How to compute the upper global basis (dual canonical basis) of an irreducible $U_q(\mathfrak{g})$-module?

Question

Let $\mathfrak{g}$ be a semisimple Lie algebra and $U_q(\mathfrak{g})$ the corresponding quantum group. Are there some general method to compute the upper global basis (dual canonical basis) of an irreducible $U_q(\mathfrak{g})$-module? Thank you very much.