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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="ja" xml:id="im_inv">

    <refnamediv>

        <refname>im_inv</refname>

        <refpurpose>原像</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[X,dim]=im_inv(A,B [,tol])

            [X,dim,Y]=im_inv(A,B, [,tol])

        </synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>A,B</term>

                <listitem>

                    <para>同じ列の数を有する実数または複素数行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>X</term>

                <listitem>

                    <para>

                        次数が<literal>A</literal>の列の数に等しい直交またはユニタリ正方行列

                    </para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>dim</term>

                <listitem>

                    <para>整数 (部分空間の次元)</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Y</term>

                <listitem>

                    <para>

                        次数が<literal>A</literal>および<literal>B</literal>の行の数に等しい直交行列.

                    </para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            <literal>[X,dim]=im_inv(A,B)</literal> は <literal>(A^-1)(B)</literal>,

            すなわち, <literal>A</literal>への像が range(<literal>B</literal>) に

            あるベクトルを計算します.

        </para>

        <para>

            <literal>X</literal>の最初の列 <literal>dim</literal> は

            <literal>(A^-1)(B)</literal>に広がっています.

        </para>

        <para>

            <literal>tol</literal> は部分空間の取り込みを確認するために

            閾値が使用されており,

            そのデフォルト値は <literal>tol = 100*%eps</literal> です.

            <literal>Y</literal> が返される時,

            <literal>[Y*A*X,Y*B]</literal> は以下のように分割されます:

            <literal>[A11,A12;0,A22]</literal>,<literal>[B1;0]</literal>

        </para>

        <para>

            ただし, <literal>B1</literal>は行フルランク  (

            <literal>rank(B)</literal>に等しい) そして <literal>A22</literal> は

            列フルランクで <literal>dim</literal> 列となります.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)];
W=rand(5,5);A=W*A;B=W*B;
[X,dim]=im_inv(A,B)
svd([A*X(:,1:dim),B])   //vectors A*X(:,1:dim) belong to range(B)
[X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B]
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="rowcomp">rowcomp</link>

            </member>

            <member>

                <link linkend="spaninter">spaninter</link>

            </member>

            <member>

                <link linkend="spanplus">spanplus</link>

            </member>

            <member>

                <link linkend="linsolve">linsolve</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

