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.TH fstair G "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
fstair - computes pencil column echelon form by qz transformations
.SH CALLING SEQUENCE
.nf
[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)
.fi
.SH PARAMETERS
.TP
A
: m x n matrix with real entries.
.TP
tol
: real positive scalar.
.TP
E
: column echelon form matrix
.TP
Q
: m x m unitary matrix
.TP
Z
: n x n unitary matrix
.TP
stair
: vector of indexes (see ereduc)
.TP
rk
: integer, estimated rank of the matrix
.TP
AE
: m x n matrix with real entries.
.TP
EE
: column echelon form matrix
.TP
QE
: m x m unitary matrix
.TP
ZE
: n x n unitary matrix
.TP
nblcks
:is the number of submatrices having full row rank >= 0 detected in
matrix A\fR.
.TP
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)
.TP
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)
.TP
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)
.TP
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)
.TP
mnei:
integer array of dimension (4). mnei(1) = row dimension of sE(eps)-A(eps)
.SH DESCRIPTION
Given a pencil \fVsE-A\fR where matrix \fVE\fR is in column echelon form the
function \fVfstair\fR computes according to the wishes of the user a
unitary transformed pencil \fVQE(sEE-AE)ZE\fR which is more or less similar
to the generalized Schur form of the pencil \fVsE-A\fR.
The function yields also part of the Kronecker structure of
the given pencil.
.LP
\fVQ,Z\fR are the unitary matrices used to compute the pencil where E
is in column echelon form (see ereduc)
.SH AUTHOR
Th.G.J. Beelen (Philips Glass Eindhoven). SLICOT
.SH SEE ALSO
quaskro, ereduc
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