* Bug 15337 fixed: mistake in l_p definition in norm() page
[scilab.git] / scilab / modules / elementary_functions / help / pt_BR / 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:ns4="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="pt">
20     <refnamediv>
21         <refname>norm</refname>
22         <refpurpose>normas de um vetor ou uma matriz</refpurpose>
23     </refnamediv>
24     <refsynopsisdiv>
25         <title>Seqüência de Chamamento</title>
26         <synopsis>
27         y = norm(x)
28         y = norm(x, normType)
29         </synopsis>
30     </refsynopsisdiv>
31     <refsection>
32         <title>Parâmetros</title>
33         <variablelist>
34             <varlistentry>
35                 <term>x</term>
36                 <listitem>
37                     <para>vetor ou matriz de reais ou complexos (armazenamento cheio ou
38                         esparso)
39                     </para>
40                 </listitem>
41             </varlistentry>
42             <varlistentry>
43                 <term>normType</term>
44                     <para>
45                         <itemizedlist>
46                             <listitem>
47                                 For a matrix <literal>x</literal>: a number among
48                                 <literal>1, 2, %inf, -%inf</literal>, or a word among
49                                 <literal>"inf"</literal> (or <literal>"i"</literal>) or
50                                 <literal>"fro"</literal> (or <literal>"f"</literal>).
51                             </listitem>
52                             <listitem>
53                                 For a vector <literal>x</literal>: any number or <literal>%inf</literal>,
54                                 <literal>-%inf</literal>; or a word <literal>"inf"</literal>
55                                 (<literal>"i"</literal>), <literal>"fro"</literal> (<literal>"f"</literal>).
56                             </listitem>
57                         </itemizedlist>
58                     </para>
59                     Default value = 2.
60             </varlistentry>
61             <varlistentry>
62                 <term>y</term>
63                 <listitem>
64                     <para>
65                         norm: single positive real number.
66                     </para>
67                 </listitem>
68             </varlistentry>
69         </variablelist>
70     </refsection>
71     <refsection>
72         <title>Descrição</title>
73         <para>For matrices</para>
74         <variablelist>
75             <varlistentry>
76                 <term>norm(x)</term>
77                 <listitem>
78                     <para>
79                         ou <literal>norm(x,2)</literal> é o maior valor singular de
80                         <literal>x</literal> (<literal>max(svd(x))</literal>).
81                     </para>
82                 </listitem>
83             </varlistentry>
84             <varlistentry>
85                 <term>norm(x,1)</term>
86                 <listitem>
87                     <para>
88                         a norma l_1 de <literal>x</literal> (a maior soma coluna a
89                         coluna : <literal>max(sum(abs(x),'r'))</literal> ).
90                     </para>
91                 </listitem>
92             </varlistentry>
93             <varlistentry>
94                 <term>norm(x,'inf'),norm(x,%inf)</term>
95                 <listitem>
96                     <para>
97                         a norma infinitesimal de <literal>x</literal> (a maior soma
98                         linha a linha : <literal>max(sum(abs(x),'c'))</literal> ).
99                     </para>
100                 </listitem>
101             </varlistentry>
102             <varlistentry>
103                 <term>norm(x,'fro')</term>
104                 <listitem>
105                     <para>norma de Frobenius i.e.
106                         <literal>sqrt(sum(diag(x'*x)))</literal>
107                     </para>
108                 </listitem>
109             </varlistentry>
110         </variablelist>
111         <para>Para vetores </para>
112         <variablelist>
113             <varlistentry>
114                 <term>norm(v,p)</term>
115                 <listitem>
116                     <para>
117                         norma l_p <literal>sum(abs(v(i))^p)^(1/p)</literal> .
118                     </para>
119                 </listitem>
120             </varlistentry>
121             <varlistentry>
122                 <term>norm(v)</term>
123                 <listitem>
124                     <para>
125                         <literal>=norm(v,2)</literal> : norma l_2
126                     </para>
127                 </listitem>
128             </varlistentry>
129             <varlistentry>
130                 <term>norm(v,'inf')</term>
131                 <listitem>
132                     <para>
133                         <literal>max(abs(v(i)))</literal>.
134                     </para>
135                 </listitem>
136             </varlistentry>
137         </variablelist>
138     </refsection>
139     <refsection>
140         <title>Exemplos</title>
141         <programlisting role="example"><![CDATA[
142 A=[1,2,3];
143 norm(A,1)
144 norm(A,'inf')
145 A=[1,2;3,4]
146 max(svd(A)) - norm(A)
147
148 A=sparse([1 0 0 33 -1])
149 norm(A)
150  ]]></programlisting>
151     </refsection>
152     <refsection role="see also">
153         <title>Ver Também</title>
154         <simplelist type="inline">
155             <member>
156                 <link linkend="h_norm">h_norm</link>
157             </member>
158             <member>
159                 <link linkend="dhnorm">dhnorm</link>
160             </member>
161             <member>
162                 <link linkend="h2norm">h2norm</link>
163             </member>
164             <member>
165                 <link linkend="abs">abs</link>
166             </member>
167         </simplelist>
168     </refsection>
169 </refentry>