japanese translation updated for linear-algebra. 93/14493/2
Rui Hirokawa [Sat, 3 May 2014 14:00:48 +0000 (23:00 +0900)]
Change-Id: I1e7b73183c06afc59bba3773904025770855ad74

59 files changed:
scilab/modules/linear_algebra/help/ja_JP/eigen/balanc.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/bdiag.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/gschur.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/gspec.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/hess.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/pbig.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/projspec.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/psmall.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/schur.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/spec.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/sva.xml
scilab/modules/linear_algebra/help/ja_JP/eigen/svd.xml
scilab/modules/linear_algebra/help/ja_JP/factorization/givens.xml
scilab/modules/linear_algebra/help/ja_JP/factorization/householder.xml
scilab/modules/linear_algebra/help/ja_JP/factorization/sqroot.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/colcomp.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/fullrf.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/fullrfk.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/im_inv.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/kernel.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/range.xml
scilab/modules/linear_algebra/help/ja_JP/kernel/rowcomp.xml
scilab/modules/linear_algebra/help/ja_JP/linear/aff2ab.xml
scilab/modules/linear_algebra/help/ja_JP/linear/chol.xml
scilab/modules/linear_algebra/help/ja_JP/linear/inv.xml
scilab/modules/linear_algebra/help/ja_JP/linear/linsolve.xml
scilab/modules/linear_algebra/help/ja_JP/linear/lsq.xml
scilab/modules/linear_algebra/help/ja_JP/linear/lu.xml
scilab/modules/linear_algebra/help/ja_JP/linear/pinv.xml
scilab/modules/linear_algebra/help/ja_JP/linear/qr.xml
scilab/modules/linear_algebra/help/ja_JP/linear/rankqr.xml
scilab/modules/linear_algebra/help/ja_JP/markov/classmarkov.xml
scilab/modules/linear_algebra/help/ja_JP/markov/eigenmarkov.xml
scilab/modules/linear_algebra/help/ja_JP/markov/genmarkov.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/cond.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/det.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/orth.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/rank.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/rcond.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/rref.xml
scilab/modules/linear_algebra/help/ja_JP/matrix/trace.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/companion.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/ereduc.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/fstair.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/glever.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/kroneck.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/lyap.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/pencan.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/penlaur.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/quaskro.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/randpencil.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/rowshuff.xml
scilab/modules/linear_algebra/help/ja_JP/pencil/sylv.xml
scilab/modules/linear_algebra/help/ja_JP/proj.xml
scilab/modules/linear_algebra/help/ja_JP/state_space/coff.xml
scilab/modules/linear_algebra/help/ja_JP/state_space/nlev.xml
scilab/modules/linear_algebra/help/ja_JP/subspaces/spaninter.xml
scilab/modules/linear_algebra/help/ja_JP/subspaces/spanplus.xml
scilab/modules/linear_algebra/help/ja_JP/subspaces/spantwo.xml

index e678877..b150c2e 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="balanc">
+    
     <refnamediv>
+        
         <refname>balanc</refname>
+        
         <refpurpose>行列またはペンシルの平衡化</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[Ab,X]=balanc(A)
+            
             [Eb,Ab,X,Y]=balanc(E,A)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A:  </term>
+                
                 <listitem>
+                    
                     <para>実数正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>X:  </term>
+                
                 <listitem>
+                    
                     <para>可逆な実数正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>E:  </term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         実数正方行列 (<literal>A</literal>と同じ次元)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Y:  </term>
+                
                 <listitem>
+                    
                     <para>可逆な実数正方行列.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             正方行列の条件数を改善するために平衡化します.
+            
         </para>
+        
         <para>
+            
             <literal>[Ab,X] = balanc(A)</literal> は,
+            
+            以下のような相似変換<literal>X</literal>を見つけます:
+            
+        </para>
+        
+        <para>
+            
             <literal>Ab = inv(X)*A*X</literal>が近似的に等しい
-            行ノルムおよび列ノルムを有する
-            相似変換<literal>X</literal>を見つけます.
+            
+            行ノルムおよび列ノルムを有する.
+            
         </para>
+        
         <para>
+            
             行列ペンシルの場合,平衡化は一般化固有値問題を改善することにより
+            
             行われます.
+            
         </para>
+        
         <para>
+            
             <literal>[Eb,Ab,X,Y] = balanc(E,A)</literal> は,
+            
             <literal>Eb=inv(X)*E*Y,  Ab=inv(X)*A*Y</literal> となるような
+            
             左および右変換
+            
             <literal>X</literal> および <literal>Y</literal> を返します.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>注意</title>
+        
         <para>
+            
             平衡化は関数<literal>bdiag</literal> および <literal>spec</literal>
+            
             で行われます.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=[1/2^10,1/2^10;2^10,2^10];
 [Ab,X]=balanc(A);
 norm(A(1,:))/norm(A(2,:))
 norm(Ab(1,:))/norm(Ab(2,:))
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="bdiag">bdiag</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="spec">spec</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="schur">schur</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 31ec600..ba3a911 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="bdiag">
+    
     <refnamediv>
+        
         <refname>bdiag</refname>
+        
         <refpurpose>ブロック対角化, 一般化固有ベクトル</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>rmax</term>
+                
                 <listitem>
+                    
                     <para>実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Ab</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の正則行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>bs</term>
+                
                 <listitem>
+                    
                     <para>整数ベクトル</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <programlisting role=""><![CDATA[ 
 [Ab [,X [,bs]]]=bdiag(A [,rmax]) 
  ]]></programlisting>
+        
         <para>
+            
             は,行列<literal>A</literal>のブロック対角化を行ないます.
+            
             bs はブロックの構造(個々のブロックの大きさ)を出力します.
+            
             <literal>X</literal> は基底変換です.
+            
             すなわち, <literal>Ab = inv(X)*A*X</literal> はブロック対角です.
+            
         </para>
+        
         <para>
+            
             <literal>rmax</literal> は<literal>X</literal>の
+            
             条件数を制御します;
+            
             デフォルト値は <literal>A</literal> の l1ノルムです.
+            
         </para>
+        
         <para>
+            
             (存在する場合,)対角形式を得るには<literal>rmax</literal>に
+            
             大きな値を指定します(例えば,<literal>rmax=1/%eps</literal>).
+            
             一般に(ランダムな実数の Aの場合) ブロックは (1x1) および (2x2) で,
+            
             <literal>X</literal> は固有値の行列です.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 //実数の場合: 1x1 および 2x2 ブロック
 a=rand(5,5);[ab,x,bs]=bdiag(a);ab
 //複素数の場合: 複素数 1x1 ブロック
 [ab,x,bs]=bdiag(a+%i*0);ab
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="schur">schur</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="sylv">sylv</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="spec">spec</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 76b5b60..2f42eb2 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="gschur">
+    
     <refnamediv>
+        
         <refname>gschur</refname>
-        <refpurpose>一般化Schur分解 (古い関数).  </refpurpose>
+        
+        <refpurpose>
+            
+            一般化Schur分解.
+            
+            <emphasis role="bold">この関数は廃止されました.</emphasis>
+            
+        </refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[As,Es]=gschur(A,E)
+            
             [As,Es,Q,Z]=gschur(A,E)
+            
             [As,Es,Z,dim] = gschur(A,E,flag)
+            
             [As,Es,Z,dim]= gschur(A,E,extern)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
-            この関数は古い関数であり,  <literal>schur</literal>関数に統合されています.
+            
+            この関数は廃止されており, <literal>schur</literal>関数に統合されています.
+            
             多くの場合, <literal>gschur</literal>関数は以前と同様に動作しますが,
+            
             将来のリリースでは削除される予定です.
+            
         </para>
+        
         <para>
+            
             最初の3つの構文は以下のように置き換えることができます
+            
         </para>
+        
         <programlisting role=""><![CDATA[ 
 [As,Es]=schur(A,E)
 [As,Es,Q,Z]=schur(A,E);Q=Q' //NOTE THE TRANPOSITION HERE
 [As,Es,Z,dim] = schur(A,E,flag) 
  ]]></programlisting>
+        
         <para>
+            
             最後の構文はさらに若干の調整が必要です:
+            
         </para>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>もし,</term>
+                
                 <listitem>
-                    <para>extern が Scilab関数の場合,
-                        新しい呼び出し手順は, Nextern を以下のように定義するとき,
+                    
+                    <para>
+                        
+                        extern が Scilab関数の場合,
+                        
+                        Nextern を以下のように定義すると,
+                        
+                        新しい呼び出し手順は,
+                        
                         <literal>[As,Es,Z,dim]= schur(A,E,Nextern)</literal>
+                        
                         となります:
+                        
                     </para>
+                    
                     <programlisting role=""><![CDATA[ 
 function t=Nextern(R)
 if R(2)==0 then
@@ -60,20 +108,37 @@ else
 end
 endfunction
  ]]></programlisting>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
-                <term>if</term>
+                
+                <term>もし,</term>
+                
                 <listitem>
-                    <para>extern は,Fortran または Cで記述された外部関数の名前です.
-                        新しい呼び出し手順は,
+                    
+                    <para>
+                        
+                        extern は,Fortran または Cで記述された外部関数の名前の場合,
+                        
                         nextern を以下のように定義すると
+                        
+                        新しい呼び出し手順は,
+                        
                         <literal>[As,Es,Z,dim]=    schur(A,E,'nextern')</literal> 
+                        
                         のようになります:
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
         <programlisting role=""><![CDATA[ 
 logical function nextern(ar,ai,beta)
 double precision ar,ai,beta
@@ -86,16 +151,30 @@ endif
 nextern=r.eq.1
 end
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="external">external</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="schur">schur</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 8cb20e0..fffb2f6 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="gspec">
+    
     <refnamediv>
+        
         <refname>gspec</refname>
-        <refpurpose>行列ペンシルの固有値 (古い関数)  </refpurpose>
+        
+        <refpurpose>
+            
+            行列ペンシルの固有値.
+            
+            <emphasis role="bold">この関数は廃止されました.</emphasis>
+            
+        </refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[al,be]=gspec(A,E)
+            
             [al,be,Z]=gspec(A,E)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             この関数は現在では <literal>spec</literal> 関数に統合されています.
+            
             呼び出し手順は以下のように置き換られています
+            
         </para>
+        
         <programlisting role=""><![CDATA[ 
 [al,be]=spec(A,E)
 [al,be,Z]=spec(A,E)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="spec">spec</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index aeef036..9ffb1de 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="hess">
+    
     <refnamediv>
+        
         <refname>hess</refname>
+        
         <refpurpose>ヘッセンベルク形式</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>H = hess(A)
+            
             [U,H] = hess(A)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>H</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>U</term>
+                
                 <listitem>
+                    
                     <para>直交またはユニタリ正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>[U,H] = hess(A)</literal> は,
+            
             <literal>A = U*H*U'</literal> および <literal>U'*U</literal> =単位行列 となるような
+            
             ユニタリ行列<literal>U</literal> およびヘッセンベルク行列<literal>H</literal>を出力します.
+            
             これにより, <literal>hess(A)</literal> は <literal>H</literal>を返します.
