Randomized LU Decomposition

Low rank approximation using randomized LU decomposition

This code computes a low rank approximation of an LU decomposition of a matrix.
Given an input matrix A of size m-by-n and a desired rank k, the function returns four matrices: L,U,P,Q such that L and U are trapezoidal matrices and P,Q are orthogonal permutation matrices (represented as vectors) such that norm(A(P,Q)-L*U) is bounded by a constant proportional the kth singular value of A with high probability.
The code and the algorithm is based on the paper (check for more details):
G. Shabat, Y. Shmueli, Y. Aizenbud, A. Averbuch; "Randomized LU Decomposition"; Applied and Computational Harmonic Analysis, DOI: 10.1016/j.acha.2016.04.006, 2016
The attached code includes GPU implementation as well.