<?xml version="1.0" encoding="UTF-8"?>
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 * 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
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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="en" xml:id="rank">
    <refnamediv>
        <refname>rank</refname>
        <refpurpose>rank</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>[i]=rank(X)
            [i]=rank(X,tol)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>real or complex matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>nonnegative real number</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>rank(X)</literal> is the numerical rank of <literal>X</literal>
            i.e. the number of singular values of X that are larger than
            <literal>norm(size(X),'inf') * norm(X) * %eps</literal>.
        </para>
        <para>
            <literal>rank(X,tol)</literal> is the number of singular values of
            <literal>X</literal> that are larger than <literal>tol</literal>.
        </para>
        <para><literal>rank([])</literal> returns 0.</para>
        <para>
            <note>
                The default value of <literal>tol</literal> is proportional to
                <literal>norm(X)</literal>. As a consequence
                <literal>rank([1.d-80,0;0,1.d-80])</literal> is 2 !.
            </note>
        </para>
    </refsection>
    <refsection>
        <title>Examples</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>See also</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>
