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  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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modules/elementary_functions/help/fr_FR/matrixoperations/norm.xml
 
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<?xml version="1.0" encoding="UTF-8"?>
 
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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:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:id="norm" xml:lang="fr">
 
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    <refnamediv>
 
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        <refname>norm</refname>
 
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        <refpurpose>normes matricielles</refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Séquence d'appel</title>
 
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        <synopsis>[y]=norm(x [,flag])</synopsis>
 
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    </refsynopsisdiv>
 
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    <refsection>
 
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        <title>Paramètres</title>
 
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        <variablelist>
 
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            <varlistentry>
 
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                <term>x</term>
 
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                <listitem>
 
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                    <para>vecteur ou matrice (réelle ou complexe, pleine ou
 
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                        creuse)
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>flag</term>
 
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                <listitem>
 
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                    <para>chaîne de caractères (type de la norme, 2 par défaut)</para>
 
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                </listitem>
 
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            </varlistentry>
 
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        </variablelist>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Description</title>
 
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        <para>Pour les matrices</para>
 
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        <variablelist>
 
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            <varlistentry>
 
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                <term>norm(x)</term>
 
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                <listitem>
 
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                    <para>
 
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                        où <literal>norm(x,2)</literal> est la plus grande valeur
 
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                        singulière de <literal>x</literal>
 
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                        (<literal>max(svd(x))</literal>).
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>norm(x,1) renvoie</term>
 
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                <listitem>
 
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                    <para>
 
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                        la norme l_1 de <literal>x</literal> (la plus grande somme
 
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                        suivant les colonnes : <literal>max(sum(abs(x),'r'))</literal>
 
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                        ).
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>norm(x,'inf'),norm(x,%inf)</term>
 
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                <listitem>
 
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                    <para>
 
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                        la norme infinie de <literal>x</literal> (la plus grande somme
 
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                        suivant les lignes : <literal>max(sum(abs(x),'c'))</literal>
 
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                        ).
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>norm(x,'fro')</term>
 
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                <listitem>
 
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                    <para>
 
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                        la norme de Frobenius de <literal>x</literal> c'est à dire
 
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                        <literal>sqrt(sum(diag(x'*x)))</literal>
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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        </variablelist>
 
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        <para>Pour les vecteurs</para>
 
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        <variablelist>
 
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            <varlistentry>
 
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                <term>norm(v,p)</term>
 
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                <listitem>
 
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                    <para>
 
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                        norme l_p (<literal>sum(v(i)^p))^(1/p)</literal> .
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>norm(v)</term>
 
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                <listitem>
 
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                    <para>
 
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                        <literal>=norm(v,2)</literal> : norme euclidienne
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>norm(v,'inf')</term>
 
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                <listitem>
 
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                    <para>
 
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                        <literal>max(abs(v(i)))</literal>.
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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        </variablelist>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Exemples</title>
 
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        <programlisting role="example"><![CDATA[ 
 
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A=[1,2,3];
 
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norm(A,1)
 
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norm(A,'inf')
 
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A=[1,2;3,4]
 
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max(svd(A))-norm(A)
 
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A=sparse([1 0 0 33 -1])
 
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norm(A)
 
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 ]]></programlisting>
 
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    </refsection>
 
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    <refsection role="see also">
 
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        <title>Voir aussi</title>
 
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        <simplelist type="inline">
 
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            <member>
 
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                <link linkend="h_norm">h_norm</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="dhnorm">dhnorm</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="h2norm">h2norm</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="abs">abs</link>
 
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            </member>
 
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        </simplelist>
 
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    </refsection>
 
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</refentry>