+            
         </para>
+        
         <para>行列のヘッセンベルク形式は最初の副対角線以下では 0となります.
+            
             この行列が対称またはエルミート行列の場合,
+            
             形は3重対角となります.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>リファレンス</title>
+        
         <para>
+            
             hess 関数は Lapack ルーチン
+            
             DGEHRD, DORGHR (実数行列の場合) および ZGEHRD, ZORGHR (複素数行列の場合)に基づいています.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(3,3);[U,H]=hess(A);
 and( abs(U*H*U'-A)<1.d-10 )
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="contr">contr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="schur">schur</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用される関数</title>
+        
         <para>
+            
             <literal>hess</literal> 関数はLapack ルーチン
+            
             DGEHRD, DORGHR (実数行列の場合) および  ZGEHRD, ZORGHR (複素数行列の場合)に
+            
             基づいています.
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 101f8f9..feaaa4c 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="pbig">
+    
     <refnamediv>
+        
         <refname>pbig</refname>
+        
         <refpurpose>固有投影</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[Q,M]=pbig(A,thres,flag)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>Parameters</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>thres</term>
+                
                 <listitem>
+                    
                     <para>実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>flag</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         文字列 (<literal>'c'</literal> または <literal>'d'</literal>)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Q,M</term>
+                
                 <listitem>
+                    
                     <para>実数行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             実部&gt;= <literal>thres</literal> (<literal>flag='c'</literal>)
+            
             または
+            
             大きさ&gt;= <literal>thres</literal>(<literal>flag='d'</literal>)
+            
             の固有値を有する固有値-部分空間への投影.
+            
         </para>
+        
         <para>
+            
             投影は<literal>Q*M</literal>により定義され,<literal>Q</literal>
+            
             は列フルランク, <literal>M</literal>は行フルランクおよび
+            
             <literal>M*Q=eye</literal>.
+            
         </para>
+        
         <para>
+            
             <literal>flag='c'</literal>の場合, 
+            
             <literal>M*A*Q</literal>の固有値 = 実部&gt;= <literal>thres</literal>
+            
             の<literal>A</literal>の固有値となります.
+            
         </para>
+        
         <para>
+            
             <literal>flag='d'</literal>の場合, 
+            
             <literal>M*A*Q</literal>の固有値 = 大きさ&gt;= <literal>thres</literal>の
+            
             <literal>A</literal>の固有値となります.
+            
         </para>
+        
         <para>
+            
             <literal>flag='c'</literal> の場合,そして
+            
             <literal>[Q1,M1]</literal> = <literal>eye()-Q*M</literal>の
+            
             フルランク分解 (<literal>fullrf</literal>)の場合,
+            
             <literal>M1*A*Q1</literal>の固有値 =
+            
             実部 &lt; <literal>thres</literal>の<literal>A</literal>の固有値となります.
+            
         </para>
+        
         <para>
+            
             <literal>flag='d'</literal>の場合,そして <literal>[Q1,M1]</literal> =
+            
             <literal>eye()-Q*M</literal>のフルランク分解 (<literal>fullrf</literal>)の場合,
+            
             <literal>M1*A*Q1</literal>の固有値 =大きさ &lt;<literal>thres</literal>の
+            
             <literal>A</literal>の固有値となります.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
 [Q,M]=pbig(A,1.5,'d');
@@ -96,30 +177,58 @@ spec(M*A*Q)
 [Q1,M1]=fullrf(eye()-Q*M);
 spec(M1*A*Q1)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="psmall">psmall</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="projspec">projspec</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrf">fullrf</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="schur">schur</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用される関数</title>
+        
         <para>
+            
             <literal>pbig</literal> は
+            
             ソートされた Schur 形式に基づいています
+            
             (Scilab関数 <literal>schur</literal>).
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 1b1a699..351331f 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="projspec">
+    
     <refnamediv>
+        
         <refname>projspec</refname>
+        
         <refpurpose>スペクトル演算子</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[S,P,D,i]=projspec(A)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>S, P, D</term>
+                
                 <listitem>
+                    
                     <para>s正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>i</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         整数 (<literal>A</literal>のゼロ固有値の添字).
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>A</literal>の0におけるスペクトル特性.
+            
         </para>
+        
         <para>
+            
             <literal>S</literal> = 0における縮小レゾルベント 
+            
             (<literal>S</literal> = -Drazin_inverse(<literal>A</literal>)).
+            
         </para>
+        
         <para>
+            
             <literal>P</literal> = 0におけるスペクトル投影.
+            
         </para>
+        
         <para>
+            
             <literal>D</literal> = 0における冪零演算子.
+            
         </para>
+        
         <para>
+            
             <literal>index</literal> = 0固有値の添字.
+            
         </para>
+        
         <para>
+            
             特異点s=0の周りでの
+            
             <literal>(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -...</literal>
+            
             が出力されます.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end')
 A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7);
@@ -80,13 +142,24 @@ trace(P)  //J-ブロックの次元の合計
 A*S-(eye()-P)
 norm(D^index,1)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="coff">coff</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index cae1a7f..e67b13b 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="psmall">
+    
     <refnamediv>
+        
         <refname>psmall</refname>
+        
         <refpurpose>スペクトル投影</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[Q,M]=psmall(A,thres,flag)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数の正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>thres</term>
+                
                 <listitem>
+                    
                     <para>実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>flag</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         文字列 (<literal>'c'</literal> または <literal>'d'</literal>)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Q,M</term>
+                
                 <listitem>
+                    
                     <para>実数行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             実部 &lt; <literal>thres</literal> (<literal>flag='c'</literal>)
+            
             または絶対値 &lt; <literal>thres</literal>(<literal>flag='d'</literal>)
+            
             となる固有値-部分空間への投影.
+            
         </para>
+        
         <para>
+            
             この投影は<literal>Q*M</literal>により定義されます.
+            
             ここで,
+            
             <literal>Q</literal>は列フルランク,<literal>M</literal>は行フルランク,
+            
             そして<literal>M*Q=eye</literal>です.
+            
         </para>
+        
         <para>
+            
             <literal>flag='c'</literal>の場合, 
+            
             <literal>M*A*Q</literal>の固有値 = 
+            
             実部&lt; <literal>thres</literal>の<literal>A</literal>の固有値.
+            
         </para>
+        
         <para>
+            
             <literal>flag='d'</literal>の場合, 
+            
             <literal>M*A*Q</literal>の固有値 = 
+            
             大きさ &lt; <literal>thres</literal>の<literal>A</literal>の固有値.
+            
         </para>
+        
         <para>
+            
             <literal>flag='c'</literal>の場合, 
+            
             <literal>[Q1,M1]</literal> = <literal>eye()-Q*M</literal>の
+            
             フルランク分解(<literal>fullrf</literal>)の場合,
+            
             <literal>M1*A*Q1</literal>の固有値 =実部&gt;=
+            
             <literal>thres</literal>の
+            
             <literal>A</literal>の固有値となります.
+            
         </para>
+        
         <para>
+            
             <literal>flag='d'</literal>の場合,
+            
             <literal>[Q1,M1]</literal> =<literal>eye()-Q*M</literal>
+            
             のフルランク分解(<literal>fullrf</literal>)の場合,
+            
             <literal>M1*A*Q1</literal>の固有値 =
+            
             大きさ&gt;=<literal>thres</literal>の
+            
             <literal>A</literal>の固有値.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
 [Q,M]=psmall(A,2.5,'d');
@@ -99,26 +183,50 @@ spec(M*A*Q)
 [Q1,M1]=fullrf(eye()-Q*M);
 spec(M1*A*Q1)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="pbig">pbig</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="proj">proj</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="projspec">projspec</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用される関数</title>
+        
         <para>
+            
             この関数はソートされた Schur形式(scilab
+            
             関数 <literal>schur</literal>)に基づいています.
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 31d8805..be68d6e 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="schur">
+    
     <refnamediv>
+        
         <refname>schur</refname>
+        
         <refpurpose>行列およびペンシルの[ソートされた] Schur 分解</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[U,T] = schur(A)
+            
             [U,dim [,T] ]=schur(A,flag)
+            
             [U,dim [,T] ]=schur(A,extern1)
+            
+            
+            
             [As,Es [,Q,Z]]=schur(A,E)
+            
             [As,Es [,Q],Z,dim] = schur(A,E,flag)
+            
             [Z,dim] = schur(A,E,flag)
+            
             [As,Es [,Q],Z,dim]= schur(A,E,extern2)
+            
             [Z,dim]= schur(A,E,extern2)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の正方行列.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>E</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>A</literal>と同じ次元の実数または複素数の正方行列.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>flag</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         文字列 (<literal>'c'</literal> または <literal>'d'</literal>)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>extern1</term>
+                
                 <listitem>
+                    
                     <para>an ``external'', 以下の参照</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>extern2</term>
+                
                 <listitem>
+                    
                     <para>an ``external'', 以下の参照</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>U</term>
+                
                 <listitem>
+                    
                     <para>直交またはユニタリ正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Q</term>
+                
                 <listitem>
+                    
                     <para>直交またはユニタリ正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Z</term>
+                
                 <listitem>
+                    
                     <para>o直交またはユニタリ正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>T</term>
+                
                 <listitem>
+                    
                     <para>上三角または準三角正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>As</term>
+                
                 <listitem>
+                    
                     <para>上三角または準三角正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Es</term>
+                
                 <listitem>
+                    
                     <para>上三角正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>dim</term>
+                
                 <listitem>
+                    
                     <para>整数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             Schur 形式, 行列およびペンシルのソートされた Schur 形式
+            
         </para>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>行列Schur形式</term>
+                
                 <listitem>
+                    
                     <variablelist>
+                        
                         <varlistentry>
+                            
                             <term>通常のSchur形式:</term>
+                            
                             <listitem>
+                                
                                 <para>
+                                    
                                     <literal>[U,T] = schur(A)</literal> は,
+                                    
                                     <literal>A = U*T*U'</literal> および <literal>U'*U =  eye(U)</literal>となるような
+                                    
                                     Schur行列<literal>T</literal> およびユニタリ行列 <literal>U</literal>
+                                    
                                     を出力します.
+                                    
                                     Schur(<literal>A</literal>)は,<literal>T</literal>を返します.
+                                    
                                     <literal>A</literal> が複素数の場合, 複素Schur形式は,行列<literal>T</literal>に返します.
+                                    
                                     複素Schur形式は,<literal>A</literal>の固有値を対角項に有する上三角行列です.
+                                    
                                     <literal>A</literal> が実数の場合, 実数Schur形式が返されます.
+                                    
                                     実数Schur形式は,対角項に実数固有値、複素数固有値を対角項の2x2ブロックに
+                                    
                                     有します.
+                                    
                                 </para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>ソートされたSchur形式</term>
+                            
                             <listitem>
+                                
                                 <para>
+                                    
                                     <literal>[U,dim]=schur(A,'c')</literal> は,
+                                    
                                     <literal>A</literal>を Schur 形式に変換する
+                                    
                                     ユニタリ行列 <literal>U</literal> を返します.
