Rui Hirokawa [Sun, 20 Apr 2014 15:48:31 +0000 (00:48 +0900)]
Change-Id: I7d3bedfa836cf6f8384ac8c0376d4fa98df63c7b

index 10791d1..44fea6a 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
*
-->
+
+
<refnamediv>
+
<refname>calerf</refname>
+
<refpurpose>誤差関数を計算する.</refpurpose>
+
</refnamediv>
+
<refsection>
-        <title>パラメータ</title>
+
+        <title>引数</title>
+
<variablelist>
+
<varlistentry>
+
<term>x</term>
+
<listitem>
+
<para>実数ベクトルまたは行列</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>flag</term>
+
<listitem>
+
<para>整数インジケータ</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>y</term>
+
<listitem>
+
<para>(xと同じ大きさの)実数ベクトルまたは行列</para>
+
</listitem>
+
</varlistentry>
+
</variablelist>
+
</refsection>
+
<refsection>
+
<title>説明</title>
+
<para>
+
<literal>calerf(x,0)</literal> は誤差関数
+
<literal>erf(x)</literal>を計算します
+
</para>
+
<para>
+
<literal>calerf(x,1)</literal> は相補誤差関数
+
f<literal>erfc(x)</literal>を計算します
+
</para>
+
<para>
+
<literal>calerf(x,2)</literal> はスケーリング付き相補誤差関数
+
<literal>erfcx(x)</literal>を計算します
+
</para>
+
</refsection>
+
<refsection>
+
<title>例</title>
+
<programlisting role="example"><![CDATA[
deff('y=f(t)','y=exp(-t^2)');
calerf(1,0)
2/sqrt(%pi)*intg(0,1,f)
]]></programlisting>
+
</refsection>
+
<refsection>
-        <title>S参照</title>
+
+        <title>アルゴリズム</title>
+
+        <para>
+
+
+            に基づきます.
+
+        </para>
+
+    </refsection>
+
+    <refsection>
+
+        <title>参照</title>
+
<simplelist type="inline">
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
</simplelist>
+
+    </refsection>
+
+    <refsection>
+
+        <title>履歴</title>
+
+        <revhistory>
+
+            <revision>
+
+                <revnumber>5.5.0</revnumber>
+
+
+            </revision>
+
+        </revhistory>
+
</refsection>
+
</refentry>
+
index 6a22d98..08df6fa 100644 (file)
@@ -1,5 +1,7 @@
<?xml version="1.0" encoding="UTF-8"?>

+
+
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
@@ -158,3 +160,5 @@ dawson(-x)

