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-rw-r--r--gsl-1.9/ode-initval/rk4imp.c390
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diff --git a/gsl-1.9/ode-initval/rk4imp.c b/gsl-1.9/ode-initval/rk4imp.c
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+/* ode-initval/rk4imp.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, Gaussian implicit */
+
+/* Author: G. Jungman
+*/
+
+/* 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.
+ Method coefficients can also be found in it.
+*/
+
+#include <config.h>
+#include <stdlib.h>
+#include <string.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_odeiv.h>
+
+#include "odeiv_util.h"
+
+typedef struct
+{
+ double *k1nu;
+ double *k2nu;
+ double *ytmp1;
+ double *ytmp2;
+ double *y0;
+ double *y0_orig;
+ double *y_onestep;
+}
+rk4imp_state_t;
+
+static void *
+rk4imp_alloc (size_t dim)
+{
+ rk4imp_state_t *state = (rk4imp_state_t *) malloc (sizeof (rk4imp_state_t));
+
+ if (state == 0)
+ {
+ GSL_ERROR_NULL ("failed to allocate space for rk4imp_state",
+ GSL_ENOMEM);
+ }
+
+ state->k1nu = (double *) malloc (dim * sizeof (double));
+
+ if (state->k1nu == 0)
+ {
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for k1nu", GSL_ENOMEM);
+ }
+
+ state->k2nu = (double *) malloc (dim * sizeof (double));
+
+ if (state->k2nu == 0)
+ {
+ free (state->k1nu);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for k2nu", GSL_ENOMEM);
+ }
+
+ state->ytmp1 = (double *) malloc (dim * sizeof (double));
+
+ if (state->ytmp1 == 0)
+ {
+ free (state->k2nu);
+ free (state->k1nu);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for ytmp1", GSL_ENOMEM);
+ }
+
+ state->ytmp2 = (double *) malloc (dim * sizeof (double));
+
+ if (state->ytmp2 == 0)
+ {
+ free (state->ytmp1);
+ free (state->k2nu);
+ free (state->k1nu);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for ytmp2", GSL_ENOMEM);
+ }
+
+ state->y0 = (double *) malloc (dim * sizeof (double));
+
+ if (state->y0 == 0)
+ {
+ free (state->ytmp2);
+ free (state->ytmp1);
+ free (state->k2nu);
+ free (state->k1nu);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
+ }
+
+ state->y0_orig = (double *) malloc (dim * sizeof (double));
+
+ if (state->y0_orig == 0)
+ {
+ free (state->y0);
+ free (state->ytmp2);
+ free (state->ytmp1);
+ free (state->k2nu);
+ free (state->k1nu);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
+ }
+
+ state->y_onestep = (double *) malloc (dim * sizeof (double));
+
+ if (state->y_onestep == 0)
+ {
+ free (state->y0_orig);
+ free (state->y0);
+ free (state->ytmp2);
+ free (state->ytmp1);
+ free (state->k2nu);
+ free (state->k1nu);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM);
+ }
+
+ return state;
+}
+
+static int
+rk4imp_step (double *y, rk4imp_state_t *state,
+ const double h, const double t,
+ const size_t dim, const gsl_odeiv_system *sys)
+{
+ /* Makes a Runge-Kutta 4th order implicit advance with step size h.
+ y0 is initial values of variables y.
+
+ The implicit matrix equations to solve are:
+
+ Y1 = y0 + h * a11 * f(t + h * c1, Y1) + h * a12 * f(t + h * c2, Y2)
+ Y2 = y0 + h * a21 * f(t + h * c1, Y1) + h * a22 * f(t + h * c2, Y2)
+
+ y = y0 + h * b1 * f(t + h * c1, Y1) + h * b2 * f(t + h * c2, Y2)
+
+ with constant coefficients a, b and c. For this method
+ they are: b=[0.5 0.5] c=[(3-sqrt(3))/6 (3+sqrt(3))/6]
+ a11=1/4, a12=(3-2*sqrt(3))/12, a21=(3+2*sqrt(3))/12 and a22=1/4
+ */
+
+ const double ir3 = 1.0 / M_SQRT3;
+ const int iter_steps = 3;
+ int nu;
+ size_t i;
+
+ double *const k1nu = state->k1nu;
+ double *const k2nu = state->k2nu;
+ double *const ytmp1 = state->ytmp1;
+ double *const ytmp2 = state->ytmp2;
+
+ /* iterative solution of Y1 and Y2.
+
+ Note: This method does not check for convergence of the
+ iterative solution!
