/* ode-initval/test_odeiv.c
*
* Copyright (C) 2004, 2009 Tuomo Keskitalo
*
* 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.
*/
/* Some functions and tests based on test.c by G. Jungman.
*/
#include <config.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_ieee_utils.h>
#include <gsl/gsl_odeiv.h>
#include "odeiv_util.h"
/* Maximum number of ODE equations */
#define MAXEQ 4
/* RHS for f=2. Solution y = 2 * t + t0 */
int
rhs_linear (double t, const double y[], double f[], void *params)
{
f[0] = 2.0;
return GSL_SUCCESS;
}
int
jac_linear (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
dfdy[0] = 0.0;
dfdt[0] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_lin = {
rhs_linear,
jac_linear,
1,
0
};
/* RHS for f=y. Equals y=exp(t) with initial value y(0)=1.0 */
int
rhs_exp (double t, const double y[], double f[], void *params)
{
f[0] = y[0];
return GSL_SUCCESS;
}
int
jac_exp (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
dfdy[0] = y[0];
dfdt[0] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_exp = {
rhs_exp,
jac_exp,
1,
0
};
/* RHS for f0 = -y1, f1 = y0
equals y = [cos(t), sin(t)] with initial values [1, 0]
*/
int
rhs_sin (double t, const double y[], double f[], void *params)
{
f[0] = -y[1];
f[1] = y[0];
return GSL_SUCCESS;
}
int
jac_sin (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
dfdy[0] = 0.0;
dfdy[1] = -1.0;
dfdy[2] = 1.0;
dfdy[3] = 0.0;
dfdt[0] = 0.0;
dfdt[1] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_sin = {
rhs_sin,
jac_sin,
2,
0
};
/* Sine/cosine with random failures */
static int rhs_xsin_reset = 0;
static int jac_xsin_reset = 0;
int
rhs_xsin (double t, const double y[], double f[], void *params)
{
static int n = 0, m = 0;
if (rhs_xsin_reset) { rhs_xsin_reset = 0; n = 0; m = 1;}
n++;
if (n >= m) {
m = n * 1.3;
return GSL_EFAILED;
} ;
if (n > 40 && n < 65) {
f[0] = GSL_NAN;
f[1] = GSL_NAN;
return GSL_EFAILED;
}
f[0] = -y[1];
f[1] = y[0];
return GSL_SUCCESS;
}
int
jac_xsin (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
static int n = 0;
if (jac_xsin_reset) { jac_xsin_reset = 0; n = 0; }
n++;
if (n > 50 && n < 55) {
dfdy[0] = GSL_NAN;
dfdy[1] = GSL_NAN;
dfdy[2] = GSL_NAN;
dfdy[3] = GSL_NAN;
dfdt[0] = GSL_NAN;
dfdt[1] = GSL_NAN;
return GSL_EFAILED;
}
dfdy[0] = 0.0;
dfdy[1] = -1.0;
dfdy[2] = 1.0;
dfdy[3] = 0.0;
dfdt[0] = 0.0;
dfdt[1] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_xsin = {
rhs_xsin,
jac_xsin,
2,
0
};
/* RHS for classic stiff example
dy0 / dt = 998 * y0 + 1998 * y1 y0(0) = 1.0
dy1 / dt = -999 * y0 - 1999 * y1 y1(0) = 0.0
solution is
y0 = 2 * exp(-t) - exp(-1000 * t)
y1 = - exp(-t) + exp(-1000 * t)
*/
int
rhs_stiff (double t, const double y[], double f[], void *params)
{
f[0] = 998.0 * y[0] + 1998.0 * y[1];
f[1] = -999.0 * y[0] - 1999.0 * y[1];
return GSL_SUCCESS;
}
int
jac_stiff (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
dfdy[0] = 998.0;
dfdy[1] = 1998.0;
dfdy[2] = -999.0;
