/* ode-initval/rk4.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.
*/
/* Runge-Kutta 4th order, Classical */
/* Author: G. Jungman
*/
/* Reference: Abramowitz & Stegun, section 25.5. equation 25.5.10
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.
*/
#include <config.h>
#include <stdlib.h>
#include <string.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_odeiv2.h>
#include "odeiv_util.h"
#include "step_utils.c"
typedef struct
{
double *k;
double *k1;
double *y0;
double *ytmp;
double *y_onestep;
}
rk4_state_t;
static void *
rk4_alloc (size_t dim)
{
rk4_state_t *state = (rk4_state_t *) malloc (sizeof (rk4_state_t));
if (state == 0)
{
GSL_ERROR_NULL ("failed to allocate space for rk4_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->k1 = (double *) malloc (dim * sizeof (double));
if (state->k1 == 0)
{
free (state->k);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k1", GSL_ENOMEM);
}
state->y0 = (double *) malloc (dim * sizeof (double));
if (state->y0 == 0)
{
free (state->k);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
}
state->ytmp = (double *) malloc (dim * sizeof (double));
if (state->ytmp == 0)
{
free (state->y0);
free (state->k);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
}
state->y_onestep = (double *) malloc (dim * sizeof (double));
if (state->y_onestep == 0)
{
free (state->ytmp);
free (state->y0);
free (state->k);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
}
return state;
}
static int
rk4_step (double *y, const rk4_state_t * state,
const double h, const double t, const size_t dim,
const gsl_odeiv2_system * sys)
{
/* Makes a Runge-Kutta 4th order advance with step size h. */
/* initial values of variables y. */
const double *y0 = state->y0;
/* work space */
double *ytmp = state->ytmp;
/* Runge-Kutta coefficients. Contains values of coefficient k1
in the beginning
*/
double *k = state->k;
size_t i;
/* k1 step */
for (i = 0; i < dim; i++)
{
y[i] += h / 6.0 * k[i];
ytmp[i] = y0[i] + 0.5 * h * k[i];
}
/* k2 step */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, k);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
{
y[i] += h / 3.0 * k[i];
ytmp[i] = y0[i] + 0.5 * h * k[i];
}
/* k3 step */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, k);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
{
y[i] += h / 3.0 * k[i];
ytmp[i] = y0[i] + h * k[i];
}
/* k4 step */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + h, ytmp, k);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
{
y[i] += h / 6.0 * k[i];
}
return GSL_SUCCESS;
}
static int
rk4_apply (void *vstate,
size_t dim,
double t,
double h,
double y[],
double yerr[],
const double dydt_in[],
double dydt_out[], const gsl_odeiv2_system * sys)
{
rk4_state_t *state = (rk4_state_t *) vstate;
size_t i;
double *const k = state->k;
double *const k1 = state->k1;
double *const y0 = state->y0;
double *const y_onestep = state->y_onestep;
DBL_MEMCPY (y0, y, dim);
if (dydt_in != NULL)
{
DBL_MEMCPY (k, dydt_in, dim);
}
else
{
int s = GSL_ODEIV_FN_EVAL (sys, t, y0, k);
if (s != GSL_SUCCESS)
{
return s;
}
}
/* Error estimation is done by step doubling procedure */
/* Save first point derivatives */
DBL_MEMCPY (k1, k, dim);
/* First traverse h with one step (save to y_onestep) */
DBL_MEMCPY (y_onestep, y, dim);
{
int s = rk4_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) */
DBL_MEMCPY (k, k1, dim);
{
int s = rk4_step (y, state, h / 2.0, t, dim, sys);
if (s != GSL_SUCCESS)
{
/* Restore original values */
DBL_MEMCPY (y, y0, dim);
return s;
}
}
/* Update before second step */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + h / 2.0, y, k);
if (s != GSL_SUCCESS)
{
/* Restore original values */
DBL_MEMCPY (y, y0, dim);
return s;
}
}
/* Save original y0 to k1 for possible failures */
DBL_MEMCPY (k1, y0, dim);
/* Update y0 for second step */
DBL_MEMCPY (y0, y, dim);
{
int s = rk4_step (y, state, h / 2.0, t + h / 2.0, dim, sys);
if (s != GSL_SUCCESS)
{
/* Restore original values */
DBL_MEMCPY (y, k1, dim);
return s;
}
}
/* Derivatives at output */
if (dydt_out != NULL)
{
int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);
if (s != GSL_SUCCESS)
{
/* Restore original values */
DBL_MEMCPY (y, k1, dim);
return s;
}
}
/* Error estimation */
for (i = 0; i < dim; i++)
{
yerr[i] = ODEIV_ERR_SAFETY * 0.5 * (y[i] - y_onestep[i]) / 15.0;
}
return GSL_SUCCESS;
}
static int
rk4_reset (void *vstate, size_t dim)
{
rk4_state_t *state = (rk4_state_t *) vstate;
DBL_ZERO_MEMSET (state->k, dim);
DBL_ZERO_MEMSET (state->k1, dim);
DBL_ZERO_MEMSET (state->y0, dim);
DBL_ZERO_MEMSET (state->ytmp, dim);
DBL_ZERO_MEMSET (state->y_onestep, dim);
return GSL_SUCCESS;
}
static unsigned int
rk4_order (void *vstate)
{
rk4_state_t *state = (rk4_state_t *) vstate;
state = 0; /* prevent warnings about unused parameters */
return 4;
}
static void
rk4_free (void *vstate)
{
rk4_state_t *state = (rk4_state_t *) vstate;
free (state->k);
free (state->k1);
free (state->y0);
free (state->ytmp);
free (state->y_onestep);
free (state);
}
static const gsl_odeiv2_step_type rk4_type = { "rk4", /* name */
1, /* can use dydt_in */
1, /* gives exact dydt_out */
&rk4_alloc,
&rk4_apply,
&stepper_set_driver_null,
&rk4_reset,
&rk4_order,
&rk4_free
};
const gsl_odeiv2_step_type *gsl_odeiv2_step_rk4 = &rk4_type;