### 35.8 Examples

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