<?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: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="psmall" xml:lang="pt">
    <refnamediv>
        <refname>psmall</refname>
        <refpurpose>projeção espectral</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>[Q,M]=psmall(A,thres,flag)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Parameters</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para>matriz quadrada de reais </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>thres</term>
                <listitem>
                    <para>número real </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>flag</term>
                <listitem>
                    <para>
                        string (<literal>'c'</literal> ou
                        <literal>'d'</literal>)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Q,M</term>
                <listitem>
                    <para>matrizes de reais</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>Projeção sobre auto-subespaço associado com autovalores com parte
            real &lt; <literal>thres</literal> (<literal>flag='c'</literal>) ou com
            módulo &lt; <literal>thres</literal> (<literal>flag='d'</literal>).
        </para>
        <para>
            A projeção é definda por <literal>Q*M</literal>,
            <literal>Q</literal> é de posto-coluna cheio, <literal>M</literal> é de
            posto-linha cheio e <literal>M*Q=eye</literal>.
        </para>
        <para>
            Se <literal>flag='c'</literal>, os autovalores de
            <literal>M*A*Q</literal> = autovalores de <literal>A</literal> com parte
            real &lt; <literal>thres</literal>.
        </para>
        <para>
            Se <literal>flag='d'</literal>, os autovalores de
            <literal>M*A*Q</literal> = autovalores de <literal>A</literal> com
            magnitude &lt; <literal>thres</literal>.
        </para>
        <para>
            Se <literal>flag='c'</literal> e se <literal>[Q1,M1]</literal> =
            fatoração em posto cheio (<literal>fullrf</literal>) de
            <literal>eye()-Q*M</literal>então os autovalores de
            <literal>M1*A*Q1</literal> = autovalores de<literal> A</literal> com parte
            real &gt;= <literal>thres</literal>.
        </para>
        <para>
            Se <literal>flag='d'</literal> e se <literal>[Q1,M1]</literal> =
            fatoração em posto cheio (<literal>fullrf</literal>) de
            <literal>eye()-Q*M</literal> então os autovalores de
            <literal>M1*A*Q1</literal> = autovalores de <literal>A</literal> com
            magnitude &gt;= <literal>thres</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
[Q,M]=psmall(A,2.5,'d');
spec(M*A*Q)
[Q1,M1]=fullrf(eye()-Q*M);
spec(M1*A*Q1)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="pbig">pbig</link>
            </member>
            <member>
                <link linkend="proj">proj</link>
            </member>
            <member>
                <link linkend="projspec">projspec</link>
            </member>
        </simplelist>
    </refsection>
    <refsection>
        <title>Used Functions</title>
        <para>Esta função é baseada na forma de Schur ordenada (Função do
            Scilab<literal> schur</literal>).
        </para>
    </refsection>
</refentry>
