quaskro
quasi-Kronecker form
Syntax
[Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F) [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A) [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(F,tol) [Q,Z,Qd,Zd,numbeps,numbeta]=quaskro(E,A,tol)
Arguments
- F
real matrix pencil
F=s*E-A(s=poly(0,'s'))- E,A
two real matrices of same dimensions
- tol
a real number (tolerance, default value=1.d-10)
- Q,Z
two square orthogonal matrices
- Qd,Zd
two vectors of integers
- numbeps
vector of integers
Description
Quasi-Kronecker form of matrix pencil: quaskro computes two
orthogonal matrices Q, Z which put the pencil F=s*E -A into
upper-triangular form:
| sE(eps)-A(eps) | X | X | |----------------|----------------|------------| | O | sE(inf)-A(inf) | X | Q(sE-A)Z = |=================================|============| | | | | O | sE(r)-A(r) |
The dimensions of the blocks are given by:
eps=Qd(1) x Zd(1), inf=Qd(2) x Zd(2),
r = Qd(3) x Zd(3)
The inf block contains the infinite modes of
the pencil.
The f block contains the finite modes of
the pencil
The structure of epsilon blocks are given by:
numbeps(1) = # of eps blocks of size 0 x 1
numbeps(2) = # of eps blocks of size 1 x 2
numbeps(3) = # of eps blocks of size 2 x 3 etc...
The complete (four blocks) Kronecker form is given by
the function kroneck which calls quaskro on
the (pertransposed) pencil sE(r)-A(r).
The code is taken from T. Beelen
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