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<a name="Computing-the-rank"></a>
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<a name="Computing-the-rank-1"></a>
<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 < p->size; i++)
{
size_t pi = p->data[i];
rank->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->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 < n; i++)
{
double vi = gsl_vector_get(v, i);
printf ("element = %d, value = %g, rank = %d\n",
i, vi, rank->data[i]);
}
gsl_permutation_free (perm);
gsl_permutation_free (rank);
}
</pre></div>
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