<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( https://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) 2008 - INRIA
 *
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
 * This file is hereby licensed under the terms of the GNU GPL v2.0,
 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * 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.
 *
 -->
<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="fr" xml:id="colcomp">
    <refnamediv>
        <refname>colcomp</refname>
        <refpurpose>compression de colonnes, noyau  </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Séquence d'appel</title>
        <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Paramètres</title>
        <variablelist>
            <varlistentry>
                <term>A  </term>
                <listitem>
                    <para>matrice réelle ou complexe
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>flag  </term>
                <listitem>
                    <para>chaîne de caractères
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol  </term>
                <listitem>
                    <para>nombre réel
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>W  </term>
                <listitem>
                    <para>matrice carré régulière (matrice de changement de base)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>rk  </term>
                <listitem>
                    <para>
                        entier (rang de"<literal>A</literal>)
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Compression des colonnes de <literal>A</literal> : <literal>Ac = A*W</literal> est à colonnes compressées, c'est à dire
        </para>
        <para>
            <literal>Ac=[0,Af]</literal> et <literal>Af</literal> est de rang maximal
            rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>.
        </para>
        <para>
            <literal>flag</literal> et <literal>tol</literal> sont des paramètres optionnels : <literal>flag = 'qr'</literal>
            ou <literal>'svd'</literal> (<literal>'svd'</literal> par défaut).
        </para>
        <para>
            <literal>tol</literal> = paramètre de tolérance (de l'ordre de <literal>%eps</literal> par défaut).
        </para>
        <para>
            Les <literal>ma-rk</literal> premières colonnes de <literal>W</literal> forment une base du noyau de <literal>A</literal> quand <literal>size(A)=[na,ma]</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Exemples</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>Voir aussi</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>
