<?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="rank">

    <refnamediv>

        <refname>rank</refname>

        <refpurpose>階数</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[i]=rank(X)

            [i]=rank(X,tol)

        </synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>X</term>

                <listitem>

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

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>tol</term>

                <listitem>

                    <para>非負実数</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            <literal>rank(X)</literal> は, <literal>X</literal>の数値的な階数(ランク),

            すなわち, <literal>norm(size(X),'inf') * norm(X) * %eps</literal> より大きな

            X の特異値の数です.

        </para>

        <para>
            <literal>rank(X,tol)</literal> は,<literal>tol</literal>
            より大きな<literal>X</literal>の特異値の数です.
        </para>
        <para><literal>rank([])</literal> returns 0.</para>
        <para>
          <note>
            <literal>tol</literal> のデフォルト値は
            <literal>norm(X)</literal>に比例することに注意してください.
            結果として,<literal>rank([1.d-80,0;0,1.d-80])</literal> は 2 になります!.
          </note>
        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
rank([1.d-80,0;0,1.d-80])
rank([1,0;0,1.d-80])
 ]]></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="rowcomp">rowcomp</link>

            </member>

            <member>

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

            </member>

            <member>

                <link linkend="lu">lu</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

