/* min/test.c * * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 #include #include #include #include #include #include #include "test.h" #include "min.h" /* stopping parameters */ const double EPSABS = 0.001 ; const double EPSREL = 0.001 ; const unsigned int MAX_ITERATIONS = 100; 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_cos, F_func1, F_func2, F_func3, F_func4; const gsl_min_fminimizer_type * fminimizer[4] ; const gsl_min_fminimizer_type ** T; gsl_ieee_env_setup (); fminimizer[0] = gsl_min_fminimizer_goldensection; fminimizer[1] = gsl_min_fminimizer_brent; fminimizer[2] = gsl_min_fminimizer_quad_golden; fminimizer[3] = 0; F_cos = create_function (f_cos) ; F_func1 = create_function (func1) ; F_func2 = create_function (func2) ; F_func3 = create_function (func3) ; F_func4 = create_function (func4) ; gsl_set_error_handler (&my_error_handler); for (T = fminimizer ; *T != 0 ; T++) { test_f (*T, "cos(x) [0 (3) 6]", &F_cos, 0.0, 3.0, 6.0, M_PI); test_f (*T, "x^4 - 1 [-3 (-1) 17]", &F_func1, -3.0, -1.0, 17.0, 0.0); test_f (*T, "sqrt(|x|) [-2 (-1) 1.5]", &F_func2, -2.0, -1.0, 1.5, 0.0); test_f (*T, "func3(x) [-2 (3) 4]", &F_func3, -2.0, 3.0, 4.0, 1.0); test_f (*T, "func4(x) [0 (0.782) 1]", &F_func4, 0, 0.782, 1.0, 0.8); test_f_e (*T, "invalid range check [4, 0]", &F_cos, 4.0, 3.0, 0.0, M_PI); test_f_e (*T, "invalid range check [1, 1]", &F_cos, 1.0, 1.0, 1.0, M_PI); test_f_e (*T, "invalid range check [-1, 1]", &F_cos, -1.0, 0.0, 1.0, M_PI); } test_bracket("cos(x) [1,2]",&F_cos,1.0,2.0,15); test_bracket("sqrt(|x|) [-1,0]",&F_func2,-1.0,0.0,15); test_bracket("sqrt(|x|) [-1,-0.6]",&F_func2,-1.0,-0.6,15); test_bracket("sqrt(|x|) [-1,1]",&F_func2,-1.0,1.0,15); exit (gsl_test_summary ()); } void test_f (const gsl_min_fminimizer_type * T, const char * description, gsl_function *f, double lower_bound, double middle, double upper_bound, double correct_minimum) { int status; size_t iterations = 0; double m, a, b; double x_lower, x_upper; gsl_min_fminimizer * s; x_lower = lower_bound; x_upper = upper_bound; s = gsl_min_fminimizer_alloc (T) ; gsl_min_fminimizer_set (s, f, middle, x_lower, x_upper) ; do { iterations++ ; status = gsl_min_fminimizer_iterate (s); m = gsl_min_fminimizer_x_minimum(s); a = gsl_min_fminimizer_x_lower(s); b = gsl_min_fminimizer_x_upper(s); #ifdef DEBUG printf("%.12f %.18f %.12f %.18f %.12f %.18f status=%d\n", a, GSL_FN_EVAL(f, a), m, GSL_FN_EVAL(f, m), b, GSL_FN_EVAL(f, b), status); #endif if (a > b) gsl_test (GSL_FAILURE, "interval is invalid (%g,%g)", a, b); if (m < a || m > b) gsl_test (GSL_FAILURE, "m lies outside interval %g (%g,%g)", m, a, b); if (status) break ; status = gsl_min_test_interval (a, b, EPSABS, EPSREL); } while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS); gsl_test (status, "%s, %s (%g obs vs %g expected) ", gsl_min_fminimizer_name(s), description, gsl_min_fminimizer_x_minimum(s), correct_minimum); /* check the validity of the returned result */ if (!WITHIN_TOL (m, correct_minimum, EPSREL, EPSABS)) { gsl_test (GSL_FAILURE, "incorrect precision (%g obs vs %g expected)", m, correct_minimum); } gsl_min_fminimizer_free (s); } void test_f_e (const gsl_min_fminimizer_type * T, const char * description, gsl_function *f, double lower_bound, double middle, double upper_bound, double correct_minimum) { int status; size_t iterations = 0; double x_lower, x_upper; double a, b; gsl_min_fminimizer * s; x_lower = lower_bound; x_upper = upper_bound; s = gsl_min_fminimizer_alloc (T) ; status = gsl_min_fminimizer_set (s, f, middle, x_lower, x_upper) ; if (status != GSL_SUCCESS) { gsl_min_fminimizer_free (s) ; gsl_test (status == GSL_SUCCESS, "%s, %s", T->name, description); return ; } do { iterations++ ; gsl_min_fminimizer_iterate (s); a = gsl_min_fminimizer_x_lower(s); b = gsl_min_fminimizer_x_upper(s); status = gsl_min_test_interval (a, b, EPSABS, EPSREL); } while (status == GSL_CONTINUE && iterations < MAX_ITERATIONS); gsl_test (!status, "%s, %s", gsl_min_fminimizer_name(s), description, gsl_min_fminimizer_x_minimum(s) - correct_minimum); gsl_min_fminimizer_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); } int test_bracket (const char * description,gsl_function *f,double lower_bound, double upper_bound, unsigned int max) { int status; double x_lower, x_upper; double f_upper,f_lower,f_minimum; double x_minimum; x_lower=lower_bound; x_upper=upper_bound; SAFE_FUNC_CALL (f,x_lower,&f_lower); SAFE_FUNC_CALL (f,x_upper,&f_upper); status=gsl_min_find_bracket(f,&x_minimum,&f_minimum,&x_lower,&f_lower,&x_upper,&f_upper,max); gsl_test (status,"%s, interval: [%g,%g], values: (%g,%g), minimum at: %g, value: %g", description,x_lower,x_upper,f_lower,f_upper,x_minimum,f_minimum); return status; }