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/* ode-initval/rk4.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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/* Runge-Kutta 4th order, Classical */
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/* Author: G. Jungman
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*/
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/* Reference: Abramowitz & Stegun, section 25.5. equation 25.5.10
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Error estimation by step doubling, see eg. Ascher, U.M., Petzold,
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L.R., Computer methods for ordinary differential and
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differential-algebraic equations, SIAM, Philadelphia, 1998.
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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_errno.h>
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#include <gsl/gsl_odeiv.h>
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#include "odeiv_util.h"
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typedef struct
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{
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double *k;
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double *k1;
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double *y0;
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double *ytmp;
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double *y_onestep;
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}
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rk4_state_t;
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static void *
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rk4_alloc (size_t dim)
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{
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rk4_state_t *state = (rk4_state_t *) malloc (sizeof (rk4_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 rk4_state", 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);
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GSL_ERROR_NULL ("failed to allocate space for k", GSL_ENOMEM);
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}
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state->k1 = (double *) malloc (dim * sizeof (double));
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if (state->k1 == 0)
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{
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free (state->k);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for k1", 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->k1);
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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->ytmp = (double *) malloc (dim * sizeof (double));
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if (state->ytmp == 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->k1);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for ytmp", 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->ytmp);
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free (state->y0);
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free (state->k);
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free (state->k1);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
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}
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return state;
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}
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static int
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rk4_step (double *y, const rk4_state_t *state,
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const double h, const double t, const size_t dim,
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const gsl_odeiv_system *sys)
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{
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/* Makes a Runge-Kutta 4th order advance with step size h. */
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/* initial values of variables y. */
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const double *y0 = state->y0;
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/* work space */
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double *ytmp = state->ytmp;
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/* Runge-Kutta coefficients. Contains values of coefficient k1
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in the beginning
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*/
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double *k = state->k;
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size_t i;
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/* k1 step */
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for (i = 0; i < dim; i++)
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{
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y[i] += h / 6.0 * k[i];
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ytmp[i] = y0[i] + 0.5 * h * k[i];
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}
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/* k2 step */
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{
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int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, 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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}
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for (i = 0; i < dim; i++)
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{
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y[i] += h / 3.0 * k[i];
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ytmp[i] = y0[i] + 0.5 * h * k[i];
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}
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/* k3 step */
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{
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int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, 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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}
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for (i = 0; i < dim; i++)
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{
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y[i] += h / 3.0 * k[i];
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ytmp[i] = y0[i] + h * k[i];
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}
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/* k4 step */
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{
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int s = GSL_ODEIV_FN_EVAL (sys, t + h, ytmp, 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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}
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for (i = 0; i < dim; i++)
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{
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y[i] += h / 6.0 * k[i];
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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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rk4_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[],
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const gsl_odeiv_system * sys)
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{
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rk4_state_t *state = (rk4_state_t *) vstate;
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size_t i;
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|
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double *const k = state->k;
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double *const k1 = state->k1;
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double *const y0 = state->y0;
|
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double *const y_onestep = state->y_onestep;
|
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|
|
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DBL_MEMCPY (y0, y, dim);
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if (dydt_in != NULL)
|
|
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{
|
|
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DBL_MEMCPY (k, dydt_in, dim);
|
|
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}
|
|
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else
|
|
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{
|
|
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int s = GSL_ODEIV_FN_EVAL (sys, t, y0, k);
|
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|
|
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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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|