+                                    
                                     更に,<literal>U</literal>の最初の列 dim は,
+                                    
                                     実部が負の固有値(安定な"連続時間"固有値空間)
+                                    
                                     に関連する<literal>A</literal>の固有値空間
+                                    
                                     の基底を構成します.
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     <literal>[U,dim]=schur(A,'d')</literal> は,
+                                    
                                     <literal>A</literal>を Schur 形式に変換する
+                                    
                                     ユニタリ行列 <literal>U</literal> を返します.
+                                    
                                     更に,<literal>U</literal>の最初の列 dim は,
+                                    
                                     大きさが1未満の固有値(安定な"離散時間"固有値空間)
+                                    
                                     に関連する<literal>A</literal>の固有値空間
+                                    
                                     の基底を構成します.
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     <literal>[U,dim]=schur(A,extern1)</literal> は,
+                                    
                                     <literal>A</literal>を Schur 形式に変換する
+                                    
                                     ユニタリ行列<literal>U</literal>を返します.
+                                    
                                     更に,<literal>U</literal>の最初の列 dim は,
+                                    
                                     外部関数 <literal>extern1</literal> (詳細は external 参照)
+                                    
                                     により選択された固有値に関連する<literal>A</literal>の固有値空間
+                                    
                                     の基底を構成します.
+                                    
                                     この external はScilab関数またはCまたはFortranプロシージャにより
+                                    
                                     次のように記述することができます: 
+                                    
                                 </para>
+                                
                                 <variablelist>
+                                    
                                     <varlistentry>
+                                        
                                         <term>Scilab関数</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 <literal>extern1</literal>が
+                                                
                                                 Scilab関数により記述される場合,
+                                                
                                                 以下の呼び出し手順を有する必要があります:
+                                                
                                                 <literal>s=extern1(Ev)</literal>, ただし <literal>Ev</literal> は固有値,
+                                                
                                                 <literal>s</literal> は論理値です.
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>C または Fortran プロシージャ</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 <literal>extern1</literal> がCまたはFortran関数により
+                                                
                                                 記述される場合,以下の呼び出し手順を有する必要があります:
+                                                
                                                 <literal>int extern1(double *EvR, double *EvI)</literal>
+                                                
                                                 ただし <literal>EvR</literal> および <literal>EvI</literal> は
+                                                
                                                 固有値の実部および虚部です.
+                                                
                                                 trueまたはゼロでない戻り値は,選択された固有値を意味します.
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                 </variablelist>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                     </variablelist>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>ペンシルSchur形式</term>
+                
                 <listitem>
+                    
                     <variablelist>
+                        
                         <varlistentry>
+                            
                             <term>通常のペンシルSchur形式</term>
+                            
                             <listitem>
+                                
                                 <para>
+                                    
                                     <literal>[As,Es] = schur(A,E)</literal> は,
+                                    
                                     対<literal>A, E</literal>の一般化Schur形式である
+                                    
                                     準三角行列<literal>As</literal>行列および三角行列<literal>Es</literal>
+                                    
                                     を出力します.
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     <literal>[As,Es,Q,Z] = schur(A,E)</literal>は,更に
+                                    
                                     <literal>As=Q'*A*Z</literal> および <literal>Es=Q'*E*Z</literal>となるような
+                                    
                                     2つのユニタリ行列<literal>Q</literal> および <literal>Z</literal>を返します.
+                                    
                                 </para>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                         <varlistentry>
+                            
                             <term>ソートされたSchur形式:</term>
+                            
                             <listitem>
+                                
                                 <para>
+                                    
                                     <literal>[As,Es,Z,dim] = schur(A,E,'c')</literal>は,
+                                    
                                     ペンシル<literal>s*E-A</literal>の実数一般化Schur形式を返します.
+                                    
                                     更に, <literal>Z</literal>の最初の列 dim は,
+                                    
                                     実部が負の固有値 (安定な"連続時間"一般化固有値空間)に関連する
+                                    
                                     固有値空間の基底を構成します.
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     <literal>[As,Es,Z,dim] = schur(A,E,'d')</literal>
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     は,ペンシル<literal>s*E-A</literal>の
+                                    
                                     実数一般化Schur形式を返します.
+                                    
                                     更に, <literal>Z</literal>の最初の列 dim は,
+                                    
                                     大きさ1未満の固有値 (安定な"離散時間"一般化固有値空間)に関連する
+                                    
                                     固有値空間の基底を構成します.
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     <literal>[As,Es,Z,dim] = schur(A,E,extern2)</literal>
+                                    
                                 </para>
+                                
                                 <para>
+                                    
                                     は,ペンシル<literal>s*E-A</literal>の実一般化Schur形式を返します.
+                                    
                                     更に, <literal>Z</literal>の最初の列 dim は,
+                                    
                                     関数<literal>extern2</literal>により指定された規則に基づき選択された
+                                    
                                     ペンシルの固有値に関する固有値空間の基底を構成します.
+                                    
                                     (詳細は external 参照)
+                                    
                                     この external は Scilab 関数またはCまたはFortranプロシージャ
+                                    
                                     により次のように記述することができます:
+                                    
                                 </para>
+                                
                                 <variablelist>
+                                    
                                     <varlistentry>
+                                        
                                         <term>Scilab関数</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 <literal>extern2</literal>がScilab関数により記述される場合,
+                                                
                                                 以下の呼び出し手順を有する必要があります:
+                                                
                                                 <literal>s=extern2(Alpha,Beta)</literal>, ただし <literal>Alpha</literal> および
+                                                
                                                 <literal>Beta</literal> は一般化固有値および論理値 <literal>s</literal>
+                                                
                                                 を定義します.
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                     <varlistentry>
+                                        
                                         <term>C またはFortranプロシージャ</term>
+                                        
                                         <listitem>
+                                            
                                             <para>
+                                                
                                                 if external <literal>extern2</literal> がCまたはFortran関数により
+                                                
                                                 記述される場合,以下の呼び出し手順を有する必要があります:
+                                                
                                             </para>
+                                            
                                             <para>
+                                                
                                                 <literal>int extern2(double *AlphaR, double *AlphaI, double *Beta)</literal>
+                                                
                                             </para>
+                                            
                                             <para>
+                                                
                                                 : <literal>A</literal> および <literal>E</literal> が実数の場合.
+                                                
                                             </para>
+                                            
                                             <para>
+                                                
                                                 <literal>int extern2(double *AlphaR, double *AlphaI, double *BetaR, double *BetaI)</literal>
+                                                
                                             </para>
+                                            
                                             <para>
+                                                
                                                 : <literal>A</literal> および <literal>E</literal> が複素数の場合.
+                                                
                                                 <literal>Alpha</literal>, および <literal>Beta</literal> は一般化固有値を定義します.
+                                                
                                                 trueまたは非ゼロの戻り値は,選択された一般化固有値を意味します.
+                                                
                                             </para>
+                                            
                                         </listitem>
+                                        
                                     </varlistentry>
+                                    
                                 </variablelist>
+                                
                             </listitem>
+                            
                         </varlistentry>
+                        
                     </variablelist>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>参考</title>
+        
         <para>
+            
             行列Schur形式の計算はLapackルーチンDGEES および ZGEESに基づいています.
+            
         </para>
+        
         <para>
+            
             ペンシルSchur形式の計算はLapackルーチンDGGES および ZGGESに基づいています.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 //行列Schur形式
 //----------------------
 A=diag([-0.9,-2,2,0.9]);X=rand(A);A=inv(X)*A*X;
 [U,T]=schur(A);T
+
 [U,dim,T]=schur(A,'c');
 T(1:dim,1:dim)      //安定な連続時間固有値
+
 function t=mytest(Ev),t=abs(Ev)<0.95,endfunction
 [U,dim,T]=schur(A,mytest);
 T(1:dim,1:dim)  
+
 // Cの同じ関数 (コンパイラが必要)
 cd TMPDIR;
 C=['int mytest(double *EvR, double *EvI) {' //the C code
    'if (*EvR * *EvR + *EvI * *EvI < 0.9025) return 1;'
    'else return 0; }';]
 mputl(C,TMPDIR+'/mytest.c')
+
+
 //構築/リンク
 lp=ilib_for_link('mytest','mytest.c',[],'c');
 link(lp,'mytest','c'); 
+
 //実行
 [U,dim,T]=schur(A,'mytest');
 //ペンシルのSchur形式
@@ -336,9 +642,12 @@ F=[-1,%s, 0,   1;
 A=coeff(F,0);E=coeff(F,1);
 [As,Es,Q,Z]=schur(A,E);
 Q'*F*Z //これはAs+%s*Esです
+
+
 [As,Es,Z,dim] = schur(A,E,'c')
 function t=mytest(Alpha,Beta),t=real(Alpha)<0,endfunction
 [As,Es,Z,dim] = schur(A,E,mytest)
+
 //Fortranの同じ関数 (コンパイラが必要)
 ftn=['integer function mytestf(ar,ai,b)' //fortranコード
      'double precision ar,ai,b'
@@ -346,31 +655,57 @@ ftn=['integer function mytestf(ar,ai,b)' //fortranコード
      'if(ar.lt.0.0d0) mytestf=1'
      'end']
 mputl('      '+ftn,TMPDIR+'/mytestf.f')
+
 //build and link
 lp=ilib_for_link('mytestf','mytestf.f',[],'F');
 link(lp,'mytestf','f'); 
+
 //実行
+
 [As,Es,Z,dim] = schur(A,E,'mytestf')
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="spec">spec</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="bdiag">bdiag</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="ricc">ricc</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="pbig">pbig</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="psmall">psmall</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 60758e7..ad29f18 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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: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="spec" xml:lang="ja">
+    
     <refnamediv>
+        
         <refname>spec</refname>
+        
         <refpurpose>行列とペンシルの固有値</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>evals=spec(A)
+            
             [R,diagevals]=spec(A)
+            
+            
+            
             evals=spec(A,B)
+            
             [alpha,beta]=spec(A,B)
+            
             [alpha,beta,Z]=spec(A,B)
+            
             [alpha,beta,Q,Z]=spec(A,B)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>B</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal> A</literal>と同じ次元の実数または複素正方行列
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>evals</term>
+                
                 <listitem>
+                    
                     <para>実数または複素ベクトル, 固有値</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>diagevals</term>
+                
                 <listitem>
+                    
                     <para>実数または(対角項に固有値を有する)複素対角行列 </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>alpha</term>
+                
                 <listitem>
+                    
                     <para>実数または複素ベクトル, al./be により固有値が得られます</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>beta</term>
+                
                 <listitem>
+                    
                     <para>実数ベクトル, al./be により固有値が得られます</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>R</term>
+                
                 <listitem>
+                    
                     <para>可逆な実数または複素正方行列, 行列右固有ベクトル.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>L</term>
+                
                 <listitem>
+                    
                     <para>可逆な実数または複素正方行列, ペンシル左固有ベクトル.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>R</term>
+                
                 <listitem>
+                    
                     <para>可逆な実数または複素正方行列, ペンシル右固有ベクトル.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>evals=spec(A)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         ベクトル<literal>evals</literal> に固有値を返します.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[R,diagevals] =spec(A)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         対角行列r <literal>evals</literal> に固有値,
+                        
                         <literal>R</literal>に固有ベクトルを返します.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>evals=spec(A,B)</term>
+                
                 <listitem>
+                    
                     <para>行列ペンシル A - s B のスペクトル,すなわち,
+                        
                         多項式行列 s B - Aの根,を返します.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[alpha,beta] = spec(A,B)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         行列ペンシル<literal>A- s B</literal>のスペクトル,
+                        
                         すなわち,多項式行列 <literal>A - s B</literal>の根を返します.
