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<a name="Computing-the-rank"></a>
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Next: <a href="Sorting-Examples.html#Sorting-Examples" accesskey="n" rel="next">Sorting Examples</a>, Previous: <a href="Selecting-the-k-smallest-or-largest-elements.html#Selecting-the-k-smallest-or-largest-elements" accesskey="p" rel="previous">Selecting the k smallest or largest elements</a>, Up: <a href="Sorting.html#Sorting" accesskey="u" rel="up">Sorting</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<h3 class="section">12.4 Computing the rank</h3>

<p>The <em>rank</em> of an element is its order in the sorted data.  The rank
is the inverse of the index permutation, <var>p</var>.  It can be computed
using the following algorithm,
</p>
<div class="example">
<pre class="example">for (i = 0; i &lt; p-&gt;size; i++) 
{
    size_t pi = p-&gt;data[i];
    rank-&gt;data[pi] = i;
}
</pre></div>

<p>This can be computed directly from the function
<code>gsl_permutation_inverse(rank,p)</code>.
</p>
<p>The following function will print the rank of each element of the vector
<var>v</var>,
</p>
<div class="example">
<pre class="example">void
print_rank (gsl_vector * v)
{
  size_t i;
  size_t n = v-&gt;size;
  gsl_permutation * perm = gsl_permutation_alloc(n);
  gsl_permutation * rank = gsl_permutation_alloc(n);

  gsl_sort_vector_index (perm, v);
  gsl_permutation_inverse (rank, perm);

  for (i = 0; i &lt; n; i++)
   {
    double vi = gsl_vector_get(v, i);
    printf (&quot;element = %d, value = %g, rank = %d\n&quot;,
             i, vi, rank-&gt;data[i]);
   }

  gsl_permutation_free (perm);
  gsl_permutation_free (rank);
}
</pre></div>




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