## Examples

The following program uses the Brent algorithm to find the minimum of the function @math{f(x) = \cos(x) + 1}, which occurs at @math{x = \pi}. The starting interval is @math{(0,6)}, with an initial guess for the minimum of @math{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)
{
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_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 %.7f\n",
iter, a, b,
m, m_expected, m - m_expected, b - a);
}
while (status == GSL_CONTINUE && iter < max_iter);

return status;
}


Here are the results of the minimization procedure.

bash\$ ./a.out
0 [0.0000000, 6.0000000] 2.0000000 -1.1415927 6.0000000
1 [2.0000000, 6.0000000] 3.2758640 +0.1342713 4.0000000
2 [2.0000000, 3.2831929] 3.2758640 +0.1342713 1.2831929
3 [2.8689068, 3.2831929] 3.2758640 +0.1342713 0.4142862
4 [2.8689068, 3.2831929] 3.2758640 +0.1342713 0.4142862
5 [2.8689068, 3.2758640] 3.1460585 +0.0044658 0.4069572
6 [3.1346075, 3.2758640] 3.1460585 +0.0044658 0.1412565
7 [3.1346075, 3.1874620] 3.1460585 +0.0044658 0.0528545
8 [3.1346075, 3.1460585] 3.1460585 +0.0044658 0.0114510
9 [3.1346075, 3.1460585] 3.1424060 +0.0008133 0.0114510
10 [3.1346075, 3.1424060] 3.1415885 -0.0000041 0.0077985
Converged:
11 [3.1415885, 3.1424060] 3.1415927 -0.0000000 0.0008175