<?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:ns4="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="spaninter" xml:lang="pt">
    <refnamediv>
        <refname>spaninter</refname>
        <refpurpose>interseção de subespaços</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title> Seqüência de Chamamento</title>
        <synopsis>[X,dim]=spaninter(A,B [,tol])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Parâmetros</title>
        <variablelist>
            <varlistentry>
                <term>A, B</term>
                <listitem>
                    <para>duas matrizes de reais ou de complexos com igual número de
                        linhas
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>matriz quadrada ortogonal ou unitária</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>dim</term>
                <listitem>
                    <para>
                        inteiro, dimensão do subesbaço Im(<literal>A</literal>) inter
                        Im(<literal>B</literal>)
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Descrição</title>
        <para>
            Computa a intereseção de Im(<literal>A</literal>) e
            Im(<literal>B</literal>).
        </para>
        <para>
            As primeiras <literal>dim</literal> colunas de <literal>X</literal>
            geram esta interseção i.e. <literal>X(:,1:dim)</literal> é uma base
            ortogonal para
        </para>
        <para>
            Im(<literal>A</literal>) inter Im(<literal>B</literal>)
        </para>
        <para>
            Na base <literal>X</literal>, <literal>A</literal> e
            <literal>B</literal> são respectivamente representados por:
        </para>
        <para>
            <literal>X'*A</literal> e <literal>X'*B</literal>.
        </para>
        <para>
            <literal>tol</literal> é um limiar (<literal>sqrt(%eps)</literal> é
            o valor padrão).
        </para>
    </refsection>
    <refsection>
        <title>Exemplos</title>
        <programlisting role="example"><![CDATA[
A=rand(5,3)*rand(3,4);     // A é 5 x 4, rank=3
B=[A(:,2),rand(5,1)]*rand(2,2);
[X,dim]=spaninter(A,B);
X1=X(:,1:dim);    //A interseção
svd(A),svd([X1,A])   // X1 no gerado(A) (span(A))
svd(B),svd([B,X1])   // X1 no gerado(B) (span(B))
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>Ver Também</title>
        <simplelist type="inline">
            <member>
                <link linkend="spanplus">spanplus</link>
            </member>
            <member>
                <link linkend="spantwo">spantwo</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
