0fe945502b3a6c00bf2c3ef8862a8fdb4b0a3806
1 <?xml version="1.0" encoding="UTF-8"?>
3     <refnamediv>
4         <refname>power</refname>
5         <refpurpose>指数演算子 (^,.^)   </refpurpose>
6     </refnamediv>
7     <refsynopsisdiv>
8         <title>呼出し手順</title>
9         <synopsis>t=A^b
10             t=A**b
11             t=A.^b
12         </synopsis>
13     </refsynopsisdiv>
14     <refsection>
15         <title>パラメータ</title>
16         <variablelist>
17             <varlistentry>
18                 <term>A,t</term>
19                 <listitem>
20                     <para>スカラー, 多項式または有理行列.</para>
21                 </listitem>
22             </varlistentry>
23             <varlistentry>
24                 <term>b</term>
25                 <listitem>
26                     <para>スカラー, ベクトルまたはスカラーの行列.</para>
27                 </listitem>
28             </varlistentry>
29         </variablelist>
30     </refsection>
31     <refsection>
32         <title>説明</title>
33         <itemizedlist>
34             <listitem>
35                 <para>
36                     <literal>"(A:square)^(b:scalar)"</literal><literal>A</literal> が正方行列で<literal>b</literal> がスカラーの場合,
37                     <literal>A^b</literal>ｇは行列<literal>A</literal>の <literal>b</literal>乗に
38                     なります.
39                 </para>
40             </listitem>
41             <listitem>
42                 <para>
43                     <literal>"(A:matrix).^(b:scalar)"</literal><literal>b</literal> がスカラーで<literal>A</literal>が行列の場合,
44                     <literal>A.^b</literal>は<literal>A</literal>の各要素を<literal>b</literal>乗
45                     (要素毎の累乗)にした行列となります.
46                     <literal>A</literal> がベクトルで <literal>b</literal> がスカラーの場合,
47                     <literal>A^b</literal> と <literal>A.^b</literal> は同じ意味となります
48                     (すなわち,要素毎の累乗).
49                 </para>
50             </listitem>
51             <listitem>
52                 <para>
53                     <literal>"(A:scalar).^(b:matrix)"</literal><literal>A</literal> がスカラーで <literal>b</literal> が行列 (またはベクトル)の場合,
54                     <literal>A^b</literal> および <literal>A.^b</literal> は,
55                     <literal> a^(b(i,j))</literal> により構成される行列 (またはベクトル) となります.
56                 </para>
57             </listitem>
58             <listitem>
59                 <para>
60                     <literal>"(A:matrix).^(b:matrix)"</literal><literal>A</literal> および <literal>b</literal>  が同じ大きさのベクトル (行列) の場合,
61                     <literal>A.^b</literal> はベクトル <literal>A(i)^b(i)</literal>  (行列<literal>A(i,j)^b(i,j)</literal>)
62                     となります.
63                 </para>
64             </listitem>
65         </itemizedlist>
66         <para>
67             注記:
68         </para>
69         <para>
70             -
71             正方行列の場合, <literal>A^p</literal>は,<literal>p</literal>が正の整数の場合,
72             行列の逐次乗算により計算され,それ以外の場合,対角化により計算されます.
73         </para>
74         <para>
75             -
76             <literal>**</literal> および <literal>^</literal> 演算子は同義です.
77         </para>
78     </refsection>
79     <refsection>
80         <title>例</title>
81         <programlisting role="example"><![CDATA[
82 A=[1 2;3 4];
83 A^2.5,
84 A.^2.5
85 (1:10)^2
86 (1:10).^2
87 s=poly(0,'s')
88 s^(1:10)
89  ]]></programlisting>
90     </refsection>
91     <refsection role="see also">
92         <title>参照</title>
93         <simplelist type="inline">
94             <member>