6908aacdbc9b8feb75584155d34c79fd6e8359ef
[scilab.git] / scilab / modules / elementary_functions / help / ja_JP / matrixoperations / norm.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2
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17
18 <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="ja">
19
20     <refnamediv>
21
22         <refname>norm</refname>
23
24         <refpurpose>行列のノルム</refpurpose>
25
26     </refnamediv>
27
28     <refsynopsisdiv>
29
30         <title>呼び出し手順</title>
31
32         <synopsis>[y]=norm(x [,flag])</synopsis>
33
34     </refsynopsisdiv>
35
36     <refsection>
37
38         <title>引数</title>
39
40         <variablelist>
41
42             <varlistentry>
43
44                 <term>x</term>
45
46                 <listitem>
47
48                     <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>
49
50                 </listitem>
51
52             </varlistentry>
53
54             <varlistentry>
55
56                 <term>flag</term>
57
58                 <listitem>
59
60                     <para>文字列 (ノルムの型) (デフォルト値 =2)</para>
61
62                 </listitem>
63
64             </varlistentry>
65
66             <varlistentry>
67
68                 <term>y</term>
69
70                 <listitem>
71
72                     <para>
73
74                         ノルム
75
76                     </para>
77
78                 </listitem>
79
80             </varlistentry>
81
82         </variablelist>
83
84     </refsection>
85
86     <refsection>
87
88         <title>説明</title>
89
90         <para>行列の場合</para>
91
92         <variablelist>
93
94             <varlistentry>
95
96                 <term>norm(x)</term>
97
98                 <listitem>
99
100                     <para>
101
102                         または<literal>norm(x,2)</literal> は
103
104                         <literal>x</literal>の最大特異値 (<literal>max(svd(x))</literal>)
105
106                         となります.
107
108                     </para>
109
110                 </listitem>
111
112             </varlistentry>
113
114             <varlistentry>
115
116                 <term>norm(x,1)</term>
117
118                 <listitem>
119
120                     <para>
121
122                         <literal>x</literal>のl_1 ノルム  (列の和の最大値:
123
124                         <literal>max(sum(abs(x),'r'))</literal> ).
125
126                     </para>
127
128                 </listitem>
129
130             </varlistentry>
131
132             <varlistentry>
133
134                 <term>norm(x,'inf'),norm(x,%inf)</term>
135
136                 <listitem>
137
138                     <para>
139
140                         <literal>x</literal>の無限大ノルム (列の和の最大値
141
142                         : <literal>max(sum(abs(x),'c'))</literal> ).
143
144                     </para>
145
146                 </listitem>
147
148             </varlistentry>
149
150             <varlistentry>
151
152                 <term>norm(x,'fro')</term>
153
154                 <listitem>
155
156                     <para>フロベニウスノルム,すなわち,
157
158                         <literal>sqrt(sum(diag(x'*x)))</literal>.
159
160                     </para>
161
162                 </listitem>
163
164             </varlistentry>
165
166         </variablelist>
167
168         <para>ベクトルの場合</para>
169
170         <variablelist>
171
172             <varlistentry>
173
174                 <term>norm(v,p)</term>
175
176                 <listitem>
177
178                     <para>
179
180                         l_p ノルム (<literal>sum(v(i)^p))^(1/p)</literal> .
181
182                     </para>
183
184                 </listitem>
185
186             </varlistentry>
187
188             <varlistentry>
189
190                 <term>norm(v), norm(v,2)</term>
191
192                 <listitem>
193
194                     <para>
195
196                         l_2 ノルム
197
198                     </para>
199
200                 </listitem>
201
202             </varlistentry>
203
204             <varlistentry>
205
206                 <term>norm(v,'inf')</term>
207
208                 <listitem>
209
210                     <para>
211
212                         <literal>max(abs(v(i)))</literal>.
213
214                     </para>
215
216                 </listitem>
217
218             </varlistentry>
219
220         </variablelist>
221
222     </refsection>
223
224     <refsection>
225
226         <title>例</title>
227
228         <programlisting role="example"><![CDATA[
229 A=[1,2,3];
230 norm(A,1)
231 norm(A,'inf')
232 A=[1,2;3,4]
233 max(svd(A))-norm(A)
234 A=sparse([1 0 0 33 -1])
235 norm(A)
236  ]]></programlisting>
237
238     </refsection>
239
240     <refsection role="see also">
241
242         <title>参照</title>
243
244         <simplelist type="inline">
245
246             <member>
247
248                 <link linkend="h_norm">h_norm</link>
249
250             </member>
251
252             <member>
253
254                 <link linkend="dhnorm">dhnorm</link>
255
256             </member>
257
258             <member>
259
260                 <link linkend="h2norm">h2norm</link>
261
262             </member>
263
264             <member>
265
266                 <link linkend="abs">abs</link>
267
268             </member>
269
270             <member>
271
272                 <link linkend="svd">svd</link>
273
274             </member>
275
276         </simplelist>
277
278     </refsection>
279
280 </refentry>
281