dfdy[3] = -1999.0;
dfdt[0] = 0.0;
dfdt[1] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_stiff = {
rhs_stiff,
jac_stiff,
2,
0
};
/* van Der Pol oscillator:
f0 = y1 y0(0) = 1.0
f1 = -y0 + mu * y1 * (1 - y0^2) y1(0) = 0.0
*/
int
rhs_vanderpol (double t, const double y[], double f[], void *params)
{
const double mu = 10.0;
f[0] = y[1];
f[1] = -y[0] + mu * y[1] * (1.0 - y[0]*y[0]);
return GSL_SUCCESS;
}
int
jac_vanderpol (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
const double mu = 10.0;
dfdy[0] = 0.0;
dfdy[1] = 1.0;
dfdy[2] = -2.0 * mu * y[0] * y[1] - 1.0;
dfdy[3] = mu * (1.0 - y[0] * y[0]);
dfdt[0] = 0.0;
dfdt[1] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_vanderpol = {
rhs_vanderpol,
jac_vanderpol,
2,
0
};
/* The Oregonator - chemical Belusov-Zhabotinskii reaction
y0(0) = 1.0, y1(0) = 2.0, y2(0) = 3.0
*/
int
rhs_oregonator (double t, const double y[], double f[], void *params)
{
const double c1=77.27;
const double c2=8.375e-6;
const double c3=0.161;
f[0] = c1 * (y[1] + y[0] * (1 - c2 * y[0] - y[1]));
f[1] = 1/c1 * (y[2] - y[1] * (1 + y[0]));
f[2] = c3 * (y[0] - y[2]);
return GSL_SUCCESS;
}
int
jac_oregonator (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
const double c1=77.27;
const double c2=8.375e-6;
const double c3=0.161;
dfdy[0] = c1 * (1 - 2 * c2 * y[0] - y[1]);
dfdy[1] = c1 * (1 - y[0]);
dfdy[2] = 0.0;
dfdy[3] = 1/c1 * (-y[1]);
dfdy[4] = 1/c1 * (-1 - y[0]);
dfdy[5] = 1/c1;
dfdy[6] = c3;
dfdy[7] = 0.0;
dfdy[8] = -c3;
dfdt[0] = 0.0;
dfdt[1] = 0.0;
dfdt[2] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_oregonator = {
rhs_oregonator,
jac_oregonator,
3,
0
};
/* Volterra-Lotka predator-prey model
f0 = (a - b * y1) * y0 y0(0) = 3.0
f1 = (-c + d * y0) * y1 y1(0) = 1.0
*/
int
rhs_vl (double t, const double y[], double f[], void *params)
{
const double a = 1.0;
const double b = 1.0;
const double c = 1.0;
const double d = 1.0;
f[0] = (a - b * y[1]) * y[0];
f[1] = (-c + d * y[0]) * y[1];
return GSL_SUCCESS;
}
int
jac_vl (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
const double a = 1.0;
const double b = 1.0;
const double c = 1.0;
const double d = 1.0;
dfdy[0] = a - b * y[1];
dfdy[1] = -b * y[0];
dfdy[2] = d * y[1];
dfdy[3] = -c + d * y[0];
dfdt[0] = 0.0;
dfdt[1] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_vl = {
rhs_vl,
jac_vl,
2,
0
};
/* Stiff trigonometric example
f0 = -50 * (y0 - cos(t)) y0(0) = 0.0
*/
int
rhs_stifftrig (double t, const double y[], double f[], void *params)
{
f[0] = -50 * (y[0] - cos(t));
return GSL_SUCCESS;
}
int
jac_stifftrig (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
dfdy[0] = -50;
dfdt[0] = -50 * sin(t);
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_stifftrig = {
rhs_stifftrig,
jac_stifftrig,
1,
0
};
/* E5 - a stiff badly scaled chemical problem by Enright, Hull &
Lindberg (1975): Comparing numerical methods for stiff systems of
ODEs. BIT, vol. 15, pp. 10-48.
