translation updated for sparse.
[scilab.git] / scilab / modules / sparse / help / ja_JP / decomposition / spchol.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2
3 <!--
4  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
5  * Copyright (C) XXXX-2008 - INRIA
6  * 
7  * This file must be used under the terms of the CeCILL.
8  * This source file is licensed as described in the file COPYING, which
9  * you should have received as part of this distribution.  The terms
10  * are also available at    
11  * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
12  *
13  -->
14
15 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="spchol">
16     
17     <refnamediv>
18         
19         <refname>spchol</refname>
20         
21         <refpurpose>疎行列コレスキー分解</refpurpose>
22         
23     </refnamediv>
24     
25     <refsynopsisdiv>
26         
27         <title>呼び出し手順</title>
28         
29         <synopsis>[R,P] = spchol(X)</synopsis>
30         
31     </refsynopsisdiv>
32     
33     <refsection>
34         
35         <title>引数</title>
36         
37         <variablelist>
38             
39             <varlistentry>
40                 
41                 <term>X</term>
42                 
43                 <listitem>
44                     
45                     <para>対称正定実疎行列</para>
46                     
47                 </listitem>
48                 
49             </varlistentry>
50             
51             <varlistentry>
52                 
53                 <term>P</term>
54                 
55                 <listitem>
56                     
57                     <para>順列行列</para>
58                     
59                 </listitem>
60                 
61             </varlistentry>
62             
63             <varlistentry>
64                 
65                 <term>R</term>
66                 
67                 <listitem>
68                     
69                     <para>コレスキー分解</para>
70                     
71                 </listitem>
72                 
73             </varlistentry>
74             
75         </variablelist>
76         
77     </refsection>
78     
79     <refsection>
80         
81         <title>説明</title>
82         
83         <para>
84             
85             <literal>[R,P] = spchol(X)</literal> は,
86             
87             <literal>P*R*R'*P' = X</literal>となるような
88             
89             上三角行列<literal>R</literal> を出力します.
90             
91         </para>
92         
93     </refsection>
94     
95     <refsection>
96         
97         <title>例</title>
98         
99         <programlisting role="example"><![CDATA[ 
100 // Factorization:
101 Xfull = [
102 3.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  2.,  0.,  0.
103 0.,  5.,  4.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.
104 0.,  4.,  5.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.
105 2.,  0.,  0.,  3.,  0.,  0.,  2.,  0.,  2.,  0.,  0.
106 0.,  0.,  0.,  0. , 5.,  0.,  0.,  0.,  0.,  0.,  4.
107 0.,  0.,  0.,  0.,  0.,  4.,  0.,  3.,  0.,  3.,  0.
108 2.,  0.,  0.,  2.,  0.,  0.,  3.,  0.,  2.,  0.,  0.
109 0.,  0.,  0.,  0.,  0.,  3.,  0.,  4.,  0.,  3.,  0.
110 2.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  3.,  0.,  0.
111 0.,  0.,  0.,  0.,  0.,  3.,  0.,  3.,  0.,  4.,  0.
112 0.,  0.,  0.,  0.,  4.,  0.,  0.,  0.,  0.,  0.,  5.];
113 X = sparse(Xfull);
114
115 [R, P] = spchol(X);
116 max(P*R*R'*P'-X)
117
118 // Factorization and solve with backslash operator:
119 Afull = [
120 2 -1  0  0  0;
121 -1  2 -1  0  0;
122 0 -1  2 -1  0;
123 0  0 -1  2 -1;
124 0  0  0 -1  2
125 ];
126 A = sparse(Afull);
127
128 [L, P] = spchol(A);
129 max(P*L*L'*P'-A)
130
131 n = size(A, "r"); e = (1:n)'; b = A * e;
132 x = P*(L'\(L\(P'*b)));
133 A*x-b
134  ]]></programlisting>
135         
136     </refsection>
137     
138     <refsection role="see also">
139         
140         <title>参照</title>
141         
142         <simplelist type="inline">
143             
144             <member>
145                 
146                 <link linkend="sparse">sparse</link>
147                 
148             </member>
149             
150             <member>
151                 
152                 <link linkend="lusolve">lusolve</link>
153                 
154             </member>
155             
156             <member>
157                 
158                 <link linkend="luget">luget</link>
159                 
160             </member>
161             
162             <member>
163                 
164                 <link linkend="chol">chol</link>
165                 
166             </member>
167             
168         </simplelist>
169         
170     </refsection>
171     
172 </refentry>
173