</refentry>

+
+
index e5b18d0..617e7db 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
*
-->
+
+
<refnamediv>
+
<refname>dlgamma</refname>
+
<refpurpose>ガンマ関数, psi関数の微分</refpurpose>
+
</refnamediv>
+
<refsynopsisdiv>
+
<title>呼び出し手順</title>
+
<synopsis>y = dlgamma(x)</synopsis>
+
</refsynopsisdiv>
+
<refsection>
+
<title>パラメータ</title>
+
<variablelist>
+
<varlistentry>
+
<term>x</term>
+
<listitem>
+
<para>実数ベクトル</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>y</term>
+
<listitem>
+
<para>同じ大きさの実数ベクトル.</para>
+
</listitem>
+
</varlistentry>
+
</variablelist>
+
</refsection>
+
<refsection>
+
<title>説明</title>
+
<para>
+
<literal>dlgamma(x)</literal> は,<literal>x</literal>
+
の全ての要素について,
+
ガンマ関数の対数微分を計算します.
+
この値はgammaln関数の微分に一致します:
+
</para>
+
<informalequation>
+
<mediaobject>
+
<imageobject>
+
<imagedata align="center" fileref="../mml/dlgamma_equation1.mml"/>
+
</imageobject>
+
</mediaobject>
+
</informalequation>
+
<para>
+
<literal>x</literal> は実数である必要があります.
+
psi 関数としても知られています.
+
</para>
+
</refsection>
+
<refsection>
+
<title>例</title>
+
<programlisting role="example"><![CDATA[
dlgamma(0.5)
]]></programlisting>
+
</refsection>
+
<refsection role="see also">
+
<title>参照</title>
+
<simplelist type="inline">
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
</simplelist>
+
</refsection>
+
+    <refsection>
+
+        <title>履歴</title>
+
+        <revhistory>
+
+            <revision>
+
+                <revnumber>5.4.0</revnumber>
+
+                <revremark>list, mlist, tlist およびハイパー行列型の
+
+                    オーバーロードが可能となりました.
+                </revremark>
+
+            </revision>
+
+        </revhistory>
+
+    </refsection>
+
</refentry>
+
@@ -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
*
-->
+
+
<refnamediv>
+
<refname>erf</refname>
+
<refpurpose>誤差関数.</refpurpose>
+
</refnamediv>
+
<refsynopsisdiv>
+
<title>呼び出し手順</title>
+
<synopsis>y = erf(x)</synopsis>
+
</refsynopsisdiv>
+
<refsection>
-        <title>パラメータ</title>
+
+        <title>引数</title>
+
<variablelist>
+
<varlistentry>
+
<term>x</term>
+
<listitem>
-                    <para>実数ベクトルまたは行列</para>
+
+                    <para>ベクトルまたは行列</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>y</term>
+
<listitem>
-                    <para>(xと同じ大きさの)実数ベクトルまたは行列 </para>
+
+                    <para>(xと同じ大きさの)ベクトルまたは行列 </para>
+
</listitem>
+
</varlistentry>
+
</variablelist>
+
</refsection>
+
<refsection>
+
<title>説明</title>
+
<para>
+
<literal>erf</literal> は誤差関数を計算します:  <latex>
+
\frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt
+
</latex>
+
</para>
+
</refsection>
+
<refsection>
+
<title>例</title>
-        <programlisting role="example"><![CDATA[
+
+        <programlisting role="example"><![CDATA[
deff('y=f(t)','y=exp(-t^2)');
erf(0.5)-2/sqrt(%pi)*intg(0,0.5,f)

-
x = [1+2*%i, -1+2*%i, 1e-6+2e-6*%i,0+2*%i];
a=erf(x)

+// 以下と等価
1-erfc(x)
]]></programlisting>
+
+    </refsection>
+
+    <refsection>
+
+        <title>アルゴリズム</title>
+
+        <para>
+
+
+            ライブラリに基づきます.
+
+        </para>
+
</refsection>
+
<refsection role="see also">
+
<title>参照</title>
+
<simplelist type="inline">
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
</simplelist>
+
</refsection>
+
+    <refsection>
+
+        <title>履歴</title>
+
+        <revhistory>
+
+            <revision>
+
+                <revnumber>5.5.0</revnumber>
+
+                <revremark>erf関数が複素数の要素をサポート</revremark>
+
+            </revision>
+
+        </revhistory>
+
+    </refsection>
+
</refentry>
+
index 7dccfc0..bed11e1 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
*
-->
+
+
<refnamediv>
+
<refname>erfc</refname>
+
<refpurpose>相補誤差関数.</refpurpose>
+
</refnamediv>
+
<refsynopsisdiv>
+
<title>呼び出し手順</title>
+
<synopsis>y = erfc(x)</synopsis>
+
</refsynopsisdiv>
+
<refsection>
+
<title>パラメータ</title>
+
<variablelist>
+
<varlistentry>
+
<term>x</term>
+
<listitem>
-                    <para>実数ベクトルまたは行列</para>
+
+                    <para>ベクトルまたは行列</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>y</term>
+
<listitem>
-                    <para>(xと同じ大きさの)実数ベクトルまたは行列</para>
+
+                    <para>(xと同じ大きさの)ベクトルまたは行列</para>
+
</listitem>
+
</varlistentry>
+
</variablelist>
+
</refsection>
+
<refsection>
+
<title>説明</title>
+
<para>
+
<literal>erfc</literal> は相補誤差関数を計算します: <latex>1- \operatorname{erf}(x)</latex>
+
</para>
+
</refsection>
+
<refsection>
+
<title>例</title>
+
<programlisting role="example"><![CDATA[
erf([0.5,0.2])+erfc([0.5,0.2])

