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/* ode-initval/rk2imp.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Runge-Kutta 2, Gaussian implicit. Also known as the implicit
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midpoint rule. */
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/* Author: G. Jungman */
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/* Error estimation by step doubling, see eg. Ascher, U.M., Petzold,
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L.R., Computer methods for ordinary differential and
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differential-algebraic equations, SIAM, Philadelphia, 1998.
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The method is also described in eg. this reference.
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*/
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#include <config.h>
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#include <stdlib.h>
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#include <string.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_errno.h>
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#include <gsl/gsl_odeiv.h>
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#include "odeiv_util.h"
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typedef struct
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{
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double *Y1;
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double *y0;
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double *ytmp;
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double *y_onestep;
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double *y0_orig;
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}
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rk2imp_state_t;
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static void *
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rk2imp_alloc (size_t dim)
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{
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rk2imp_state_t *state = (rk2imp_state_t *) malloc (sizeof (rk2imp_state_t));
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if (state == 0)
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{
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GSL_ERROR_NULL ("failed to allocate space for rk2imp_state",
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GSL_ENOMEM);
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}
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state->Y1 = (double *) malloc (dim * sizeof (double));
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if (state->Y1 == 0)
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{
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for Y1", GSL_ENOMEM);
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}
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state->ytmp = (double *) malloc (dim * sizeof (double));
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if (state->ytmp == 0)
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{
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free (state->Y1);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
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}
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state->y0 = (double *) malloc (dim * sizeof (double));
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if (state->y0 == 0)
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{
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free (state->Y1);
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free (state->ytmp);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
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}
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state->y_onestep = (double *) malloc (dim * sizeof (double));
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if (state->y_onestep == 0)
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{
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free (state->Y1);
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free (state->ytmp);
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free (state->y0);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM);
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}
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state->y0_orig = (double *) malloc (dim * sizeof (double));
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if (state->y0_orig == 0)
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{
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free (state->y_onestep);
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free (state->Y1);
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free (state->ytmp);
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free (state->y0);
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free (state);
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GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
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}
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return state;
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}
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static int
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rk2imp_step (double *y, rk2imp_state_t *state,
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const double h, const double t,
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const size_t dim, const gsl_odeiv_system *sys)
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{
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/* Makes a Runge-Kutta 2nd order implicit advance with step size h.
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y0 is initial values of variables y.
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The implicit matrix equations to solve are:
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Y1 = y0 + h/2 * f(t + h/2, Y1)
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y = y0 + h * f(t + h/2, Y1)
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*/
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const double *y0 = state->y0;
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double *Y1 = state->Y1;
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double *ytmp = state->ytmp;
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int max_iter=3;
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int nu;
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size_t i;
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/* iterative solution of Y1 = y0 + h/2 * f(t + h/2, Y1)
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Y1 should include initial values at call.
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Note: This method does not check for convergence of the
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iterative solution!
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*/
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for (nu = 0; nu < max_iter; nu++)
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{
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for (i = 0; i < dim; i++)
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{
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ytmp[i] = y0[i] + 0.5 * h * Y1[i];
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}
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{
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int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, Y1);
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if (s != GSL_SUCCESS)
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{
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return s;
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}
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}
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}
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/* assignment */
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for (i = 0; i < dim; i++)
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{
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y[i] = y0[i] + h * Y1[i];
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}
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return GSL_SUCCESS;
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}
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static int
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rk2imp_apply (void *vstate,
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size_t dim,
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double t,
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double h,
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double y[],
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double yerr[],
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const double dydt_in[],
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double dydt_out[], const gsl_odeiv_system * sys)
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{
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rk2imp_state_t *state = (rk2imp_state_t *) vstate;
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size_t i;
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double *Y1 = state->Y1;
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double *y0 = state->y0;
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double *y_onestep = state->y_onestep;
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double *y0_orig = state->y0_orig;
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/* Error estimation is done by step doubling procedure */
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/* initialization step */
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DBL_MEMCPY (y0, y, dim);
