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<a name="Basic-Usage"></a>
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<p>
Next: <a href="Matrix-Algebra.html#Matrix-Algebra" accesskey="n" rel="next">Matrix Algebra</a>, Up: <a href="Diagonal-and-Permutation-Matrices.html#Diagonal-and-Permutation-Matrices" accesskey="u" rel="up">Diagonal and Permutation Matrices</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Creating-and-Manipulating-Diagonal_002fPermutation-Matrices"></a>
<h3 class="section">21.1 Creating and Manipulating Diagonal/Permutation Matrices</h3>
<p>A diagonal matrix is defined as a matrix that has zero entries outside the main
diagonal; that is,
<code>D(i,j) == 0</code> if <code>i != j</code>.
Most often, square diagonal matrices are considered; however, the definition
can equally be applied to non-square matrices, in which case we usually speak
of a rectangular diagonal matrix.
</p>
<p>A permutation matrix is defined as a square matrix that has a single element
equal to unity in each row and each column; all other elements are zero. That
is, there exists a permutation (vector)
<code>p</code> such that <code>P(i,j) == 1</code> if <code>j == p(i)</code> and
<code>P(i,j) == 0</code> otherwise.
</p>
<p>Octave provides special treatment of real and complex rectangular diagonal
matrices, as well as permutation matrices. They are stored as special objects,
using efficient storage and algorithms, facilitating writing both readable and
efficient matrix algebra expressions in the Octave language. The special
treatment may be disabled by using the functions <em>disable_diagonal_matrix</em>
and <em>disable_permutation_matrix</em>.
</p>
<a name="XREFdisable_005fdiagonal_005fmatrix"></a><dl>
<dt><a name="index-disable_005fdiagonal_005fmatrix"></a><em><var>val</var> =</em> <strong>disable_diagonal_matrix</strong> <em>()</em></dt>
<dt><a name="index-disable_005fdiagonal_005fmatrix-1"></a><em><var>old_val</var> =</em> <strong>disable_diagonal_matrix</strong> <em>(<var>new_val</var>)</em></dt>
<dt><a name="index-disable_005fdiagonal_005fmatrix-2"></a><em></em> <strong>disable_diagonal_matrix</strong> <em>(<var>new_val</var>, "local")</em></dt>
<dd><p>Query or set the internal variable that controls whether diagonal
matrices are stored in a special space-efficient format.
</p>
<p>The default value is true. If this option is disabled Octave will store
diagonal matrices as full matrices.
</p>
<p>When called from inside a function with the <code>"local"</code> option, the
variable is changed locally for the function and any subroutines it calls.
The original variable value is restored when exiting the function.
</p>
<p><strong>See also:</strong> <a href="Ranges.html#XREFdisable_005frange">disable_range</a>, <a href="#XREFdisable_005fpermutation_005fmatrix">disable_permutation_matrix</a>.
</p></dd></dl>
<a name="XREFdisable_005fpermutation_005fmatrix"></a><dl>
<dt><a name="index-disable_005fpermutation_005fmatrix"></a><em><var>val</var> =</em> <strong>disable_permutation_matrix</strong> <em>()</em></dt>
<dt><a name="index-disable_005fpermutation_005fmatrix-1"></a><em><var>old_val</var> =</em> <strong>disable_permutation_matrix</strong> <em>(<var>new_val</var>)</em></dt>
<dt><a name="index-disable_005fpermutation_005fmatrix-2"></a><em></em> <strong>disable_permutation_matrix</strong> <em>(<var>new_val</var>, "local")</em></dt>
<dd><p>Query or set the internal variable that controls whether permutation
matrices are stored in a special space-efficient format.
</p>
<p>The default value is true. If this option is disabled Octave will store
permutation matrices as full matrices.
</p>
<p>When called from inside a function with the <code>"local"</code> option, the
variable is changed locally for the function and any subroutines it calls.
The original variable value is restored when exiting the function.
</p>
<p><strong>See also:</strong> <a href="Ranges.html#XREFdisable_005frange">disable_range</a>, <a href="#XREFdisable_005fdiagonal_005fmatrix">disable_diagonal_matrix</a>.
</p></dd></dl>
<p>The space savings are significant as demonstrated by the following code.
</p>
<div class="example">
<pre class="example">x = diag (rand (10, 1));
xf = full (x);
sizeof (x)
⇒ 80
sizeof (xf)
⇒ 800
</pre></div>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">• <a href="Creating-Diagonal-Matrices.html#Creating-Diagonal-Matrices" accesskey="1">Creating Diagonal Matrices</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="Creating-Permutation-Matrices.html#Creating-Permutation-Matrices" accesskey="2">Creating Permutation Matrices</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="Explicit-and-Implicit-Conversions.html#Explicit-and-Implicit-Conversions" accesskey="3">Explicit and Implicit Conversions</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
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<p>
Next: <a href="Matrix-Algebra.html#Matrix-Algebra" accesskey="n" rel="next">Matrix Algebra</a>, Up: <a href="Diagonal-and-Permutation-Matrices.html#Diagonal-and-Permutation-Matrices" accesskey="u" rel="up">Diagonal and Permutation Matrices</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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