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fstair(G) Scilab Function fstair(G)
NAME
fstair - computes pencil column echelon form by qz transformations
CALLING SEQUENCE
[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)
PARAMETERS
A : m x n matrix with real entries.
tol : real positive scalar.
E : column echelon form matrix
Q : m x m unitary matrix
Z : n x n unitary matrix
stair
: vector of indexes (see ereduc)
rk : integer, estimated rank of the matrix
AE : m x n matrix with real entries.
EE : column echelon form matrix
QE : m x m unitary matrix
ZE : n x n unitary matrix
nblcks
:is the number of submatrices having full row rank >= 0 detected in
matrix A.
muk: integer array of dimension (n). Contains the column dimensions mu(k)
(k=1,...,nblcks) of the submatrices having full column
rank in the pencil sE(eps)-A(eps)
nuk: integer array of dimension (m+1). Contains the row dimensions nu(k)
(k=1,...,nblcks) of the submatrices having full row
rank in the pencil sE(eps)-A(eps)
muk0:
integer array of dimension (n). Contains the column dimensions mu(k)
(k=1,...,nblcks) of the submatrices having full column
rank in the pencil sE(eps,inf)-A(eps,inf)
nuk: integer array of dimension (m+1). Contains the row dimensions nu(k)
(k=1,...,nblcks) of the submatrices having full row
rank in the pencil sE(eps,inf)-A(eps,inf)
mnei:
integer array of dimension (4). mnei(1) = row dimension of sE(eps)-
A(eps)
DESCRIPTION
Given a pencil sE-A where matrix E is in column echelon form the function
fstair computes according to the wishes of the user a unitary transformed
pencil QE(sEE-AE)ZE which is more or less similar to the generalized Schur
form of the pencil sE-A. The function yields also part of the Kronecker
structure of the given pencil.
Q,Z are the unitary matrices used to compute the pencil where E is in
column echelon form (see ereduc)
AUTHOR
Th.G.J. Beelen (Philips Glass Eindhoven). SLICOT
SEE ALSO
quaskro, ereduc
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