* Bug 15337 fixed: mistake in l_p definition in norm() page
[scilab.git] / scilab / modules / elementary_functions / help / fr_FR / matrixoperations / norm.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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16 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
17           xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
18           xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
19           xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="fr">
20     <refnamediv>
21         <refname>norm</refname>
22         <refpurpose>normes d'un vecteur ou d'une matrice</refpurpose>
23     </refnamediv>
24     <refsynopsisdiv>
25         <title>Séquence d'appel</title>
26         <synopsis>
27         y = norm(x)
28         y = norm(x, normType)
29         </synopsis>
30     </refsynopsisdiv>
31     <refsection>
32         <title>Paramètres</title>
33         <variablelist>
34             <varlistentry>
35                 <term>x</term>
36                 <listitem>
37                     <para>vecteur ou matrice (réelle ou complexe, pleine ou creuse)
38                     </para>
39                 </listitem>
40             </varlistentry>
41             <varlistentry>
42                 <term>normType</term>
43                 <listitem>
44                     <para>
45                         <itemizedlist>
46                             <listitem>
47                                 Matrice <literal>x</literal>: un nombre parmi
48                                 <literal>1, 2, %inf, -%inf</literal>, ou un mot parmi
49                                 <literal>"inf"</literal> (ou <literal>"i"</literal>) ou
50                                 <literal>"fro"</literal> (ou <literal>"f"</literal>).
51                             </listitem>
52                             <listitem>
53                                 Vecteur <literal>x</literal>: un nombre réel quelconque ou
54                                 <literal>%inf</literal>,
55                                 <literal>-%inf</literal>; ou mot <literal>"inf"</literal>
56                                 (<literal>"i"</literal>), <literal>"fro"</literal>
57                                 (<literal>"f"</literal>).
58                             </listitem>
59                         </itemizedlist>
60                     </para>
61                     Valeur par défaut : 2.
62                 </listitem>
63             </varlistentry>
64             <varlistentry>
65                 <term>y</term>
66                 <listitem>
67                     <para>
68                         norme : nombre réel positif unique.
69                     </para>
70                 </listitem>
71             </varlistentry>
72         </variablelist>
73     </refsection>
74     <refsection>
75         <title>Description</title>
76         <para>Pour les matrices</para>
77         <variablelist>
78             <varlistentry>
79                 <term>norm(x)</term>
80                 <listitem>
81                     <para>
82                         où <literal>norm(x,2)</literal> est la plus grande valeur
83                         singulière de <literal>x</literal>
84                         (<literal>max(svd(x))</literal>).
85                     </para>
86                 </listitem>
87             </varlistentry>
88             <varlistentry>
89                 <term>norm(x,1) renvoie</term>
90                 <listitem>
91                     <para>
92                         la norme l_1 de <literal>x</literal> (la plus grande somme
93                         suivant les colonnes : <literal>max(sum(abs(x),'r'))</literal>
94                         ).
95                     </para>
96                 </listitem>
97             </varlistentry>
98             <varlistentry>
99                 <term>norm(x,'inf'),norm(x,%inf)</term>
100                 <listitem>
101                     <para>
102                         la norme infinie de <literal>x</literal> (la plus grande somme
103                         suivant les lignes : <literal>max(sum(abs(x),'c'))</literal>
104                         ).
105                     </para>
106                 </listitem>
107             </varlistentry>
108             <varlistentry>
109                 <term>norm(x,'fro')</term>
110                 <listitem>
111                     <para>
112                         la norme de Frobenius de <literal>x</literal> c'est à dire
113                         <literal>sqrt(sum(diag(x'*x)))</literal>
114                     </para>
115                 </listitem>
116             </varlistentry>
117         </variablelist>
118         <para>Pour les vecteurs</para>
119         <variablelist>
120             <varlistentry>
121                 <term>norm(v,p)</term>
122                 <listitem>
123                     <para>
124                         norme l_p <literal>sum(abs(v(i))^p)^(1/p)</literal> .
125                     </para>
126                 </listitem>
127             </varlistentry>
128             <varlistentry>
129                 <term>norm(v)</term>
130                 <listitem>
131                     <para>
132                         <literal>=norm(v,2)</literal> : norme euclidienne
133                     </para>
134                 </listitem>
135             </varlistentry>
136             <varlistentry>
137                 <term>norm(v,'inf')</term>
138                 <listitem>
139                     <para>
140                         <literal>max(abs(v(i)))</literal>.
141                     </para>
142                 </listitem>
143             </varlistentry>
144         </variablelist>
145     </refsection>
146     <refsection>
147         <title>Exemples</title>
148         <programlisting role="example"><![CDATA[
149 A = [1,2,3];
150 norm(A,1)
151 norm(A,'inf')
152 A = [1,2;3,4]
153 max(svd(A)) - norm(A)
154
155 A = sparse([1 0 0 33 -1])
156 norm(A)
157  ]]></programlisting>
158     </refsection>
159     <refsection role="see also">
160         <title>Voir aussi</title>
161         <simplelist type="inline">
162             <member>
163                 <link linkend="h_norm">h_norm</link>
164             </member>
165             <member>
166                 <link linkend="dhnorm">dhnorm</link>
167             </member>
168             <member>
169                 <link linkend="h2norm">h2norm</link>
170             </member>
171             <member>
172                 <link linkend="abs">abs</link>
173             </member>
174         </simplelist>
175     </refsection>
176 </refentry>