f0 = -a * y0 - b * y0 * y2 y0(0) = 1.76e-3
f1 = a * y0 - m * c * y1 * y2 y1(0) = 0.0
f2 = a * y0 - b * y0 * y2 - m * c * y1 * y2 + c * y3 y2(0) = 0.0
f3 = b * y0 * y2 - c * y3 y3(0) = 0.0
*/
int
rhs_e5 (double t, const double y[], double f[], void *params)
{
const double a = 7.89e-10;
const double b = 1.1e7;
const double c = 1.13e3;
const double m = 1.0e6;
f[0] = -a * y[0] - b * y[0] * y[2];
f[1] = a * y[0] - m * c * y[1] * y[2];
f[3] = b * y[0] * y[2] - c * y[3];
f[2] = f[1] - f[3];
return GSL_SUCCESS;
}
int
jac_e5 (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
const double a = 7.89e-10;
const double b = 1.1e7;
const double c = 1.13e3;
const double m = 1.0e6;
dfdy[0] = -a - b * y[2];
dfdy[1] = 0.0;
dfdy[2] = -b * y[0];
dfdy[3] = 0.0;
dfdy[4] = a;
dfdy[5] = -m * c * y[2];
dfdy[6] = -m * c * y[1];
dfdy[7] = 0.0;
dfdy[8] = a - b * y[2];
dfdy[9] = -m * c * y[2];
dfdy[10] = -b * y[0] - m * c * y[1];
dfdy[11] = c;
dfdy[12] = b * y[2];
dfdy[13] = 0.0;
dfdy[14] = b * y[0];
dfdy[15] = -c;
dfdt[0] = 0.0;
dfdt[1] = 0.0;
dfdt[2] = 0.0;
dfdt[3] = 0.0;
return GSL_SUCCESS;
}
gsl_odeiv_system rhs_func_e5 = {
rhs_e5,
jac_e5,
4,
0
};
void
test_odeiv_stepper (const gsl_odeiv_step_type *T, const gsl_odeiv_system *sys,
const double h, const double t, const char desc[],
const double ystart[], const double yfin[],
const double relerr)
{
/* tests stepper T with one fixed length step advance of system sys
and compares with given values yfin
*/
double y[MAXEQ] = {0.0};
double yerr[MAXEQ] = {0.0};
size_t ne = sys->dimension;
size_t i;
gsl_odeiv_step *step = gsl_odeiv_step_alloc (T, ne);
DBL_MEMCPY (y, ystart, MAXEQ);
{
int s = gsl_odeiv_step_apply (step, t, h, y, yerr, 0, 0, sys);
if (s != GSL_SUCCESS)
{
gsl_test(s, "test_odeiv_stepper: %s step_apply returned %d", desc, s);
}
}
for (i = 0; i < ne; i++)
{
gsl_test_rel (y[i], yfin[i], relerr,
"%s %s step(%d)",
gsl_odeiv_step_name (step), desc,i);
}
gsl_odeiv_step_free (step);
}
void
test_stepper (const gsl_odeiv_step_type *T)
{
/* Tests stepper T with a step of selected systems */
double y[MAXEQ] = {0.0};
double yfin[MAXEQ] = {0.0};
/* Step length */
double h;
/* Required tolerance */
double err_target;
/* linear */
h = 1e-1;
err_target = 1e-10;
y[0] = 0.58;
yfin[0] = y[0] + 2 * h;
test_odeiv_stepper (T, &rhs_func_lin, h, 0.0, "linear",
y, yfin, err_target);
/* exponential */
h = 1e-4;
err_target = 1e-8;
y[0] = exp(2.7);
yfin[0] = exp(2.7 + h);
test_odeiv_stepper (T, &rhs_func_exp, h, 2.7, "exponential",
y, yfin, err_target);
/* cosine-sine */
h = 1e-3;
err_target = 1e-6;
y[0] = cos(1.2);
y[1] = sin(1.2);
yfin[0] = cos(1.2 + h);
yfin[1] = sin(1.2 + h);
test_odeiv_stepper (T, &rhs_func_sin, h, 1.2, "cosine-sine",
y, yfin, err_target);
/* classic stiff */
h = 1e-7;
err_target = 1e-4;
y[0] = 1.0;
y[1] = 0.0;
{
const double e1 = exp (-h);
const double e2 = exp (-1000.0 * h);
yfin[0] = 2.0 * e1 - e2;
yfin[1] = -e1 + e2;
}
test_odeiv_stepper (T, &rhs_func_stiff, h, 0.0, "classic_stiff",
y, yfin, err_target);
}
void
test_evolve_system (const gsl_odeiv_step_type * T,
const gsl_odeiv_system * sys,
double t0, double t1, double hstart,
double y[], double yfin[],
double err_target, const char *desc)
{
/* Tests system sys with stepper T. Step length is controlled by
error estimation from the stepper.