+                        
                         一般化固有値 alpha と beta は行列 
+                        
                         <literal>A - alpha./beta B</literal> が特異行列となる値です.
+                        
                         固有値は <literal>al./be</literal> により指定され,
+                        
                         <literal>beta(i) = 0</literal>の場合,i番目の固有値は無限大となります.
+                        
                         (<literal>B = eye(A)</literal>の場合, <literal>alpha./beta</literal>は
+                        
                         <literal>spec(A)</literal>となります).
+                        
                         通常,beta=0や両方がゼロの場合に関して都合が良い解釈が存在するため,
+                        
                         (alpha,beta)の組み合わせで表されます.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[alpha,beta,R] = spec(A,B)</term>
+                
                 <listitem>
+                    
                     <para>上記に加えてペンシルの一般化右固有ベクトルとなる
+                        
                         行列 <literal>R</literal>を返します.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[al,be,L,R] = spec(A,B)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         上記に加えてペンシルの一般化右および左固有ベクトルである行列
+                        
                         <literal>L</literal> および<literal>R</literal>を返します.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[al,be,Z] = spec(A,E)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         一般化右固有ベクトルである行列 <literal>Z</literal> を返します.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[al,be,Q,Z] = spec(A,E)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         一般化右および左固有ベクトルである行列 <literal>Q</literal>
+                        
                         および <literal>Z</literal>を返します.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
         <para>大きな完全 / 疎行列の場合, Arnoldi モジュールを使用することができます.</para>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <para>行列の固有値計算は Lapack ルーチンに基づいています</para>
+        
         <itemizedlist>
+            
             <listitem>
+                
                 <para>行列が対称でない場合, DGEEV および ZGEEV.</para>
+                
             </listitem>
+            
             <listitem>
+                
                 <para>行列が対称の場合, DSYEV および ZHEEV.</para>
+                
             </listitem>
+            
         </itemizedlist>
+        
         <para>複素対象行列は複素共役の非対角項と実数の対角項を有します.</para>
+        
         <para>ペンシル固有値計算は Lapack ルーチン
+            
             DGGEV および ZGGEVに基づいています.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>実数および複素行列</title>
+        
         <para>
+            
             例えば evals や R のような出力変数の型は入力行列 A および B の型と
+            
             同じである必要はないことに注意してください.
+            
             以下のパラグラフでは、行列 A の固有値および固有ベクトルを
+            
             計算する際の出力変数の型を解析します.
+            
         </para>
+        
         <itemizedlist>
+            
             <listitem>
+                
                 <para>実数 A 行列</para>
+                
                 <itemizedlist>
+                    
                     <listitem>
+                        
                         <para>対称</para>
+                        
                         <para>固有値と固有ベクトルは実数.</para>
+                        
                     </listitem>
+                    
                     <listitem>
+                        
                         <para>非対称</para>
+                        
                         <para>固有値と固有ベクトルは複素数.</para>
+                        
                     </listitem>
+                    
                 </itemizedlist>
+                
             </listitem>
+            
             <listitem>
+                
                 <para>複素 A 行列</para>
+                
                 <itemizedlist>
+                    
                     <listitem>
+                        
                         <para>対称</para>
+                        
                         <para>固有値は実数だが固有ベクトルは複素数.</para>
+                        
                     </listitem>
+                    
                     <listitem>
+                        
                         <para>非対称</para>
+                        
                         <para>固有値,固有ベクトルは複素数.</para>
+                        
                     </listitem>
+                    
                 </itemizedlist>
+                
             </listitem>
+            
         </itemizedlist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 // MATRIX EIGENVALUES
 A=diag([1,2,3]);
 X=rand(3,3);
 A=inv(X)*A*X;
 spec(A)
+
 x=poly(0,'x');
 pol=det(x*eye()-A)
 roots(pol)
+
 [S,X]=bdiag(A);
 clean(inv(X)*A*X)
+
 // PENCIL EIGENVALUES
 A=rand(3,3);
 [al,be,R] = spec(A,eye(A));
@@ -243,31 +463,60 @@ A=A+%i*rand(A);
 E=rand(A);
 roots(det(A-%s*E))   //complex case
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="poly">poly</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="det">det</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="schur">schur</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="bdiag">bdiag</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="colcomp">colcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="dsaupd">dsaupd</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="dnaupd">dnaupd</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 1739f23..64e9f80 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="sva">
+    
     <refnamediv>
+        
         <refname>sva</refname>
+        
         <refpurpose>特異値近似</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[U,s,V]=sva(A,k)
+            
             [U,s,V]=sva(A,tol)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>k</term>
+                
                 <listitem>
+                    
                     <para>整数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>非負の実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             特異値近似.
+            
         </para>
+        
         <para>
+            
             <literal>k</literal>を&gt;=1の整数とするとき,
+            
             <literal>[U,S,V]=sva(A,k)</literal> は,
+            
             rank(<literal>B</literal>)=<literal>k</literal>として
+            
             <literal>B=U*S*V'</literal>が<literal>A</literal>の最良のL2近似となる
+            
             ような
+            
             <literal>U,S</literal> および<literal>V</literal>を返します.
+            
         </para>
+        
         <para>
+            
             実数<literal>tol</literal>を指定した<literal>[U,S,V]=sva(A,tol)</literal>は,
+            
             <literal>A-B</literal>のL2ノルムである<literal>B=U*S*V'</literal>の
+            
             最大値が<literal>tol</literal>となるような
+            
             <literal>U,S</literal> および <literal>V</literal> を返します.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(5,4)*rand(4,5);
 [U,s,V]=sva(A,2);
@@ -74,13 +132,24 @@ svd(A)
 svd(B)
 clean(svd(A-B))
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="svd">svd</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index da8cd56..d5e536a 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="svd">
+    
     <refnamediv>
+        
         <refname>svd</refname>
+        
         <refpurpose>特異値分解</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>s=svd(X)
+            
             [U,S,V]=svd(X)
+            
             [U,S,V]=svd(X,0) (obsolete)
+            
             [U,S,V]=svd(X,"e")
+            
             [U,S,V,rk]=svd(X [,tol])
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>実数または複素行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>s</term>
+                
                 <listitem>
+                    
                     <para>実数ベクトル (特異値)</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>S</term>
+                
                 <listitem>
+                    
                     <para>実数対角行列 (特異値)</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>U,V</term>
+                
                 <listitem>
+                    
                     <para>直交またはユニタリ正方行列(特異値).</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>[U,S,V] = svd(X)</literal> は
+            
             <literal>X</literal> と同次元で
+            
             降順に非負の対角要素を有する
+            
             対角行列 <literal>S</literal>および
+            
             <literal>X = U*S*V'</literal>となる
+            
             ユニタリ行列 <literal>U</literal> と <literal>V</literal>
-            を出力する.
+            
+            を出力します.
+            
         </para>
+        
         <para>
+            
             <literal>[U,S,V] = svd(X,0)</literal> は
-            "エコノミーサイズ"分解を出力する.
+            
+            "エコノミーサイズ"分解を出力します.
+            
             <literal>X</literal> がm行n列 (m &gt; n)の場合,
+            
             <literal>U</literal> の最初のn列のみが計算され,
-            <literal>S</literal>は n行n列となる.
+            
+            <literal>S</literal>は n行n列となります.
+            
         </para>
+        
         <para>
+            
             <literal>s= svd(X)</literal> は
-            特異値を含むベクトル<literal>s</literal>を返す.
+            
+            特異値を含むベクトル<literal>s</literal>を返します.
+            
         </para>
+        
         <para>
+            
             <literal>[U,S,V,rk]=svd(X,tol)</literal> は
+            
             <literal>rk</literal>に加えて,
+            
             <literal>X</literal> の数値ランク,すなわち
-            <literal>tol</literal>より大きな特異値の数を出力する.
+            
+            <literal>tol</literal>より大きな特異値の数を出力します.
+            
         </para>
+        
         <para>
+            
             <literal>tol</literal>のデフォルト値は
-            <literal>rank</literal>とのもの同じである.
+            
+            <literal>rank</literal>と同じです.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 X=rand(4,2)*rand(2,4)
 svd(X)
 sqrt(spec(X*X'))
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection>
+        
         <title>参考</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="rank">rank</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="colcomp">colcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="rowcomp">rowcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="sva">sva</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="spec">spec</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用される関数</title>
+        
         <para>
+            
             svd 分解はLapackのルーチン DGESVD (実数行列の場合)および
+            
             ZGESVD (複素数の場合)に基づいている.
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index e49df4a..7eae55a 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="givens">
+    
     <refnamediv>
+        
         <refname>givens</refname>
+        
         <refpurpose>ギブンス変換</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>U=givens(xy)
+            
             U=givens(x,y)
+            
             [U,c]=givens(xy)
+            
             [U,c]=givens(x,y)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>x,y</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>xy</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の要素数2の列ベクトル</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>U</term>
+                
                 <listitem>
+                    
                     <para>2x2 ユニタリ行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>c</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の要素数2の列ベクトル</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title><literal>xy = [x;y]</literal>として
+        
         <para>
+            
             <literal>U= givens(x, y)</literal> または <literal>U = givens(xy)</literal> 
+            
             は,次のような<literal>2</literal>x<literal>2</literal> の
+            
             ユニタリ行列 <literal>U</literal> を返します:
+            
         </para>
+        
         <para>
+            
             <literal>U*xy=[r;0]=c</literal>.
+            
         </para>
+        
         <para>
+            
             <note>
+                
                 <literal>givens(x,y)</literal> および <literal>givens([x;y])</literal> は等価であることに
+                
                 注意してください.
+                
             </note>
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=[3,4;5,6];
 U=givens(A(:,1));
 U*A
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index c86903d..9643f73 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="householder">
+    
     <refnamediv>
+        
         <refname>householder</refname>
+        
         <refpurpose>ハウスホルダー直交鏡映行列</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>u=householder(v [,w])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>v</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の列ベクトル</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>w</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>v</literal>と同じ大きさの実数または複素数の列ベクトル.
+                        
                         デフォルト値は<literal>eye(v)</literal>
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>u</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の列ベクトル</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             同じ大きさの列ベクトル
+            
             <literal>v</literal>, <literal> w</literal> を指定すると, 
+            
             <literal>householder(v,w)</literal> は,
+            
             <literal> (eye()-2*u*u')*v</literal>が<literal>w</literal>に比例するような
+            
             ユニタリ列ベクトル<literal>u</literal>を返します.
+            
             <literal>(eye()-2*u*u')</literal> はハウスホルダー直交鏡映行列です.
+            
         </para>
+        
         <para>
+            
             <literal>w</literal> のデフォルト値は <literal> eye(v)</literal>です. 
