots/dnewton.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> |
| |
| /* 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; |