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<title>GNU Scientific Library – Reference Manual: Minimization Examples</title>
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<a name="Minimization-Examples"></a>
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<p>
Next: <a href="Minimization-References-and-Further-Reading.html#Minimization-References-and-Further-Reading" accesskey="n" rel="next">Minimization References and Further Reading</a>, Previous: <a href="Minimization-Algorithms.html#Minimization-Algorithms" accesskey="p" rel="previous">Minimization Algorithms</a>, Up: <a href="One-dimensional-Minimization.html#One-dimensional-Minimization" accesskey="u" rel="up">One dimensional Minimization</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Examples-25"></a>
<h3 class="section">34.8 Examples</h3>
<p>The following program uses the Brent algorithm to find the minimum of
the function <em>f(x) = \cos(x) + 1</em>, which occurs at <em>x = \pi</em>.
The starting interval is <em>(0,6)</em>, with an initial guess for the
minimum of <em>2</em>.
</p>
<div class="example">
<pre class="verbatim">#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_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;
}
</pre></div>
<p>Here are the results of the minimization procedure.
</p>
<div class="smallexample">
<pre class="smallexample">$ ./a.out
</pre><pre class="verbatim"> 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
</pre></div>
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