diff options
Diffstat (limited to 'gsl-1.9/ode-initval/rk2imp.c')
-rw-r--r-- | gsl-1.9/ode-initval/rk2imp.c | 336 |
1 files changed, 336 insertions, 0 deletions
diff --git a/gsl-1.9/ode-initval/rk2imp.c b/gsl-1.9/ode-initval/rk2imp.c new file mode 100644 index 0000000..53c31c4 --- /dev/null +++ b/gsl-1.9/ode-initval/rk2imp.c @@ -0,0 +1,336 @@ +/* ode-initval/rk2imp.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 2, Gaussian implicit. Also known as the implicit + midpoint rule. */ + +/* 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. + The method is also described in eg. this reference. +*/ + +#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 *Y1; + double *y0; + double *ytmp; + double *y_onestep; + double *y0_orig; +} +rk2imp_state_t; + +static void * +rk2imp_alloc (size_t dim) +{ + rk2imp_state_t *state = (rk2imp_state_t *) malloc (sizeof (rk2imp_state_t)); + + if (state == 0) + { + GSL_ERROR_NULL ("failed to allocate space for rk2imp_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->ytmp = (double *) malloc (dim * sizeof (double)); + + if (state->ytmp == 0) + { + free (state->Y1); + free (state); + GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM); + } + + state->y0 = (double *) malloc (dim * sizeof (double)); + + if (state->y0 == 0) + { + free (state->Y1); + free (state->ytmp); + free (state); + GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM); + } + + state->y_onestep = (double *) malloc (dim * sizeof (double)); + + if (state->y_onestep == 0) + { + free (state->Y1); + free (state->ytmp); + free (state->y0); + free (state); + GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM); + } + + state->y0_orig = (double *) malloc (dim * sizeof (double)); + + if (state->y0_orig == 0) + { + free (state->y_onestep); + free (state->Y1); + free (state->ytmp); + free (state->y0); + free (state); + GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM); + } + + return state; +} + +static int +rk2imp_step (double *y, rk2imp_state_t *state, + const double h, const double t, + const size_t dim, const gsl_odeiv_system *sys) +{ + /* Makes a Runge-Kutta 2nd order implicit advance with step size h. + y0 is initial values of variables y. + + The implicit matrix equations to solve are: + + Y1 = y0 + h/2 * f(t + h/2, Y1) + + y = y0 + h * f(t + h/2, Y1) + */ + + const double *y0 = state->y0; + double *Y1 = state->Y1; + double *ytmp = state->ytmp; + int max_iter=3; + int nu; + size_t i; + + /* iterative solution of Y1 = y0 + h/2 * f(t + h/2, Y1) + Y1 should include initial values at call. + + Note: This method does not check for convergence of the + iterative solution! + */ + + for (nu = 0; nu < max_iter; nu++) + { + for (i = 0; i < dim; i++) + { + ytmp[i] = y0[i] + 0.5 * h * Y1[i]; + } + + { + int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, Y1); + + if (s != GSL_SUCCESS) + { + return s; + } + } + } + + /* assignment */ + + for (i = 0; i < dim; i++) + { + y[i] = y0[i] + h * Y1[i]; + } + + return GSL_SUCCESS; +} + +static int +rk2imp_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) +{ + rk2imp_state_t *state = (rk2imp_state_t *) vstate; + + size_t i; + + double *Y1 = state->Y1; + double *y0 = state->y0; + double *y_onestep = state->y_onestep; + double *y0_orig = state->y0_orig; + + /* Error estimation is done by step doubling procedure */ + + /* initialization step */ + + DBL_MEMCPY (y0, y, dim); + + /* Save initial values for possible failures */ + DBL_MEMCPY (y0_orig, y, dim); + + if (dydt_in != NULL) + { + DBL_MEMCPY (Y1, dydt_in, dim); + } + + else + { + int s = GSL_ODEIV_FN_EVAL (sys, t, y, Y1); + + if (s != GSL_SUCCESS) + { + return s; + } + } + + /* First traverse h with one step (save to y_onestep) */ + + DBL_MEMCPY (y_onestep, y, dim); + + { + int s = rk2imp_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 = rk2imp_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, Y1); + + if (s != GSL_SUCCESS) + { + /* Restore original y vector */ + DBL_MEMCPY (y, y0_orig, dim); + + return s; + } + } + + { + int s = rk2imp_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 +rk2imp_reset (void *vstate, size_t dim) +{ + rk2imp_state_t *state = (rk2imp_state_t *) vstate; + + DBL_ZERO_MEMSET (state->Y1, dim); + DBL_ZERO_MEMSET (state->ytmp, dim); + DBL_ZERO_MEMSET (state->y0, dim); + DBL_ZERO_MEMSET (state->y_onestep, dim); + DBL_ZERO_MEMSET (state->y0_orig, dim); + + return GSL_SUCCESS; +} + +static unsigned int +rk2imp_order (void *vstate) +{ + rk2imp_state_t *state = (rk2imp_state_t *) vstate; + state = 0; /* prevent warnings about unused parameters */ + return 2; +} + +static void +rk2imp_free (void *vstate) +{ + rk2imp_state_t *state = (rk2imp_state_t *) vstate; + + free (state->Y1); + free (state->ytmp); + free (state->y0); + free (state->y_onestep); + free (state->y0_orig); + free (state); +} + +static const gsl_odeiv_step_type rk2imp_type = { "rk2imp", /* name */ + 1, /* can use dydt_in */ + 1, /* gives exact dydt_out */ + &rk2imp_alloc, + &rk2imp_apply, + &rk2imp_reset, + &rk2imp_order, + &rk2imp_free +}; + +const gsl_odeiv_step_type *gsl_odeiv_step_rk2imp = &rk2imp_type; |