<?xml version="1.0" encoding="UTF-8"?>
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 * Copyright (C) 2012 - 2016 - Scilab Enterprises
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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:ns3="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="fullrf" xml:lang="pt">
    <refnamediv>
        <refname>fullrf</refname>
        <refpurpose>fatoração de posto completo (ou cheio)</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title> Seqüência de Chamamento </title>
        <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Parâmetros</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para>matriz de reais ou complexos </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>número real (limiar para determinação do posto) </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Q,M</term>
                <listitem>
                    <para>matriz de reais ou complexos </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>rk</term>
                <listitem>
                    <para>
                        inteiro(posto de <literal>A</literal>)
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Descrição</title>
        <para>
            Fatoração de posto cheio : <literal>fullrf</literal> retorna
            <literal>Q</literal> e <literal>M</literal> tais que <literal>A =
                Q*M
            </literal>
            com Im(<literal>Q</literal>)=Im(<literal>A</literal>) e
            Nuc(<literal>M</literal>)=Nuc(<literal>A</literal>), <literal>Q</literal>
            de posto-coluna cheio, <literal>M</literal> de posto-linha cheio e
            <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>.
        </para>
        <para>
            <literal>tol</literal> é um parâmetro real opcional (valor real
            padrão é <literal>sqrt(%eps)</literal>). O posto <literal>rk</literal> de
            <literal>A</literal> é definido como o número de valores singulares
            maiores que <literal>norm(A)*tol</literal>.
        </para>
        <para>
            Se A é simétrica, <literal>fullrf</literal> retorna
            <literal>M=Q'</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Exemplos</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)) (span = "gerado")
 ]]></programlisting>
    </refsection>
    <refsection>
        <title> Ver Também </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>
