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<title>GNU Scientific Library &ndash; Reference Manual: Minimization Examples</title>

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<a name="Minimization-Examples"></a>
<div class="header">
<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> &nbsp; [<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">35.8 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 &lt;stdio.h&gt;
#include &lt;gsl/gsl_errno.h&gt;
#include &lt;gsl/gsl_math.h&gt;
#include &lt;gsl/gsl_min.h&gt;

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 = &amp;fn1;
  F.params = 0;

  T = gsl_min_fminimizer_brent;
  s = gsl_min_fminimizer_alloc (T);
  gsl_min_fminimizer_set (s, &amp;F, m, a, b);

  printf (&quot;using %s method\n&quot;,
          gsl_min_fminimizer_name (s));

  printf (&quot;%5s [%9s, %9s] %9s %10s %9s\n&quot;,
          &quot;iter&quot;, &quot;lower&quot;, &quot;upper&quot;, &quot;min&quot;,
          &quot;err&quot;, &quot;err(est)&quot;);

  printf (&quot;%5d [%.7f, %.7f] %.7f %+.7f %.7f\n&quot;,
          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 (&quot;Converged:\n&quot;);

      printf (&quot;%5d [%.7f, %.7f] &quot;
              &quot;%.7f %+.7f %.7f\n&quot;,
              iter, a, b,
              m, m - m_expected, b - a);
    }
  while (status == GSL_CONTINUE &amp;&amp; iter &lt; 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">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
</pre></div>




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