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The following program uses the Brent algorithm to find the minimum of the function f(x) = \cos(x) + 1, which occurs at x = \pi. The starting interval is (0,6), with an initial guess for the minimum of 2.
#include <stdio.h> #include <gsl/gsl_errno.h> #include <gsl/gsl_math.h> #include <gsl/gsl_min.h> double fn1 (double x, void * params) { (void)(params); /* avoid unused parameter warning */ return cos(x) + 1.0; } int main (void) { int status; int iter = 0, max_iter = 100; const gsl_min_fminimizer_type *T; gsl_min_fminimizer *s; double m = 2.0, m_expected = M_PI; double a = 0.0, b = 6.0; gsl_function F; F.function = &fn1; F.params = 0; T = gsl_min_fminimizer_brent; s = gsl_min_fminimizer_alloc (T); gsl_min_fminimizer_set (s, &F, m, a, b); printf ("using %s method\n", gsl_min_fminimizer_name (s)); printf ("%5s [%9s, %9s] %9s %10s %9s\n", "iter", "lower", "upper", "min", "err", "err(est)"); printf ("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n", iter, a, b, m, m - m_expected, b - a); do { iter++; 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); status = gsl_min_test_interval (a, b, 0.001, 0.0); if (status == GSL_SUCCESS) printf ("Converged:\n"); printf ("%5d [%.7f, %.7f] " "%.7f %+.7f %.7f\n", iter, a, b, m, m - m_expected, b - a); } while (status == GSL_CONTINUE && iter < max_iter); gsl_min_fminimizer_free (s); return status; }
Here are the results of the minimization procedure.
$ ./a.out
using brent method iter [ lower, upper] min err err(est) 0 [0.0000000, 6.0000000] 2.0000000 -1.1415927 6.0000000 1 [2.0000000, 6.0000000] 3.5278640 +0.3862713 4.0000000 2 [2.0000000, 3.5278640] 3.1748217 +0.0332290 1.5278640 3 [2.0000000, 3.1748217] 3.1264576 -0.0151351 1.1748217 4 [3.1264576, 3.1748217] 3.1414743 -0.0001183 0.0483641 5 [3.1414743, 3.1748217] 3.1415930 +0.0000004 0.0333474 Converged: 6 [3.1414743, 3.1415930] 3.1415927 +0.0000000 0.0001187