/* ode-initval2/rkck.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 3 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(5), Cash-Karp */ /* Reference: Cash, J.R., Karp, A.H., ACM Transactions of Mathematical Software, vol. 16 (1990) 201-222. */ /* Author: G. Jungman */ #include #include #include #include #include #include "odeiv_util.h" #include "step_utils.c" /* Cash-Karp constants */ static const double ah[] = { 1.0 / 5.0, 0.3, 3.0 / 5.0, 1.0, 7.0 / 8.0 }; static const double b21 = 1.0 / 5.0; static const double b3[] = { 3.0 / 40.0, 9.0 / 40.0 }; static const double b4[] = { 0.3, -0.9, 1.2 }; static const double b5[] = { -11.0 / 54.0, 2.5, -70.0 / 27.0, 35.0 / 27.0 }; static const double b6[] = { 1631.0 / 55296.0, 175.0 / 512.0, 575.0 / 13824.0, 44275.0 / 110592.0, 253.0 / 4096.0 }; static const double c1 = 37.0 / 378.0; static const double c3 = 250.0 / 621.0; static const double c4 = 125.0 / 594.0; static const double c6 = 512.0 / 1771.0; /* These are the differences of fifth and fourth order coefficients for error estimation */ static const double ec[] = { 0.0, 37.0 / 378.0 - 2825.0 / 27648.0, 0.0, 250.0 / 621.0 - 18575.0 / 48384.0, 125.0 / 594.0 - 13525.0 / 55296.0, -277.0 / 14336.0, 512.0 / 1771.0 - 0.25 }; typedef struct { double *k1; double *k2; double *k3; double *k4; double *k5; double *k6; double *y0; double *ytmp; } rkck_state_t; static void * rkck_alloc (size_t dim) { rkck_state_t *state = (rkck_state_t *) malloc (sizeof (rkck_state_t)); if (state == 0) { GSL_ERROR_NULL ("failed to allocate space for rkck_state", GSL_ENOMEM); } state->k1 = (double *) malloc (dim * sizeof (double)); if (state->k1 == 0) { free (state); GSL_ERROR_NULL ("failed to allocate space for k1", GSL_ENOMEM); } state->k2 = (double *) malloc (dim * sizeof (double)); if (state->k2 == 0) { free (state->k1); free (state); GSL_ERROR_NULL ("failed to allocate space for k2", GSL_ENOMEM); } state->k3 = (double *) malloc (dim * sizeof (double)); if (state->k3 == 0) { free (state->k2); free (state->k1); free (state); GSL_ERROR_NULL ("failed to allocate space for k3", GSL_ENOMEM); } state->k4 = (double *) malloc (dim * sizeof (double)); if (state->k4 == 0) { free (state->k3); free (state->k2); free (state->k1); free (state); GSL_ERROR_NULL ("failed to allocate space for k4", GSL_ENOMEM); } state->k5 = (double *) malloc (dim * sizeof (double)); if (state->k5 == 0) { free (state->k4); free (state->k3); free (state->k2); free (state->k1); free (state); GSL_ERROR_NULL ("failed to allocate space for k5", GSL_ENOMEM); } state->k6 = (double *) malloc (dim * sizeof (double)); if (state->k6 == 0) { free (state->k5); free (state->k4); free (state->k3); free (state->k2); free (state->k1); free (state); GSL_ERROR_NULL ("failed to allocate space for k6", GSL_ENOMEM); } state->y0 = (double *) malloc (dim * sizeof (double)); if (state->y0 == 0) { free (state->k6); free (state->k5); free (state->k4); free (state->k3); free (state->k2); free (state->k1); free (state); GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM); } state->ytmp = (double *) malloc (dim * sizeof (double)); if (state->ytmp == 0) { free (state->y0); free (state->k6); free (state->k5); free (state->k4); free (state->k3); free (state->k2); free (state->k1); free (state); GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM); } return