+            
             この場合,ベクトル<literal> (eye()-2*u*u')*v</literal> はベクトル 
+            
             <literal> eye(v)*norm(v)</literal>です.
+            
         </para>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="givens">givens</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index b9cb69c..0498d89 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="sqroot">
+    
     <refnamediv>
+        
         <refname>sqroot</refname>
+        
         <refpurpose>W*W' エルミート分解</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>sqroot(X)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>対称非負定実または複素行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>X=W*W'</literal> となるようなWを返します(SVDを使用).
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 X=rand(5,2)*rand(2,5);X=X*X';
 W=sqroot(X)
@@ -46,16 +76,30 @@ X=rand(5,2)+%i*rand(5,2);X=X*X';
 W=sqroot(X)
 norm(W*W'-X,1)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="chol">chol</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="svd">svd</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 13d08b1..31a6a6b 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="colcomp">
+    
     <refnamediv>
+        
         <refname>colcomp</refname>
+        
         <refpurpose>列圧縮,カーネル,ヌル空間</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[W,rk]=colcomp(A [,flag] [,tol])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>flag</term>
+                
                 <listitem>
+                    
                     <para>文字列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>W</term>
+                
                 <listitem>
+                    
                     <para>正方正則行列 (基底変換)</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>rk</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         整数 (<literal>A</literal>のランク)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>A</literal>の列圧縮: <literal>Ac = A*W</literal> は
+            
             列圧縮,すなわち <literal>Ac=[0,Af]</literal> となります.
+            
         </para>
+        
         <para>
+            
             ただし, <literal>Af</literal> はフル列ランクを有します:
+            
             rank(<literal>Af</literal>) = rank(<literal>A</literal>) = <literal>rk</literal>.
+            
         </para>
+        
         <para>
+            
             <literal>flag</literal> および <literal>tol</literal> は
+            
             オプションのパラメータ: <literal>flag = 'qr'</literal> 
+            
             または <literal>'svd'</literal> (デフォルトは
+            
             <literal>'svd'</literal>)です.
+            
         </para>
+        
         <para>
+            
             <literal>tol</literal> = 許容誤差パラメータ (デフォルト値は
+            
             <literal>%eps</literal>のオーダー).
+            
         </para>
+        
         <para>
+            
             <literal>W</literal>の最初の<literal>ma-rk</literal>列は,
+            
             <literal>size(A)=(na,ma)</literal>とするとき,
+            
             <literal>A</literal>のカーネルに広がります.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,5);
 [X,r]=colcomp(A);
 norm(A*X(:,1:$-r),1)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="rowcomp">rowcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrf">fullrf</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrfk">fullrfk</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="kernel">kernel</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 6872615..6085443 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="fullrf">
+    
     <refnamediv>
+        
         <refname>fullrf</refname>
+        
         <refpurpose>フルランク分解</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[Q,M,rk]=fullrf(A,[tol])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>実数 (ランク定義時の閾値)</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Q,M</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>rk</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         整数 (<literal>A</literal>のランク)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             フルランク分解 : <literal>fullrf</literal> は,
+            
             <literal>A = Q*M</literal>となるような
+            
             <literal>Q</literal> および <literal>M</literal>を返します.
+            
             ただし,
+            
             range(<literal>Q</literal>)=range(<literal>A</literal>) および
+            
             ker(<literal>M</literal>)=ker(<literal>A</literal>),
+            
             <literal>Q</literal> フル列ランク , <literal>M</literal> フル行ランク,
+            
             <literal>rk = rank(A) = #columns(Q) = #rows(M)</literal>です.
+            
         </para>
+        
         <para>
+            
             <literal>tol</literal> はオプションの実数パラメータです
+            
             (デフォルト値は <literal>sqrt(%eps)</literal>です).
+            
             <literal>A</literal>のランク<literal>rk</literal>は
+            
             <literal>norm(A)*tol</literal>より大きな
+            
             特異値の数として定義されます.
+            
         </para>
+        
         <para>
+            
             Aが対称の場合,
+            
             <literal>fullrf</literal> は <literal>M=Q'</literal>を返します.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,5);
 [Q,M]=fullrf(A);
@@ -83,25 +151,48 @@ norm(Q*M-A,1)
 [X,d]=rowcomp(A);Y=X';
 svd([A,Y(:,1:d),Q])        //span(Q) = span(A) = span(Y(:,1:2))
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="svd">svd</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrfk">fullrfk</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="rowcomp">rowcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="colcomp">colcomp</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index dbac0cf..8ce763a 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="fullrfk">
+    
     <refnamediv>
+        
         <refname>fullrfk</refname>
+        
         <refpurpose>A^kのフルランク分解</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[Bk,Ck]=fullrfk(A,k)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>k</term>
+                
                 <listitem>
+                    
                     <para>整数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Bk,Ck</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             この関数は,<literal>A^k</literal>のフルランク分解,
+            
             すなわち, <literal>Bk*Ck=A^k</literal> を計算します.
+            
             ただし, <literal>Bk</literal> は列フルランク,
+            
             <literal>Ck</literal>は行フルランクです.
+            
             range(<literal>Bk</literal>)=range(<literal>A^k</literal>) 
+            
             および ker(<literal>Ck</literal>)=ker(<literal>A^k</literal>)となります.
+            
         </para>
+        
         <para>
+            
             <literal>k=1</literal>の場合, <literal>fullrfk</literal> は
+            
             <literal>fullrf</literal>と等価になります.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,5);[Bk,Ck]=fullrfk(A,3);
 norm(Bk*Ck-A^3,1)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="fullrf">fullrf</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="range">range</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 2acc8d7..de6c340 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="im_inv">
+    
     <refnamediv>
+        
         <refname>im_inv</refname>
+        
         <refpurpose>原像</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[X,dim]=im_inv(A,B [,tol])
+            
             [X,dim,Y]=im_inv(A,B, [,tol])
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A,B</term>
+                
                 <listitem>
+                    
                     <para>同じ列の数を有する実数または複素数行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         次数が<literal>A</literal>の列の数に等しい直交またはユニタリ正方行列
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>dim</term>
+                
                 <listitem>
-                    <para>整数 (サブスペースの次元)</para>
+                    
+                    <para>整数 (部分空間の次元)</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Y</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         次数が<literal>A</literal>および<literal>B</literal>の行の数に等しい直交行列.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>[X,dim]=im_inv(A,B)</literal> は <literal>(A^-1)(B)</literal>,
+            
             すなわち, <literal>A</literal>への像が range(<literal>B</literal>) に
+            
             あるベクトルを計算します.
+            
         </para>
+        
         <para>
+            
             <literal>X</literal>の最初の列 <literal>dim</literal> は
+            
             <literal>(A^-1)(B)</literal>に広がっています.
+            
         </para>
+        
         <para>
-            <literal>tol</literal> はサブ空間の取り込みを確認するために
+            
+            <literal>tol</literal> は部分空間の取り込みを確認するために
+            
             閾値が使用されており,
+            
             そのデフォルト値は <literal>tol = 100*%eps</literal> です.
+            
             <literal>Y</literal> が返される時,
+            
             <literal>[Y*A*X,Y*B]</literal> は以下のように分割されます:
+            
             <literal>[A11,A12;0,A22]</literal>,<literal>[B1;0]</literal>
+            
         </para>
+        
         <para>
+            
             ただし, <literal>B1</literal>は行フルランク  (
+            
             <literal>rank(B)</literal>に等しい) そして <literal>A22</literal> は
+            
             列フルランクで <literal>dim</literal> 列となります.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=[rand(2,5);[zeros(3,4),rand(3,1)]];B=[[1,1;1,1];zeros(3,2)];
 W=rand(5,5);A=W*A;B=W*B;
@@ -88,22 +161,42 @@ W=rand(5,5);A=W*A;B=W*B;
 svd([A*X(:,1:dim),B])   //vectors A*X(:,1:dim) belong to range(B)
 [X,dim,Y]=im_inv(A,B);[Y*A*X,Y*B]
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="rowcomp">rowcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="spaninter">spaninter</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="spanplus">spanplus</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="linsolve">linsolve</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 1693cac..f468817 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="kernel">
+    
     <refnamediv>
+        
         <refname>kernel</refname>
+        
         <refpurpose>カーネル, ヌル空間</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>W=kernel(A [,tol,[,flag])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数のフル行列または実数疎行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>flag</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         文字列 <literal>'svd'</literal> (デフォルト) または <literal>'qr'</literal>
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>W</term>
+                
                 <listitem>
+                    
                     <para>列フルランク行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>W=kernel(A)</literal> は<literal>A</literal>のカーネル (ヌル空間)を返します. 
+            
             A が列フルランクの場合, 空の行列 [] が返されます.
+            
         </para>
+        
         <para>
+            
             <literal>flag</literal> および <literal>tol</literal> は
+            
             オプションのパラメータです: <literal>flag = 'qr'</literal> 
+            
             または <literal>'svd'</literal> (デフォルトは <literal>'svd'</literal>).
+            
         </para>
+        
         <para>
+            
             <literal>tol</literal> = 許容誤差パラメータ (デフォルト値は <literal>%eps</literal> のオーダ).
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(3,1)*rand(1,3);
 A*kernel(A)
 A=sparse(A);
 clean(A*kernel(A))
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="colcomp">colcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrf">fullrf</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrfk">fullrfk</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="linsolve">linsolve</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index b64aacd..3090517 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="range">
+    
     <refnamediv>
+        
         <refname>range</refname>
+        
         <refpurpose>A^kの範囲</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[X,dim]=range(A,k)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数正方行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>k</term>
+                
                 <listitem>
+                    
                     <para>整数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>直交実数行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>dim</term>
+                
                 <listitem>
+                    
                     <para>整数 (部分空間の次元)</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
-            範囲 <literal>A^k</literal>を計算します ; the first dim rows of <literal>X</literal> の
+            
+            範囲 <literal>A^k</literal>を計算します ; <literal>X</literal> の
+            
             最初の dim 行は, <literal>A^k</literal>の範囲に広がります.
+            
             <literal>X</literal>の最後の行は,
+            
             この直交相補な範囲に広がります.
+            
             <literal>X*X'</literal> は単位行列です.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(4,2)*rand(2,4);   // 4 列ベクトル, 2 独立.
 [X,dim]=range(A,1);dim   // 範囲を計算
+
 y1=A*rand(4,1);          //Aの範囲のベクトル
 y2=rand(4,1);            //Aの範囲にないベクトル
 norm(X(dim+1:$,:)*y1)    //最後のエントリはゼロ, y1 はAの範囲
 norm(X(dim+1:$,:)*y2)    //最後のエントリは非ゼロ
-I=X(1:dim,:)'            //I が範囲の基底is a basis of the range
-coeffs=X(1:dim,:)*y1     // 基底Iに関連るy1の要素
+
+I=X(1:dim,:)'            //I が範囲の基底
+coeffs=X(1:dim,:)*y1     // 基底Iに関連するy1の要素
+
 norm(I*coeffs-y1)        //check
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="fullrfk">fullrfk</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="rowcomp">rowcomp</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用される関数</title>
+        
         <para>
+            
             <literal>range</literal> 関数は,
+            
             <link linkend="svd">svd</link>分解を使用する
+            
             <link linkend="rowcomp">rowcomp</link> 関数
+            
             に基づいています.
