Bug #13369 fixed: samplef works on zero frequency values
[scilab.git] / scilab / modules / core / help / en_US / 1_keywords / hat.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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12  -->
13 <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="en" xml:id="hat">
14     <refnamediv>
15         <refname>hat</refname>
16         <refpurpose>(^) exponentiation</refpurpose>
17     </refnamediv>
18     <refsynopsisdiv>
19         <title>Calling Sequence</title>
20         <synopsis>A^b</synopsis>
21     </refsynopsisdiv>
22     <refsection>
23         <title>Description</title>
24         <para>
25             Exponentiation of matrices or vectors by a constant vector.
26         </para>
27         <para>
28             If <literal>A</literal> is a vector or a rectangular matrix the exponentiation is done
29             element-wise, with the usual meaning.
30         </para>
31         <para>
32             For square <literal>A</literal> matrix the exponentiation is done in the matrix sense.
33         </para>
34         <para>
35             For boolean, polynomial and rational matrices, the exponent must be an
36             integer.
37         </para>
38         <refsection>
39             <title>Remarks </title>
40             <para>
41                 <literal>123.^b</literal> is interpreted as <literal>(123).^b</literal>. In such
42                 cases dot is part of the operator, not of the number.
43             </para>
44             <para>
45                 For two real or complex numbers <literal>x1</literal> and
46                 <literal>x2</literal> the value of  <literal>x1^x2</literal> is the "principal value"
47                 determined by <literal>x1^x2 = exp(x2*log(x1))</literal>.
48             </para>
49         </refsection>
50     </refsection>
51     <refsection>
52         <title>Examples</title>
53         <programlisting role="example"><![CDATA[ 
54 2^4
55 (-0.5)^(1/3)
56 [1 2;2 4]^(1+%i)
57 s=poly(0,"s");
58 [1 2 s]^4
59 [s 1;1  s]^(-1)
60  ]]></programlisting>
61     </refsection>
62     <refsection role="see also">
63         <title>See Also</title>
64         <simplelist type="inline">
65             <member>
66                 <link linkend="exp">exp</link>
67             </member>
68             <member>
69                 <link linkend="log">log</link>
70             </member>
71         </simplelist>
72     </refsection>
73 </refentry>