sp_lu — Performs a LU decomposition on a sparse matrix
[L[,U[,P]]] = sp_lu(M[,alpha])
the real sparse matrix on which we will perform the LU decomposition
a coefficient used in the partial pivoting (default value: 1).
partial pivoting and Markowitz criterion:
|a[p][k]| >= alpha * max_i |a[i][k]|
the L sparse matrix from the LU decomposition
the U sparse matrix from the LU decomposition
The permutation matrix such that L*U = P*A