+ */
+
+ for (nu = 0; nu < iter_steps; nu++)
+ {
+ for (i = 0; i < dim; i++)
+ {
+ ytmp1[i] =
+ y[i] + h * (0.25 * k1nu[i] + 0.5 * (0.5 - ir3) * k2nu[i]);
+ ytmp2[i] =
+ y[i] + h * (0.25 * k2nu[i] + 0.5 * (0.5 + ir3) * k1nu[i]);
+ }
+ {
+ int s =
+ GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h * (1.0 - ir3), ytmp1, k1nu);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+ }
+ {
+ int s =
+ GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h * (1.0 + ir3), ytmp2, k2nu);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+ }
+ }
+
+ /* assignment */
+
+ for (i = 0; i < dim; i++)
+ {
+ const double d_i = 0.5 * (k1nu[i] + k2nu[i]);
+ y[i] += h * d_i;
+ }
+
+ return GSL_SUCCESS;
+}
+
+static int
+rk4imp_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)
+{
+ rk4imp_state_t *state = (rk4imp_state_t *) vstate;
+
+ size_t i;
+
+ double *y0 = state->y0;
+ double *y0_orig = state->y0_orig;
+ double *y_onestep = state->y_onestep;
+ double *k1nu = state->k1nu;
+ double *k2nu = state->k2nu;
+
+ /* Initialization step */
+ DBL_MEMCPY (y0, y, dim);
+
+ /* Save initial values in case of failure */
+ DBL_MEMCPY (y0_orig, y, dim);
+
+ if (dydt_in != 0)
+ {
+ DBL_MEMCPY (k1nu, dydt_in, dim);
+ }
+ else
+ {
+ int s = GSL_ODEIV_FN_EVAL (sys, t, y, k1nu);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+ }
+
+ DBL_MEMCPY (k2nu, k1nu, dim);
+
+ /* First traverse h with one step (save to y_onestep) */
+
+ DBL_MEMCPY (y_onestep, y, dim);
+
+ {
+ int s = rk4imp_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) */
+
+ {
+ int s = rk4imp_step (y, state, h/2.0, t, dim, sys);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original y vector */
+ DBL_MEMCPY (y, y0_orig, dim);
+ return s;
+ }
+ }
+
+ DBL_MEMCPY (y0, y, dim);
+
+ {
+ int s = GSL_ODEIV_FN_EVAL (sys, t + h/2.0, y, k1nu);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original y vector */
+ DBL_MEMCPY (y, y0_orig, dim);
+ return s;
+ }
+ }
+
+ DBL_MEMCPY (k2nu, k1nu, dim);
+
+ {
+ int s = rk4imp_step (y, state, h/2.0, t + h/2.0, dim, sys);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original y vector */
+ DBL_MEMCPY (y, y0_orig, 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 y vector */
+ DBL_MEMCPY (y, y0_orig, dim);
+ return s;
+ }
+ }
+
+ /* Error estimation */
+
+ /* Denominator in step doubling error equation
+ * yerr = 0.5 * | y(onestep) - y(twosteps) | / (2^order - 1)
+ */
+
+ for (i = 0; i < dim; i++)
+ {
+ yerr[i] = 8.0 * 0.5 * (y[i] - y_onestep[i]) / 15.0;
+ }
+
+ return GSL_SUCCESS;
+}
+
+static int
+rk4imp_reset (void *vstate, size_t dim)
+{
+ rk4imp_state_t *state = (rk4imp_state_t *) vstate;
+
+ DBL_ZERO_MEMSET (state->y_onestep, dim);
+ DBL_ZERO_MEMSET (state->y0_orig, dim);
+ DBL_ZERO_MEMSET (state->y0, dim);
+ DBL_ZERO_MEMSET (state->k1nu, dim);
+ DBL_ZERO_MEMSET (state->k2nu, dim);
+ DBL_ZERO_MEMSET (state->ytmp1, dim);
+ DBL_ZERO_MEMSET (state->ytmp2, dim);
+
+ return GSL_SUCCESS;
+}
+
+static unsigned int
+rk4imp_order (void *vstate)
+{
+ rk4imp_state_t *state = (rk4imp_state_t *) vstate;
+ state = 0; /* prevent warnings about unused parameters */
+ return 4;
+}
+
+static void
+rk4imp_free (void *vstate)
+{
+ rk4imp_state_t *state = (rk4imp_state_t *) vstate;
+
+ free (state->y_onestep);
+ free (state->y0_orig);
+ free (state->y0);
+ free (state->k1nu);
+ free (state->k2nu);
+ free (state->ytmp1);
+ free (state->ytmp2);
+ free (state);
+}
+
+static const gsl_odeiv_step_type rk4imp_type = { "rk4imp", /* name */
+ 1, /* can use dydt_in? */
+ 1, /* gives exact dydt_out? */
+ &rk4imp_alloc,
+ &rk4imp_apply,
+ &rk4imp_reset,
+ &rk4imp_order,
+ &rk4imp_free
+};
+
+const gsl_odeiv_step_type *gsl_odeiv_step_rk4imp = &rk4imp_type;
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