summaryrefslogtreecommitdiff
path: root/gsl-1.9/ode-initval/rkf45.c
diff options
context:
space:
mode:
Diffstat (limited to 'gsl-1.9/ode-initval/rkf45.c')
-rw-r--r--gsl-1.9/ode-initval/rkf45.c372
1 files changed, 372 insertions, 0 deletions
diff --git a/gsl-1.9/ode-initval/rkf45.c b/gsl-1.9/ode-initval/rkf45.c
new file mode 100644
index 0000000..7750144
--- /dev/null
+++ b/gsl-1.9/ode-initval/rkf45.c
@@ -0,0 +1,372 @@
+/* ode-initval/rkf45.c
+ *
+ * Copyright (C) 2001, 2004 Brian Gough
+ *
+ * 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 2 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-Fehlberg 4(5)*/
+
+/* Reference eg. Hairer, E., Norsett S.P., Wanner, G. Solving ordinary
+ differential equations I, Nonstiff Problems, 2nd revised edition,
+ Springer, 2000.
+*/
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_odeiv.h>
+
+#include "odeiv_util.h"
+
+/* Runge-Kutta-Fehlberg coefficients. Zero elements left out */
+
+static const double ah[] = { 1.0/4.0, 3.0/8.0, 12.0/13.0, 1.0, 1.0/2.0 };
+static const double b3[] = { 3.0/32.0, 9.0/32.0 };
+static const double b4[] = { 1932.0/2197.0, -7200.0/2197.0, 7296.0/2197.0};
+static const double b5[] = { 8341.0/4104.0, -32832.0/4104.0, 29440.0/4104.0, -845.0/4104.0};
+static const double b6[] = { -6080.0/20520.0, 41040.0/20520.0, -28352.0/20520.0, 9295.0/20520.0, -5643.0/20520.0};
+
+static const double c1 = 902880.0/7618050.0;
+static const double c3 = 3953664.0/7618050.0;
+static const double c4 = 3855735.0/7618050.0;
+static const double c5 = -1371249.0/7618050.0;
+static const double c6 = 277020.0/7618050.0;
+
+/* These are the differences of fifth and fourth order coefficients
+ for error estimation */
+
+static const double ec[] = { 0.0,
+ 1.0 / 360.0,
+ 0.0,
+ -128.0 / 4275.0,
+ -2197.0 / 75240.0,
+ 1.0 / 50.0,
+ 2.0 / 55.0
+};
+
+typedef struct
+{
+ double *k1;
+ double *k2;
+ double *k3;
+ double *k4;
+ double *k5;
+ double *k6;
+ double *y0;
+ double *ytmp;
+}
+rkf45_state_t;
+
+static void *
+rkf45_alloc (size_t dim)
+{
+ rkf45_state_t *state = (rkf45_state_t *) malloc (sizeof (rkf45_state_t));
+
+ if (state == 0)
+ {
+ GSL_ERROR_NULL ("failed to allocate space for rkf45_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
+rkf45_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)
+{
+ rkf45_state_t *state = (rkf45_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] + ah[0] * 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] + c5 * k5[i] + c6 * k6[i];
+ y[i] += h * d_i;
+ }
+
+ /* Derivatives at output */
+
+ 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
+rkf45_reset (void *vstate, size_t dim)
+{
+ rkf45_state_t *state = (rkf45_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
+rkf45_order (void *vstate)
+{
+ rkf45_state_t *state = (rkf45_state_t *) vstate;
+ state = 0; /* prevent warnings about unused parameters */
+ return 5;
+}
+
+static void
+rkf45_free (void *vstate)
+{
+ rkf45_state_t *state = (rkf45_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 rkf45_type = { "rkf45", /* name */
+ 1, /* can use dydt_in */
+ 0, /* gives exact dydt_out */
+ &rkf45_alloc,
+ &rkf45_apply,
+ &rkf45_reset,
+ &rkf45_order,
+ &rkf45_free
+};
+
+const gsl_odeiv_step_type *gsl_odeiv_step_rkf45 = &rkf45_type;
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-01 12:08:30 +0000