1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Created by GNU Texinfo 6.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Octave: Basic Usage</title>
<meta name="description" content="GNU Octave: Basic Usage">
<meta name="keywords" content="GNU Octave: Basic Usage">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="Diagonal-and-Permutation-Matrices.html#Diagonal-and-Permutation-Matrices" rel="up" title="Diagonal and Permutation Matrices">
<link href="Creating-Diagonal-Matrices.html#Creating-Diagonal-Matrices" rel="next" title="Creating Diagonal Matrices">
<link href="Diagonal-and-Permutation-Matrices.html#Diagonal-and-Permutation-Matrices" rel="prev" title="Diagonal and Permutation Matrices">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.indentedblock {margin-right: 0em}
blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smalllisp {margin-left: 3.2em}
kbd {font-style: oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nolinebreak {white-space: nowrap}
span.roman {font-family: initial; font-weight: normal}
span.sansserif {font-family: sans-serif; font-weight: normal}
ul.no-bullet {list-style: none}
-->
</style>
</head>
<body lang="en">
<a name="Basic-Usage"></a>
<div class="header">
<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>
</div>
<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>Built-in Function: <em><var>val</var> =</em> <strong>disable_diagonal_matrix</strong> <em>()</em></dt>
<dt><a name="index-disable_005fdiagonal_005fmatrix-1"></a>Built-in Function: <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>Built-in Function: <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>Built-in Function: <em><var>val</var> =</em> <strong>disable_permutation_matrix</strong> <em>()</em></dt>
<dt><a name="index-disable_005fpermutation_005fmatrix-1"></a>Built-in Function: <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>Built-in Function: <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>
</table>
<hr>
<div class="header">
<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>
</div>
</body>
</html>
|
