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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from residue.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="residue" 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:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>residue</refname>
<refpurpose></refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
[r, p, k, e] = residue (b, a)
[b, a] = residue (r, p, k)
[b, a] = residue (r, p, k, e)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>b:</term>
<listitem><para> Real or complex valued vector or matrix</para></listitem></varlistentry>
<varlistentry><term>a:</term>
<listitem><para> Real or complex valued vector or matrix</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
The first calling form computes the partial fraction expansion for the quotient of the polynomials, b and a.
This function works for transfer functions which are proper fractions.
NOTE that the polynomials 'b' and 'a' should have real coefficients(because of the function 'filter' used in polyval)
</para>
<para>The second and the third calling forms perform the inverse operation of the first calling form.</para>
<para>
<latex>
\begin{eqnarray}
\frac{B(s)}{A(s)}=\sum_{m=1}^{M}\frac{r(m)}{(s-p(m))^{e(m)}}+\sum_{i=1}^{N}k(i)*{s^{N-i}}
\end{eqnarray}
</latex>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
1.
b = [1, 1, 1];
a = [1, -5, 8, -4];
[r, p, k, e] = residue (b, a)
// result r = [-2; 7; 3]
// result p = [2; 2; 1]
// result k = [](0x0)
// result e = [1; 2; 1]
]]></programlisting>
</refsection>
</refentry>
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