* Bug 15337 fixed: mistake in l_p definition in norm() page
[scilab.git] / scilab / modules / elementary_functions / help / ja_JP / 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="ja">
20     <refnamediv>
21         <refname>norm</refname>
22         <refpurpose>行列のノルム</refpurpose>
23     </refnamediv>
24     <refsynopsisdiv>
25         <title>呼び出し手順</title>
26         <synopsis>
27         y = norm(x)
28         y = norm(x, normType)
29         </synopsis>
30     </refsynopsisdiv>
31     <refsection>
32         <title>引数</title>
33         <variablelist>
34             <varlistentry>
35                 <term>x</term>
36                 <listitem>
37                     <para>実数または複素数のベクトルまたは(通常または疎の)行列 </para>
38                 </listitem>
39             </varlistentry>
40             <varlistentry>
41                 <term>normType</term>
42                     <para>
43                         <itemizedlist>
44                             <listitem>
45                                 For a matrix <literal>x</literal>: a number among
46                                 <literal>1, 2, %inf, -%inf</literal>, or a word among
47                                 <literal>"inf"</literal> (or <literal>"i"</literal>) or
48                                 <literal>"fro"</literal> (or <literal>"f"</literal>).
49                             </listitem>
50                             <listitem>
51                                 For a vector <literal>x</literal>: any number or <literal>%inf</literal>,
52                                 <literal>-%inf</literal>; or a word <literal>"inf"</literal>
53                                 (<literal>"i"</literal>), <literal>"fro"</literal> (<literal>"f"</literal>).
54                             </listitem>
55                         </itemizedlist>
56                     </para>
57                     Default value = 2.
58             </varlistentry>
59             <varlistentry>
60                 <term>y</term>
61                 <listitem>
62                     <para>
63                         ノルム
64                     </para>
65                 </listitem>
66             </varlistentry>
67         </variablelist>
68     </refsection>
69     <refsection>
70         <title>説明</title>
71         <para>行列の場合</para>
72         <variablelist>
73             <varlistentry>
74                 <term>norm(x)</term>
75                 <listitem>
76                     <para>
77                         または<literal>norm(x,2)</literal> は
78                         <literal>x</literal>の最大特異値 (<literal>max(svd(x))</literal>)
79                         となります.
80                     </para>
81                 </listitem>
82             </varlistentry>
83             <varlistentry>
84                 <term>norm(x,1)</term>
85                 <listitem>
86                     <para>
87                         <literal>x</literal>のl_1 ノルム  (列の和の最大値:
88                         <literal>max(sum(abs(x),'r'))</literal> ).
89                     </para>
90                 </listitem>
91             </varlistentry>
92             <varlistentry>
93                 <term>norm(x,'inf'),norm(x,%inf)</term>
94                 <listitem>
95                     <para>
96                         <literal>x</literal>の無限大ノルム (列の和の最大値
97                         : <literal>max(sum(abs(x),'c'))</literal> ).
98                     </para>
99                 </listitem>
100             </varlistentry>
101             <varlistentry>
102                 <term>norm(x,'fro')</term>
103                 <listitem>
104                     <para>フロベニウスノルム,すなわち,
105                         <literal>sqrt(sum(diag(x'*x)))</literal>.
106                     </para>
107                 </listitem>
108             </varlistentry>
109         </variablelist>
110         <para>ベクトルの場合</para>
111         <variablelist>
112             <varlistentry>
113                 <term>norm(v,p)</term>
114                 <listitem>
115                     <para>
116                         l_p ノルム <literal>sum(abs(v(i))^p)^(1/p)</literal> .
117                     </para>
118                 </listitem>
119             </varlistentry>
120             <varlistentry>
121                 <term>norm(v), norm(v,2)</term>
122                 <listitem>
123                     <para>
124                         l_2 ノルム
125                     </para>
126                 </listitem>
127             </varlistentry>
128             <varlistentry>
129                 <term>norm(v,'inf')</term>
130                 <listitem>
131                     <para>
132                         <literal>max(abs(v(i)))</literal>.
133                     </para>
134                 </listitem>
135             </varlistentry>
136         </variablelist>
137     </refsection>
138     <refsection>
139         <title>例</title>
140         <programlisting role="example"><![CDATA[
141 A = [1,2,3];
142 norm(A,1)
143 norm(A,'inf')
144 A = [1,2;3,4]
145 max(svd(A)) - norm(A)
146
147 A = sparse([1 0 0 33 -1])
148 norm(A)
149  ]]></programlisting>
150     </refsection>
151     <refsection role="see also">
152         <title>参照</title>
153         <simplelist type="inline">
154             <member>
155                 <link linkend="h_norm">h_norm</link>
156             </member>
157             <member>
158                 <link linkend="dhnorm">dhnorm</link>
159             </member>
160             <member>
161                 <link linkend="h2norm">h2norm</link>
162             </member>
163             <member>
164                 <link linkend="abs">abs</link>
165             </member>
166             <member>
167                 <link linkend="svd">svd</link>
168             </member>
169         </simplelist>
170     </refsection>
171 </refentry>