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Diffstat (limited to 'gsl-1.9/ode-initval/rk8pd.c')
| -rw-r--r-- | gsl-1.9/ode-initval/rk8pd.c | 537 |
1 files changed, 537 insertions, 0 deletions
diff --git a/gsl-1.9/ode-initval/rk8pd.c b/gsl-1.9/ode-initval/rk8pd.c new file mode 100644 index 0000000..37bffe9 --- /dev/null +++ b/gsl-1.9/ode-initval/rk8pd.c @@ -0,0 +1,537 @@ +/* ode-initval/rk8pd.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 8(9), Prince-Dormand + * + * High Order Embedded Runge-Kutta Formulae + * P.J. Prince and J.R. Dormand + * J. Comp. Appl. Math.,7, pp. 67-75, 1981 + */ + +/* Author: G. Jungman + */ +#include <config.h> +#include <stdlib.h> +#include <string.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_odeiv.h> + +#include "odeiv_util.h" + +/* Prince-Dormand constants */ + +static const double Abar[] = { + 14005451.0 / 335480064.0, + 0.0, + 0.0, + 0.0, + 0.0, + -59238493.0 / 1068277825.0, + 181606767.0 / 758867731.0, + 561292985.0 / 797845732.0, + -1041891430.0 / 1371343529.0, + 760417239.0 / 1151165299.0, + 118820643.0 / 751138087.0, + -528747749.0 / 2220607170.0, + 1.0 / 4.0 +}; + +static const double A[] = { + 13451932.0 / 455176623.0, + 0.0, + 0.0, + 0.0, + 0.0, + -808719846.0 / 976000145.0, + 1757004468.0 / 5645159321.0, + 656045339.0 / 265891186.0, + -3867574721.0 / 1518517206.0, + 465885868.0 / 322736535.0, + 53011238.0 / 667516719.0, + 2.0 / 45.0 +}; + +static const double ah[] = { + 1.0 / 18.0, + 1.0 / 12.0, + 1.0 / 8.0, + 5.0 / 16.0, + 3.0 / 8.0, + 59.0 / 400.0, + 93.0 / 200.0, + 5490023248.0 / 9719169821.0, + 13.0 / 20.0, + 1201146811.0 / 1299019798.0 +}; + +static const double b21 = 1.0 / 18.0; +static const double b3[] = { 1.0 / 48.0, 1.0 / 16.0 }; +static const double b4[] = { 1.0 / 32.0, 0.0, 3.0 / 32.0 }; +static const double b5[] = { 5.0 / 16.0, 0.0, -75.0 / 64.0, 75.0 / 64.0 }; +static const double b6[] = { 3.0 / 80.0, 0.0, 0.0, 3.0 / 16.0, 3.0 / 20.0 }; +static const double b7[] = { + 29443841.0 / 614563906.0, + 0.0, + 0.0, + 77736538.0 / 692538347.0, + -28693883.0 / 1125000000.0, + 23124283.0 / 1800000000.0 +}; +static const double b8[] = { + 16016141.0 / 946692911.0, + 0.0, + 0.0, + 61564180.0 / 158732637.0, + 22789713.0 / 633445777.0, + 545815736.0 / 2771057229.0, + -180193667.0 / 1043307555.0 +}; +static const double b9[] = { + 39632708.0 / 573591083.0, + 0.0, + 0.0, + -433636366.0 / 683701615.0, + -421739975.0 / 2616292301.0, + 100302831.0 / 723423059.0, + 790204164.0 / 839813087.0, + 800635310.0 / 3783071287.0 +}; +static const double b10[] = { + 246121993.0 / 1340847787.0, + 0.0, + 0.0, + -37695042795.0 / 15268766246.0, + -309121744.0 / 1061227803.0, + -12992083.0 / 490766935.0, + 6005943493.0 / 2108947869.0, + 393006217.0 / 1396673457.0, + 123872331.0 / 1001029789.0 +}; +static const double b11[] = { + -1028468189.0 / 846180014.0, + 0.0, + 0.0, + 8478235783.0 / 508512852.0, + 1311729495.0 / 1432422823.0, + -10304129995.0 / 1701304382.0, + -48777925059.0 / 3047939560.0, + 15336726248.0 / 1032824649.0, + -45442868181.0 / 3398467696.0, + 3065993473.0 / 597172653.0 +}; +static const double b12[] = { + 185892177.0 / 718116043.0, + 0.0, + 0.0, + -3185094517.0 / 