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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
-->
<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" version="5.0-subset Scilab" xml:lang="fr" xml:id="colcomp">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<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>
<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>
<refsection>
<title>Auteurs</title>
<para>F.D.; </para>
</refsection>
</refentry>
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