| | | Scilab Reference Manual | |
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quaskro — quasi-Kronecker form
[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)
| 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 |
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
| << qr | randpencil >> |