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<a name="Applying-Permutations"></a>
<div class="header">
<p>
Next: <a href="Reading-and-writing-permutations.html#Reading-and-writing-permutations" accesskey="n" rel="next">Reading and writing permutations</a>, Previous: <a href="Permutation-functions.html#Permutation-functions" accesskey="p" rel="previous">Permutation functions</a>, Up: <a href="Permutations.html#Permutations" accesskey="u" rel="up">Permutations</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Applying-Permutations-1"></a>
<h3 class="section">9.6 Applying Permutations</h3>

<dl>
<dt><a name="index-gsl_005fpermute"></a>Function: <em>int</em> <strong>gsl_permute</strong> <em>(const size_t * <var>p</var>, double * <var>data</var>, size_t <var>stride</var>, size_t <var>n</var>)</em></dt>
<dd><p>This function applies the permutation <var>p</var> to the array <var>data</var> of
size <var>n</var> with stride <var>stride</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fpermute_005finverse"></a>Function: <em>int</em> <strong>gsl_permute_inverse</strong> <em>(const size_t * <var>p</var>, double * <var>data</var>, size_t <var>stride</var>, size_t <var>n</var>)</em></dt>
<dd><p>This function applies the inverse of the permutation <var>p</var> to the
array <var>data</var> of size <var>n</var> with stride <var>stride</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fpermute_005fvector"></a>Function: <em>int</em> <strong>gsl_permute_vector</strong> <em>(const gsl_permutation * <var>p</var>, gsl_vector * <var>v</var>)</em></dt>
<dd><p>This function applies the permutation <var>p</var> to the elements of the
vector <var>v</var>, considered as a row-vector acted on by a permutation
matrix from the right, <em>v' = v P</em>.  The <em>j</em>-th column of the
permutation matrix <em>P</em> is given by the <em><var>p</var>_j</em>-th column of the
identity matrix. The permutation <var>p</var> and the vector <var>v</var> must
have the same length.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fpermute_005fvector_005finverse"></a>Function: <em>int</em> <strong>gsl_permute_vector_inverse</strong> <em>(const gsl_permutation * <var>p</var>, gsl_vector * <var>v</var>)</em></dt>
<dd><p>This function applies the inverse of the permutation <var>p</var> to the
elements of the vector <var>v</var>, considered as a row-vector acted on by
an inverse permutation matrix from the right, <em>v' = v P^T</em>.  Note
that for permutation matrices the inverse is the same as the transpose.
The <em>j</em>-th column of the permutation matrix <em>P</em> is given by
the <em><var>p</var>_j</em>-th column of the identity matrix. The permutation <var>p</var>
and the vector <var>v</var> must have the same length.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fpermute_005fmatrix"></a>Function: <em>int</em> <strong>gsl_permute_matrix</strong> <em>(const gsl_permutation * <var>p</var>, gsl_matrix * <var>A</var>)</em></dt>
<dd><p>This function applies the permutation <var>p</var> to the matrix <var>A</var> from
the right, <em>A' = A P</em>.  The <em>j</em>-th column of the
permutation matrix <em>P</em> is given by the <em><var>p</var>_j</em>-th column of the
identity matrix. This effectively permutes the columns of <var>A</var> according
to the permutation <var>p</var>, and so the number of columns of <var>A</var> must
equal the size of the permutation <var>p</var>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fpermutation_005fmul"></a>Function: <em>int</em> <strong>gsl_permutation_mul</strong> <em>(gsl_permutation * <var>p</var>, const gsl_permutation * <var>pa</var>, const gsl_permutation * <var>pb</var>)</em></dt>
<dd><p>This function combines the two permutations <var>pa</var> and <var>pb</var> into a
single permutation <var>p</var>, where <em><var>p</var> = <var>pa</var> * <var>pb</var></em>. 
The permutation <var>p</var> is equivalent to applying <var>pb</var> first and
then <var>pa</var>.
</p></dd></dl>

<hr>
<div class="header">
<p>
Next: <a href="Reading-and-writing-permutations.html#Reading-and-writing-permutations" accesskey="n" rel="next">Reading and writing permutations</a>, Previous: <a href="Permutation-functions.html#Permutation-functions" accesskey="p" rel="previous">Permutation functions</a>, Up: <a href="Permutations.html#Permutations" accesskey="u" rel="up">Permutations</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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