*/
int steps = 0;
size_t i;
double t = t0;
double h = hstart;
/* Tolerance factor in testing errors */
const double factor = 10;
gsl_odeiv_step * step = gsl_odeiv_step_alloc (T, sys->dimension);
gsl_odeiv_control *c =
gsl_odeiv_control_standard_new (err_target, err_target, 1.0, 0.0);
gsl_odeiv_evolve *e = gsl_odeiv_evolve_alloc (sys->dimension);
double * y_orig = malloc (sys->dimension * sizeof(double));
while (t < t1)
{
double t_orig = t;
int s;
memcpy (y_orig, y, sys->dimension * sizeof(double));
s= gsl_odeiv_evolve_apply (e, c, step, sys, &t, t1, &h, y);
if (s != GSL_SUCCESS)
{
/* check that t and y are unchanged */
gsl_test_abs(t, t_orig, 0.0, "%s, t must be restored on failure",
gsl_odeiv_step_name (step));
for (i = 0; i < sys->dimension; i++)
{
gsl_test_abs (y[i], y_orig[i], 0.0,
"%s, y must be restored on failure",
gsl_odeiv_step_name (step), desc, i);
}
if (sys != &rhs_func_xsin) {
/* apart from xsin, other functions should not return errors */
gsl_test(s, "%s evolve_apply returned %d",
gsl_odeiv_step_name (step), s);
break;
}
}
if (steps > 100000)
{
gsl_test(GSL_EFAILED,
"%s evolve_apply reached maxiter",
gsl_odeiv_step_name (step));
break;
}
steps++;
}
/* err_target is target error of one step. Test if stepper has made
larger error than (tolerance factor times) the number of steps
times the err_target */
for (i = 0; i < sys->dimension; i++)
{
gsl_test_abs (y[i], yfin[i], factor * e->count * err_target,
"%s %s evolve(%d)",
gsl_odeiv_step_name (step), desc, i);
}
free (y_orig);
gsl_odeiv_evolve_free (e);
gsl_odeiv_control_free (c);
gsl_odeiv_step_free (step);
}
int
sys_driver (const gsl_odeiv_step_type * T,
const gsl_odeiv_system * sys,
double t0, double t1, double hstart,
double y[], double epsabs, double epsrel,
const char desc[])
{
/* This function evolves a system sys with stepper T from t0 to t1.
Step length is varied via error control with possibly different
absolute and relative error tolerances.