x = [1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i];
erfc(x)
+
]]></programlisting>
+
+    </refsection>
+
+    <refsection>
+
+        <title>アルゴリズム</title>
+
+        <para>
+
+
+            ライブラリに基づきます.
+
+        </para>
+
</refsection>
+
<refsection role="see also">
+
<title>参照</title>
+
<simplelist type="inline">
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
</simplelist>
+
</refsection>
+
+    <refsection>
+
+        <title>履歴</title>
+
+        <revhistory>
+
+            <revision>
+
+                <revnumber>5.5.0</revnumber>
+
+                <revremark>erfc関数が複素数の要素をサポート</revremark>
+
+            </revision>
+
+        </revhistory>
+
+    </refsection>
+
</refentry>
+
index fb9ce92..6cb2dd4 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
*
-->
+
+
<refnamediv>
+
<refname>erfcx</refname>
+
<refpurpose>スケーリング付き相補誤差関数.</refpurpose>
+
</refnamediv>
+
<refsynopsisdiv>
+
<title>呼び出し手順</title>
+
<synopsis>y = erfcx(x)</synopsis>
+
</refsynopsisdiv>
+
<refsection>
-        <title>パラメータ</title>
+
+        <title>引数</title>
+
<variablelist>
+
<varlistentry>
+
<term>x</term>
+
<listitem>
-                    <para>実数ベクトルまたは行列</para>
+
+                    <para>ベクトルまたは行列</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>y</term>
+
<listitem>
-                    <para>(xと同じ大きさの)実数ベクトルまたは行列</para>
+
+                    <para>(xと同じ大きさの)ベクトルまたは行列</para>
+
</listitem>
+
</varlistentry>
+
</variablelist>
+
</refsection>
+
<refsection>
+
<title>説明</title>
+
<para>
+
<literal>erfcx</literal> はスケーリング付き相互関数を計算します:<latex>e^{x^2} \operatorname{erfc}(x)</latex>
+
</para>
+
</refsection>

+
+
<refsection>
+
<title>例</title>
+
<programlisting role="example"><![CDATA[
x = [1+2*%i,-1+2*%i,1e-6+2e-6*%i,0+2*%i];
erfcx(x)
-// ==
+// 以下と等価
exp (x.^2) .* erfc(x)
]]></programlisting>
+
</refsection>

+    <refsection>
+
+        <title>アルゴリズム</title>
+
+        <para>
+
+
+            ライブラリに基づきます.
+
+        </para>
+
+    </refsection>
+
+
<refsection role="see also">
+
<title>参照</title>
+
<simplelist type="inline">
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
</simplelist>
+
</refsection>
+
+    <refsection>
+
+        <title>履歴</title>
+
+        <revhistory>
+
+            <revision>
+
+                <revnumber>5.5.0</revnumber>
+
+                <revremark>erfcx関数が複素数の要素をサポート</revremark>
+
+            </revision>
+
+        </revhistory>
+
+    </refsection>
+
</refentry>
+
index ebd3a63..c259569 100644 (file)
@@ -1,5 +1,7 @@
<?xml version="1.0" encoding="UTF-8"?>

+
+
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
@@ -149,7 +151,7 @@ erfi(x)

<revnumber>5.5.0</revnumber>

-                <revremark>関数erfiは複素数引数をサポートします</revremark>
+                <revremark>関数erfiが複素数引数をサポート</revremark>

</revision>

@@ -159,3 +161,5 @@ erfi(x)