state; } static int rkck_apply (void *vstate, size_t dim, double t, double h, double y[], double yerr[], const double dydt_in[], double dydt_out[], const gsl_odeiv2_system * sys) { rkck_state_t *state = (rkck_state_t *) vstate; size_t i; double *const k1 = state->k1; double *const k2 = state->k2; double *const k3 = state->k3; double *const k4 = state->k4; double *const k5 = state->k5; double *const k6 = state->k6; double *const ytmp = state->ytmp; double *const y0 = state->y0; DBL_MEMCPY (y0, y, dim); /* k1 step */ if (dydt_in != NULL) { DBL_MEMCPY (k1, dydt_in, dim); } else { int s = GSL_ODEIV_FN_EVAL (sys, t, y, k1); if (s != GSL_SUCCESS) { return s; } } for (i = 0; i < dim; i++) ytmp[i] = y[i] + b21 * h * k1[i]; /* k2 step */ { int s = GSL_ODEIV_FN_EVAL (sys, t + ah[0] * h, ytmp, k2); if (s != GSL_SUCCESS) { return s; } } for (i = 0; i < dim; i++) ytmp[i] = y[i] + h * (b3[0] * k1[i] + b3[1] * k2[i]); /* k3 step */ { int s = GSL_ODEIV_FN_EVAL (sys, t + ah[1] * h, ytmp, k3); if (s != GSL_SUCCESS) { return s; } } for (i = 0; i < dim; i++) ytmp[i] = y[i] + h * (b4[0] * k1[i] + b4[1] * k2[i] + b4[2] * k3[i]); /* k4 step */ { int s = GSL_ODEIV_FN_EVAL (sys, t + ah[2] * h, ytmp, k4); if (s != GSL_SUCCESS) { return s; } } for (i = 0; i < dim; i++) ytmp[i] = y[i] + h * (b5[0] * k1[i] + b5[1] * k2[i] + b5[2] * k3[i] + b5[3] * k4[i]); /* k5 step */ { int s = GSL_ODEIV_FN_EVAL (sys, t + ah[3] * h, ytmp, k5); if (s != GSL_SUCCESS) { return s; } } for (i = 0; i < dim; i++) ytmp[i] = y[i] + h * (b6[0] * k1[i] + b6[1] * k2[i] + b6[2] * k3[i] + b6[3] * k4[i] + b6[4] * k5[i]); /* k6 step and final sum */ { int s = GSL_ODEIV_FN_EVAL (sys, t + ah[4] * h, ytmp, k6); if (s != GSL_SUCCESS) { return s; } } for (i = 0; i < dim; i++) { const double d_i = c1 * k1[i] + c3 * k3[i] + c4 * k4[i] + c6 * k6[i]; y[i] += h * d_i; } /* Evaluate dydt_out[]. */ if (dydt_out != NULL) { int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out); if (s != GSL_SUCCESS) { /* Restore initial values */ DBL_MEMCPY (y, y0, dim); return s; } } /* difference between 4th and 5th order */ for (i = 0; i < dim; i++) { yerr[i] = h * (ec[1] * k1[i] + ec[3] * k3[i] + ec[4] * k4[i] + ec[5] * k5[i] + ec[6] * k6[i]); } return GSL_SUCCESS; } static int rkck_reset (void *vstate, size_t dim) { rkck_state_t *state = (rkck_state_t *) vstate; DBL_ZERO_MEMSET (state->k1, dim); DBL_ZERO_MEMSET (state->k2, dim); DBL_ZERO_MEMSET (state->k3, dim); DBL_ZERO_MEMSET (state->k4, dim); DBL_ZERO_MEMSET (state->k5, dim); DBL_ZERO_MEMSET (state->k6, dim); DBL_ZERO_MEMSET (state->ytmp, dim); DBL_ZERO_MEMSET (state->y0, dim); return GSL_SUCCESS; } static unsigned int rkck_order (void *vstate) { rkck_state_t *state = (rkck_state_t *) vstate; state = 0; /* prevent warnings about unused parameters */ return 5; /* FIXME: should this be 4? */ } static void rkck_free (void *vstate) { rkck_state_t *state = (rkck_state_t *) vstate; free (state->ytmp); free (state->y0); free (state->k6); free (state->k5); free (state->k4); free (state->k3); free (state->k2); free (state->k1); free (state); } static const gsl_odeiv2_step_type rkck_type = { "rkck", /* name */ 1, /* can use dydt_in */ 1, /* gives exact dydt_out */ &rkck_alloc, &rkck_apply, &stepper_set_driver_null, &rkck_reset, &rkck_order, &rkck_free }; const gsl_odeiv2_step_type *gsl_odeiv2_step_rkck = &rkck_type;