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 372e1bd..dc29889 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="rowcomp">
+    
     <refnamediv>
+        
         <refname>rowcomp</refname>
+        
         <refpurpose>行圧縮, 範囲</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[W,rk]=rowcomp(A [,flag [,tol]])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>flag</term>
+                
                 <listitem>
+                    
                     <para>オプションの文字列, 指定可能な値は
+                        
                         <literal>'svd'</literal> または <literal>'qr'</literal>です. 
+                        
                         デフォルト値  <literal>'svd'</literal>はです.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>オプションの非負の実数. デフォルト値は 
+                        
                         <literal>sqrt(%eps)*norm(A,1)</literal>.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>W</term>
+                
                 <listitem>
+                    
                     <para>正方正則行列 (基底の変更)</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>rk</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         整数 (<literal>A</literal>のランク)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>A</literal>の行圧縮. <literal>Ac = W*A</literal> は行圧縮された行列です: すなわち, 
+            
             <literal>Af</literal>を行フルランクとして
+            
             <literal>Ac=[Af;0]</literal> となります.
+            
         </para>
+        
         <para>
+            
             <literal>flag</literal> および <literal>tol</literal> はオプションのパラメータです: <literal>flag='qr'</literal> 
+            
             または <literal>'svd'</literal> (デフォルト <literal>'svd'</literal>).
+            
         </para>
+        
         <para>
+            
             <literal>tol</literal> は許容誤差パラメータです.
+            
         </para>
+        
         <para>
+            
             <literal>W'</literal>の最初の<literal>rk</literal> 列には,
+            
             <literal>A</literal>の範囲が広がります.
+            
         </para>
+        
         <para>
+            
             <literal>W</literal>の最初の(上側の)<literal>rk</literal> 行には,
+            
             <literal>A</literal>の行範囲が広がります.
+            
         </para>
+        
         <para>
+            
             非ゼロベクトル <literal>x</literal> は,
+            
             <literal>W*x</literal>が<literal>Ac</literal>に基づき行圧縮された場合,
+            
             すなわち,その最後の要素のノルムが最初の要素に対して小さい場合に限り,
+            
             range(<literal>A</literal>)に属します.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,4);              // 4 列ベクトル, 2 つは独立.
 [X,dim]=rowcomp(A);Xp=X';
@@ -100,26 +184,50 @@ x=A*rand(4,1);                      //x は span(A)に属します
 y=X*x  
 norm(y(dim+1:$))/norm(y(1:dim))     // 小さい
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="colcomp">colcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrf">fullrf</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrfk">fullrfk</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用される関数</title>
+        
         <para>
+            
             <literal>rowcomp</literal> 関数は<link linkend="svd">svd</link> または
+            
             <link linkend="qr">qr</link> 分解d.
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 156ead1..f15783c 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="aff2ab">
+    
     <refnamediv>
+        
         <refname>aff2ab</refname>
+        
         <refpurpose>線形 (アフィン)関数を A,b に変換</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[A,b]=aff2ab(afunction,dimX,D [,flag])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>Parameters</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>afunction</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         scilab 関数 <literal> Y =fct(X,D) </literal> 
-                        ただし, <literal>X, D, Y</literal> は行列の <literal>list</literal>
+                        
+                        ただし, <literal>X, D, Y</literal> は行列の<literal>リスト</literal>
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>dimX</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         p x 2 整数行列 (<literal>p</literal> は
+                        
                         <literal>X</literal>の行列の数)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>D</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         実数行列の<literal>list</literal>  (または任意の有効なScilab オブジェクト).
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>flag</term>
+                
                 <listitem>
+                    
                     <para>
-                        オプションのパラメータ (<literal>flag='f'</literal> または <literal>flag='sp'</literal>)
+                        
+                        オプションのパラメータ (<literal>flag='f'</literal> 
+                        
+                        または <literal>flag='sp'</literal>)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>b</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>A</literal>と同じ行次元を有する実数ベクトル
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
-            <literal>aff2ab</literal>  はアフィン関数の(正準形式の)行列表現を返します.
+            
+            <literal>aff2ab</literal>は,アフィン関数の(正準形式の)行列表現を返します.
+            
         </para>
+        
         <para>
+            
             <literal>afunction</literal> は以下の規定の構文を有する関数です:
+            
             <literal> Y=afunction(X,D) </literal> 
+            
             ただし, <literal> X=list(X1,X2,...,Xp) </literal> は
+            
             p 個の実数行列のリスト,<literal> Y=list(Y1,...,Yq) </literal> は
+            
             <literal> Xi</literal>に線形に依存するq 個の実数行列のリストです.
+            
             (オプションの) 入力 <literal> D</literal> は, X の関数として
+            
             Yを計算するために必要なパラメータを有しています.
+            
         </para>
+        
         <para>
+            
             <literal> dimX</literal> は p x 2 行列です: <literal>dimX(i)=[nri,nci]</literal>
+            
             は行列<literal>Xi</literal>の行と列の実際の数です.
+            
             これらの次元は,結果の行列<literal>A</literal>の列の次元である
+            
             <literal>na</literal> を以下のように定義します:
+            
             <literal>na=nr1*nc1 +...+ nrp*ncp</literal>.
+            
         </para>
+        
         <para>
+            
             オプションのパラメータ <literal>flag='sp'</literal> が指定された場合,
+            
             結果の行列 <literal>A</literal>は疎行列として返されます.
+            
         </para>
+        
         <para>
+            
             この関数は,未知変数が行列であるような
+            
             線形方程式のシステムを解くために有用です.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 // リアプノフ方程式ソルバ (未知変数1つ, 拘束条件1つ)
 deff('Y=lyapunov(X,D)','[A,Q]=D(:);Xm=X(:); Y=list(A''*Xm+Xm*A-Q)')
@@ -137,13 +235,24 @@ A=rand(3,3);dimX=[3,3];[Af,bf]=aff2ab(f,dimX,list(A));
 Xsol=vec2list(Xf+KerAf*rand(q,1),dimX);
 C=Xsol(:); A*C-C*A
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="linsolve">linsolve</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 1866a5f..3838ddb 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="chol">
+    
     <refnamediv>
+        
         <refname>chol</refname>
+        
         <refpurpose>コレスキー分解</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[R]=chol(X)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の正定対称行列.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>X</literal> が正定の場合, <literal>R = chol(X)</literal> は,
+            
             <literal>R'*R = X</literal>となるような
+            
             上三角行列<literal>R</literal>を出力します.
+            
         </para>
+        
         <para>
+            
             <literal>chol(X)</literal> は<literal>X</literal>の対角項
+            
             と上三角部のみを使用します.
+            
             下三角部は上三角部の転置(複素共役)とみなされます.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>参考文献</title>
+        
         <para>
+            
             コレスキー分解はLapackルーチン DPOTRF (実数行列の場合)および ZPOTRF (複素行列の場合)
+            
             に基づきます.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 W=rand(5,5)+%i*rand(5,5);
 X=W*W';
 R=chol(X);
 norm(R'*R-X)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="spchol">spchol</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="svd">svd</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="bdiag">bdiag</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="fullrf">fullrf</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index a0f14ae..64e289d 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="inv">
+    
     <refnamediv>
+        
         <refname>inv</refname>
+        
         <refpurpose>逆行列</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>inv(X)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の正方行列, 多項式行列および
+                        
                         伝達関数または状態空間表現の有理行列.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
-            <literal>inv(X)</literal> は正方行列 <literal>X</literal>の逆行列
-            となる. 
+            
+            <literal>inv(X)</literal> は,正方行列 <literal>X</literal>の逆行列
+            
+            となります. 
+            
             <literal>X</literal> のスケーリングが
-            悪い場合や特異行列に近い場合には警告を出力する.
+            
+            悪い場合や特異行列に近い場合には警告を出力します.
+            
         </para>
+        
         <para>
+            
             多項式行列または伝達関数表現の有理行列の場合,
-            <literal>inv(X)</literal> は <literal>invr(X)</literal>に等しくなる.
+            
+            <literal>inv(X)</literal> は <literal>invr(X)</literal>に等しくなります.
+            
         </para>
+        
         <para>
+            
             状態空間表現の線形システム(<literal>syslin</literal> リスト)の場合,
-            <literal>invr(X)</literal> は <literal>invsyslin(X)</literal>に等しくなる.
+            
+            <literal>invr(X)</literal> は <literal>invsyslin(X)</literal>に等しくなります.
+            
         </para>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <para>
+            
             数値行列用の<literal>inv</literal> 関数は Lapack ルーチン
+            
             DGETRF, DGETRI (実数行列の場合)および  ZGETRF, ZGETRI
-            (複素数の場合)に基づいている.
+            
+            (複素数の場合)に基づいています.
+            
             多項式および有理行列に関する <literal>inv</literal> は
-            Scilab関数<literal>invr</literal>に基づいている.
+            
+            Scilab関数<literal>invr</literal>に基づいています.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(3,3);inv(A)*A
 x=poly(0,'x');
@@ -71,37 +124,72 @@ A=ssrand(2,2,3);
 W=inv(A)*A
 clean(ss2tf(W))
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection>
+        
         <title>参考</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="slash">slash</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="backslash">backslash</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="pinv">pinv</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="lufact">lufact</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="lusolve">lusolve</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="invr">invr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="coff">coff</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="coffg">coffg</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 097b0b4..f34d07e 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="linsolve">
+    
     <refnamediv>
+        
         <refname>linsolve</refname>
+        
         <refpurpose>線形方程式ソルバ</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         a <literal>na x ma</literal> 実数行列 (疎行列の場合もあり)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>b</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>na x 1</literal>ベクトル (<literal>A</literal>の行と同じ次元)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>x0</term>
+                
                 <listitem>
+                    
                     <para>実数ベクトル</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>kerA</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>ma x k</literal> 実数行列
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>linsolve</literal>  は,
+            
             <literal> A*x+b=0</literal>の解を全て計算します.
+            
         </para>
+        
         <para>
+            
             <literal>x0</literal> は特解 (存在する場合),
+            
             <literal> kerA </literal> は<literal>A</literal>のヌル空間です.
+            
             任意の<literal>w</literal>について<literal>x=x0+kerA*w</literal>は,
+            
             <literal> A*x+b=0</literal>を満たします.
+            
         </para>
+        
         <para>
-            互換性のある <literal>x0</literal> がエントリに指定された場合, <literal>x0</literal>が返されます. 
+            
+            互換性のある <literal>x0</literal> がエントリに指定された場合, 
+            
+            <literal>x0</literal>が返されます. 
+            
             そうでない場合,<literal>x0</literal>と互換性のあるもの(存在する場合)が返されます.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(5,3)*rand(3,8);
 b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //compatible b
@@ -91,28 +158,54 @@ tic();
 res = A\b;
 mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="inv">inv</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="pinv">pinv</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="colcomp">colcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="im_inv">im_inv</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="umfpack">umfpack</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="backslash">backslash</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 5fd914a..51c5518 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="lsq">
+    
     <refnamediv>
+        
         <refname>lsq</refname>
+        
         <refpurpose>線形最小二乗問題.  </refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>X=lsq(A,B [,tol])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の (m x n) 行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>B</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の (m x p) 行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>Aの実効ランクを定義するために使用される正のスカラー
+                        
                         (Aのピボット操作付きQR分解における最前部にある部分三角行列R11の次数として
+                        
                         定義され,条件数の推定値は&lt;= 1/tolとなります.
