gmm::lu_factor(M, ipvt) : compute the LU factorization of M in M. ipvt should be
                   an std::vector<size_t> (of size gmm::mat_nrows(M))
                   which will contain the indices of the pivots.

gmm::lu_solve(LU, ipvt, x, b) : solve the system LUx = b. LU is the LU
                         factorization which has to be computed first.

gmm::lu_solve(M, x, b) : solve the system Mx=b calling the lu factorization on
                  a copy of M.

gmm::lu_solve_transposed(LU, ipvt, x, b) : solve the system transposed(LU)x = b.
                                    LU is the LU factorization which
                                    has to be computed first.

gmm::lu_inverse(LU, ipvt, A) : compute the inverse of LU in A. LU is the LU
                        factorization which has to be computed first

gmm::lu_inverse(A) : invert A calling the LU factorization and the latter
              procedure.

gmm::lu_det(LU, ipvt) : compute the determinant of LU. LU is the LU
                 factorization which has to be computed first

gmm::lu_det(A) : compute the determinant of A calling the LU factorization
          and the latter function.