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  <refnamediv>
    <refname>_levin</refname>
    <refpurpose>Resolve the Yule-Walker equations:</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Syntax</title>
   <synopsis>
   [ar,sigma2,rc]=_levin(r)
   
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Description</title>
   <para>
|r(0)   r(1)   ... r(N-1)|| a(1) | |sigma2|
|r(1)   r(0)   ... r(n-1)|| a(2) | |  0   |
|  :      :    ...    :  ||   :  |=|  0   |
|  :      :    ...    :  ||   :  | |  0   |
|r(N-1) r(N-2) ...  r(0) ||a(N-1)| |  0   |
   </para>
   <para>
using Levinson's algorithm.
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Parameters</title>
   <variablelist>
        <varlistentry>
            <term>r      :</term>
            <listitem><para>Correlation coefficients</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>ar     :</term>
            <listitem><para>Auto-Regressive model parameters</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>sigma2 :</term>
            <listitem><para>Scale constant</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>rc     :</term>
            <listitem><para>Reflection coefficients</para></listitem>
        </varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
// Solve the Yule-Walker equations using Levinson's algorithm
// Correlation coefficients
r = [1, 0.8, 0.5, 0.2]
// Solve the Yule-Walker equations
[ar, sigma2, rc] = _levin(r)
   ]]></programlisting>
</refsection>
</refentry>
