/* ode-initval/rkck.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 4(5), Cash-Karp */
/* Reference: Cash, J.R., Karp, A.H., ACM Transactions of Mathematical
Software, vol. 16 (1990) 201-222. */
/* Author: G. Jungman
*/
#include <config.h>
#include <stdlib.h>
#include <string.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_odeiv.h>
#include "odeiv_util.h"
/* Cash-Karp constants */
static const double ah[] = { 1.0 / 5.0, 0.3, 3.0 / 5.0, 1.0, 7.0 / 8.0 };
static const double b21 = 1.0 / 5.0;
static const double b3[] = { 3.0 / 40.0, 9.0 / 40.0 };
static const double b4[] = { 0.3, -0.9, 1.2 };
static const double b5[] = { -11.0 / 54.0, 2.5, -70.0 / 27.0, 35.0 / 27.0 };
static const double b6[] =
{ 1631.0 / 55296.0, 175.0 / 512.0, 575.0 / 13824.0, 44275.0 / 110592.0,
253.0 / 4096.0 };
static const double c1 = 37.0 / 378.0;
static const double c3 = 250.0 / 621.0;
static const double c4 = 125.0 / 594.0;
static const double c6 = 512.0 / 1771.0;
/* These are the differences of fifth and fourth order coefficients
for error estimation */
static const double ec[] = { 0.0,
37.0 / 378.0 - 2825.0 / 27648.0,
0.0,
250.0 / 621.0 - 18575.0 / 48384.0,
125.0 / 594.0 - 13525.0 / 55296.0,
-277.0 / 14336.0,
512.0 / 1771.0 - 0.25
};
typedef struct
{
double *k1;
double *k2;
double *k3;
double *k4;
double *k5;
double *k6;
double *y0;
double *ytmp;
}
rkck_state_t;
static void *
rkck_alloc (size_t dim)
{
rkck_state_t *state = (rkck_state_t *) malloc (sizeof (rkck_state_t));
if (state == 0)
{
GSL_ERROR_NULL ("failed to allocate space for rkck_state", GSL_ENOMEM);
}
state->k1 = (double *) malloc (dim * sizeof (double));
if (state->k1 == 0)
{
free (state);
GSL_ERROR_NULL ("failed to allocate space for k1", GSL_ENOMEM);
}
state->k2 = (double *) malloc (dim * sizeof (double));
if (state->k2 == 0)
{
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k2", GSL_ENOMEM);
}
state->k3 = (double *) malloc (dim * sizeof (double));
if (state->k3 == 0)
{
free (state->k2);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k3", GSL_ENOMEM);
}
state->k4 = (double *) malloc (dim * sizeof (double));
if (state->k4 == 0)
{
free (state->k3);
free (state->k2);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k4", GSL_ENOMEM);
}
state->k5 = (double *) malloc (dim * sizeof (double));
if (state->k5 == 0)
{
free (state->k4);
free (state->k3);
free (state->k2);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k5", GSL_ENOMEM);
}
state->k6 = (double *) malloc (dim * sizeof (double));
if (state->k6 == 0)
{
free (state->k5);
free (state->k4);
free (state->k3);
free (state->k2);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for k6", GSL_ENOMEM);
}
state->y0 = (double *) malloc (dim * sizeof (double));
if (state->y0 == 0)
{
free (state->k6);
free (state->k5);
free (state->k4);
free (state->k3);
free (state->k2);
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->k6);
free (state->k5);
free (state->k4);
free (state->k3);
free (state->k2);
free (state->k1);
free (state);
GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
}
return state;
}
static int
rkck_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)
{
rkck_state_t *state = (rkck_state_t *) vstate;
size_t i;
double *const k1 = state->k1;
double *const k2 = state->k2;
double *const k3 = state->k3;
double *const k4 = state->k4;
double *const k5 = state->k5;
double *const k6 = state->k6;
double *const ytmp = state->ytmp;
double *const y0 = state->y0;
DBL_MEMCPY (y0, y, dim);
/* k1 step */
if (dydt_in != NULL)
{
DBL_MEMCPY (k1, dydt_in, dim);
}
else
{
int s = GSL_ODEIV_FN_EVAL (sys, t, y, k1);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
ytmp[i] = y[i] + b21 * h * k1[i];
/* k2 step */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + ah[0] * h, ytmp, k2);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
ytmp[i] = y[i] + h * (b3[0] * k1[i] + b3[1] * k2[i]);
/* k3 step */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + ah[1] * h, ytmp, k3);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
ytmp[i] = y[i] + h * (b4[0] * k1[i] + b4[1] * k2[i] + b4[2] * k3[i]);
/* k4 step */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + ah[2] * h, ytmp, k4);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
ytmp[i] =
y[i] + h * (b5[0] * k1[i] + b5[1] * k2[i] + b5[2] * k3[i] +
b5[3] * k4[i]);
/* k5 step */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + ah[3] * h, ytmp, k5);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
ytmp[i] =
y[i] + h * (b6[0] * k1[i] + b6[1] * k2[i] + b6[2] * k3[i] +
b6[3] * k4[i] + b6[4] * k5[i]);
/* k6 step and final sum */
{
int s = GSL_ODEIV_FN_EVAL (sys, t + ah[4] * h, ytmp, k6);
if (s != GSL_SUCCESS)
{
return s;
}
}
for (i = 0; i < dim; i++)
{
const double d_i = c1 * k1[i] + c3 * k3[i] + c4 * k4[i] + c6 * k6[i];
y[i] += h * d_i;
}
/* Evaluate dydt_out[]. */
if (dydt_out != NULL)
{
int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);
if (s != GSL_SUCCESS)
{
/* Restore initial values */
DBL_MEMCPY (y, y0, dim);
return s;
}
}
/* difference between 4th and 5th order */
for (i = 0; i < dim; i++)
{
yerr[i] = h * (ec[1] * k1[i] + ec[3] * k3[i] + ec[4] * k4[i]
+ ec[5] * k5[i] + ec[6] * k6[i]);
}
return GSL_SUCCESS;
}
static int
rkck_reset (void *vstate, size_t dim)
{
rkck_state_t *state = (rkck_state_t *) vstate;
DBL_ZERO_MEMSET (state->k1, dim);
DBL_ZERO_MEMSET (state->k2, dim);
DBL_ZERO_MEMSET (state->k3, dim);
DBL_ZERO_MEMSET (state->k4, dim);
DBL_ZERO_MEMSET (state->k5, dim);
DBL_ZERO_MEMSET (state->k6, dim);
DBL_ZERO_MEMSET (state->ytmp, dim);
DBL_ZERO_MEMSET (state->y0, dim);
return GSL_SUCCESS;
}
static unsigned int
rkck_order (void *vstate)
{
rkck_state_t *state = (rkck_state_t *) vstate;
state = 0; /* prevent warnings about unused parameters */
return 5; /* FIXME: should this be 4? */
}
static void
rkck_free (void *vstate)
{
rkck_state_t *state = (rkck_state_t *) vstate;
free (state->ytmp);
free (state->y0);
free (state->k6);
free (state->k5);
free (state->k4);
free (state->k3);
free (state->k2);
free (state->k1);
free (state);
}
static const gsl_odeiv_step_type rkck_type = { "rkck", /* name */
1, /* can use dydt_in */
1, /* gives exact dydt_out */
&rkck_alloc,
&rkck_apply,
&rkck_reset,
&rkck_order,
&rkck_free
};
const gsl_odeiv_step_type *gsl_odeiv_step_rkck = &rkck_type;