scilab/modules/core/help/en_US/1_keywords/hat.xml

   1         <?xml version="1.0" encoding="UTF-8"?>
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  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>