+                        
                         tolのデフォルト値は <literal>sqrt(%eps)</literal>に設定されます )
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の (n x p) 行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>X=lsq(A,B)</literal> は方程式 <literal>A*X=B</literal>の
+            
             最小二乗解の最小ノルムを計算します.
+            
             一方, <literal>X=A \ B</literal>は
+            
             各列に最大<literal>rank(A)</literal>個の非ゼロ要素を有する最小二乗解を計算します.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>参考文献</title>
+        
         <para>
+            
             <literal>lsq</literal> 関数はLApack 関数 DGELSY (実行列の場合)および
+            
             ZGELSY (複素行列の場合)に基づいています.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 //Build the data
 x=(1:10)';
@@ -89,22 +151,42 @@ X1=lsq(A,b)
 X2=A\b
 [A*X1-b, A*X2-b] //the residuals are the same
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="backslash">backslash</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="inv">inv</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="pinv">pinv</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="rank">rank</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 824c234..6ce19d0 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="lu">
+    
     <refnamediv>
+        
         <refname>lu</refname>
+        
         <refpurpose>ピボット選択付きのLU 分解</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[L,U]= lu(A)
+            
             [L,U,E]= lu(A)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>Parameters</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列 (m x n).</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>L</term>
+                
                 <listitem>
+                    
                     <para> 実数または複素数の行列  (m x min(m,n)).</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>U</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列  (min(m,n) x n ).</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>E</term>
+                
                 <listitem>
+                    
                     <para>a (n x n) 置換行列.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>[L,U]= lu(A)</literal> は,
+            
             <literal>U</literal>を上三角行列,
+            
             <literal>L</literal>を何らかの特別な構造を持たない一般的な行列として,
+            
             <literal>A = L*U</literal> となるような
+            
             2つの行列 <literal>L</literal> および
+            
             <literal>U</literal> を出力します.
+            
             実際は,行列<literal>A</literal>は<literal>E*A=B*U</literal>
+            
             のように分解されます.
+            
             ただし, 行列<literal>B</literal>は下三角行列,
+            
             行列<literal>L</literal>は<literal>L=E'*B</literal>から計算されます.
+            
         </para>
+        
         <para>
+            
             <literal>A</literal> がランク <literal>k</literal>を有している場合, 
+            
             <literal>U</literal>の行 <literal>k+1</literal> から
+            
             <literal>n</literal> までは 0 となります.
+            
         </para>
+        
         <para>
+            
             <literal>[L,U,E]= lu(A)</literal> は,
+            
             上三角行列<literal>U</literal>および
+            
             置換行列を <literal>E</literal>とした下三角行列 <literal>E*L</literal>,
+            
             により<literal>E*A = L*U</literal>となるような
+            
             3つの行列 <literal>L</literal>, <literal>U</literal> および
+            
             <literal>E</literal>を出力します.
+            
         </para>
+        
         <para>
+            
             <literal>A</literal> が実数行列の場合, 
+            
             関数<literal>lufact</literal> および  <literal>luget</literal>を
+            
             用いることにより,
+            
             置換行列を得ることができます.
+            
             <literal>A</literal>がフルランクでない場合,行列 <literal>L</literal>
+            
             の列圧縮も得ることができる.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例 #1</title>
+        
         <para>
+            
             以下の例では,大きさ4のヒルバート行列を作成し,
+            
             A=LU と分解します.
+            
             行列 L は下三角行列ではないことに注意してください.
+            
             下三角行列Lを取得するには,
+            
             出力引数 E を Scilab に指定する必要があります.
+            
         </para>
+        
         <programlisting role="example"><![CDATA[ 
 a = testmatrix("hilb",4);
 [l,u]=lu(a)
 norm(l*u-a)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例 #2</title>
+        
         <para>
+            
             以下の例では,大きさ4のヒルバート行列を作成し,
+            
             EA=LU と分解します.
+            
             行列 L は下三角行列であることに注意してください.
+            
         </para>
+        
         <programlisting role="example"><![CDATA[ 
 a = testmatrix("hilb",4);
 [l,u,e]=lu(a)
 norm(l*u-e*a)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例 #3</title>
+        
         <para>
+            
             以下の例では, lufact および luget 関数を使用する
+            
             方法を示しています.
+            
         </para>
+        
         <programlisting role="example"><![CDATA[ 
 a=rand(4,4);
 [l,u]=lu(a)
@@ -134,32 +238,62 @@ U=full(U);
 Q=full(Q);
 norm(P*L*U*Q-a)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="lufact">lufact</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="luget">luget</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="lusolve">lusolve</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="svd">svd</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用する関数</title>
+        
         <para>
+            
             lu 分解 Lapack ルーチン DGETRF (実数行列の場合)
+            
             および ZGETRF (複素数の場合) に基づいています.
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 91ffb35..1b59ae1 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="pinv">
+    
     <refnamediv>
+        
         <refname>pinv</refname>
+        
         <refpurpose>擬似逆行列</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>pinv(A,[tol])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             <literal>X= pinv(A)</literal> は,
+            
             <literal>A'</literal>と同じ次元の以下のような
+            
             行列<literal>X</literal>を出力します:
+            
         </para>
+        
         <para>
+            
             <literal>A*X*A = A, X*A*X = X</literal>  そして
+            
             <literal>A*X</literal> および <literal>X*A</literal>
-            はエルミート行列です.
+            
+            は共にエルミート行列です.
+            
         </para>
+        
         <para>
+            
             計算は特異値分解に基づいており,
+            
             許容値よりも小さい特異値は 0 として扱われます:
+            
             この許容誤差は <literal>X=pinv(A,tol)</literal>
+            
             でアクセスされます.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(5,2)*rand(2,4);
 norm(A*pinv(A)*A-A,1)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="rank">rank</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="svd">svd</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用される関数</title>
+        
         <para>
+            
             <literal>pinv</literal> 関数は特異値分解に基づいています
+            
             (Scilab関数 <literal>svd</literal>).
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 366a21f..d1b1acd 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="qr">
+    
     <refnamediv>
+        
         <refname>qr</refname>
+        
         <refpurpose>QR 分解</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[Q,R]=qr(X [,"e"])
+            
             [Q,R,E]=qr(X [,"e"])
+            
             [Q,R,rk,E]=qr(X [,tol])
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>X</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tol</term>
+                
                 <listitem>
+                    
                     <para>非負の実数</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Q</term>
+                
                 <listitem>
+                    
                     <para>正方直交またはユニタリ行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>R</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>X</literal>と同じ次元の行列
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>E</term>
+                
                 <listitem>
+                    
                     <para>置換行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>rk</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         整数 (<literal>X</literal>のQRランク)
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>[Q,R] = qr(X)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>X= Q*R</literal>となるような
+                        
                         <literal>X</literal>と同じ次元の
+                        
                         上三角行列<literal>R</literal>および直交(複素数の場合はユニタリ)行列
+                        
                         <literal>Q</literal>を出力します.
+                        
                         <literal>[Q,R] = qr(X,"e")</literal>は次にように
+                        
                         "エコノミーサイズ"で出力します:
+                        
                         <literal>X</literal> が m行n列 (m &gt; n)の場合,
+                        
                         <literal>Q</literal>の最初のn列のみが
+                        
                         <literal>R</literal>の最初のn行と同時に計算されます.
+                        
                     </para>
+                    
                     <para>
+                        
                         <literal>Q*R = X</literal> から,
+                        
                         行列 <literal>X</literal>のk番目の列は,
+                        
                         (係数 <literal> R(1,k), ..., R(k,k) </literal>を用いて)
+                        
                         <literal>Q</literal>の最初のk列の線形結合で表されます. 
+                        
                         <literal>Q</literal>の最初のk列は,<literal>X</literal>の最初のk列
+                        
                         に広がる部分空間の直交基底を作成します.
+                        
                         <literal>X</literal>の列<literal>k</literal>(すなわち, <literal>X(:,k)</literal> )
+                        
                         が<literal>X</literal>の最初の<literal>p</literal>列の線形結合の場合,
+                        
                         エントリ<literal>R(p+1,k), ..., R(k,k)</literal>は 0 となります.
+                        
                         この場合,<literal>R</literal>は上台形となります.
+                        
                         <literal>X</literal> がランク<literal>rk</literal>を有する場合,
+                        
                         行 <literal>R(rk+1,:), R(rk+2,:), ...</literal> は 0 となります.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[Q,R,E] = qr(X)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>X*E =    Q*R</literal>となるような
+                        
                         (列)置換行列<literal>E</literal>,
+                        
                         降順の対角要素を有する上三角行列 <literal>R</literal>,
+                        
                         直交(またはユニタリ)<literal>Q</literal>
+                        
                         を出力します.
+                        
                         <literal>rk</literal>が<literal>X</literal>のランクの場合,
+                        
                         <literal>R</literal>の主対角項に沿った
+                        
                         最初の<literal>rk</literal>個のエントリ,
+                        
                         すなわち,<literal>R(1,1), R(2,2), ..., R(rk,rk)</literal>は
+                        
                         全て0以外となります.
+                        
                         <literal>[Q,R,E] =  qr(X,"e")</literal> は
+                        
                         "エコノミーサイズ"で出力します:
+                        
                         <literal>X</literal> が m行n列 (m &gt; n)の場合,
+                        
                         <literal>Q</literal>の最初のn列のみが
+                        
                         <literal>R</literal>の最初のn行と同時に計算されます.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[Q,R,rk,E] = qr(X ,tol)</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>rk</literal> = <literal>X</literal>のランクの推定値
+                        
                         を返します.
+                        
                         すなわち, <literal>rk</literal>は,
+                        
                         指定した閾値<literal>tol</literal>より大きな
+                        
                         <literal>R</literal>の対角要素の数となります.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>[Q,R,rk,E] = qr(X) </term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>rk</literal> = <literal>X</literal>のランクの推定値
+                        
                         を返します.
+                        
                         すなわち,<literal>rk</literal> は
+                        
                         <literal>tol=R(1,1)*%eps*max(size(R))</literal>より大きな
+                        
                         <literal>R</literal>の対角要素の数となります.
+                        
                         <literal>R</literal>の条件数を用いる
+                        
                         ランク計算型のQR分解については,<literal>rankqr</literal>を
+                        
                         参照してください.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 // QR factorization, generic case
 // X is tall (full rank)
@@ -170,33 +315,64 @@ A=rand(5,2)*rand(2,5);
 norm(Q'*A-R)
 svd([A,Q(:,1:rk)])    //span(A) =span(Q(:,1:rk))
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="rankqr">rankqr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="rank">rank</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="svd">svd</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="rowcomp">rowcomp</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="colcomp">colcomp</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用する関数</title>
+        
         <para>
+            
             qr 分解はLapack ルーチン DGEQRF, DGEQPF,
+            
             DORGQR (実数行列)および  ZGEQRF, ZGEQPF, ZORGQR (複素数の場合)
+            
             に基づいています.