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/* Save initial values for possible failures */
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DBL_MEMCPY (y0_orig, y, dim);
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if (dydt_in != NULL)
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{
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DBL_MEMCPY (Y1, dydt_in, dim);
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}
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else
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{
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int s = GSL_ODEIV_FN_EVAL (sys, t, y, Y1);
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if (s != GSL_SUCCESS)
|
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{
|
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return s;
|
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}
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|
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}
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|
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/* First traverse h with one step (save to y_onestep) */
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|
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DBL_MEMCPY (y_onestep, y, dim);
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|
|
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{
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|
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int s = rk2imp_step (y_onestep, state, h, t, dim, sys);
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if (s != GSL_SUCCESS)
|
|
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{
|
|
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return s;
|
|
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}
|
|
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}
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|
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/* Then with two steps with half step length (save to y) */
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|
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{
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|
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int s = rk2imp_step (y, state, h / 2.0, t, dim, sys);
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|
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if (s != GSL_SUCCESS)
|
|
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{
|
|
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/* Restore original y vector */
|
|
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DBL_MEMCPY (y, y0_orig, dim);
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|
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return s;
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|
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}
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|
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}
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DBL_MEMCPY (y0, y, dim);
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|
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{
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int s = GSL_ODEIV_FN_EVAL (sys, t + h / 2.0, y, Y1);
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|
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if (s != GSL_SUCCESS)
|
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{
|
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/* Restore original y vector */
|
|
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DBL_MEMCPY (y, y0_orig, dim);
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|
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return s;
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}
|
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}
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|
|
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{
|
|
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int s = rk2imp_step (y, state, h / 2.0, t + h / 2.0, dim, sys);
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|
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if (s != GSL_SUCCESS)
|
|
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{
|
|
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/* Restore original y vector */
|
|
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DBL_MEMCPY (y, y0_orig, dim);
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|
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return s;
|
|
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}
|
|
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}
|
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|
|
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/* Derivatives at output */
|
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|
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if (dydt_out != NULL)
|
|
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{
|
|
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int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);
|
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|
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if (s != GSL_SUCCESS)
|
|
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{
|
|
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/* Restore original y vector */
|
|
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DBL_MEMCPY (y, y0_orig, dim);
|
|
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|
|
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return s;
|
|
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}
|
|
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}
|
|
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|
|
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/* Error estimation */
|
|
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|
|
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for (i = 0; i < dim; i++)
|
|
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{
|
|
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yerr[i] = 4.0 * (y[i] - y_onestep[i]) / 3.0;
|
|
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}
|
|
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|
|
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return GSL_SUCCESS;
|
|
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}
|
|
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|
|
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static int
|
|
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rk2imp_reset (void *vstate, size_t dim)
|
|
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{
|
|
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rk2imp_state_t *state = (rk2imp_state_t *) vstate;
|
|
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|
|
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DBL_ZERO_MEMSET (state->Y1, dim);
|
|
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DBL_ZERO_MEMSET (state->ytmp, dim);
|
|
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DBL_ZERO_MEMSET (state->y0, dim);
|
|
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DBL_ZERO_MEMSET (state->y_onestep, dim);
|
|
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DBL_ZERO_MEMSET (state->y0_orig, dim);
|
|
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|
|
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return GSL_SUCCESS;
|
|
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}
|
|
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|
|
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static unsigned int
|
|
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rk2imp_order (void *vstate)
|
|
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67cb25 |
{
|
|
Packit |
67cb25 |
rk2imp_state_t *state = (rk2imp_state_t *) vstate;
|
|
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67cb25 |
state = 0; /* prevent warnings about unused parameters */
|
|
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return 2;
|
|
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}
|
|
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|
|
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static void
|
|
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rk2imp_free (void *vstate)
|
|
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67cb25 |
{
|
|
Packit |
67cb25 |
rk2imp_state_t *state = (rk2imp_state_t *) vstate;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
free (state->Y1);
|
|
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67cb25 |
free (state->ytmp);
|
|
Packit |
67cb25 |
free (state->y0);
|
|
Packit |
67cb25 |
free (state->y_onestep);
|
|
Packit |
67cb25 |
free (state->y0_orig);
|
|
Packit |
67cb25 |
free (state);
|
|
Packit |
67cb25 |
}
|
|
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67cb25 |
|
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Packit |
67cb25 |
static const gsl_odeiv_step_type rk2imp_type = { "rk2imp", /* name */
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67cb25 |
1, /* can use dydt_in */
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67cb25 |
1, /* gives exact dydt_out */
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&rk2imp_alloc,
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&rk2imp_apply,
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&rk2imp_reset,
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67cb25 |
&rk2imp_order,
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67cb25 |
&rk2imp_free
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67cb25 |
};
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67cb25 |
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67cb25 |
const gsl_odeiv_step_type *gsl_odeiv_step_rk2imp = &rk2imp_type;
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