* Bug 16145 fixed: intg() integrate() intc() default atol
[scilab.git] / scilab / modules / differential_equations / help / ja_JP / integrate.xml
index 8c1aef1..4602074 100644 (file)
@@ -1,10 +1,9 @@
 <?xml version="1.0" encoding="UTF-8"?>
-
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
- *
  * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ * Copyright (C) 2020 - Samuel GOUGEON
  *
  * This file is hereby licensed under the terms of the GNU GPL v2.0,
  * pursuant to article 5.3.4 of the CeCILL v.2.1.
  * along with this program.
  *
  -->
-
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="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="integrate" xml:lang="ja">
-
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns3="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="integrate" xml:lang="ja">
     <refnamediv>
-
         <refname>integrate</refname>
-
         <refpurpose>求積法による式の積分</refpurpose>
-
     </refnamediv>
-
     <refsynopsisdiv>
-
         <title>呼び出し手順</title>
-
-        <synopsis>x=integrate(expr,v,x0,x1 [,atol [,rtol]])</synopsis>
-
+        <synopsis>
+          y = integrate(expr, v, x0, x1)
+          y = integrate(expr, v, x0, x1, atol)
+          y = integrate(expr, v, x0, x1, atol, rtol)
+        </synopsis>
     </refsynopsisdiv>
-
     <refsection>
-
         <title>引数</title>
-
         <variablelist>
-
             <varlistentry>
-
                 <term>expr</term>
-
                 <listitem>
-
-                    <para>文字列, Scilab 式を定義</para>
-
+                    文字列, Scilab 式を定義
+                    <para/>
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>v</term>
-
                 <listitem>
-
-                    <para>文字列, 積分変数名</para>
-
+                    文字列, 積分変数名
+                    <para/>
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>x0</term>
-
                 <listitem>
-
-                    <para>実数, 積分区間の下限</para>
-
+                    実数, 積分区間の下限
+                    <para/>
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>x1</term>
-
                 <listitem>
-
-                    <para>実数のベクトル, 積分区間の上限</para>
-
+                    実数のベクトル, 積分区間の上限
+                    <para/>
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>atol</term>
-
                 <listitem>
-
-                    <para>実数 (絶対許容誤差) デフォルト値: 1.-8</para>
-
+                    実数 (絶対許容誤差) デフォルト値: 1e-13
+                    <para/>
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>rtol</term>
-
                 <listitem>
-
-                    <para>実数, (相対許容誤差) デフォルト値:
-
-                        1e-14
-
-                    </para>
-
+                    実数, (相対許容誤差) デフォルト値: 1e-8
+                    <para/>
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
-                <term>x</term>
-
+                <term>y</term>
                 <listitem>
-
-                    <para>実数のベクトル,
-
-                        各<literal>x1(i)</literal>に関する積分値.
-
-                    </para>
-
+                    実数のベクトル, 各<literal>x1(i)</literal>に関する積分値.
+                    <para/>
                 </listitem>
-
             </varlistentry>
-
         </variablelist>
-
     </refsection>
-
     <refsection>
-
         <title>説明</title>
-
         <para>
-
-            以下を計算します :
-
-            <subscript>
-
-                <inlinemediaobject>
-
-                    <imageobject>
-
-                        <imagedata>
-
-                            <mml:math display="block">
-
-                                <mml:mi mathvariant="normal">x</mml:mi>
-
-                                <mml:mrow>
-
-                                    <mml:mrow>
-
-                                        <mml:mo>(</mml:mo><mml:mi mathvariant="normal">i</mml:mi><mml:mo>)</mml:mo>
-
-                                    </mml:mrow>
-
-                                    <mml:mo>=</mml:mo>
-
-                                    <mml:mrow>
-
-                                        <mml:msubsup>
-
-                                            <mml:mo>∫</mml:mo>
-
-                                            <mml:msub>
-
-                                                <mml:mi mathvariant="normal">x</mml:mi><mml:mn>0</mml:mn>
-
-                                            </mml:msub>
-
-                                            <mml:mrow>
-
-                                                <mml:msub>
-
