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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:ns5="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="kroneck" xml:lang="pt">
    <refnamediv>
        <refname>kroneck</refname>
        <refpurpose>forma de Kronecker de feixe de matrizes</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title> Seqüência de Chamamento </title>
        <synopsis>
            [Q, Z, Qd, Zd, numbeps, numbeta] = kroneck(F)
            [Q, Z, Qd, Zd, numbeps, numbeta] = kroneck(E,A)
        </synopsis>
    </refsynopsisdiv>
    <refsection role="parameters">
        <title>Parâmetros</title>
        <variablelist>
            <varlistentry>
                <term>F</term>
                <listitem>
                    <para>
                        feixe de matrizes de reais <literal>F=s*E-A</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>E,A</term>
                <listitem>
                    <para>duas matrizes de reais de mesma dimensão</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Q,Z</term>
                <listitem>
                    <para>duas matrizes quadradas ortogonais </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Qd,Zd</term>
                <listitem>
                    <para>dois vetores de inteiros </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>numbeps,numeta</term>
                <listitem>
                    <para>dois vetores de inteiros</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection role="description">
        <title>Descrição</title>
        <para>
            Forma de Kronecker de feixe de matrizes: <literal>kroneck</literal>
            computa duas matrizes ortogonais <literal>Q, Z</literal> que põem o feixe
            <literal>F=s*E -A</literal> na forma triangular superior:
        </para>
        <screen><![CDATA[
           | sE(eps)-A(eps) |        X       |      X     |      X        |
           |----------------|----------------|------------|---------------|
           |        O       | sE(inf)-A(inf) |      X     |      X        |
Q(sE-A)Z = |---------------------------------|----------------------------|
           |                |                |            |               |
           |        0       |       0        | sE(f)-A(f) |      X        |
           |--------------------------------------------------------------|
           |                |                |            |               |
           |        0       |       0        |      0     | sE(eta)-A(eta)|
 ]]></screen>
        <para>As dimensões dos quatro blocos são dadas por:</para>
        <para>
            <literal>eps=Qd(1) x Zd(1)</literal>, <literal>inf=Qd(2) x
                Zd(2)
            </literal>
            ,<literal>f = Qd(3) x Zd(3)</literal>,
            <literal>eta=Qd(4)xZd(4)</literal>
        </para>
        <para>
            O bloco <literal>inf</literal> contém modos infinitos de
            feixes.
        </para>
        <para>
            O bloco <literal>f</literal> contém modos finitos de feixes.
        </para>
        <para>A estrutura dos blocos epsilon e eta é dada por </para>
        <para>
            <literal>numbeps(1)</literal> = <literal>#</literal> de blocos eps
            de tamanho 0 x 1
        </para>
        <para>
            <literal>numbeps(2)</literal> = <literal>#</literal> de blocos eps
            de tamanho 1 x 2
        </para>
        <para>
            <literal>numbeps(3)</literal> = <literal>#</literal> de blocos eps
            de tamanho 2 x 3 etc...
        </para>
        <para>
            <literal>numbeta(1)</literal> = <literal>#</literal> de blocos eta
            de tamanho 1 x 0
        </para>
        <para>
            <literal>numbeta(2)</literal> = <literal>#</literal> de blocos eta
            de tamanho 2 x 1
        </para>
        <para>
            <literal>numbeta(3)</literal> = <literal>#</literal> de blocos eta
            de tamanho 3 x 2 etc...
        </para>
        <para>O código foi retirado de T. Beelen (Slicot-WGS group).</para>
    </refsection>
    <refsection role="examples">
        <title>Exemplos</title>
        <programlisting role="example"><![CDATA[
F = randpencil([1,1,2],[2,3],[-1,3,1],[0,3]);
Q = rand(17,17);
Z = rand(18,18);
F = Q*F*Z;
//feixe aleatório com eps1=1,eps2=1,eps3=1; 2 blocos J @ infty (infinito)
//com dimensões 2 e
//3 autovalores finitos em -1,3,1 e eta1=0,eta2=3
[Q, Z, Qd, Zd, numbeps, numbeta] = kroneck(F);
[Qd(1),Zd(1)]    //parte eps. é sum(epsi) x (sum(epsi) + número de epsi) (sum="soma")
[Qd(2),Zd(2)]    //parte infinita
[Qd(3),Zd(3)]    //parte finita
[Qd(4),Zd(4)]    //parte eta é (sum(etai) + number(eta1)) x sum(etai) (number=número)
numbeps
numbeta
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title> Ver Também</title>
        <simplelist type="inline">
            <member>
                <link linkend="schur">schur</link>
            </member>
            <member>
                <link linkend="spec">spec</link>
            </member>
            <member>
                <link linkend="systmat">systmat</link>
            </member>
            <member>
                <link linkend="pencan">pencan</link>
            </member>
            <member>
                <link linkend="randpencil">randpencil</link>
            </member>
            <member>
                <link linkend="trzeros">trzeros</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
