<?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>実数または複素数の正定対称行列.</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>

    </refsection>

    <refsection>

        <title>参考文献</title>

        <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>

    </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>

