123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273 |
- /* ode-initval/gear1.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
- *
- * 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.
- */
- /* Gear 1. This is the implicit Euler a.k.a backward Euler method. */
- /* Author: G. Jungman
- */
- /* Error estimation by step doubling, see eg. Ascher, U.M., Petzold,
- L.R., Computer methods for ordinary differential and
- differential-algebraic equations, SIAM, Philadelphia, 1998.
- The method is also described in eg. this reference.
- */
- #include "gsl__config.h"
- #include <stdlib.h>
- #include <string.h>
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_odeiv.h"
- #include "gsl_ode-initval__odeiv_util.h"
- typedef struct
- {
- double *k;
- double *y0;
- double *y0_orig;
- double *y_onestep;
- }
- gear1_state_t;
- static void *
- gear1_alloc (size_t dim)
- {
- gear1_state_t *state = (gear1_state_t *) malloc (sizeof (gear1_state_t));
- if (state == 0)
- {
- GSL_ERROR_NULL ("failed to allocate space for gear1_state", GSL_ENOMEM);
- }
- state->k = (double *) malloc (dim * sizeof (double));
- if (state->k == 0)
- {
- free (state);
- GSL_ERROR_NULL ("failed to allocate space for k", GSL_ENOMEM);
- }
- state->y0 = (double *) malloc (dim * sizeof (double));
- if (state->y0 == 0)
- {
- free (state->k);
- free (state);
- GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
- }
- state->y0_orig = (double *) malloc (dim * sizeof (double));
- if (state->y0_orig == 0)
- {
- free (state->y0);
- free (state->k);
- free (state);
- GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
- }
- state->y_onestep = (double *) malloc (dim * sizeof (double));
- if (state->y_onestep == 0)
- {
- free (state->y0_orig);
- free (state->y0);
- free (state->k);
- free (state);
- GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM);
- }
- return state;
- }
- static int
- gear1_step (double *y, gear1_state_t *state,
- const double h, const double t,
- const size_t dim, const gsl_odeiv_system *sys)
- {
- /* Makes an implicit Euler advance with step size h.
- y0 is the initial values of variables y.
- The implicit matrix equations to solve are:
- k = y0 + h * f(t + h, k)
- y = y0 + h * f(t + h, k)
- */
- const int iter_steps = 3;
- int nu;
- size_t i;
- double *y0 = state->y0;
- double *k = state->k;
- /* Iterative solution of k = y0 + h * f(t + h, k)
- Note: This method does not check for convergence of the
- iterative solution!
- */
- for (nu = 0; nu < iter_steps; nu++)
- {
- int s = GSL_ODEIV_FN_EVAL(sys, t + h, y, k);
- if (s != GSL_SUCCESS)
- {
- return s;
- }
- for (i=0; i<dim; i++)
- {
- y[i] = y0[i] + h * k[i];
- }
- }
-
- return GSL_SUCCESS;
- }
- static int
- gear1_apply(void * vstate,
- size_t dim,
- double t,
- double h,
- double y[],
- double yerr[],
- const double dydt_in[],
- double dydt_out[],
- const gsl_odeiv_system * sys)
- {
- gear1_state_t *state = (gear1_state_t *) vstate;
- size_t i;
- double *y0 = state->y0;
- double *y0_orig = state->y0_orig;
- double *y_onestep = state->y_onestep;
- /* initialization */
- DBL_MEMCPY(y0, y, dim);
- /* Save initial values for possible failures */
- DBL_MEMCPY (y0_orig, y, dim);
- /* First traverse h with one step (save to y_onestep) */
- DBL_MEMCPY (y_onestep, y, dim);
- {
- int s = gear1_step (y_onestep, state, h, t, dim, sys);
- if (s != GSL_SUCCESS)
- {
- return s;
- }
- }
- /* Then with two steps with half step length (save to y) */
- {
- int s = gear1_step (y, state, h / 2.0, t, dim, sys);
- if (s != GSL_SUCCESS)
- {
- /* Restore original y vector */
- DBL_MEMCPY (y, y0_orig, dim);
- return s;
- }
- }
- DBL_MEMCPY (y0, y, dim);
- {
- int s = gear1_step (y, state, h / 2.0, t + h / 2.0, dim, sys);
- if (s != GSL_SUCCESS)
- {
- /* Restore original y vector */
- DBL_MEMCPY (y, y0_orig, dim);
- return s;
- }
- }
-
- /* Cleanup update */
- if (dydt_out != NULL)
- {
- int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);
-
- if (s != GSL_SUCCESS)
- {
- /* Restore original y vector */
- DBL_MEMCPY (y, y0_orig, dim);
- return s;
- }
- }
-
- /* Error estimation */
- for (i = 0; i < dim; i++)
- {
- yerr[i] = 4.0 * (y[i] - y_onestep[i]);
- }
- return GSL_SUCCESS;
- }
- static int
- gear1_reset (void *vstate, size_t dim)
- {
- gear1_state_t *state = (gear1_state_t *) vstate;
- DBL_ZERO_MEMSET (state->y_onestep, dim);
- DBL_ZERO_MEMSET (state->y0_orig, dim);
- DBL_ZERO_MEMSET (state->y0, dim);
- DBL_ZERO_MEMSET (state->k, dim);
- return GSL_SUCCESS;
- }
- static unsigned int
- gear1_order (void *vstate)
- {
- gear1_state_t *state = (gear1_state_t *) vstate;
- state = 0; /* prevent warnings about unused parameters */
- return 1;
- }
- static void
- gear1_free (void *vstate)
- {
- gear1_state_t *state = (gear1_state_t *) vstate;
- free (state->y_onestep);
- free (state->y0_orig);
- free (state->y0);
- free (state->k);
- free (state);
- }
- static const gsl_odeiv_step_type gear1_type = { "gear1", /* name */
- 0, /* can use dydt_in? */
- 1, /* gives exact dydt_out? */
- &gear1_alloc,
- &gear1_apply,
- &gear1_reset,
- &gear1_order,
- &gear1_free
- };
- const gsl_odeiv_step_type *gsl_odeiv_step_gear1 = &gear1_type;
|