667107341.0, + -477755414.0 / 1098053517.0, + -703635378.0 / 230739211.0, + 5731566787.0 / 1027545527.0, + 5232866602.0 / 850066563.0, + -4093664535.0 / 808688257.0, + 3962137247.0 / 1805957418.0, + 65686358.0 / 487910083.0 +}; +static const double b13[] = { + 403863854.0 / 491063109.0, + 0.0, + 0.0, + -5068492393.0 / 434740067.0, + -411421997.0 / 543043805.0, + 652783627.0 / 914296604.0, + 11173962825.0 / 925320556.0, + -13158990841.0 / 6184727034.0, + 3936647629.0 / 1978049680.0, + -160528059.0 / 685178525.0, + 248638103.0 / 1413531060.0, + 0.0 +}; + +typedef struct +{ + double *k[13]; + double *ytmp; + double *y0; +} +rk8pd_state_t; + +static void * +rk8pd_alloc (size_t dim) +{ + rk8pd_state_t *state = (rk8pd_state_t *) malloc (sizeof (rk8pd_state_t)); + int i, j; + + if (state == 0) + { + GSL_ERROR_NULL ("failed to allocate space for rk8pd_state", GSL_ENOMEM); + } + + state->ytmp = (double *) malloc (dim * sizeof (double)); + + if (state->ytmp == 0) + { + 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->ytmp); + free (state); + GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM); + } + + for (i = 0; i < 13; i++) + { + state->k[i] = (double *) malloc (dim * sizeof (double)); + + if (state->k[i] == 0) + { + for (j = 0; j < i; j++) + { + free (state->k[j]); + } + free (state->y0); + free (state->ytmp); + free (state); + GSL_ERROR_NULL ("failed to allocate space for k's", GSL_ENOMEM); + } + } + + return state; +} + + +static int +rk8pd_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) +{ + rk8pd_state_t *state = (rk8pd_state_t *) vstate; + + size_t i; + + double *const ytmp = state->ytmp; + double *const y0 = state->y0; + /* Note that k1 is stored in state->k[0] due to zero-based indexing */ + double *const k1 = state->k[0]; + double *const k2 = state->k[1]; + double *const k3 = state->k[2]; + double *const k4 = state->k[3]; + double *const k5 = state->k[4]; + double *const k6 = state->k[5]; + double *const k7 = state->k[6]; + double *const k8 = state->k[7]; + double *const k9 = state->k[8]; + double *const k10 = state->k[9]; + double *const k11 = state->k[10]; + double *const k12 = state->k[11]; + double *const k13 = state->k[12]; + + 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[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[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[3] * k4[i] + b6[4] * k5[i]); + + /* k6 step */ + { + 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++) + ytmp[i] = + y[i] + h * (b7[0] * k1[i] + b7[3] * k4[i] + b7[4] * k5[i] + + b7[5] * k6[i]); + + /* k7 step */ + { + int s = GSL_ODEIV_FN_EVAL (sys, t + ah[5] * h, ytmp, k7); + + if (s != GSL_SUCCESS) + { + return s; + } + } + + for (i = 0; i < dim; i++) + ytmp[i] = + y[i] + h * (b8[0] * k1[i] + b8[3] * k4[i] + b8[4] * k5[i] + + b8[5] * k6[i] + b8[6] * k7[i]); + + /* k8 step */ + { + int s = GSL_ODEIV_FN_EVAL (sys, t + ah[6] * h, ytmp, k8); + + if (s != GSL_SUCCESS) + { + return s; + } + } + + for (i = 0; i < dim; i++) + ytmp[i] = + y[i] + h * (b9[0] * k1[i] + b9[3] * k4[i] + b9[4] * k5[i] + + b9[5] * k6[i] + b9[6] * k7[i] + b9[7] * k8[i]); + + /* k9 step */ + { + int s = GSL_ODEIV_FN_EVAL (sys, t + ah[7] * h, ytmp, k9); + + if (s != GSL_SUCCESS) + { + return s; + } + } + + for (i = 0; i < dim; i++) + ytmp[i] = + y[i] + h * (b10[0] * k1[i] + b10[3] * k4[i] + b10[4] * k5[i] + + b10[5] * k6[i] + b10[6] * k7[i] + b10[7] * k8[i] + + b10[8] * k9[i]); + + /* k10 step */ + { + int s = GSL_ODEIV_FN_EVAL (sys, t + ah[8] * h, ytmp, k10); + + if (s != GSL_SUCCESS) + { + return s; + } + } + + for (i = 0; i < dim; i++) + ytmp[i] = + y[i] + h * (b11[0] * k1[i] + b11[3] * k4[i] + b11[4] * k5[i] + + b11[5] * k6[i] + b11[6] * k7[i] + b11[7] * k8[i] + + b11[8] * k9[i] + b11[9] * k10[i]); + + /* k11 step */ + { + int s = GSL_ODEIV_FN_EVAL (sys, t + ah[9] * h, ytmp, k11); + + if (s != GSL_SUCCESS) + { + return s; + } + } + + for (i = 0; i < dim; i++) + ytmp[i] = + y[i] + h * (b12[0] * k1[i] + b12[3] * k4[i] + b12[4] * k5[i] + + b12[5] * k6[i] + b12[6] * k7[i] + b12[7] * k8[i] + + b12[8] * k9[i] + b12[9] * k10[i] + b12[10] * k11[i]); + + /* k12 step */ + { + int s = GSL_ODEIV_FN_EVAL (sys, t + h, ytmp, k12); + + if (s != GSL_SUCCESS) + { + return s; + } + } + + for (i = 0; i < dim; i++) + ytmp[i] = + y[i] + h * (b13[0] * k1[i] + b13[3] * k4[i] + b13[4] * k5[i] + + b13[5] * k6[i] + b13[6] * k7[i] + b13[7] * k8[i] + + b13[8] * k9[i] + b13[9] * k10[i] + b13[10] * k11[i] + + b13[11] * k12[i]); + + /* k13 step */ + { + int s = GSL_ODEIV_FN_EVAL (sys, t + h, ytmp, k13); + + if (s != GSL_SUCCESS) + { + return s; + } + } + + /* final sum */ + for (i = 0; i < dim; i++) + { + const double ksum8 = + Abar[0] * k1[i] + Abar[5] * k6[i] + Abar[6] * k7[i] + + Abar[7] * k8[i] + Abar[8] * k9[i] + Abar[9] * k10[i] + + Abar[10] * k11[i] + Abar[11] * k12[i] + Abar[12] * k13[i]; + y[i] += h * ksum8; + } + + /* 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; + } + } + + /* error estimate */ + for (i = 0; i < dim; i++) + { + const double ksum8 = + Abar[0] * k1[i] + Abar[5] * k6[i] + Abar[6] * k7[i] + + Abar[7] * k8[i] + Abar[8] * k9[i] + Abar[9] * k10[i] + + Abar[10] * k11[i] + Abar[11] * k12[i] + Abar[12] * k13[i]; + const double ksum7 = + A[0] * k1[i] + A[5] * k6[i] + A[6] * k7[i] + A[7] * k8[i] + + A[8] * k9[i] + A[9] * k10[i] + A[10] * k11[i] + A[11] * k12[i]; + yerr[i] = h * (ksum7 - ksum8); + } + + return GSL_SUCCESS; +} + +static int +rk8pd_reset (void *vstate, size_t dim) +{ + rk8pd_state_t *state = (rk8pd_state_t *) vstate; + + int i; + + for (i = 0; i < 13; i++) + { + DBL_ZERO_MEMSET (state->k[i], dim); + } + + DBL_ZERO_MEMSET (state->y0, dim); + DBL_ZERO_MEMSET (state->ytmp, dim); + + return GSL_SUCCESS; +} + +static unsigned int +rk8pd_order (void *vstate) +{ + rk8pd_state_t *state = (rk8pd_state_t *) vstate; + state = 0; /* prevent warnings about unused parameters */ + return 8; +} + +static void +rk8pd_free (void *vstate) +{ + rk8pd_state_t *state = (rk8pd_state_t *) vstate; + int i; + + for (i = 0; i < 13; i++) + { + free (state->k[i]); + } + free (state->y0); + free (state->ytmp); + free (state); +} + +static const gsl_odeiv_step_type rk8pd_type = { "rk8pd", /* name */ + 1, /* can use dydt_in */ + 1, /* gives exact dydt_out */ + &rk8pd_alloc, + &rk8pd_apply, + &rk8pd_reset, + &rk8pd_order, + &rk8pd_free +}; + +const gsl_odeiv_step_type *gsl_odeiv_step_rk8pd = &rk8pd_type; |