Rank revealing lu decomposition

calculates rank revealing lu decomposition

rrlu computes a rank revealing LU factorization of a general m-by-n real full matrix A using partial pivoting with row and column interchanges.

The factorization has the form
A(P,Q) = L * U
where P and Q are permutation vectors, L is lower triangular
(lower trapezoidal if m > n), and U is upper triangular
(upper trapezoidal if m < n).

if VERSION = 0
then L has unit diagonal elements and the matrix U takes form
U = [ U1 U2 ] (*)
[ 0 0 ]
where U1 in upper triangulal with nonzero elements on diagonal

if VERSION = 1
then U has unit diagonal elements and the matrix L takes form
L = [ L1 0 ] (**)
[ L2 0 ]

where L1 in lower triangulal with nonzero elements on diagonal

rrlu allows to find left or right null space faster than QR or SVD decomposition, but in some cases is less accurate.