residu

residue

Calling Sequence

[V]=residu(P,Q1,Q2)

Arguments

:P, Q1, Q2 polynomials or matrix polynomials with real or complex

coefficients.

:

Description

V=residu(P,Q1,Q2) returns the matrix V such that V(i,j) is the sum of the residues of the rational fraction P(i,j)/(Q1(i,j)*Q2(i,j)) calculated at the zeros of Q1(i,j).

Q1(i,j) and Q2(i,j) must not have any common root.

Examples

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

See Also

• pfss partial fraction decomposition
• bdiag block diagonalization, generalized eigenvectors
• roots roots of polynomials
• poly polynomial definition
• gtild tilde operation