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fstair — computes pencil column echelon form by qz transformations
[AE,EE,QE,ZE,blcks,muk,nuk,muk0,nuk0,mnei]=fstair(A,E,Q,Z,stair,rk,tol)
| 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) |
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)
Th.G.J. Beelen (Philips Glass Eindhoven). SLICOT
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