* Bug #13810 fixed - householder(v, k*v) returned column of %nan. Input parameters...
[scilab.git] / scilab / modules / linear_algebra / help / en_US / factorization / givens.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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16 <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="givens">
17     <refnamediv>
18         <refname>givens</refname>
19         <refpurpose>Givens transformation</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Calling Sequence</title>
23         <synopsis>U=givens(xy)
24             U=givens(x,y)
25             [U,c]=givens(xy)
26             [U,c]=givens(x,y)
27         </synopsis>
28     </refsynopsisdiv>
29     <refsection>
30         <title>Arguments</title>
31         <variablelist>
32             <varlistentry>
33                 <term>x,y</term>
34                 <listitem>
35                     <para>two real or complex numbers</para>
36                 </listitem>
37             </varlistentry>
38             <varlistentry>
39                 <term>xy</term>
40                 <listitem>
41                     <para> real or complex size 2 column vector</para>
42                 </listitem>
43             </varlistentry>
44             <varlistentry>
45                 <term>U</term>
46                 <listitem>
47                     <para>2x2 unitary matrix</para>
48                 </listitem>
49             </varlistentry>
50             <varlistentry>
51                 <term>c</term>
52                 <listitem>
53                     <para> real or complex size 2 column vector</para>
54                 </listitem>
55             </varlistentry>
56         </variablelist>
57     </refsection>
58     <refsection>
59         <title>Description</title>
60         <para>
61             <literal>U= givens(x, y)</literal> or <literal>U = givens(xy)</literal> with <literal>xy = [x;y]</literal>
62             returns a <literal>2</literal>x<literal>2</literal> unitary matrix <literal>U</literal> such that:
63         </para>
64         <para>
65             <literal>U*xy=[r;0]=c</literal>.
66         </para>
67         <para>
68             <note>
69                 Note that <literal>givens(x,y)</literal> and <literal>givens([x;y])</literal> are equivalent.
70             </note>
71         </para>
72     </refsection>
73     <refsection>
74         <title>Examples</title>
75         <programlisting role="example"><![CDATA[ 
76 A=[3,4;5,6];
77 U=givens(A(:,1));
78 U*A
79  ]]></programlisting>
80     </refsection>
81     <refsection role="see also">
82         <title>See Also</title>
83         <simplelist type="inline">
84             <member>
85                 <link linkend="qr">qr</link>
86             </member>
87         </simplelist>
88     </refsection>
89 </refentry>