/* roots/test.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Reid Priedhorsky, Brian Gough
*
* 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.
*/
#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_roots.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_ieee_utils.h>
#include "roots.h"
#include "test.h"
/* stopping parameters */
const double EPSREL = (10 * GSL_DBL_EPSILON);
const double EPSABS = (10 * GSL_DBL_EPSILON);
const unsigned int MAX_ITERATIONS = 150;
void my_error_handler (const char *reason, const char *file,
int line, int err);
#define WITHIN_TOL(a, b, epsrel, epsabs) \
((fabs((a) - (b)) < (epsrel) * GSL_MIN(fabs(a), fabs(b)) + (epsabs)))
int
main (void)
{
gsl_function F_sin, F_cos, F_func1, F_func2, F_func3, F_func4,
F_func5, F_func6;
gsl_function_fdf FDF_sin, FDF_cos, FDF_func1, FDF_func2, FDF_func3, FDF_func4,
FDF_func5, FDF_func6, FDF_func7;
const gsl_root_fsolver_type * fsolver[4] ;
const gsl_root_fdfsolver_type * fdfsolver[4] ;
const gsl_root_fsolver_type ** T;
const gsl_root_fdfsolver_type ** S;
gsl_ieee_env_setup();
fsolver[0] = gsl_root_fsolver_bisection;
fsolver[1] = gsl_root_fsolver_brent;
fsolver[2] = gsl_root_fsolver_falsepos;
fsolver[3] = 0;
fdfsolver[0] = gsl_root_fdfsolver_newton;
fdfsolver[1] = gsl_root_fdfsolver_secant;
fdfsolver[2] = gsl_root_fdfsolver_steffenson;
fdfsolver[3] = 0;
F_sin = create_function (sin_f) ;
F_cos = create_function (cos_f) ;
F_func1 = create_function (func1) ;
F_func2 = create_function (func2) ;
F_func3 = create_function (func3) ;
F_func4 = create_function (func4) ;
F_func5 = create_function (func5) ;
F_func6 = create_function (func6) ;
FDF_sin = create_fdf (sin_f, sin_df, sin_fdf) ;
FDF_cos = create_fdf (cos_f, cos_df, cos_fdf) ;
FDF_func1 = create_fdf (func1, func1_df, func1_fdf) ;
FDF_func2 = create_fdf (func2, func2_df, func2_fdf) ;
FDF_func3 = create_fdf (func3, func3_df, func3_fdf) ;
FDF_func4 = create_fdf (func4, func4_df, func4_fdf) ;
FDF_func5 = create_fdf (func5, func5_df, func5_fdf) ;
FDF_func6 = create_fdf (func6, func6_df, func6_fdf) ;
FDF_func7 = create_fdf(func7, func7_df, func7_fdf) ;
gsl_set_error_handler (&my_error_handler);
for (T = fsolver ; *T != 0 ; T++)
{
test_f (*T, "sin(x) [3, 4]", &F_sin, 3.0, 4.0, M_PI);
test_f (*T, "sin(x) [-4, -3]", &F_sin, -4.0, -3.0, -M_PI);
test_f (*T, "sin(x) [-1/3, 1]", &F_sin, -1.0 / 3.0, 1.0, 0.0);
test_f (*T, "cos(x) [0, 3]", &F_cos, 0.0, 3.0, M_PI / 2.0);
test_f (*T, "cos(x) [-3, 0]", &F_cos, -3.0, 0.0, -M_PI / 2.0);
test_f (*T, "x^20 - 1 [0.1, 2]", &F_func1, 0.1, 2.0, 1.0);
test_f (*T, "sqrt(|x|)*sgn(x)", &F_func2, -1.0 / 3.0, 1.0, 0.0);
test_f (*T, "x^2 - 1e-8 [0, 1]", &F_func3, 0.0, 1.0, sqrt (1e-8));
test_f (*T, "x exp(-x) [-1/3, 2]", &F_func4, -1.0 / 3.0, 2.0, 0.0);
test_f (*T, "(x - 1)^7 [0.9995, 1.0002]", &F_func6, 0.9995, 1.0002, 1.0);
test_f_e (*T, "invalid range check [4, 0]", &F_sin, 4.0, 0.0, M_PI);
test_f_e (*T, "invalid range check [1, 1]", &F_sin, 1.0, 1.0, M_PI);
test_f_e (*T, "invalid range check [0.1, 0.2]", &F_sin, 0.1, 0.2, M_PI);
}
for (S = fdfsolver ; *S != 0 ; S++)
{
test_fdf (*S,"sin(x) {3.4}", &FDF_sin, 3.4, M_PI);
test_fdf (*S,"sin(x) {-3.3}", &FDF_sin, -3.3, -M_PI);
test_fdf (*S,"sin(x) {0.5}", &FDF_sin, 0.5, 0.0);
test_fdf (*S,"cos(x) {0.6}", &FDF_cos, 0.6, M_PI / 2.0);
test_fdf (*S,"cos(x) {-2.5}", &FDF_cos, -2.5, -M_PI / 2.0);
test_fdf (*S,"x^{20} - 1 {0.9}", &FDF_func1, 0.9, 1.0);
test_fdf (*S,"x^{20} - 1 {1.1}", &FDF_func1, 1.1, 1.0);
test_fdf (*S,"sqrt(|x|)*sgn(x) {1.001}", &FDF_func2, 0.001, 0.0);
test_fdf (*S,"x^2 - 1e-8 {1}", &FDF_func3, 1.0, sqrt (1e-8));
test_fdf (*S,"x exp(-x) {-2}", &FDF_func4, -2.0, 0.0);
test_fdf_e (*S,"max iterations x -> +Inf, x exp(-x) {2}", &FDF_func4, 2.0, 0.0);
test_fdf_e (*S,"max iterations x -> -Inf, 1/(1 + exp(-x)) {0}", &FDF_func5, 0.0, 0.0);
test_fdf(*S, "-pi * x + e {1.5}", &FDF_func7, 1.5, M_E / M_PI);
}
test_fdf (gsl_root_fdfsolver_steffenson,
"(x - 1)^7 {0.9}", &FDF_func6, 0.9, 1.0);
/* now summarize the results */
exit (gsl_test_summary ());
}
/* Using gsl_root_bisection, find the root of the function pointed to by f,
using the interval [lower_bound, upper_bound]. Check if f succeeded and
