<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( http://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="glever">
    <refnamediv>
        <refname>glever</refname>
        <refpurpose>inverse d'un faisceau de matrices  </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Séquence d'appel</title>
        <synopsis>[Bfs,Bis,chis]=glever(E,A [,s])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Paramètres</title>
        <variablelist>
            <varlistentry>
                <term>E, A  </term>
                <listitem>
                    <para>matrices carrées réelles de même dimensions
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>s  </term>
                <listitem>
                    <para>
                        chaîne de caractères (indéterminée des polynômes, '<literal>s</literal>' par défaut )
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Bfs,Bis  </term>
                <listitem>
                    <para>deux matrices polynomiales
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>chis  </term>
                <listitem>
                    <para>polynôme
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Calcul de
        </para>
        <para>
            (s*E-A)^-1
        </para>
        <para>
            par l'algorithme généralisé de Leverrier pour un faisceau de matrices.
        </para>
        <programlisting role=""><![CDATA[
(s*E-A)^-1 = (Bfs/chis) - Bis.
 ]]></programlisting>
        <para>
            <literal>chis</literal> = polynôme caractéristique (à une constante multiplicative près).
        </para>
        <para>
            <literal>Bfs</literal>  = matrice polynomiale de numérateurs
        </para>
        <para>
            <literal>Bis</literal>
            = matrice polynomiale ( - développement de <literal>(s*E-A)^-1</literal> à l'infini).
        </para>
        <para>
            Noter le signe - devant <literal>Bis</literal>.
        </para>
        <para>
        </para>
    </refsection>
    <refsection>
        <title>Attention</title>
        <para>
            Cette fonction utilise <literal>cleanp</literal> pour simplifier <literal>Bfs,Bis</literal> et <literal>chis</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Exemples</title>
        <programlisting role="example"><![CDATA[
s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1];
[Bfs,Bis,chis]=glever(F)
inv(F)-((Bfs/chis) - Bis)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>Voir aussi</title>
        <simplelist type="inline">
            <member>
                <link linkend="rowshuff">rowshuff</link>
            </member>
            <member>
                <link linkend="det">det</link>
            </member>
            <member>
                <link linkend="invr">invr</link>
            </member>
            <member>
                <link linkend="coffg">coffg</link>
            </member>
            <member>
                <link linkend="pencan">pencan</link>
            </member>
            <member>
                <link linkend="penlaur">penlaur</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