</refentry>

+
+
index 93598e7..2029b0e 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
*
-->
+
+
<refnamediv>
+
<refname>gamma</refname>
+
<refpurpose>ガンマ関数.</refpurpose>
+
</refnamediv>
+
<refsynopsisdiv>
+
<title>呼び出し手順</title>
+
<synopsis>y = gamma(x)</synopsis>
+
</refsynopsisdiv>
+
<refsection>
+
<title>引数</title>
+
<variablelist>
+
<varlistentry>
+
<term>x</term>
+
<listitem>
+
<para>実数ベクトルまたは行列</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>y</term>
+
<listitem>
+
<para>(xと同じ大きさの)実数ベクトルまたは行列.</para>
+
</listitem>
+
</varlistentry>
+
</variablelist>
+
</refsection>
+
<refsection>
+
<title>説明</title>
+
<para>
+
<literal>gamma(x)</literal> は,
+
<literal>x</literal>の全要素についてガンマ関数を計算します.
+
ガンマ関数は以下のように定義されます:
+
</para>
+
<informalequation>
+
<mediaobject>
+
<imageobject>
+
<imagedata align="center" fileref="../mml/gamma_equation1.mml"/>
+
</imageobject>
+
</mediaobject>
+
</informalequation>
+
<para>そして,階乗関数を実数に一般化します.
+
(<literal>gamma(n+1) = n!</literal>).
+
</para>
+
</refsection>
+
<refsection>
+
<title>例</title>
+
<programlisting role="example"><![CDATA[
// 簡単な例
gamma(0.5)
gamma(6)-prod(1:5)
]]></programlisting>
+
<programlisting role="example"><![CDATA[
// [a,b]のガンマ関数のグラフ
a = -3; b = 5;
@@ -74,35 +123,68 @@ xset("color",c)
xtitle("The gamma function on ["+string(a)+","+string(b)+"]")
show_window()
]]></programlisting>
+
<scilab:image>
+
a = -3; b = 5;
+
x = linspace(a,b,40000)';
+
y = gamma(x);
+
plot2d(x, y, style=0, axesflag=5, rect=[a, -10, b, 10])
+
xtitle("The gamma function on ["+string(a)+","+string(b)+"]")
+
</scilab:image>
+
</refsection>
+
<refsection role="see also">
+
<title>参照</title>
+
<simplelist type="inline">
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
</simplelist>
+
</refsection>
+
<refsection>
+
<title>履歴</title>
+
<revhistory>
+
<revision>
+
<revnumber>5.4.0</revnumber>
+
<revremark>
-                    list, mlist, tlistおよびhypermatrix型のオーバーロードが
+
+                    list, mlist, tlistおよびハイパー行列型のオーバーロードが
+
可能となりました.
+
</revremark>
+
</revision>
+
</revhistory>
+
</refsection>
+
</refentry>
+
index 3a53216..253a34f 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
*
-->
+
+
<refnamediv>
+
<refname>gammaln</refname>
+
<refpurpose>ガンマ関数の対数.</refpurpose>
+
</refnamediv>
+
<refsynopsisdiv>
+
<title>呼び出し手順</title>
+
<synopsis>y = gammaln(x)</synopsis>
+
</refsynopsisdiv>
+
<refsection>
-        <title>パラメータ</title>
+
+        <title>引数</title>
+
<variablelist>
+
<varlistentry>
+
<term>x</term>
+
<listitem>
+
<para>実数ベクトル</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>y</term>
+
<listitem>
+
<para>同じ大きさの実数ベクトル.</para>
+
</listitem>
+
</varlistentry>
+
</variablelist>
+
</refsection>
+
<refsection>
+
<title>説明</title>
+
<para>
+
<literal>gammaln(x)</literal> は<literal>x</literal>
+
の全ての要素に関してオーバーフローおよびアンダーフローを回避しつつ
+
ガンマ関数の対数を計算します.
+
<literal>x</literal>は実数とする必要があります.
+
</para>
+
</refsection>
+
<refsection>
+
<title>例</title>
+
<programlisting role="example"><![CDATA[
gammaln(0.5)
]]></programlisting>
+
</refsection>
+
<refsection role="see also">
+
<title>参照</title>
+
<simplelist type="inline">
+
<member>
+
+
</member>
+
<member>
+
