This function computes the LU decomposition (with partial pivoting) of matrix \(A\)
\[A = L U\]
where \(A\) is a dense matrix of size \(n \times n\), \(L\) is a lower triangular matrix with unit diagonal, and \(U\) is a upper triangular matrix. This function implement partial pivoting. The maximum matrix size supported in FPGA is templated by NMAX.