<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( https://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) INRIA -
 *
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
 * This file is hereby licensed under the terms of the GNU GPL v2.0,
 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
 * along with this program.
 *
 -->
<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="ja" xml:id="equil1">
    <refnamediv>
        <refname>equil1</refname>
        <refpurpose>行列の平衡 (非負定) の組</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>[T [,siz]]=equil1(P,Q [,tol])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>パラメータ</title>
        <variablelist>
            <varlistentry>
                <term>P, Q</term>
                <listitem>
                    <para>非負定の対称行列</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>T</term>
                <listitem>
                    <para>正則行列</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>siz</term>
                <listitem>
                    <para>3要素の整数ベクトル</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>閾値</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            <literal>equil1</literal> は次のような <literal>t</literal> を計算します:
        </para>
        <para>
            <literal>P1=T*P*T'</literal>  および <literal>Q1=inv(T)'*Q*inv(T)</literal>
            は以下のようになります:
        </para>
        <para>
            <literal>P1 = diag(S1,S2,0,0)</literal>  および <literal>Q1 = diag(S1,0,S3,0)</literal>
            ただし,
            <literal>S1,S2,S3</literal> は各次元が<literal>siz=[n1,n2,n3]</literal>の正定対角行列です.
        </para>
        <para>
            <literal>tol</literal> はSVDのランク定義の閾値です.
        </para>
    </refsection>
    <refsection>
        <title>例</title>
        <programlisting role="example"><![CDATA[
S1=rand(2,2);S1=S1*S1';
S2=rand(2,2);S2=S2*S2';
S3=rand(2,2);S3=S3*S3';
P=blockdiag(S1,S2,zeros(4,4));
Q=blockdiag(S1,zeros(2,2),S3,zeros(2,2));
X=rand(8,8);
P=X*P*X';Q=inv(X)'*Q*inv(X);
[T,siz]=equil1(P,Q);
P1=clean(T*P*T')
Q1=clean(inv(T)'*Q*inv(T))
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="balreal">balreal</link>
            </member>
            <member>
                <link linkend="minreal">minreal</link>
            </member>
            <member>
                <link linkend="equil">equil</link>
            </member>
            <member>
                <link linkend="hankelsv">hankelsv</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
