quaskro
=======

quasi-Kronecker form



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [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



See Also
~~~~~~~~


+ `kroneck`_ Kronecker form of matrix pencil
+ `gschur`_ generalized Schur form (obsolete).
+ `gspec`_ eigenvalues of matrix pencil (obsolete)


.. _kroneck: kroneck.html
.. _gspec: gspec.html
.. _gschur: gschur.html