4aca6ad472168aee14e4b343ad635a5f1b88fa97
[scilab.git] / scilab / modules / elementary_functions / help / pt_BR / matrixoperations / norm.xml
1 <?xml version="1.0" encoding="ISO-8859-1"?>
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16 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="pt">
17     <refnamediv>
18         <refname>norm</refname>
19         <refpurpose>norma de matrizes</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Seqüência de Chamamento</title>
23         <synopsis>[y]=norm(x [,flag])</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Parâmetros</title>
27         <variablelist>
28             <varlistentry>
29                 <term>x</term>
30                 <listitem>
31                     <para>vetor ou matriz de reais ou complexos (armazenamento cheio ou
32                         esparso)
33                     </para>
34                 </listitem>
35             </varlistentry>
36             <varlistentry>
37                 <term>flag</term>
38                 <listitem>
39                     <para>string (tipo da norma) (valor padrão = 2)</para>
40                 </listitem>
41             </varlistentry>
42         </variablelist>
43     </refsection>
44     <refsection>
45         <title>Descrição</title>
46         <para>For matrices</para>
47         <variablelist>
48             <varlistentry>
49                 <term>norm(x)</term>
50                 <listitem>
51                     <para>
52                         ou <literal>norm(x,2)</literal> é o maior valor singular de
53                         <literal>x</literal> (<literal>max(svd(x))</literal>).
54                     </para>
55                 </listitem>
56             </varlistentry>
57             <varlistentry>
58                 <term>norm(x,1)</term>
59                 <listitem>
60                     <para>
61                         a norma l_1 de <literal>x</literal> (a maior soma coluna a
62                         coluna : <literal>max(sum(abs(x),'r'))</literal> ).
63                     </para>
64                 </listitem>
65             </varlistentry>
66             <varlistentry>
67                 <term>norm(x,'inf'),norm(x,%inf)</term>
68                 <listitem>
69                     <para>
70                         a norma infinitesimal de <literal>x</literal> (a maior soma
71                         linha a linha : <literal>max(sum(abs(x),'c'))</literal> ).
72                     </para>
73                 </listitem>
74             </varlistentry>
75             <varlistentry>
76                 <term>norm(x,'fro')</term>
77                 <listitem>
78                     <para>norma de Frobenius i.e.
79                         <literal>sqrt(sum(diag(x'*x)))</literal>
80                     </para>
81                 </listitem>
82             </varlistentry>
83         </variablelist>
84         <para>Para vetores </para>
85         <variablelist>
86             <varlistentry>
87                 <term>norm(v,p)</term>
88                 <listitem>
89                     <para>
90                         norma l_p (<literal>sum(v(i)^p))^(1/p)</literal> .
91                     </para>
92                 </listitem>
93             </varlistentry>
94             <varlistentry>
95                 <term>norm(v)</term>
96                 <listitem>
97                     <para>
98                         <literal>=norm(v,2)</literal> : norma l_2
99                     </para>
100                 </listitem>
101             </varlistentry>
102             <varlistentry>
103                 <term>norm(v,'inf')</term>
104                 <listitem>
105                     <para>
106                         <literal>max(abs(v(i)))</literal>.
107                     </para>
108                 </listitem>
109             </varlistentry>
110         </variablelist>
111     </refsection>
112     <refsection>
113         <title>Exemplos</title>
114         <programlisting role="example"><![CDATA[
115 A=[1,2,3];
116 norm(A,1)
117 norm(A,'inf')
118 A=[1,2;3,4]
119 max(svd(A))-norm(A)
120
121 A=sparse([1 0 0 33 -1])
122 norm(A)
123  ]]></programlisting>
124     </refsection>
125     <refsection role="see also">
126         <title>Ver Também</title>
127         <simplelist type="inline">
128             <member>
129                 <link linkend="h_norm">h_norm</link>
130             </member>
131             <member>
132                 <link linkend="dhnorm">dhnorm</link>
133             </member>
134             <member>
135                 <link linkend="h2norm">h2norm</link>
136             </member>
137             <member>
138                 <link linkend="abs">abs</link>
139             </member>
140         </simplelist>
141     </refsection>
142 </refentry>