Massive indent of all codes:
[scilab.git] / scilab / modules / linear_algebra / help / en_US / factorization / householder.xml
1     <?xml version="1.0" encoding="UTF-8"?>
2     <!--
3  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4  * Copyright (C) 2008 - INRIA
5  * 
6  * This file must be used under the terms of the CeCILL.
7  * This source file is licensed as described in the file COPYING, which
8  * you should have received as part of this distribution.  The terms
9  * are also available at    
10  * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
11  *
12  -->
13     <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="householder">
14         <refnamediv>
15             <refname>householder</refname>
16             <refpurpose>Householder orthogonal reflexion matrix</refpurpose>
17         </refnamediv>
18         <refsynopsisdiv>
19             <title>Calling Sequence</title>
20             <synopsis>u=householder(v [,w])</synopsis>
21         </refsynopsisdiv>
22         <refsection>
23             <title>Arguments</title>
24             <variablelist>
25                 <varlistentry>
26                     <term>v</term>
27                     <listitem>
28                         <para>real or complex column vector</para>
29                     </listitem>
30                 </varlistentry>
31                 <varlistentry>
32                     <term>w</term>
33                     <listitem>
34                         <para>
35                             real or complex column vector with same size as <literal>v</literal>. Default value is <literal>eye(v)</literal>
36                         </para>
37                     </listitem>
38                 </varlistentry>
39                 <varlistentry>
40                     <term>u</term>
41                     <listitem>
42                         <para>real or complex column vector</para>
43                     </listitem>
44                 </varlistentry>
45             </variablelist>
46         </refsection>
47         <refsection>
48             <title>Description</title>
49             <para>
50                 given 2 column vectors <literal>v</literal>, <literal> w</literal> of same size, <literal>householder(v,w)</literal> returns a unitary 
51                 column vector <literal>u</literal>, such that <literal> (eye()-2*u*u')*v</literal> is proportional to <literal>w</literal>.
52                 <literal>(eye()-2*u*u')</literal> is the orthogonal Householder reflexion matrix .
53             </para>
54             <para>
55                 <literal>w</literal> default value is <literal> eye(v)</literal>. In this case vector <literal> (eye()-2*u*u')*v</literal> is the 
56                 vector  <literal> eye(v)*norm(v)</literal>.
57             </para>
58         </refsection>
59         <refsection role="see also">
60             <title>See Also</title>
61             <simplelist type="inline">
62                 <member>
63                     <link linkend="qr">qr</link>
64                 </member>
65                 <member>
66                     <link linkend="givens">givens</link>
67                 </member>
68             </simplelist>
69         </refsection>
70     </refentry>