translation updated for sparse.
[scilab.git] / scilab / modules / sparse / help / ja_JP / decomposition / spchol.xml
index f8468a5..f9369d8 100644 (file)
@@ -1,5 +1,6 @@
-        <?xml version="1.0" encoding="UTF-8"?>
-    <!--
+<?xml version="1.0" encoding="UTF-8"?>
+
+<!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) XXXX-2008 - INRIA
  * 
  * This source file is licensed as described in the file COPYING, which
  * you should have received as part of this distribution.  The terms
  * are also available at    
- * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ * http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
  *
  -->
-    <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">
-        <refnamediv>
-            <refname>spchol</refname>
-            <refpurpose>疎行列コレスキー分解</refpurpose>
-        </refnamediv>
-        <refsynopsisdiv>
-            <title>呼び出し手順</title>
-            <synopsis>[R,P] = spchol(X)</synopsis>
-        </refsynopsisdiv>
-        <refsection>
-            <title>パラメータ</title>
-            <variablelist>
-                <varlistentry>
-                    <term>X</term>
-                    <listitem>
-                        <para>対称正定実疎行列</para>
-                    </listitem>
-                </varlistentry>
-                <varlistentry>
-                    <term>P</term>
-                    <listitem>
-                        <para>順列行列</para>
-                    </listitem>
-                </varlistentry>
-                <varlistentry>
-                    <term>R</term>
-                    <listitem>
-                        <para>コレスキー分解</para>
-                    </listitem>
-                </varlistentry>
-            </variablelist>
-        </refsection>
-        <refsection>
-            <title>説明</title>
-            <para>
-                <literal>[R,P] = spchol(X)</literal> は,
-                <literal>P*R*R'*P' = X</literal>となるような
-                上三角行列<literal>R</literal> を出力します.
-            </para>
-        </refsection>
-        <refsection>
-            <title>例</title>
-            <programlisting role="example"><![CDATA[ 
-X=[
-3.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  2.,  0.,  0. ;
-0.,  5.,  4.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0. ;
-0.,  4.,  5.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0. ;
-2.,  0.,  0.,  3.,  0.,  0.,  2.,  0.,  2.,  0.,  0. ;
-0.,  0.,  0.,  0. , 5.,  0.,  0.,  0.,  0.,  0.,  4. ;
-0.,  0.,  0.,  0.,  0.,  4.,  0.,  3.,  0.,  3.,  0. ;
-2.,  0.,  0.,  2.,  0.,  0.,  3.,  0.,  2.,  0.,  0. ;
-0.,  0.,  0.,  0.,  0.,  3.,  0.,  4.,  0.,  3.,  0. ;
-2.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  3.,  0.,  0. ;
-0.,  0.,  0.,  0.,  0.,  3.,  0.,  3.,  0.,  4.,  0. ;
+
+<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">
+    
+    <refnamediv>
+        
+        <refname>spchol</refname>
+        
+        <refpurpose>疎行列コレスキー分解</refpurpose>
+        
+    </refnamediv>
+    
+    <refsynopsisdiv>
+        
+        <title>呼び出し手順</title>
+        
+        <synopsis>[R,P] = spchol(X)</synopsis>
+        
+    </refsynopsisdiv>
+    
+    <refsection>
+        
+        <title>引数</title>
+        
+        <variablelist>
+            
+            <varlistentry>
+                
+                <term>X</term>
+                
+                <listitem>
+                    
+                    <para>対称正定実疎行列</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>P</term>
+                
+                <listitem>
+                    
+                    <para>順列行列</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+            <varlistentry>
+                
+                <term>R</term>
+                
+                <listitem>
+                    
+                    <para>コレスキー分解</para>
+                    
+                </listitem>
+                
+            </varlistentry>
+            
+        </variablelist>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>説明</title>
+        
+        <para>
+            
+            <literal>[R,P] = spchol(X)</literal> は,
+            
+            <literal>P*R*R'*P' = X</literal>となるような
+            
+            上三角行列<literal>R</literal> を出力します.
+            
+        </para>
+        
+    </refsection>
+    
+    <refsection>
+        
+        <title>例</title>
+        
+        <programlisting role="example"><![CDATA[ 
+// Factorization:
+Xfull = [
+3.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  2.,  0.,  0.
+0.,  5.,  4.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.
+0.,  4.,  5.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.
+2.,  0.,  0.,  3.,  0.,  0.,  2.,  0.,  2.,  0.,  0.
+0.,  0.,  0.,  0. , 5.,  0.,  0.,  0.,  0.,  0.,  4.
+0.,  0.,  0.,  0.,  0.,  4.,  0.,  3.,  0.,  3.,  0.
+2.,  0.,  0.,  2.,  0.,  0.,  3.,  0.,  2.,  0.,  0.
+0.,  0.,  0.,  0.,  0.,  3.,  0.,  4.,  0.,  3.,  0.
+2.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  3.,  0.,  0.
+0.,  0.,  0.,  0.,  0.,  3.,  0.,  3.,  0.,  4.,  0.
 0.,  0.,  0.,  0.,  4.,  0.,  0.,  0.,  0.,  0.,  5.];
-X=sparse(X);[R,P] = spchol(X);
+X = sparse(Xfull);
+
+[R, P] = spchol(X);
 max(P*R*R'*P'-X)
+
+// Factorization and solve with backslash operator:
+Afull = [
+2 -1  0  0  0;
+-1  2 -1  0  0;
+0 -1  2 -1  0;
+0  0 -1  2 -1;
+0  0  0 -1  2
+];
+A = sparse(Afull);
+
+[L, P] = spchol(A);
+max(P*L*L'*P'-A)
+
+n = size(A, "r"); e = (1:n)'; b = A * e;
+x = P*(L'\(L\(P'*b)));
+A*x-b
  ]]></programlisting>
-        </refsection>
-        <refsection role="see also">
-            <title>参照</title>
-            <simplelist type="inline">
-                <member>
-                    <link linkend="sparse">sparse</link>
-                </member>
-                <member>
-                    <link linkend="lusolve">lusolve</link>
-                </member>
-                <member>
-                    <link linkend="luget">luget</link>
-                </member>
-                <member>
-                    <link linkend="chol">chol</link>
-                </member>
-            </simplelist>
-        </refsection>
-    </refentry>
+        
+    </refsection>
+    
+    <refsection role="see also">
+        
+        <title>参照</title>
+        
+        <simplelist type="inline">
+            
+            <member>
+                
+                <link linkend="sparse">sparse</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="lusolve">lusolve</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="luget">luget</link>
+                
+            </member>
+            
+            <member>
+                
+                <link linkend="chol">chol</link>
+                
+            </member>
+            
+        </simplelist>
+        
+    </refsection>
+    
+</refentry>
+