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-rw-r--r--gsl-1.9/ode-initval/rkck.c371
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diff --git a/gsl-1.9/ode-initval/rkck.c b/gsl-1.9/ode-initval/rkck.c
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+/* 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 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 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;
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