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)

See Also

quaskro ,   ereduc ,  

Author

Th.G.J. Beelen (Philips Glass Eindhoven). SLICOT