/* ode-initval/gear2.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 2 */
/* Author: G. Jungman
*/
#include <config.h>
#include <stdlib.h>
#include <string.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include "odeiv_util.h"
#include <gsl/gsl_odeiv.h>
/* gear2 state object */
typedef struct
{
int primed; /* flag indicating that yim1 is ready */
double t_primed; /* system was primed for this value of t */
double last_h; /* last step size */
gsl_odeiv_step *primer; /* stepper to use for priming */
double *yim1; /* y_{i-1} */
double *k; /* work space */
double *y0; /* work space */
double *y0_orig;
double *y_onestep;
int stutter;
}
gear2_state_t;
static void *
gear2_alloc (size_t dim)
{
gear2_state_t *state = (gear2_state_t *) malloc (sizeof (gear2_state_t));
if (state == 0)
{
GSL_ERROR_NULL ("failed to allocate space for gear2_state", GSL_ENOMEM);
}
state->yim1 = (double *) malloc (dim * sizeof (double));
if (state->yim1 == 0)
{
free (state);
GSL_ERROR_NULL ("failed to allocate space for yim1", GSL_ENOMEM);
}
state->k = (double *) malloc (dim * sizeof (double));
if (state->k == 0)
{
free (state->yim1);
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->yim1);
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->yim1);
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->yim1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
}
state->primed = 0;
state->primer = gsl_odeiv_step_alloc (gsl_odeiv_step_rk4imp, dim);
if (state->primer == 0)
{
free (state->y_onestep);
free (state->y0_orig);
free (state->y0);
free (state->k);
free (state->yim1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for primer", GSL_ENOMEM);
}
state->last_h = 0.0;
return state;
}
static int
gear2_step (double *y, gear2_state_t * state,
const double h, const double t,
const size_t dim, const gsl_odeiv_system * sys)
{
/* Makes a Gear2 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 *yim1 = state->yim1;
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] = ((4.0 * y0[i] - yim1[i]) + 2.0 * h * k[i]) / 3.0;
}
}
return GSL_SUCCESS;
}
static int
gear2_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)
{
gear2_state_t *state = (gear2_state_t *) vstate;
state->stutter = 0;
if (state->primed == 0 || t == state->t_primed || h != state->last_h)
{
/* Execute a single-step method to prime the process. Note that
* we do this if the step size changes, so frequent step size
* changes will cause the method to stutter.
*
* Note that we reuse this method if the time has not changed,
* which can occur when the adaptive driver is attempting to find
* an appropriate step-size on its first iteration */
int status;
DBL_MEMCPY (state->yim1, y, dim);
status =
gsl_odeiv_step_apply (state->primer, t, h, y, yerr, dydt_in, dydt_out,
sys);
/* Make note of step size and indicate readiness for a Gear step. */
state->primed = 1;
state->t_primed = t;
state->last_h = h;
state->stutter = 1;
return status;
}
else
{
/* We have a previous y value in the buffer, and the step
* sizes match, so we go ahead with the Gear step.
*/
double *const k = state->k;
double *const y0 = state->y0;
double *const y0_orig = state->y0_orig;
double *const yim1 = state->yim1;
double *y_onestep = state->y_onestep;
int s;
size_t i;
/* initialization */
DBL_MEMCPY (y0, y, dim);
/* Save initial values for possible failures */
DBL_MEMCPY (y0_orig, y, dim);
/* iterative solution */
if (dydt_out != NULL)
{
DBL_MEMCPY (k, dydt_out, dim);
}
/* First traverse h with one step (save to y_onestep) */
DBL_MEMCPY (y_onestep, y, dim);
s = gear2_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) */
s = gear2_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);
s = gear2_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)
{
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;
}
}
/* Estimate error and update the state buffer. */
for (i = 0; i < dim; i++)
{
yerr[i] = 4.0 * (y[i] - y_onestep[i]);
yim1[i] = y0[i];
}
/* Make note of step size. */
state->last_h = h;
return 0;
}
}
static int
gear2_reset (void *vstate, size_t dim)
{
gear2_state_t *state = (gear2_state_t *) vstate;
DBL_ZERO_MEMSET (state->yim1, dim);
DBL_ZERO_MEMSET (state->k, dim);
DBL_ZERO_MEMSET (state->y0, dim);
state->primed = 0;
state->last_h = 0.0;
return GSL_SUCCESS;
}
static unsigned int
gear2_order (void *vstate)
{
gear2_state_t *state = (gear2_state_t *) vstate;
state = 0; /* prevent warnings about unused parameters */
return 3;
}
static void
gear2_free (void *vstate)
{
gear2_state_t *state = (gear2_state_t *) vstate;
free (state->yim1);
free (state->k);
free (state->y0);
free (state->y0_orig);
free (state->y_onestep);
gsl_odeiv_step_free (state->primer);
free (state);
}
static const gsl_odeiv_step_type gear2_type = { "gear2", /* name */
1, /* can use dydt_in */
0, /* gives exact dydt_out */
&gear2_alloc,
&gear2_apply,
&gear2_reset,
&gear2_order,
&gear2_free
};
const gsl_odeiv_step_type *gsl_odeiv_step_gear2 = &gear2_type;