## Version 1.2.0

This routine forms an incomplete $LU$ factorization of an $n×n$ sparse unsymmetric matrix $A$. No ﬁll-in is allowed. The entries of $A$ are stored by rows. If $A$ has zeros on the diagonal, the routine ﬁrst ﬁnds a row permutation $Q$ which makes the matrix have nonzeros on the diagonal. The incomplete $LU$ factorization of the permuted matrix $QA$ is then formed. $L$ is lower triangular and $U$ is unit upper triangular. The incomplete factorization may be used as a preconditioner when solving the linear system $Ax=b$. A second entry performs the preconditioning operations
where $P={\left(LU\right)}^{-1}Q$ is the preconditioner.