<?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="ja" xml:id="chol">
    <refnamediv>
        <refname>chol</refname>
        <refpurpose>コレスキー分解</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>R = chol(X)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>引数</title>
        <variablelist>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>正方正定値実対称行列または複素ハーミティアン行列.</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            <literal>X</literal> が正定の場合, <literal>R = chol(X)</literal> は,
            <literal>R'*R = X</literal>となるような
            上三角行列<literal>R</literal>を出力します.
        </para>
        <para>
            <literal>chol(X)</literal> は<literal>X</literal>の対角項
            と上三角部のみを使用します.
            下三角部は上三角部の転置(複素共役)とみなされます.
        </para>
        <note>
          <para>
              コレスキー分解はLapackルーチン DPOTRF (実数行列の場合)および ZPOTRF (複素行列の場合)
              に基づきます.
          </para>
        </note>
    </refsection>
    <refsection>
        <title>例</title>
        <programlisting role="example"><![CDATA[
W = rand(5,5) + %i*rand(5,5);
X = W*W';
R = chol(X)
norm(R'*R-X)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="spchol">spchol</link>
            </member>
            <member>
                <link linkend="qr">qr</link>
            </member>
            <member>
                <link linkend="svd">svd</link>
            </member>
            <member>
                <link linkend="bdiag">bdiag</link>
            </member>
            <member>
                <link linkend="fullrf">fullrf</link>
            </member>
        </simplelist>
    </refsection>
</refentry>