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.TH RESIDU G "April 1993" "Scilab Group" "Scilab Function"
.SH NAME
residu - residue
.SH CALLING SEQUENCE
.nf
[V]=residu(P,Q1,Q2)
.fi
.SH PARAMETERS
.TP
P, Q1, Q2
: polynomials or matrix polynomials with real or complex coefficients.
.SH DESCRIPTION
.Vb V=residu(P,Q1,Q2)
returns the matrix \fVV\fR such that \fVV(i,j)\fR
is the sum of the residues of the rational fraction
\fVP(i,j)/(Q1(i,j)*Q2(i,j))\fR calculated at the zeros of \fVQ1(i,j)\fR.
.LP
\fVQ1(i,j)\fR and \fVQ2(i,j)\fR must not have any common root.
.SH EXAMPLE
.nf
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
.fi
.SH SEE ALSO
pfss, bdiag, roots, poly, gtild
.SH AUTHOR
F.D.
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