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<title>GNU Scientific Library &ndash; Reference Manual: Interpolation Example programs</title>

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<a name="Interpolation-Example-programs"></a>
<div class="header">
<p>
Next: <a href="Interpolation-References-and-Further-Reading.html#Interpolation-References-and-Further-Reading" accesskey="n" rel="next">Interpolation References and Further Reading</a>, Previous: <a href="Higher_002dlevel-Interface.html#Higher_002dlevel-Interface" accesskey="p" rel="previous">Higher-level Interface</a>, Up: <a href="Interpolation.html#Interpolation" accesskey="u" rel="up">Interpolation</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Examples-19"></a>
<h3 class="section">27.7 Examples</h3>

<p>The following program demonstrates the use of the interpolation and
spline functions.  It computes a cubic spline interpolation of the
10-point dataset <em>(x_i, y_i)</em> where <em>x_i = i + \sin(i)/2</em> and
<em>y_i = i + \cos(i^2)</em> for <em>i = 0 \dots 9</em>.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;math.h&gt;
#include &lt;gsl/gsl_errno.h&gt;
#include &lt;gsl/gsl_spline.h&gt;

int
main (void)
{
  int i;
  double xi, yi, x[10], y[10];

  printf (&quot;#m=0,S=2\n&quot;);

  for (i = 0; i &lt; 10; i++)
    {
      x[i] = i + 0.5 * sin (i);
      y[i] = i + cos (i * i);
      printf (&quot;%g %g\n&quot;, x[i], y[i]);
    }

  printf (&quot;#m=1,S=0\n&quot;);

  {
    gsl_interp_accel *acc 
      = gsl_interp_accel_alloc ();
    gsl_spline *spline 
      = gsl_spline_alloc (gsl_interp_cspline, 10);

    gsl_spline_init (spline, x, y, 10);

    for (xi = x[0]; xi &lt; x[9]; xi += 0.01)
      {
        yi = gsl_spline_eval (spline, xi, acc);
        printf (&quot;%g %g\n&quot;, xi, yi);
      }
    gsl_spline_free (spline);
    gsl_interp_accel_free (acc);
  }
  return 0;
}
</pre></div>

<p>The output is designed to be used with the <small>GNU</small> plotutils
<code>graph</code> program,
</p>
<div class="example">
<pre class="example">$ ./a.out &gt; interp.dat
$ graph -T ps &lt; interp.dat &gt; interp.ps
</pre></div>


<p>The result shows a smooth interpolation of the original points.  The
interpolation method can be changed simply by varying the first argument of
<code>gsl_spline_alloc</code>.
</p>
<p>The next program demonstrates a periodic cubic spline with 4 data
points.  Note that the first and last points must be supplied with 
the same y-value for a periodic spline.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;math.h&gt;
#include &lt;gsl/gsl_errno.h&gt;
#include &lt;gsl/gsl_spline.h&gt;

int
main (void)
{
  int N = 4;
  double x[4] = {0.00, 0.10,  0.27,  0.30};
  double y[4] = {0.15, 0.70, -0.10,  0.15}; 
             /* Note: y[0] == y[3] for periodic data */

  gsl_interp_accel *acc = gsl_interp_accel_alloc ();
  const gsl_interp_type *t = gsl_interp_cspline_periodic; 
  gsl_spline *spline = gsl_spline_alloc (t, N);

  int i; double xi, yi;

  printf (&quot;#m=0,S=5\n&quot;);
  for (i = 0; i &lt; N; i++)
    {
      printf (&quot;%g %g\n&quot;, x[i], y[i]);
    }

  printf (&quot;#m=1,S=0\n&quot;);
  gsl_spline_init (spline, x, y, N);

  for (i = 0; i &lt;= 100; i++)
    {
      xi = (1 - i / 100.0) * x[0] + (i / 100.0) * x[N-1];
      yi = gsl_spline_eval (spline, xi, acc);
      printf (&quot;%g %g\n&quot;, xi, yi);
    }
  
  gsl_spline_free (spline);
  gsl_interp_accel_free (acc);
  return 0;
}
</pre></div>


<p>The output can be plotted with <small>GNU</small> <code>graph</code>.
</p>
<div class="example">
<pre class="example">$ ./a.out &gt; interp.dat
$ graph -T ps &lt; interp.dat &gt; interp.ps
</pre></div>


<p>The result shows a periodic interpolation of the original points. The
slope of the fitted curve is the same at the beginning and end of the
data, and the second derivative is also.
</p>
<hr>
<div class="header">
<p>
Next: <a href="Interpolation-References-and-Further-Reading.html#Interpolation-References-and-Further-Reading" accesskey="n" rel="next">Interpolation References and Further Reading</a>, Previous: <a href="Higher_002dlevel-Interface.html#Higher_002dlevel-Interface" accesskey="p" rel="previous">Higher-level Interface</a>, Up: <a href="Interpolation.html#Interpolation" accesskey="u" rel="up">Interpolation</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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