<?xml version="1.0" encoding="UTF-8"?>
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<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">
    <refnamediv>
        <refname>equil</refname>
        <refpurpose>balancing of pair of symmetric matrices</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>T = equil(P, Q)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>P, Q</term>
                <listitem>
                    <para>two positive definite symmetric matrices</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>T</term>
                <listitem>
                    <para>nonsingular matrix</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>equil</literal> returns <literal>t</literal> such that:
        </para>
        <para>
            <literal>T*P*T'</literal> and  <literal>inv(T)'*Q*inv(T)</literal>  are both equal to a same
            diagonal and positive matrix.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
P=rand(4,4);P=P*P';
Q=rand(4,4);Q=Q*Q';
T=equil(P,Q)
clean(T*P*T')
clean(inv(T)'*Q*inv(T))
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="equil1">equil1</link>
            </member>
            <member>
                <link linkend="balanc">balanc</link>
            </member>
            <member>
                <link linkend="ctr_gram">ctr_gram</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