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 305e725..b6013b2 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="rankqr">
+    
     <refnamediv>
+        
         <refname>rankqr</refname>
+        
         <refpurpose>QR分解に基づく階数</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[Q,R,JPVT,RANK,SVAL]=rankqr(A, [RCOND,JPVT])</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>A</term>
+                
                 <listitem>
+                    
                     <para>実数または複素数の行列</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>RCOND</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>A</literal>の実効階数(ランク)を定義するために使用される実数です.
+                        
                         この階数は,
+                        
                         <literal>A</literal>のピボット選択付きのQR分解の中の
+                        
                         最大の先頭の部分三角行列<literal>R11</literal>の次数として定義されます.
+                        
                         その推定された条件数は &lt; <literal>1/RCOND</literal> となります.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>JPVT</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         エントリの整数ベクトル, <literal>JPVT(i)</literal> が 0でない場合,
+                        
                         <literal> A</literal>の<literal>i</literal>列目は
+                        
                         <literal>AP</literal>の先頭と交換され,
+                        
                         それ以外の場合,<literal>i</literal>は自由な列となります.
+                        
                         処理終了時に<literal>JPVT(i) = k</literal>の場合,
+                        
                         <literal>A*P</literal>の<literal>i</literal>列目は,
+                        
                         <literal>A</literal>の<literal>k</literal>列目となっています.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>RANK</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         <literal>A</literal>の実効ランク,すなわち,
+                        
                         部分行列<literal>R11</literal>の次数.
+                        
                         これは,<literal>A</literal>の完全な直交分解における
+                        
                         部分行列<literal>T1</literal>の次数と同じです.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>SVAL</term>
+                
                 <listitem>
+                    
                     <para>
+                        
                         3つの要素を有する実数ベクトル;三角分解<literal>R</literal>の
+                        
                         特異値の推定値.
+                        
                     </para>
+                    
                     <para>
+                        
                         <literal>SVAL(1)</literal> は,
+                        
                         <literal>R(1:RANK,1:RANK)</literal>の最大特異値です;
+                        
                     </para>
+                    
                     <para>
+                        
                         <literal>SVAL(2)</literal> は,
+                        
                         <literal>R(1:RANK,1:RANK)</literal>の最小特異値です;
+                        
                     </para>
+                    
                     <para>
+                        
                         <literal>SVAL(3)</literal> は,
+                        
                         <literal>RANK</literal> &lt; <literal>MIN(M,N)</literal>の場合,
+                        
                         <literal>R(1:RANK+1,1:RANK+1)</literal>,
+                        
                         そうでない場合, <literal>R(1:RANK,1:RANK)</literal>の最小特異値です.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             実数または複素数のM行N列一般行列<literal>A</literal>の(オプションで)
+            
             ランク出力を伴なうQR分解を計算します.
+            
             ランクが不完全になる可能性があり,実効ランクを条件数のインクリメンタル推定により
+            
             推定します.
+            
         </para>
+        
         <para>
+            
             このルーチンは列ピボット選択付きのQR分解を使用します:
+            
         </para>
+        
         <programlisting role=""><![CDATA[ 
 A * P = Q * R,  where  R = [ R11 R12 ],
                            [  0  R22 ]
  ]]></programlisting>
+        
         <para>
+            
             <literal>R11</literal>は,条件数の推定値が<literal>1/RCOND</literal>未満となる
+            
             最大の部分行列として定義されます.
+            
             <literal>R11</literal>, <literal>RANK</literal>の次数は,
+            
             <literal>A</literal>の実効階数です.
+            
         </para>
+        
         <para>
+            
             三角分解が階数出力を伴なう場合 (これは先頭の列が健全(well-conditioned)な場合です),
+            
             <literal>SVAL(1)</literal>は<literal>A</literal>の最大特異値の
+            
             推定値となり,<literal>SVAL(2)</literal> および
+            
             <literal>SVAL(3)</literal>は,それぞれ <literal>A</literal>の
+            
             <literal>RANK</literal>番目および<literal>(RANK+1)</literal>番目の
+            
             特異値の推定値となります.
+            
         </para>
+        
         <para>
+            
             これらの値を評価することにより,選択した<literal>RCOND</literal>の
+            
             値により階数が良好に定義されることを確認することができます.
+            
             比 <literal>SVAL(1)/SVAL(2)</literal> は,
+            
             <literal>R(1:RANK,1:RANK)</literal>の条件数の推定値です.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 A=rand(5,3)*rand(3,7);
 [Q,R,JPVT,RANK,SVAL]=rankqr(A,%eps)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="qr">qr</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="rank">rank</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>使用される関数</title>
+        
         <para>
+            
             Slicot library routines MB03OD, ZB03OD.
+            
         </para>
+        
     </refsection>
+    
 </refentry>
+
index 529b291..48055e4 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="classmarkov">
+    
     <refnamediv>
+        
         <refname>classmarkov</refname>
-        <refpurpose>マルコフ行列の再帰的(recurrent)および一時的(transient)なクラス</refpurpose>
+        
+        <refpurpose>マルコフ行列の再帰的かつ一時的なクラス</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[perm,rec,tr,indsRec,indsT]=classmarkov(M)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>M</term>
+                
                 <listitem>
+                    
                     <para>実数 N x N マルコフ行列. 各行のエントリの合計を
+                        
                         1に加えたもの
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>perm</term>
+                
                 <listitem>
-                    <para>整数置換ベクトル.</para>
+                    
+                    <para>整数交換ベクトル.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>rec, tr</term>
+                
                 <listitem>
+                    
                     <para>整数ベクトル, 数値 (各再帰的クラスにおける状態量の数,
+                        
                         一時的な状態量の数).
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>indsRec,indsT</term>
+                
                 <listitem>
+                    
                     <para>整数ベクトル. (再帰的および一時的な状態量の添字).</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             以下のような置換ベクトル<literal>perm</literal>を返します
+            
         </para>
+        
         <programlisting role=""><![CDATA[ 
 M(perm,perm) = [M11 0 0 0 0   0]
                [0 M22 0 0     0]
@@ -65,35 +114,63 @@ M(perm,perm) = [M11 0 0 0 0   0]
                [0 0       Mrr 0]
                [* *        *  Q]
  ]]></programlisting>
+        
         <para>
+            
             各 <literal>Mii</literal> は<literal>rec(i)  i=1,..,r</literal>次の
+            
             マルコフ行列です.
-            <literal>Q</literal> は<literal>tr</literal>次のサブマルコフ行列です.
+            
+            <literal>Q</literal>は,<literal>tr</literal>次のサブマルコフ行列です.
+            
             1 から sum(rec)の状態量は再帰的で,
+            
             r+1からnは一時的な状態量です.
+            
             <literal>perm=[indsRec,indsT]</literal>となります.
+            
             ただし, indsRec は大きさ sum(rec)のベクトル,
+            
             indsT は大きさ trのベクトルです.
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 //P は2つの再帰的なクラス (2および1個の状態量を有する) 2つの一時的な状態量
 P=genmarkov([2,1],2,'perm')
 [perm,rec,tr,indsRec,indsT]=classmarkov(P);
 P(perm,perm)
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="genmarkov">genmarkov</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="eigenmarkov">eigenmarkov</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 17f2e1a..11762fb 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="eigenmarkov">
+    
     <refnamediv>
+        
         <refname>eigenmarkov</refname>
+        
         <refpurpose>正規化された左および右マルコフ固有ベクトル</refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>[M,Q]=eigenmarkov(P)</synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>P</term>
+                
                 <listitem>
+                    
                     <para>実数 N x N マルコフ行列. 1に加える各行のエントリの合計.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>M</term>
+                
                 <listitem>
+                    
                     <para>N個の列を有する実数行列.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>Q</term>
+                
                 <listitem>
+                    
                     <para>N個の行を有する実数行列.</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
         </variablelist>
+        
     </refsection>
+    
     <refsection>
+        
         <title>説明</title>
+        
         <para>
+            
             マルコフ推移行列 P の固有値 1 に関連する
+            
             正規化された左および右固有ベクトルを返します.
+            
             この固有値の多重度が m で, Pが N x N の場合,
+            
             M は m x N 行列で Q は N x m 行列となります.
+            
             M(k,:) はk番目のエルゴード集合(再帰的クラス)に関連する
+            
             確率分布ベクトルです.
+            
             M(k,x) は x が k番目の再帰的クラスにない場合には
+            
             0となります.
+            
             Q(x,k) はx から始まる k 番目の再帰的クラスに最終的にある確率です.
+            
             大きな<literal>k</literal>に関して<literal>P^k</literal> が
+            
             収束する場合(1以外に単位円上に固有値がない),
+            
             極限は<literal>Q*M</literal>となります(固有投影).
+            
         </para>
+        
     </refsection>
+    
     <refsection>
+        
         <title>例</title>
+        
         <programlisting role="example"><![CDATA[ 
 //P は2つの再帰的なクラス (2および1個の状態量を有する) 2つの一時的な状態量
 P=genmarkov([2,1],2) 
@@ -68,16 +121,30 @@ P=genmarkov([2,1],2)
 P*Q-Q
 Q*M-P^20
  ]]></programlisting>
+        
     </refsection>
+    
     <refsection role="see also">
+        
         <title>参照</title>
+        
         <simplelist type="inline">
+            
             <member>
+                
                 <link linkend="genmarkov">genmarkov</link>
+                
             </member>
+            
             <member>
+                
                 <link linkend="classmarkov">classmarkov</link>
+                
             </member>
+            
         </simplelist>
+        
     </refsection>
+    
 </refentry>
+
index 741fda9..287e19b 100644 (file)
@@ -1,4 +1,5 @@
 <?xml version="1.0" encoding="UTF-8"?>
+
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * 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="genmarkov">
+    
     <refnamediv>
+        
         <refname>genmarkov</refname>
+        
         <refpurpose>
+            
             再帰的および一時的なクラスを有するランダムなマルコフ行列を生成する
+            
         </refpurpose>
+        
     </refnamediv>
+    
     <refsynopsisdiv>
+        
         <title>呼び出し手順</title>
+        
         <synopsis>M=genmarkov(rec,tr)
+            
             M=genmarkov(rec,tr,flag)
+            
         </synopsis>
+        
     </refsynopsisdiv>
+    
     <refsection>
-        <title>パラメータ</title>
+        
+        <title>引数</title>
+        
         <variablelist>
+            
             <varlistentry>
+                
                 <term>rec</term>
+                
                 <listitem>
+                    
                     <para>整数行ベクトル (次元は再帰的クラスの数).</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>tr</term>
+                
                 <listitem>
+                    
                     <para>整数 (一時的な状態量の数)</para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>M</term>
+                
                 <listitem>
+                    
                     <para>実数のマルコフ行列. 
+                        
                         1に追加する各行のエントリの合計.
+                        
                     </para>
+                    
                 </listitem>
+                
             </varlistentry>
+            
             <varlistentry>
+                
                 <term>flag</term>
+         &nbs