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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="equil">
17     <refnamediv>
18         <refname>equil</refname>
19         <refpurpose>balancing of pair of symmetric matrices</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Calling Sequence</title>
23         <synopsis>T=equil(P,Q)</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Arguments</title>
27         <variablelist>
28             <varlistentry>
29                 <term>P, Q</term>
30                 <listitem>
31                     <para>two positive definite symmetric matrices</para>
32                 </listitem>
33             </varlistentry>
34             <varlistentry>
35                 <term>T</term>
36                 <listitem>
37                     <para>nonsingular matrix</para>
38                 </listitem>
39             </varlistentry>
40         </variablelist>
41     </refsection>
42     <refsection>
43         <title>Description</title>
44         <para>
45             <literal>equil</literal> returns <literal>t</literal> such that:
46         </para>
47         <para>
48             <literal>T*P*T'</literal> and  <literal>inv(T)'*Q*inv(T)</literal>  are both equal to a same 
49             diagonal and positive matrix.
50         </para>
51     </refsection>
52     <refsection>
53         <title>Examples</title>
54         <programlisting role="example"><![CDATA[ 
55 P=rand(4,4);P=P*P';
56 Q=rand(4,4);Q=Q*Q';
57 T=equil(P,Q)
58 clean(T*P*T')
59 clean(inv(T)'*Q*inv(T))
60  ]]></programlisting>
61     </refsection>
62     <refsection role="see also">
63         <title>See Also</title>
64         <simplelist type="inline">
65             <member>
66                 <link linkend="equil1">equil1</link>
67             </member>
68             <member>
69                 <link linkend="balanc">balanc</link>
70             </member>
71             <member>
72                 <link linkend="ctr_gram">ctr_gram</link>
73             </member>
74         </simplelist>
75     </refsection>
76 </refentry>