| /* 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; |