-                                                    <mml:mi mathvariant="normal">x</mml:mi><mml:mn>1</mml:mn>
-
-                                                </mml:msub>
-
-                                                <mml:mrow>
-
-                                                    <mml:mo>(</mml:mo><mml:mi mathvariant="normal">i</mml:mi><mml:mo>)</mml:mo>
-
-                                                </mml:mrow>
-
-                                            </mml:mrow>
-
-                                        </mml:msubsup>
-
-                                        <mml:mi mathvariant="normal">f</mml:mi>
-
-                                    </mml:mrow>
-
-                                </mml:mrow>
-
-                                <mml:mrow>
-
-                                    <mml:mo>(</mml:mo><mml:mi mathvariant="normal">v</mml:mi><mml:mo>)</mml:mo>
-
-                                </mml:mrow>
-
-                                <mml:mi>d</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:annotation mml:encoding="StarMath 5.0">x(i)=int_{x_0}^{x_1(i)}
-
-                                    f(v)dv
-
-                                </mml:annotation>
-
-                            </mml:math>
-
-                        </imagedata>
-
-                    </imageobject>
-
-                </inlinemediaobject>
-
-            </subscript>
-
-            for
-
-            <literal>i=1:size(x1,'*')</literal>
-
-        </para>
-
-        <para>
-
-            ただし
-
-            <inlinemediaobject>
-
-                <imageobject>
-
-                    <imagedata>
-
-                        <mml:math display="block">
-
-                            <mml:mi mathvariant="normal">f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">v</mml:mi><mml:mo>)</mml:mo>
-
-                        </mml:math>
-
-                    </imagedata>
-
-                </imageobject>
-
-            </inlinemediaobject>
-
-            は式
-
-            <literal>expr</literal>で指定されます.
-
+            以下を計算します
+            <latex alt="y(i) = integral_{x_0}^{x_1(i)} f(v).dv">
+                y(i) = \int_{x_0}^{x_1(i)} f(v)\,dv
+            </latex>
+            for <literal>i=1:size(x1,'*')</literal>, ただし <emphasis>f(v)</emphasis>
+            は式 <literal>expr</literal>で指定されます.
         </para>
-
         <para>
-
             この処理は以下の精度指標を満足することが期待されます:
-
-            <literal>abs(I-x)&lt;= max(atol,rtol*abs(I))</literal> ただし
-
+            <literal>abs(I-y) &lt;= max(atol, rtol*abs(I))</literal> ただし
             <literal>I</literal>はこの積分の真値を意味します.
-
         </para>
-
-    </refsection>
-
-    <refsection>
-
-        <title>制約</title>
-
         <para>
-
-            式を指定する際に
-
-            <literal>%</literal>から始まる変数名を使用することはできません.
-
+            <warning>
+                制約: 式を指定する際に <literal>%</literal>から始まる変数名を使用することはできません.
+            </warning>
         </para>
-
     </refsection>
-
     <refsection>
-
         <title>例</title>
-
         <programlisting role="example"><![CDATA[
-x0=0;x1=0:0.1:2*%pi;
-X=integrate('sin(x)','x',x0,x1);
-norm(cos(x1)-(1-X))
- x1=-10:0.1:10;
-X=integrate(['if x==0 then 1,';
-             'else sin(x)/x,end'],'x',0,x1)
- ]]></programlisting>
+x1 = 0:0.1:2*%pi;
+Y = integrate('sin(x)', 'x', 0, x1);
+norm(cos(x1)-(1-Y))
 
+x1 = -10:0.1:10;
+Y = integrate(['if x==0 then 1,';
+               'else sin(x)/x,end'], 'x', 0, x1)
+ ]]></programlisting>
     </refsection>
-
     <refsection role="see also">
-
         <title>参照</title>
-
         <simplelist type="inline">
-
             <member>
-
                 <link linkend="intg">intg</link>
-
             </member>
-
             <member>
-
                 <link linkend="inttrap">inttrap</link>
-
             </member>
-
             <member>
-
                 <link linkend="intsplin">intsplin</link>
-
             </member>
-
             <member>
-
                 <link linkend="ode">ode</link>
-
             </member>
-
         </simplelist>
-
     </refsection>
-
-</refentry>
-
+    <refsection role="history">
+        <title>履歴</title>
+        <revhistory>
+            <revision>
+                <revnumber>6.1.0</revnumber>
+                <revdescription>
+                    Default atol value increased from
+                    10<superscript>-14</superscript> to 10<superscript>-13</superscript>.
+                </revdescription>
+            </revision>
+        </revhistory>
+    </refsection>
+</refentry>
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