summaryrefslogtreecommitdiff
path: root/gsl-1.9/ode-initval/rk2simp.c
diff options
context:
space:
mode:
Diffstat (limited to 'gsl-1.9/ode-initval/rk2simp.c')
-rw-r--r--gsl-1.9/ode-initval/rk2simp.c382
1 files changed, 382 insertions, 0 deletions
diff --git a/gsl-1.9/ode-initval/rk2simp.c b/gsl-1.9/ode-initval/rk2simp.c
new file mode 100644
index 0000000..61248ac
--- /dev/null
+++ b/gsl-1.9/ode-initval/rk2simp.c
@@ -0,0 +1,382 @@
+/* ode-initval/rk2simp.c
+ *
+ * Copyright (C) 2004 Tuomo Keskitalo
+ *
+ * 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 2, Gaussian implicit. Also known as implicit midpoint rule.
+
+ Non-linear equations solved by linearization, LU-decomposition
+ and matrix inversion. For reference, see eg.
+
+ Ascher, U.M., Petzold, L.R., Computer methods for ordinary
+ differential and differential-algebraic equations, SIAM,
+ Philadelphia, 1998.
+ */
+
+#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 <gsl/gsl_linalg.h>
+
+#include "odeiv_util.h"
+
+typedef struct
+{
+ double *Y1;
+ double *y0;
+ double *y0_orig;
+ double *ytmp;
+ double *dfdy; /* Jacobian */
+ double *dfdt; /* time derivatives, not used */
+ double *y_onestep;
+ gsl_permutation *p;
+}
+rk2simp_state_t;
+
+static void *
+rk2simp_alloc (size_t dim)
+{
+ rk2simp_state_t *state =
+ (rk2simp_state_t *) malloc (sizeof (rk2simp_state_t));
+
+ if (state == 0)
+ {
+ GSL_ERROR_NULL ("failed to allocate space for rk2simp_state",
+ GSL_ENOMEM);
+ }
+
+ state->Y1 = (double *) malloc (dim * sizeof (double));
+
+ if (state->Y1 == 0)
+ {
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for Y1", GSL_ENOMEM);
+ }
+
+ state->y0 = (double *) malloc (dim * sizeof (double));
+
+ if (state->y0 == 0)
+ {
+ free (state->Y1);
+ 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->Y1);
+ free (state->y0);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
+ }
+
+ state->ytmp = (double *) malloc (dim * sizeof (double));
+
+ if (state->ytmp == 0)
+ {
+ free (state->Y1);
+ free (state->y0);
+ free (state->y0_orig);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
+ }
+
+ state->dfdy = (double *) malloc (dim * dim * sizeof (double));
+
+ if (state->dfdy == 0)
+ {
+ free (state->Y1);
+ free (state->y0);
+ free (state->y0_orig);
+ free (state->ytmp);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for dfdy", GSL_ENOMEM);
+ }
+
+ state->dfdt = (double *) malloc (dim * sizeof (double));
+
+ if (state->dfdt == 0)
+ {
+ free (state->Y1);
+ free (state->y0);
+ free (state->y0_orig);
+ free (state->ytmp);
+ free (state->dfdy);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for dfdt", GSL_ENOMEM);
+ }
+
+ state->y_onestep = (double *) malloc (dim * sizeof (double));
+
+ if (state->y_onestep == 0)
+ {
+ free (state->Y1);
+ free (state->y0);
+ free (state->y0_orig);
+ free (state->ytmp);
+ free (state->dfdy);
+ free (state->dfdt);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM);
+ }
+
+ state->p = gsl_permutation_alloc (dim);
+
+ if (state->p == 0)
+ {
+ free (state->Y1);
+ free (state->y0);
+ free (state->y0_orig);
+ free (state->ytmp);
+ free (state->dfdy);
+ free (state->dfdt);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for p", GSL_ENOMEM);
+ }
+
+ return state;
+}
+
+
+static int
+rk2simp_step (double *y, rk2simp_state_t * state,
+ const double h, const double t,
+ const size_t dim, const gsl_odeiv_system * sys)
+{
+ /* Makes a Runge-Kutta 2nd order semi-implicit advance with step size h.
+ y0 is initial values of variables y.
+
+ The linearized semi-implicit equations to calculate are:
+
+ Y1 = y0 + h/2 * (1 - h/2 * df/dy)^(-1) * f(t + h/2, y0)
+
+ y = y0 + h * f(t + h/2, Y1)
+ */
+
+ const double *y0 = state->y0;
+ double *Y1 = state->Y1;
+ double *ytmp = state->ytmp;
+
+ size_t i;
+ int s, ps;
+
+ gsl_matrix_view J = gsl_matrix_view_array (state->dfdy, dim, dim);
+
+ /* First solve Y1.
