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<?xml version="1.0" encoding="UTF-8"?>
<!--
    * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
    * Copyright (C) 2004-2007 - INRIA - Vincent COUVERT 
    * 
    * This file must be used under the terms of the CeCILL.
    * This source file is licensed as described in the file COPYING, which
    * you should have received as part of this distribution.  The terms
    * are also available at    
    * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
    *
    -->
<refentry version="5.0-subset Scilab" xml:id="mtlb_var" xml:lang="en"
          xmlns="http://docbook.org/ns/docbook"
          xmlns:xlink="http://www.w3.org/1999/xlink"
          xmlns:svg="http://www.w3.org/2000/svg"
          xmlns:ns4="http://www.w3.org/1999/xhtml"
          xmlns:mml="http://www.w3.org/1998/Math/MathML"
          xmlns:db="http://docbook.org/ns/docbook">
  <info>
    <pubdate>$LastChangedDate$</pubdate>
  </info>

  <refnamediv>
    <refname>mtlb_var</refname>

    <refpurpose>Matlab var emulation function</refpurpose>
  </refnamediv>

  <refsection>
    <title>Parameters</title>

    <variablelist>
      <varlistentry>
        <term>x</term>

        <listitem>
          <para>a real or a complex vector or matrix.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>s</term>

        <listitem>
          <para>a real scalar or real vector.</para>

          <itemizedlist>
            <listitem>
              <para>If x is a vector, s is the variance of x.</para>
            </listitem>

            <listitem>
              <para>If x is a matrix, s is a row vector containing the
              variance of each column of x.</para>
            </listitem>
          </itemizedlist>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>w</term>

        <listitem>
          <para>type of normalization to use. Valid values are, depending on
          the number of columns m of x :</para>

          <itemizedlist>
            <listitem>
              <para>w = 0 : normalizes with m-1, provides the best unbiased
              estimator of the variance (this is the default).</para>
            </listitem>

            <listitem>
              <para>w = 1: normalizes with m, this provides the second moment
              around the mean.</para>
            </listitem>
          </itemizedlist>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>dim</term>

        <listitem>
          <para>the dimension along which the variance is computed (default is
          1, i.e. column by column). If dim is 2, the variance is computed row
          by row.</para>
        </listitem>
      </varlistentry>
    </variablelist>
  </refsection>

  <refsection>
    <title>Description</title>

    <para>This function computes the variance of the values of a vector or
    matrix x. It provides the same service as Octave and Matlab. It differs
    from Scilab's variance primitive:</para>

    <itemizedlist>
      <listitem>
        <para>mtlb_var returns a real (i.e. with a zero imaginary part)
        variance, even if x is a complex vector or matrix. The Scilab variance
        primitive returns a complex value if the input vector x is complex and
        if no option additionnal is used.</para>
      </listitem>

      <listitem>
        <para>Whatever the type of the input data x (i.e. vector or matrix),
        mtlb_var computes the variance either on dimension 1 or on dimension 2
        while, if no option is passed to the Scilab's variance primitive, the
        variance is computed on all dimension at once.</para>
      </listitem>
    </itemizedlist>
  </refsection>

  <refsection>
    <title>Examples</title>

    <para>The following 3 examples illustrates the use of the mtlb_var
    function. In the first case, a column vector is passed to the function,
    which returns the value 750. In the second case, a matrix is passed to the
    function, which returns the row vector [0.16 0.09]. In the third case, a
    complex column vector is passed to the function, which returns a value
    close to 2.</para>

    <programlisting role="example"> 
x = [10; 20; 30; 40; 50; 60; 70; 80; 90];
computed = mtlb_var(x);

x = [0.9    0.7  
    0.1    0.1  
    0.5    0.4];
computed = mtlb_var(x);

N=1000;
x = grand(N,1,'nor',0,1) + %i*grand(N,1,'nor',0,1);
computed = mtlb_var(x);
   </programlisting>
  </refsection>

  <refsection>
    <title>See Also</title>

    <simplelist type="inline">
      <member><link linkend="variance">variance</link></member>
    </simplelist>
  </refsection>

  <refsection>
    <title>Authors</title>

    <simplelist type="vert">
      <member>Michael Baudin</member>
    </simplelist>
  </refsection>
</refentry>