|
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/* Error estimation is done by step doubling procedure */
|
|
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|
|
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/* Save first point derivatives*/
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|
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|
|
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DBL_MEMCPY (k1, k, dim);
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|
|
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/* First traverse h with one step (save to y_onestep) */
|
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|
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DBL_MEMCPY (y_onestep, y, dim);
|
|
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|
|
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{
|
|
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int s = rk4_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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|
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/* Then with two steps with half step length (save to y) */
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DBL_MEMCPY (k, k1, dim);
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|
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|
|
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{
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|
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int s = rk4_step (y, state, h/2.0, t, dim, sys);
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|
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if (s != GSL_SUCCESS)
|
|
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{
|
|
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/* Restore original values */
|
|
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DBL_MEMCPY (y, y0, dim);
|
|
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return s;
|
|
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}
|
|
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}
|
|
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|
|
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/* Update before second step */
|
|
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{
|
|
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int s = GSL_ODEIV_FN_EVAL (sys, t + h/2.0, y, k);
|
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|
|
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if (s != GSL_SUCCESS)
|
|
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{
|
|
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/* Restore original values */
|
|
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DBL_MEMCPY (y, y0, dim);
|
|
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return s;
|
|
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}
|
|
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}
|
|
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|
|
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/* Save original y0 to k1 for possible failures */
|
|
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DBL_MEMCPY (k1, y0, dim);
|
|
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|
|
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/* Update y0 for second step */
|
|
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DBL_MEMCPY (y0, y, dim);
|
|
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|
|
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{
|
|
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int s = rk4_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 values */
|
|
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DBL_MEMCPY (y, k1, dim);
|
|
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return s;
|
|
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}
|
|
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}
|
|
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|
|
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/* Derivatives at output */
|
|
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|
|
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if (dydt_out != NULL) {
|
|
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int 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 values */
|
|
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DBL_MEMCPY (y, k1, dim);
|
|
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return s;
|
|
Packit |
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}
|
|
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}
|
|
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|
|
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/* Error estimation
|
|
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|
|
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yerr = C * 0.5 * | y(onestep) - y(twosteps) | / (2^order - 1)
|
|
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|
|
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constant C is approximately 8.0 to ensure 90% of samples lie within
|
|
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67cb25 |
the error (assuming a gaussian distribution with prior p(sigma)=1/sigma.)
|
|
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|
|
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*/
|
|
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|
|
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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]) / 15.0;
|
|
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67cb25 |
}
|
|
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67cb25 |
|
|
Packit |
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return GSL_SUCCESS;
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static int
|
|
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rk4_reset (void *vstate, size_t dim)
|
|
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67cb25 |
{
|
|
Packit |
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rk4_state_t *state = (rk4_state_t *) vstate;
|
|
Packit |
67cb25 |
|
|
Packit |
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DBL_ZERO_MEMSET (state->k, dim);
|
|
Packit |
67cb25 |
DBL_ZERO_MEMSET (state->k1, dim);
|
|
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67cb25 |
DBL_ZERO_MEMSET (state->y0, dim);
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DBL_ZERO_MEMSET (state->ytmp, dim);
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67cb25 |
DBL_ZERO_MEMSET (state->y_onestep, dim);
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67cb25 |
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67cb25 |
return GSL_SUCCESS;
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67cb25 |
}
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|
Packit |
67cb25 |
|
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Packit |
67cb25 |
static unsigned int
|
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67cb25 |
rk4_order (void *vstate)
|
|
Packit |
67cb25 |
{
|
|
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67cb25 |
rk4_state_t *state = (rk4_state_t *) vstate;
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|
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67cb25 |
state = 0; /* prevent warnings about unused parameters */
|
|
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67cb25 |
return 4;
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|
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67cb25 |
}
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|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static void
|
|
Packit |
67cb25 |
rk4_free (void *vstate)
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
rk4_state_t *state = (rk4_state_t *) vstate;
|
|
Packit |
67cb25 |
free (state->k);
|
|
Packit |
67cb25 |
free (state->k1);
|
|
Packit |
67cb25 |
free (state->y0);
|
|
Packit |
67cb25 |
free (state->ytmp);
|
|
Packit |
67cb25 |
free (state->y_onestep);
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|
Packit |
67cb25 |
free (state);
|
|
Packit |
67cb25 |
}
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
static const gsl_odeiv_step_type rk4_type = { "rk4", /* name */
|
|
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67cb25 |
1, /* can use dydt_in */
|
|
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67cb25 |
1, /* gives exact dydt_out */
|
|
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67cb25 |
&rk4_alloc,
|
|
Packit |
67cb25 |
&rk4_apply,
|
|
Packit |
67cb25 |
&rk4_reset,
|
|
Packit |
67cb25 |
&rk4_order,
|
|
Packit |
67cb25 |
&rk4_free
|
|
Packit |
67cb25 |
};
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
const gsl_odeiv_step_type *gsl_odeiv_step_rk4 = &rk4_type;
|