that it was accurate enough. */
void
test_f (const gsl_root_fsolver_type * T, const char * description, gsl_function *f,
double lower_bound, double upper_bound, double correct_root)
{
int status;
size_t iterations = 0;
double r, a, b;
double x_lower, x_upper;
gsl_root_fsolver * s;
x_lower = lower_bound;
x_upper = upper_bound;
s = gsl_root_fsolver_alloc(T);
gsl_root_fsolver_set(s, f, x_lower, x_upper) ;
do
{
iterations++ ;
gsl_root_fsolver_iterate (s);
r = gsl_root_fsolver_root(s);
a = gsl_root_fsolver_x_lower(s);
b = gsl_root_fsolver_x_upper(s);
if (a > b)
gsl_test (GSL_FAILURE, "interval is invalid (%g,%g)", a, b);
if (r < a || r > b)
gsl_test (GSL_FAILURE, "r lies outside interval %g (%g,%g)", r, a, b);
status = gsl_root_test_interval (a,b, EPSABS, EPSREL);
}
while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS);
gsl_test (status, "%s, %s (%g obs vs %g expected) ",
gsl_root_fsolver_name(s), description,
gsl_root_fsolver_root(s), correct_root);
if (iterations == MAX_ITERATIONS)
{
gsl_test (GSL_FAILURE, "exceeded maximum number of iterations");
}
/* check the validity of the returned result */
if (!WITHIN_TOL (r, correct_root, EPSREL, EPSABS))
{
gsl_test (GSL_FAILURE, "incorrect precision (%g obs vs %g expected)",
r, correct_root);
}
gsl_root_fsolver_free(s);
}
void
test_f_e (const gsl_root_fsolver_type * T,
const char * description, gsl_function *f,
double lower_bound, double upper_bound, double correct_root)
{
int status;
size_t iterations = 0;
double x_lower, x_upper;
gsl_root_fsolver * s;
x_lower = lower_bound;
x_upper = upper_bound;
s = gsl_root_fsolver_alloc(T);
status = gsl_root_fsolver_set(s, f, x_lower, x_upper) ;
gsl_test (status != GSL_EINVAL, "%s (set), %s", T->name, description);
if (status == GSL_EINVAL)
{
gsl_root_fsolver_free(s);
return ;
}
do
{
iterations++ ;
gsl_root_fsolver_iterate (s);
x_lower = gsl_root_fsolver_x_lower(s);
x_upper = gsl_root_fsolver_x_lower(s);
status = gsl_root_test_interval (x_lower, x_upper,
EPSABS, EPSREL);
}
while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS);
gsl_test (!status, "%s, %s", gsl_root_fsolver_name(s), description,
gsl_root_fsolver_root(s) - correct_root);
gsl_root_fsolver_free(s);
}
void
test_fdf (const gsl_root_fdfsolver_type * T, const char * description,
gsl_function_fdf *fdf, double root, double correct_root)
{
int status;
size_t iterations = 0;
double prev = 0 ;
gsl_root_fdfsolver * s = gsl_root_fdfsolver_alloc(T);
gsl_root_fdfsolver_set (s, fdf, root) ;
do
{
iterations++ ;
prev = gsl_root_fdfsolver_root(s);
gsl_root_fdfsolver_iterate (s);
status = gsl_root_test_delta(gsl_root_fdfsolver_root(s), prev,
EPSABS, EPSREL);
}
while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS);
gsl_test (status, "%s, %s (%g obs vs %g expected) ",
gsl_root_fdfsolver_name(s), description,
gsl_root_fdfsolver_root(s), correct_root);
if (iterations == MAX_ITERATIONS)
{
gsl_test (GSL_FAILURE, "exceeded maximum number of iterations");
}
/* check the validity of the returned result */
if (!WITHIN_TOL (gsl_root_fdfsolver_root(s), correct_root,
EPSREL, EPSABS))
{
gsl_test (GSL_FAILURE, "incorrect precision (%g obs vs %g expected)",
gsl_root_fdfsolver_root(s), correct_root);
}
gsl_root_fdfsolver_free(s);
}
void
test_fdf_e (const gsl_root_fdfsolver_type * T,
const char * description, gsl_function_fdf *fdf,
double root, double correct_root)
{
int status;
size_t iterations = 0;
double prev = 0 ;
gsl_root_fdfsolver * s = gsl_root_fdfsolver_alloc(T);
status = gsl_root_fdfsolver_set (s, fdf, root) ;
gsl_test (status, "%s (set), %s", T->name, description);
do
{
iterations++ ;
prev = gsl_root_fdfsolver_root(s);
gsl_root_fdfsolver_iterate (s);
status = gsl_root_test_delta(gsl_root_fdfsolver_root(s), prev,
EPSABS, EPSREL);
}
while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS);
gsl_test (!status, "%s, %s", gsl_root_fdfsolver_name(s),
description, gsl_root_fdfsolver_root(s) - correct_root);
gsl_root_fdfsolver_free(s);
}
void
my_error_handler (const char *reason, const char *file, int line, int err)
{
if (0)
printf ("(caught [%s:%d: %s (%d)])\n", file, line, reason, err);
}