ereduc

ereduc — computes matrix column echelon form by qz transformations

Calling sequence

[E,Q,Z [,stair [,rk]]]=ereduc(X,tol)

Parameters

X : 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,

`*`	`ISTAIR(i) = + j` if the boundary element `E(i,j)` is a corner point.
`*`	`ISTAIR(i) = - j` if the boundary element `E(i,j)` is not a corner point.

(i=1,...,M)

rk : integer, estimated rank of the matrix

Description

Given an m x n matrix X (not necessarily regular) the function ereduc computes a unitary transformed matrix E=Q*X*Z which is in column echelon form (trapezoidal form). Furthermore the rank of matrix X is determined.

Examples



X=[1 2 3;4 5 6]
[E,Q,Z ,stair ,rk]=ereduc(X,1.d-15)

Author

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