*/
int s = 0;
int steps = 0;
double t = t0;
double h = hstart;
gsl_odeiv_step * step = gsl_odeiv_step_alloc (T, sys->dimension);
gsl_odeiv_control *c =
gsl_odeiv_control_standard_new (epsabs, epsrel, 1.0, 0.0);
gsl_odeiv_evolve *e = gsl_odeiv_evolve_alloc (sys->dimension);
while (t < t1)
{
s = gsl_odeiv_evolve_apply (e, c, step, sys, &t, t1, &h, y);
if (s != GSL_SUCCESS)
{
gsl_test(s, "sys_driver: %s evolve_apply returned %d",
gsl_odeiv_step_name (step), s);
break;
}
if (steps > 1e7)
{
gsl_test(GSL_EMAXITER,
"sys_driver: %s evolve_apply reached maxiter at t=%g",
gsl_odeiv_step_name (step), t);
s = GSL_EMAXITER;
break;
}
steps++;
}
gsl_test(s, "%s %s [%g,%g], %d steps completed",
gsl_odeiv_step_name (step), desc, t0, t1, steps);
gsl_odeiv_evolve_free (e);
gsl_odeiv_control_free (c);
gsl_odeiv_step_free (step);
return s;
}
void
test_compare_vanderpol (void)
{
/* Compares output of van Der Pol oscillator with several steppers */
/* system dimension */
const size_t sd = 2;
const gsl_odeiv_step_type *steppers[20];
const gsl_odeiv_step_type **T;
/* Required error tolerance for each stepper. */
double err_target[20];
/* number of ODE solvers */
const size_t ns = 11;
/* initial values for each ode-solver */
double y[11][2];
double *yp = &y[0][0];
size_t i, j, k;
int status = 0;
/* Parameters for the problem and stepper */
const double start = 0.0;
const double end = 100.0;
const double epsabs = 1e-8;
const double epsrel = 1e-8;
const double initstepsize = 1e-5;
/* Initialize */
steppers[0] = gsl_odeiv_step_rk2;
err_target[0] = 1e-6;
steppers[1] = gsl_odeiv_step_rk4;
err_target[1] = 1e-6;
steppers[2] = gsl_odeiv_step_rkf45;
err_target[2] = 1e-6;
steppers[3] = gsl_odeiv_step_rkck;
err_target[3] = 1e-6;
steppers[4] = gsl_odeiv_step_rk8pd;
err_target[4] = 1e-6;
steppers[5] = gsl_odeiv_step_rk2imp;
err_target[5] = 1e-5;
steppers[6] = gsl_odeiv_step_rk2simp;
err_target[6] = 1e-5;
steppers[7] = gsl_odeiv_step_rk4imp;
err_target[7] = 1e-6;
steppers[8] = gsl_odeiv_step_bsimp;
err_target[8] = 1e-7;
steppers[9] = gsl_odeiv_step_gear1;
err_target[9] = 1e-2;
steppers[10] = gsl_odeiv_step_gear2;
err_target[10] = 1e-6;
steppers[11] = 0;
T = steppers;
for (i = 0; i < ns; i++)
{
y[i][0] = 1.0;
y[i][1] = 0.0;
}
/* Call each solver for the problem */
i = 0;
while (*T != 0)
{
{
int s = sys_driver (*T, &rhs_func_vanderpol,
start, end, initstepsize, &yp[i],
epsabs, epsrel, "vanderpol");
if (s != GSL_SUCCESS)
{
status++;
}
}
T++;
i += sd;
}
if (status != GSL_SUCCESS)
{
return;
}
/* Compare results */
T = steppers;
for (i = 0; i < ns; i++)
for (j = i+1; j < ns; j++)
for (k = 0; k < sd; k++)
{
const double val1 = yp[sd * i + k];
const double val2 = yp[sd * j + k];
gsl_test_abs (val1, val2,
( GSL_MAX(err_target[i], err_target[j]) ),
"%s/%s vanderpol",
T[i]->name, T[j]->name);
}
}
void
test_compare_oregonator (void)
{
/* Compares output of the Oregonator with several steppers */
/* system dimension */
const size_t sd = 3;