+
</member>
+
</simplelist>
+
</refsection>
+
+    <refsection>
+
+        <title>履歴</title>
+
+        <revhistory>
+
+            <revision>
+
+                <revnumber>5.4.0</revnumber>
+
+                <revremark>
+
+                    list, mlist, tlistおよびハイパー行列型のオーバーロードが
+
+                    可能となりました.
+
+                </revremark>
+
+            </revision>
+
+        </revhistory>
+
+    </refsection>
+
</refentry>
+
index 723abc4..25e6e93 100644 (file)
<?xml version="1.0" encoding="UTF-8"?>
+
+
<refnamediv>
+
<refname>%asn</refname>
-        <refpurpose>楕円積分 l</refpurpose>
+
+        <refpurpose>
+
+            楕円積分.
+
+            <emphasis role="bold">この関数は廃止されます.</emphasis>
+
+        </refpurpose>
+
</refnamediv>
+
<refsynopsisdiv>
+
<title>呼び出し手順</title>
+
<synopsis>[y]=%asn(x,m)</synopsis>
+
</refsynopsisdiv>
+
<refsection>
+
<title>パラメータ</title>
+
<variablelist>
+
<varlistentry>
+
<term>x</term>
+
<listitem>
+
<para>
+
積分の上限 (<literal>x&gt;0</literal>) (ベクトルにすることが可能)
+
</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>m</term>
+
<listitem>
+
<para>
+
積分のパラメータ (<literal>0&lt;m&lt;1</literal>)
+
</para>
+
</listitem>
+
</varlistentry>
+
<varlistentry>
+
<term>y</term>
+
<listitem>
+
<para>積分値</para>
+
</listitem>
+
</varlistentry>
+
</variablelist>
+
</refsection>
+
<refsection>
+
<title>説明</title>
+
<para>
+
楕円積分を計算します.
+
</para>
+
<para>
+
<literal>x</literal>がベクトルの場合, <literal>y</literal> は
+
<literal>x</literal>と同じ次元のベクトルとなります.
+
+        </para>
+
+        <warning>この関数は廃止されます.</warning>
+
+        <para>
+
+
+            方が良いでしょう.
+
</para>
+
</refsection>
+
<refsection>
+
<title>例</title>
+
<programlisting role="example"><![CDATA[
-m=0.8;z=%asn(1/sqrt(m),m);K=real(z);Ktilde=imag(z);
+m=0.8;
+z=%asn(1/sqrt(m),m);
+K=real(z);
+Ktilde=imag(z);
x2max=1/sqrt(m);
-x1=0:0.05:1;x2=1:((x2max-1)/20):x2max;x3=x2max:0.05:10;
+x1=0:0.05:1;
+x2=1:((x2max-1)/20):x2max;
+x3=x2max:0.05:10;
x=[x1,x2,x3];
y=%asn(x,m);
rect=[0,-Ktilde,1.1*K,2*Ktilde];
@@ -59,5 +129,80 @@ plot2d(real(y)',imag(y)',1,'011',' ',rect)
deff('y=f(t)','y=1/sqrt((1-t^2)*(1-m*t^2))');
intg(0,0.9,f)-%asn(0.9,m)  //実数の場合のみ動作します!
]]></programlisting>
+
+        <scilab:image>
+
+            warning("off")
+
+            m=0.8;
+
+            z=%asn(1/sqrt(m),m);
+
+            K=real(z);
+
+            Ktilde=imag(z);
+
+            x2max=1/sqrt(m);
+
+            x1=0:0.05:1;
+
+            x2=1:((x2max-1)/20):x2max;
+
+            x3=x2max:0.05:10;
+
+            x=[x1,x2,x3];
+
+            y=%asn(x,m);
+
+            rect=[0,-Ktilde,1.1*K,2*Ktilde];
+
+            plot2d(real(y)',imag(y)',1,'011',' ',rect)
+
+            warning("on")
+
+        </scilab:image>
+
+    </refsection>
+
+    <refsection role="see also">
+
+        <title>参照</title>
+
+        <simplelist type="inline">
+
+            <member>
+
+
+            </member>
+
+        </simplelist>
+
</refsection>
+
+    <refsection>
+
+        <title>履歴</title>
+
+        <revhistory>
+
+            <revision>
+
+                <revnumber>5.5.0</revnumber>
+
+                <revdescription>
+
+                    関数が廃止対象となりました. 5.5.1で削除されます.
+