<?xml version="1.0" encoding="UTF-8"?>
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 * 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
 * along with this program.
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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="en" xml:id="colcomp">
    <refnamediv>
        <refname>colcomp</refname>
        <refpurpose>column compression, kernel, nullspace</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para>real or complex matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>flag</term>
                <listitem>
                    <para>character string</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>real number</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>W</term>
                <listitem>
                    <para>square non-singular matrix (change of basis)</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>rk</term>
                <listitem>
                    <para>
                        integer (rank of <literal>A</literal>)
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Column compression of <literal>A</literal>: <literal>Ac = A*W</literal> is
            column compressed i.e
        </para>
        <para>
            <literal>Ac=[0,Af]</literal> with <literal>Af</literal> full column rank,
            rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>.
        </para>
        <para>
            <literal>flag</literal> and <literal>tol</literal> are optional parameters: <literal>flag = 'qr'</literal>
            or <literal>'svd'</literal> (default is <literal>'svd'</literal>).
        </para>
        <para>
            <literal>tol</literal> = tolerance parameter (of order <literal>%eps</literal> as default value).
        </para>
        <para>
            The <literal>ma-rk</literal> first columns of <literal>W</literal> span the kernel of <literal>A</literal>
            when <literal>size(A)=(na,ma)</literal>
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=rand(5,2)*rand(2,5);
[X,r]=colcomp(A);
norm(A*X(:,1:$-r),1)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="rowcomp">rowcomp</link>
            </member>
            <member>
                <link linkend="fullrf">fullrf</link>
            </member>
            <member>
                <link linkend="fullrfk">fullrfk</link>
            </member>
            <member>
                <link linkend="kernel">kernel</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
