The Stan Math Library has a function called csr_matrix_times_vector,
which inputs a matrix in compressed row storage form and a dense vector and
returns their product without fillin. To use the
csr_matrix_times_vector function with a large
sparse matrix, it is optimal in terms of memory to simply pass the three vectors
that characterize the compressed row storage form of the matrix to the
data block of the Stan program.
The extract_sparse_parts function provides a convenient means of
obtaining these vectors.