*Bug #14330 fixed - luget was really slow.
[scilab.git] / scilab / modules / core / help / ja_JP / 1_keywords / backslash.xml
index f6bd86e..41f9b05 100644 (file)
 <?xml version="1.0" encoding="UTF-8"?>
 
 <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="backslash">
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     <refnamediv>
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         <refname>backslash</refname>
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         <refpurpose>(\) 左行列除算.</refpurpose>
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     </refnamediv>
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     <refsynopsisdiv>
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         <title>呼び出し手順</title>
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         <synopsis>X=A\B</synopsis>
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     </refsynopsisdiv>
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     <refsection>
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         <title>説明</title>
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         <para>
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             バックスラッシュは左行列除算を定義します.
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             <literal>X=A\B</literal> は <literal>A*X=B</literal>の解です.
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         </para>
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         <para>
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             <literal>A</literal> が正方で非特異の場合,
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             <literal>X=A\B</literal> は <literal>X=inv(A)*B</literal>
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             と等価です.しかし,計算はより正確で浮動小数点演算の負荷は小さくなります.
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             すなわち,線形システムの方程式<code>A*X=B</code>の解を計算する際には,
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             バックスラッシュ演算子を使用するべきであり,<function>inv</function>関数の
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             使用は避けるべきです.
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         </para>
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         <para>
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             <literal>A</literal>が正方の場合, 解<literal>X</literal>は
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             LU分解または線形最小二乗ソルバのどちらかにより計算できます.
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             <literal>A</literal>の条件数が<code>1/(10*%eps)</code>よりも小さい場合
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             (つまり,<literal>A</literal>の条件が良い場合),ピボット選択付きLU分解が使用されます.
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             そうでない場合(<literal>A</literal>の条件が悪い場合),
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             <literal>X</literal> は<literal>A</literal>の完全直交分解を用いて
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             <literal>||A*X-B||</literal>を最小化する最小ノルム解となります
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             (すなわち,<literal>X</literal>は線形最小二乗問題の解です).
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         </para>
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         <para>
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             <literal>A</literal> が正方でない場合, <literal>X</literal> は最小二乗解となります.
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             すなわち, <code>norm(A*X-B)</code> は,最小値 (ユークリッドノルム)となります.
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             <literal>A</literal> が列フルランクの場合,最小二乗解, <literal>X=A\B</literal>, は
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             唯一の解 (<literal>norm(A*X-B)</literal>を最小化する唯一の
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             <literal>X</literal>が存在)となります.
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             <literal>A</literal> が列フルランクでない場合, 最小二乗解は唯一ではなくなり,
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             <literal>X=A\B</literal>は一般に最小ノルム解ではなくなります
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             (最小ノルム解は <literal>X=pinv(A)*B</literal>です).
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         </para>
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         <para>
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             <literal>A.\B</literal>  は<literal>(i,j)</literal> エントリが
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             <literal>A(i,j)\B(i,j)</literal>となる行列となります.
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             <literal>A.\B</literal> は
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             <literal>A*ones(B).\B</literal> (または <literal>A.\(B*ones(A))</literal>
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             と等価になります.
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         </para>
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         <para>
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             <literal>A\.B</literal>  は定義されていない演算子です.
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             この演算子は, <literal>*</literal> または <literal>/</literal> のように
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             新しい演算子を定義する際に使用できます
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             (<link linkend="overloading">オーバーロード</link>参照).
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         </para>
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     </refsection>
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     <refsection>
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         <title>例</title>
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         <programlisting role="example"><![CDATA[
 A=[
    9.   -36.    30.
@@ -157,7 +157,7 @@ A*x-b, A*y-b
 // 複数の線形ソルバのベンチマーク
 
 [A,descr,ref,mtype] = ReadHBSparse(SCI+..
-   "/modules/umfpack/examples/bcsstk24.rsa");
+   "/modules/umfpack/demos/bcsstk24.rsa");
 
 b = zeros(size(A,1),1);
 
@@ -173,79 +173,79 @@ tic();
 res = A\b;
 mprintf('\ntime with backslash: %.3f\n',toc());
  ]]></programlisting>
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     </refsection>
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     <refsection role="see also">
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         <title>参照</title>
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         <simplelist type="inline">
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             <member>
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                 <link linkend="slash">slash</link>
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             </member>
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             <member>
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                 <link linkend="inv">inv</link>
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             </member>
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             <member>
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                 <link linkend="pinv">pinv</link>
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             </member>
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             <member>
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                 <link linkend="percent">percent</link>
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             </member>
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             <member>
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                 <link linkend="ieee">ieee</link>
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             </member>
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             <member>
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                 <link linkend="linsolve">linsolve</link>
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             </member>
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             <member>
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                 <link linkend="umfpack">umfpack</link>
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             </member>
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         </simplelist>
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     </refsection>
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     <refsection>
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         <title>履歴</title>
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         <revhistory>
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             <revision>
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                 <revnumber>5.4.1</revnumber>
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                 <revremark>バックスラッシュの条件数の閾値が増加しました.</revremark>
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             </revision>
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         </revhistory>
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     </refsection>
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 </refentry>