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

   1 <?xml version="1.0" encoding="UTF-8"?>
   2 <!--
   3  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
   4  * Copyright (C) INRIA
   5  *
   6  * Copyright (C) 2012 - 2016 - Scilab Enterprises
   7  *
   8  * This file is hereby licensed under the terms of the GNU GPL v2.0,
   9  * pursuant to article 5.3.4 of the CeCILL v.2.1.
  10  * This file was originally licensed under the terms of the CeCILL v2.1,
  11  * and continues to be available under such terms.
  12  * For more information, see the COPYING file which you should have received
  13  * along with this program.
  14  *
  15  -->
  16 <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">
  17     <refnamediv>
  18         <refname>hat</refname>
  19         <refpurpose>(^) exponentiation</refpurpose>
  20     </refnamediv>
  21     <refsynopsisdiv>
  22         <title>Syntax</title>
  23         <synopsis>A^b</synopsis>
  24     </refsynopsisdiv>
  25     <refsection>
  26         <title>Description</title>
  27         <para>
  28             Exponentiation of matrices or vectors by a constant vector.
  29         </para>
  30         <para>
  31             If <literal>A</literal> is a vector, the exponentiation is done
  32             element-wise, with the usual meaning.
  33         </para>
  34         <para>
  35             For a square <literal>A</literal> matrix, the exponentiation is done in the matrix sense.
  36         </para>
  37         <para>
  38             For boolean, polynomial and rational matrices, the exponent must be an
  39             integer.
  40         </para>
  41         <refsection>
  42             <title>Remarks </title>
  43             <para>
  44                 <literal>123.^b</literal> is interpreted as <literal>(123).^b</literal>. In such
  45                 cases dot is part of the operator, not of the number.
  46             </para>
  47             <para>
  48                 For two real or complex numbers <literal>x1</literal> and
  49                 <literal>x2</literal> the value of  <literal>x1^x2</literal> is the "principal value"
  50                 determined by <literal>x1^x2 = exp(x2*log(x1))</literal>.
  51             </para>
  52             <para>
  53                 <warning>
  54                     Exponentiation is right-associative in Scilab contrarily to Matlab® and Octave.
  55                    For example 2^3^4 is equal to 2^(3^4) in Scilab but is equal to (2^3)^4 in Matlab®
  56                    and Octave.
  57                 </warning>
  58             </para>
  59         </refsection>
  60     </refsection>
  61     <refsection>
  62         <title>Examples</title>
  63         <programlisting role="example"><![CDATA[
  64 2^4
  65 (-0.5)^(1/3)
  66 [1 2;2 4]^(1+%i)
  67 s=poly(0,"s");
  68 [1 2 s]^4
  69 [s 1;1  s]^(-1)
  70  ]]></programlisting>
  71     </refsection>
  72     <refsection role="see also">
  73         <title>See also</title>
  74         <simplelist type="inline">
  75             <member>
  76                 <link linkend="power">power</link>
  77             </member>
  78             <member>
  79                 <link linkend="exp">exp</link>
  80             </member>
  81             <member>
  82                 <link linkend="log">log</link>
  83             </member>
  84             <member>
  85                 <link linkend="log2">log2</link>
  86             </member>
  87             <member>
  88                 <link linkend="inv">inv</link>
  89             </member>
  90         </simplelist>
  91     </refsection>
  92 </refentry>