+ Calculate the inverse matrix (1 - h/2 * df/dy)^-1
+ */
+
+ /* Create matrix to J */
+
+ s = GSL_ODEIV_JA_EVAL (sys, t, y0, state->dfdy, state->dfdt);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+
+ gsl_matrix_scale (&J.matrix, -h / 2.0);
+ gsl_matrix_add_diagonal(&J.matrix, 1.0);
+
+ /* Invert it by LU-decomposition to invmat */
+
+ s += gsl_linalg_LU_decomp (&J.matrix, state->p, &ps);
+
+ if (s != GSL_SUCCESS)
+ {
+ return GSL_EFAILED;
+ }
+
+ /* Evaluate f(t + h/2, y0) */
+
+ s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, y0, ytmp);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+
+ /* Calculate Y1 = y0 + h/2 * ((1-h/2 * df/dy)^-1) ytmp */
+
+ {
+ gsl_vector_const_view y0_view = gsl_vector_const_view_array(y0, dim);
+ gsl_vector_view ytmp_view = gsl_vector_view_array(ytmp, dim);
+ gsl_vector_view Y1_view = gsl_vector_view_array(Y1, dim);
+
+ s = gsl_linalg_LU_solve (&J.matrix, state->p,
+ &ytmp_view.vector, &Y1_view.vector);
+
+ gsl_vector_scale (&Y1_view.vector, 0.5 * h);
+ gsl_vector_add (&Y1_view.vector, &y0_view.vector);
+ }
+
+ /* And finally evaluation of f(t + h/2, Y1) and calculation of y */
+
+ s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, Y1, ytmp);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+
+ for (i = 0; i < dim; i++)
+ {
+ y[i] = y0[i] + h * ytmp[i];
+ }
+
+ return s;
+}
+
+static int
+rk2simp_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)
+{
+ rk2simp_state_t *state = (rk2simp_state_t *) vstate;
+
+ size_t i;
+
+ double *y0 = state->y0;
+ double *y0_orig = state->y0_orig;
+ double *y_onestep = state->y_onestep;
+
+ /* Error estimation is done by step doubling procedure */
+
+ DBL_MEMCPY (y0, y, dim);
+
+ /* Save initial values in case of failure */
+ DBL_MEMCPY (y0_orig, y, dim);
+
+ /* First traverse h with one step (save to y_onestep) */
+ DBL_MEMCPY (y_onestep, y, dim);
+
+ {
+ int s = rk2simp_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 = rk2simp_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 = rk2simp_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 */
+
+ for (i = 0; i < dim; i++)
+ {
+ yerr[i] = 4.0 * (y[i] - y_onestep[i]) / 3.0;
+ }
+
+ return GSL_SUCCESS;
+}
+
+
+static int
+rk2simp_reset (void *vstate, size_t dim)
+{
+ rk2simp_state_t *state = (rk2simp_state_t *) vstate;
+
+ DBL_ZERO_MEMSET (state->Y1, dim);
+ DBL_ZERO_MEMSET (state->y0, dim);
+ DBL_ZERO_MEMSET (state->y0_orig, dim);
+ DBL_ZERO_MEMSET (state->ytmp, dim);
+ DBL_ZERO_MEMSET (state->dfdt, dim * dim);
+ DBL_ZERO_MEMSET (state->dfdt, dim);
+ DBL_ZERO_MEMSET (state->y_onestep, dim);
+
+ return GSL_SUCCESS;
+}
+
+static unsigned int
+rk2simp_order (void *vstate)
+{
+ rk2simp_state_t *state = (rk2simp_state_t *) vstate;
+ state = 0; /* prevent warnings about unused parameters */
+ return 2;
+}
+
+static void
+rk2simp_free (void *vstate)
+{
+ rk2simp_state_t *state = (rk2simp_state_t *) vstate;
+ free (state->Y1);
+ free (state->y0);
+ free (state->y0_orig);
+ free (state->ytmp);
+ free (state->dfdy);
+ free (state->dfdt);
+ free (state->y_onestep);
+ gsl_permutation_free (state->p);
+ free (state);
+}
+
+static const gsl_odeiv_step_type rk2simp_type = {
+ "rk2simp", /* name */
+ 0, /* can use dydt_in? */
+ 1, /* gives exact dydt_out? */
+ &rk2simp_alloc,
+ &rk2simp_apply,
+ &rk2simp_reset,
+ &rk2simp_order,
+ &rk2simp_free
+};
+
+const gsl_odeiv_step_type *gsl_odeiv_step_rk2simp = &rk2simp_type;
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-01 03:52:30 +0000