const gsl_odeiv_step_type *steppers[20];
const gsl_odeiv_step_type **T;
/* Required error tolerance for each stepper. */
double err_target[20];
/* number of ODE solvers */
const size_t ns = 2;
/* initial values for each ode-solver */
double y[2][3];
double *yp = &y[0][0];
size_t i, j, k;
int status = 0;
/* Parameters for the problem and stepper */
const double start = 0.0;
const double end = 360.0;
const double epsabs = 1e-8;
const double epsrel = 1e-8;
const double initstepsize = 1e-5;
/* Initialize */
steppers[0] = gsl_odeiv_step_rk2simp;
err_target[0] = 1e-6;
steppers[1] = gsl_odeiv_step_bsimp;
err_target[1] = 1e-6;
steppers[2] = 0;
T = steppers;
for (i = 0; i < ns; i++)
{
y[i][0] = 1.0;
y[i][1] = 2.0;
y[i][2] = 3.0;
}
/* Call each solver for the problem */
i = 0;
while (*T != 0)
{
{
int s = sys_driver (*T, &rhs_func_oregonator,
start, end, initstepsize, &yp[i],
epsabs, epsrel, "oregonator");
if (s != GSL_SUCCESS)
{
status++;
}
}
T++;
i += sd;
}
if (status != GSL_SUCCESS)
{
return;
}
/* Compare results */
T = steppers;
for (i = 0; i < ns; i++)
for (j = i+1; j < ns; j++)
for (k = 0; k < sd; k++)
{
const double val1 = yp[sd * i + k];
const double val2 = yp[sd * j + k];
gsl_test_rel (val1, val2,
( GSL_MAX(err_target[i], err_target[j]) ),
"%s/%s oregonator",
T[i]->name, T[j]->name);
}
}
void
test_evolve_linear (const gsl_odeiv_step_type * T, double h, double err)
{
double y[1];
double yfin[1];
y[0] = 1.0;
yfin[0] = 9.0;
test_evolve_system (T, &rhs_func_lin, 0.0, 4.0, h, y, yfin, err,
"linear[0,4]");
}
void
test_evolve_exp (const gsl_odeiv_step_type * T, double h, double err)
{
double y[1];
double yfin[1];
y[0] = 1.0;
yfin[0] = exp (2.0);
test_evolve_system (T, &rhs_func_exp, 0.0, 2.0, h, y, yfin, err,
"exp[0,2]");
}
void
test_evolve_sin (const gsl_odeiv_step_type * T, double h, double err)
{
double y[2];
double yfin[2];
y[0] = 1.0;
y[1] = 0.0;
yfin[0] = cos (2.0);
yfin[1] = sin (2.0);
test_evolve_system (T, &rhs_func_sin, 0.0, 2.0, h, y, yfin, err,
"sine[0,2]");
}
void
test_evolve_xsin (const gsl_odeiv_step_type * T, double h, double err)
{
double y[2];
double yfin[2];
y[0] = 1.0;
y[1] = 0.0;
yfin[0] = cos (2.0);
yfin[1] = sin (2.0);
rhs_xsin_reset = 1;
jac_xsin_reset = 1;
test_evolve_system (T, &rhs_func_xsin, 0.0, 2.0, h, y, yfin, err,
"sine[0,2] w/errors");
}
void
test_evolve_stiff1 (const gsl_odeiv_step_type * T, double h, double err)
{
double y[2];
double yfin[2];
y[0] = 1.0;
y[1] = 0.0;
{
double arg = 1.0;
double e1 = exp (-arg);
double e2 = exp (-1000.0 * arg);
yfin[0] = 2.0 * e1 - e2;
yfin[1] = -e1 + e2;
}
test_evolve_system (T, &rhs_func_stiff, 0.0, 1.0, h, y, yfin, err,
"stiff[0,1]");
}
void
test_evolve_stiff5 (const gsl_odeiv_step_type * T, double h, double err)
{
double y[2];
double yfin[2];
y[0] = 1.0;
y[1] = 0.0;
{
double arg = 5.0;
double e1 = exp (-arg);
double e2 = exp (-1000.0 * arg);
yfin[0] = 2.0 * e1 - e2;
yfin[1] = -e1 + e2;
}
test_evolve_system (T, &rhs_func_stiff, 0.0, 5.0, h, y, yfin, err,
