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/* ode-initval/gear2.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Gear 2 */
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/* Author: G. Jungman
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*/
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#include <config.h>
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#include <stdlib.h>
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#include <string.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_errno.h>
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#include "odeiv_util.h"
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#include <gsl/gsl_odeiv.h>
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/* gear2 state object */
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typedef struct
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{
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int primed; /* flag indicating that yim1 is ready */
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double t_primed; /* system was primed for this value of t */
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double last_h; /* last step size */
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gsl_odeiv_step *primer; /* stepper to use for priming */
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double *yim1; /* y_{i-1} */
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double *k; /* work space */
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double *y0; /* work space */
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double *y0_orig;
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double *y_onestep;
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int stutter;
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}
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gear2_state_t;
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static void *
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gear2_alloc (size_t dim)
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{
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gear2_state_t *state = (gear2_state_t *) malloc (sizeof (gear2_state_t));
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if (state == 0)
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{
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GSL_ERROR_NULL ("failed to allocate space for gear2_state", GSL_ENOMEM);
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}
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state->yim1 = (double *) malloc (dim * sizeof (double));
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if (state->yim1 == 0)
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{
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for yim1", GSL_ENOMEM);
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}
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state->k = (double *) malloc (dim * sizeof (double));
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if (state->k == 0)
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{
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free (state->yim1);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for k", GSL_ENOMEM);
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}
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state->y0 = (double *) malloc (dim * sizeof (double));
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if (state->y0 == 0)
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{
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free (state->k);
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free (state->yim1);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
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}
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state->y0_orig = (double *) malloc (dim * sizeof (double));
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if (state->y0_orig == 0)
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{
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free (state->y0);
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free (state->k);
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free (state->yim1);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
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}
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state->y_onestep = (double *) malloc (dim * sizeof (double));
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if (state->y_onestep == 0)
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{
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free (state->y0_orig);
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free (state->y0);
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free (state->k);
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free (state->yim1);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
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}
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state->primed = 0;
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state->primer = gsl_odeiv_step_alloc (gsl_odeiv_step_rk4imp, dim);
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if (state->primer == 0)
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{
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free (state->y_onestep);
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free (state->y0_orig);
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free (state->y0);
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free (state->k);
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free (state->yim1);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for primer", GSL_ENOMEM);
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}
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state->last_h = 0.0;
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return state;
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}
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static int
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gear2_step (double *y, gear2_state_t * state,
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const double h, const double t,
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const size_t dim, const gsl_odeiv_system * sys)
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{
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/* Makes a Gear2 advance with step size h.
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y0 is the initial values of variables y.
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The implicit matrix equations to solve are:
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k = y0 + h * f(t + h, k)
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y = y0 + h * f(t + h, k)
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*/
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const int iter_steps = 3;
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int nu;
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size_t i;
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double *y0 = state->y0;
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double *yim1 = state->yim1;
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double *k = state->k;
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/* Iterative solution of k = y0 + h * f(t + h, k)
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Note: This method does not check for convergence of the
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iterative solution!
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*/
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for (nu = 0; nu < iter_steps; nu++)
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{
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int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, k);
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if (s != GSL_SUCCESS)
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{
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return s;
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}
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for (i = 0; i < dim; i++)
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{
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y[i] = ((4.0 * y0[i] - yim1[i]) + 2.0 * h * k[i]) / 3.0;
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}
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}
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return GSL_SUCCESS;
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}
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static int
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gear2_apply (void *vstate,
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size_t dim,
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double t,
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double h,
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double y[],
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double yerr[],
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const double dydt_in[],
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double dydt_out[], const gsl_odeiv_system * sys)
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{
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gear2_state_t *state = (gear2_state_t *) vstate;
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state->stutter = 0;
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if (state->primed == 0 || t == state->t_primed || h != state->last_h)
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{
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/* Execute a single-step method to prime the process. Note that
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* we do this if the step size changes, so frequent step size
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* changes will cause the method to stutter.
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*
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* Note that we reuse this method if the time has not changed,
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* which can occur when the adaptive driver is attempting to find
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* an appropriate step-size on its first iteration */
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int status;
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DBL_MEMCPY (state->yim1, y, dim);
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status =
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gsl_odeiv_step_apply (state->primer, t, h, y, yerr, dydt_in, dydt_out,
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sys);
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/* Make note of step size and indicate readiness for a Gear step. */
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state->primed = 1;
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state->t_primed = t;
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state->last_h = h;
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state->stutter = 1;
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return status;
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}
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else
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{
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/* We have a previous y value in the buffer, and the step
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* sizes match, so we go ahead with the Gear step.
