DGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).
See http://www.netlib.org/lapack/double/dgetrf.f for more information