<?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="fullrf">

    <refnamediv>

        <refname>fullrf</refname>

        <refpurpose>フルランク分解</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>A</term>

                <listitem>

                    <para>実数または複素数の行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>tol</term>

                <listitem>

                    <para>実数 (ランク定義時の閾値)</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Q,M</term>

                <listitem>

                    <para>実数または複素数の行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>rk</term>

                <listitem>

                    <para>

                        整数 (<literal>A</literal>のランク)

                    </para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            フルランク分解 : <literal>fullrf</literal> は,

            <literal>A = Q*M</literal>となるような

            <literal>Q</literal> および <literal>M</literal>を返します.

            ただし,

            range(<literal>Q</literal>)=range(<literal>A</literal>) および

            ker(<literal>M</literal>)=ker(<literal>A</literal>),

            <literal>Q</literal> フル列ランク , <literal>M</literal> フル行ランク,

            <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>です.

        </para>

        <para>

            <literal>tol</literal> はオプションの実数パラメータです

            (デフォルト値は <literal>sqrt(%eps)</literal>です).

            <literal>A</literal>のランク<literal>rk</literal>は

            <literal>norm(A)*tol</literal>より大きな

            特異値の数として定義されます.

        </para>

        <para>

            Aが対称の場合,

            <literal>fullrf</literal> は <literal>M=Q'</literal>を返します.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
A=rand(5,2)*rand(2,5);
[Q,M]=fullrf(A);
norm(Q*M-A,1)
[X,d]=rowcomp(A);Y=X';
svd([A,Y(:,1:d),Q])        //span(Q) = span(A) = span(Y(:,1:2))
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="svd">svd</link>

            </member>

            <member>

                <link linkend="qr">qr</link>

            </member>

            <member>

                <link linkend="fullrfk">fullrfk</link>

            </member>

            <member>

                <link linkend="rowcomp">rowcomp</link>

            </member>

            <member>

                <link linkend="colcomp">colcomp</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

