3aba2b7fa5cd21e08fd7b69575512c97b1925b97
[scilab.git] / scilab / modules / elementary_functions / help / ru_RU / 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" 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" xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="ru">
17     <refnamediv>
18         <refname>norm</refname>
19         <refpurpose>норма матрицы</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Синтаксис</title>
23         <synopsis>[y]=norm(x [,flag])</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Аргументы</title>
27         <variablelist>
28             <varlistentry>
29                 <term>x</term>
30                 <listitem>
31                     <para>
32                         вещественный или комплексный вектор/матрица (полной или разрежённой
33                         формы)
34                     </para>
35                 </listitem>
36             </varlistentry>
37             <varlistentry>
38                 <term>flag</term>
39                 <listitem>
40                     <para>строка (тип нормы) (значение по умолчанию 2)</para>
41                 </listitem>
42             </varlistentry>
43         </variablelist>
44     </refsection>
45     <refsection>
46         <title>Описание</title>
47         <para>Для матриц</para>
48         <variablelist>
49             <varlistentry>
50                 <term>norm(x), norm(x,2)</term>
51                 <listitem>
52                     <para>
53                         наибольшее сингулярное значение <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                         l_1-норма <literal>x</literal> (наибольшая сумма столбцов:
62                         <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                         Бесконечная норма <literal>x</literal> (наибольшая сумма строк:
71                         <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>
79                         Норма Фробениуса, т. е.
80                         <literal>sqrt(sum(diag(x'*x)))</literal>.
81                     </para>
82                 </listitem>
83             </varlistentry>
84         </variablelist>
85         <para>Для векторов</para>
86         <variablelist>
87             <varlistentry>
88                 <term>norm(v,p)</term>
89                 <listitem>
90                     <para>
91                         l_p-норма  (<literal>sum(v(i)^p))^(1/p)</literal> .
92                     </para>
93                 </listitem>
94             </varlistentry>
95             <varlistentry>
96                 <term>norm(v), norm(v,2)</term>
97                 <listitem>
98                     <para>
99                         Норма l_2.
100                     </para>
101                 </listitem>
102             </varlistentry>
103             <varlistentry>
104                 <term>norm(v,'inf')</term>
105                 <listitem>
106                     <para>
107                         <literal>max(abs(v(i)))</literal>.
108                     </para>
109                 </listitem>
110             </varlistentry>
111         </variablelist>
112     </refsection>
113     <refsection>
114         <title>Примеры</title>
115         <programlisting role="example"><![CDATA[
116 A=[1,2,3];
117 norm(A,1)
118 norm(A,'inf')
119 A=[1,2;3,4]
120 max(svd(A))-norm(A)
121
122 A=sparse([1 0 0 33 -1])
123 norm(A)
124  ]]></programlisting>
125     </refsection>
126     <refsection role="see also">
127         <title>Смотрите также</title>
128         <simplelist type="inline">
129             <member>
130                 <link linkend="h_norm">h_norm</link>
131             </member>
132             <member>
133                 <link linkend="dhnorm">dhnorm</link>
134             </member>
135             <member>
136                 <link linkend="h2norm">h2norm</link>
137             </member>
138             <member>
139                 <link linkend="abs">abs</link>
140             </member>
141             <member>
142                 <link linkend="svd">svd</link>
143             </member>
144         </simplelist>
145     </refsection>
146 </refentry>