We analyze large non-uniform optical antenna arrays of nanorods, which form optical vortices, axicons and lenses, by using a numerically efficient technique, called the Characteristics Basis Function Method (CBFM). The efficiency is realized by deriving an accurate, efficient simplified representation of nanorod, and by using the CBFM, which not only reduces the number of unknowns significantly without sacrificing the computational accuracy, but also enables us to handle large, truncated and non-uniform arrays. The method is numerically rigorous and includes all of the mutual coupling effects to obtain accurate results. Furthermore, it is readily parallelizable and can be generalized to handle more complex shapes of nanoantennas, without any difficulty.