"stiff[0,5]");
}
/* Test cases from Frank Reininghaus <frank78ac@googlemail.com> */
int rhs_stepfn (double t, const double * y, double * dydt, void * params) {
if (t >= 1.0)
dydt [0] = 1;
else
dydt [0] = 0;
return GSL_SUCCESS;
}
void test_stepfn (void) {
/* infinite loop for epsabs = 1e-18, but not for 1e-17 */
double epsabs = 1e-18;
double epsrel = 1e-6;
const gsl_odeiv_step_type * T = gsl_odeiv_step_rk2;
gsl_odeiv_step * s = gsl_odeiv_step_alloc (T, 1);
gsl_odeiv_control * c = gsl_odeiv_control_y_new (epsabs, epsrel);
gsl_odeiv_evolve * e = gsl_odeiv_evolve_alloc (1);
gsl_odeiv_system sys = {rhs_stepfn, 0, 1, 0};
double t = 0.0;
double h = 1e-6;
double y = 0.0;
int i = 0;
int status;
while (t < 2.0 && i < 1000000) {
status = gsl_odeiv_evolve_apply (e, c, s, &sys, &t, 2, &h, &y);
#ifdef DEBUG
printf("i=%d status=%d t=%g h=%g y=%g\n", i, status, t, h, y);
#endif
if (status != GSL_SUCCESS)
break;
i++;
}
gsl_test_abs(t, 2.0, 1e-16, "evolve step function, t (stepfn/rk2)");
gsl_test_rel(y, 1.0, epsrel, "evolve step function, y (stepfn/rk2)");
gsl_odeiv_evolve_free (e);
gsl_odeiv_control_free (c);
gsl_odeiv_step_free (s);
}
int rhs_stepfn2 (double t, const double * y, double * dydt, void * params) {
if (t >= 0.0)
dydt [0] = 1e300;
else
dydt [0] = 0;
return GSL_SUCCESS;
}
void test_stepfn2 (void) {
/* infinite loop for epsabs = 1e-25, but not for 1e-24 */
double epsabs = 1e-25;
double epsrel = 1e-6;
const gsl_odeiv_step_type * T = gsl_odeiv_step_rk2;
gsl_odeiv_step * s = gsl_odeiv_step_alloc (T, 1);
gsl_odeiv_control * c = gsl_odeiv_control_y_new (epsabs, epsrel);
gsl_odeiv_evolve * e = gsl_odeiv_evolve_alloc (1);
gsl_odeiv_system sys = {rhs_stepfn2, 0, 1, 0};
double t = -1.0;
double h = 1e-6;
double y = 0.0;
int i = 0;
int status;
while (t < 1.0 && i < 10000) {
status = gsl_odeiv_evolve_apply (e, c, s, &sys, &t, 1.0, &h, &y);
#ifdef DEBUG
printf("i=%d status=%d t=%g h=%g y=%g\n", i, status, t, h, y);
#endif
if (status != GSL_SUCCESS)
break;
i++;
}
gsl_test_abs(t, 1.0, 1e-16, "evolve big step function, t (stepfn2/rk2)");
gsl_test_rel(y, 1e300, epsrel, "evolve big step function, y (stepfn2/rk2)");
gsl_odeiv_evolve_free (e);
gsl_odeiv_control_free (c);
gsl_odeiv_step_free (s);
}
int rhs_stepfn3 (double t, const double * y, double * dydt, void * params) {
static int calls = 0;
if (t >= 0.0)
dydt [0] = 1e300;
else
dydt [0] = 0;
calls++;
return (calls < 100000) ? GSL_SUCCESS : -999;
}
void test_stepfn3 (void) {
/* infinite loop for epsabs = 1e-26, but not for 1e-25 */
double epsabs = 1e-26;
double epsrel = 1e-6;
const gsl_odeiv_step_type * T = gsl_odeiv_step_rkf45;
gsl_odeiv_step * s = gsl_odeiv_step_alloc (T, 1);
gsl_odeiv_control * c = gsl_odeiv_control_y_new (epsabs, epsrel);
gsl_odeiv_evolve * e = gsl_odeiv_evolve_alloc (1);
gsl_odeiv_system sys = {rhs_stepfn3, 0, 1, 0};
double t = -1.0;
double h = 1e-6;
double y = 0.0;
int i = 0;
int status;
while (t < 1.0 && i < 10000) {
