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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE
*
* 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_V2.1-en.txt
*
-->
<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="residu">
<refnamediv>
<refname>residu</refname>
<refpurpose>residue</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[V]=residu(P,Q1,Q2)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>P, Q1, Q2</term>
<listitem>
<para>polynomials or matrix polynomials with real or complex coefficients.</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>V=residu(P,Q1,Q2)</literal> returns the matrix <literal>V</literal>
such that <literal>V(i,j)</literal> is the sum of the residues of the
rational fraction <literal>P(i,j)/(Q1(i,j)*Q2(i,j))</literal> calculated
at the zeros of <literal>Q1(i,j)</literal>.
</para>
<para>
<literal>Q1(i,j)</literal> and <literal>Q2(i,j)</literal> must not have any common root.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
s=poly(0,'s');
H=[s/(s+1)^2,1/(s+2)];N=numer(H);D=denom(H);
w=residu(N.*horner(N,-s),D,horner(D,-s)); //N(s) N(-s) / D(s) D(-s)
sqrt(sum(w)) //This is H2 norm
h2norm(tf2ss(H))
p=(s-1)*(s+1)*(s+2)*(s+10);a=(s-5)*(s-1)*(s*s)*((s+1/2)**2);
b=(s-3)*(s+2/5)*(s+3);
residu(p,a,b)+531863/4410 //Exact
z=poly(0,'z');a=z^3+0.7*z^2+0.5*z-0.3;b=z^3+0.3*z^2+0.2*z+0.1;
atild=gtild(a,'d');btild=gtild(b,'d');
residu(b*btild,z*a,atild)-2.9488038 //Exact
a=a+0*%i;b=b+0*%i;
real(residu(b*btild,z*a,atild)-2.9488038) //Complex case
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="pfss">pfss</link>
</member>
<member>
<link linkend="bdiag">bdiag</link>
</member>
<member>
<link linkend="roots">roots</link>
</member>
<member>
<link linkend="poly">poly</link>
</member>
<member>
<link linkend="gtild">gtild</link>
</member>
</simplelist>
</refsection>
</refentry>
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