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*/
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double *const k = state->k;
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double *const y0 = state->y0;
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double *const y0_orig = state->y0_orig;
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double *const yim1 = state->yim1;
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double *y_onestep = state->y_onestep;
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int s;
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size_t i;
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/* initialization */
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DBL_MEMCPY (y0, y, dim);
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/* Save initial values for possible failures */
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DBL_MEMCPY (y0_orig, y, dim);
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/* iterative solution */
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if (dydt_out != NULL)
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{
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DBL_MEMCPY (k, dydt_out, dim);
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}
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|
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/* First traverse h with one step (save to y_onestep) */
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DBL_MEMCPY (y_onestep, y, dim);
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s = gear2_step (y_onestep, state, h, t, dim, sys);
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if (s != GSL_SUCCESS)
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{
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return s;
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}
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|
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/* Then with two steps with half step length (save to y) */
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s = gear2_step (y, state, h / 2.0, t, dim, sys);
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if (s != GSL_SUCCESS)
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{
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/* Restore original y vector */
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DBL_MEMCPY (y, y0_orig, dim);
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return s;
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}
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|
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DBL_MEMCPY (y0, y, dim);
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s = gear2_step (y, state, h / 2.0, t + h / 2.0, dim, sys);
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|
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if (s != GSL_SUCCESS)
|
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{
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/* Restore original y vector */
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DBL_MEMCPY (y, y0_orig, dim);
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return s;
|
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}
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|
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/* Cleanup update */
|
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|
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if (dydt_out != NULL)
|
|
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{
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s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);
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|
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if (s != GSL_SUCCESS)
|
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{
|
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/* Restore original y vector */
|
|
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DBL_MEMCPY (y, y0_orig, dim);
|
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return s;
|
|
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}
|
|
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}
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|
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/* Estimate error and update the state buffer. */
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for (i = 0; i < dim; i++)
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{
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yerr[i] = 4.0 * (y[i] - y_onestep[i]);
|
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yim1[i] = y0[i];
|
|
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}
|
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|
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/* Make note of step size. */
|
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state->last_h = h;
|
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|
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return 0;
|
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}
|
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}
|
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|
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static int
|
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gear2_reset (void *vstate, size_t dim)
|
|
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67cb25 |
{
|
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gear2_state_t *state = (gear2_state_t *) vstate;
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|
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67cb25 |
|
|
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DBL_ZERO_MEMSET (state->yim1, dim);
|
|
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67cb25 |
DBL_ZERO_MEMSET (state->k, dim);
|
|
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DBL_ZERO_MEMSET (state->y0, dim);
|
|
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67cb25 |
|
|
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state->primed = 0;
|
|
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67cb25 |
state->last_h = 0.0;
|
|
Packit |
67cb25 |
return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static unsigned int
|
|
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67cb25 |
gear2_order (void *vstate)
|
|
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67cb25 |
{
|
|
Packit |
67cb25 |
gear2_state_t *state = (gear2_state_t *) vstate;
|
|
Packit |
67cb25 |
state = 0; /* prevent warnings about unused parameters */
|
|
Packit |
67cb25 |
return 3;
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|
Packit |
67cb25 |
}
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|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
gear2_free (void *vstate)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
gear2_state_t *state = (gear2_state_t *) vstate;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
free (state->yim1);
|
|
Packit |
67cb25 |
free (state->k);
|
|
Packit |
67cb25 |
free (state->y0);
|
|
Packit |
67cb25 |
free (state->y0_orig);
|
|
Packit |
67cb25 |
free (state->y_onestep);
|
|
Packit |
67cb25 |
gsl_odeiv_step_free (state->primer);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
free (state);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static const gsl_odeiv_step_type gear2_type = { "gear2", /* name */
|
|
Packit |
67cb25 |
1, /* can use dydt_in */
|
|
Packit |
67cb25 |
0, /* gives exact dydt_out */
|
|
Packit |
67cb25 |
&gear2_alloc,
|
|
Packit |
67cb25 |
&gear2_apply,
|
|
Packit |
67cb25 |
&gear2_reset,
|
|
Packit |
67cb25 |
&gear2_order,
|
|
Packit |
67cb25 |
&gear2_free
|
|
Packit |
67cb25 |
};
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
const gsl_odeiv_step_type *gsl_odeiv_step_gear2 = &gear2_type;
|