status = gsl_odeiv_evolve_apply (e, c, s, &sys, &t, 1.0, &h, &y);
#ifdef DEBUG
printf("i=%d status=%d t=%g h=%g y=%g\n", i, status, t, h, y);
#endif
if (status != GSL_SUCCESS)
break;
i++;
}
gsl_test_abs(t, 1.0, 1e-16, "evolve big step function, t (stepfn3/rkf45)");
gsl_test_rel(y, 1e300, epsrel, "evolve big step function, y (stepfn3/rkf45)");
gsl_odeiv_evolve_free (e);
gsl_odeiv_control_free (c);
gsl_odeiv_step_free (s);
}
int rhs_cos (double t, const double * y, double * dydt, void * params) {
dydt [0] = cos (t);
return GSL_SUCCESS;
}
int jac_cos (double t, const double y[], double *dfdy, double dfdt[],
void *params)
{
dfdy[0] = 0.0;
dfdt[0] = -sin(t);
return GSL_SUCCESS;
}
/* Test evolution in negative direction */
void
test_evolve_negative_h (const gsl_odeiv_step_type * T, double h, double err)
{
/* Tolerance factor in testing errors */
const double factor = 10;
gsl_odeiv_step * step = gsl_odeiv_step_alloc (T, 1);
gsl_odeiv_control * c = gsl_odeiv_control_standard_new (err, err, 1.0, 0.0);
gsl_odeiv_evolve * e = gsl_odeiv_evolve_alloc (1);
gsl_odeiv_system sys = {rhs_cos, jac_cos, 1, 0};
double t = 0;
double t1 = -4.0;
double y = 0.0;
double yfin = sin (t1);
/* Make initial h negative */
h = -fabs(h);
while (t > t1) {
int status = gsl_odeiv_evolve_apply (e, c, step, &sys, &t, t1, &h, &y);
if (status != GSL_SUCCESS)
{
gsl_test(status, "%s evolve_apply returned %d for negative h",
gsl_odeiv_step_name (step), status);
break;
}
}
gsl_test_abs (y, yfin, factor * e->count * err,
"evolution with negative h (using %s)",
gsl_odeiv_step_name (step));
gsl_odeiv_evolve_free (e);
gsl_odeiv_control_free (c);
gsl_odeiv_step_free (step);
}
int
main (void)
{
int i;
struct ptype
{
const gsl_odeiv_step_type *type;
double h;
}
p[20];
p[0].type = gsl_odeiv_step_rk2;
p[0].h = 1.0e-3;
p[1].type = gsl_odeiv_step_rk4;
p[1].h = 1.0e-3;
p[2].type = gsl_odeiv_step_rkf45;
p[2].h = 1.0e-3;
p[3].type = gsl_odeiv_step_rkck;
p[3].h = 1.0e-3;
p[4].type = gsl_odeiv_step_rk8pd;
p[4].h = 1.0e-3;
p[5].type = gsl_odeiv_step_rk2imp;
p[5].h = 1.0e-3;
p[6].type = gsl_odeiv_step_rk2simp;
p[6].h = 1.0e-3;
p[7].type = gsl_odeiv_step_rk4imp;
p[7].h = 1.0e-3;
p[8].type = gsl_odeiv_step_bsimp;
p[8].h = 1.0e-3;
p[9].type = gsl_odeiv_step_gear1;
p[9].h = 1.0e-3;
p[10].type = gsl_odeiv_step_gear2;
p[10].h = 1.0e-3;
p[11].type = 0;
gsl_ieee_env_setup ();
for (i = 0; p[i].type != 0; i++)
{
test_stepper(p[i].type);
}
for (i = 0; p[i].type != 0; i++)
{
test_evolve_linear (p[i].type, p[i].h, 1e-10);
test_evolve_exp (p[i].type, p[i].h, 1e-6);
test_evolve_sin (p[i].type, p[i].h, 1e-8);
test_evolve_xsin (p[i].type, p[i].h, 1e-8);
test_evolve_xsin (p[i].type, 0.1, 1e-8); /* test with large step size */
test_evolve_stiff1 (p[i].type, p[i].h, 1e-7);
test_evolve_stiff5 (p[i].type, p[i].h, 1e-7);
test_evolve_negative_h (p[i].type, p[i].h, 1e-7);
}
test_compare_vanderpol();
test_compare_oregonator();
test_stepfn();
test_stepfn2();
test_stepfn3();
exit (gsl_test_summary ());
}