5. Finally, the energy of an atom A can be evaluated as the sum of simple dot product of the accumulated S α ′ for each scale, with the appropriate v A,α ′ , defined in eqn. (18). Each dot product is independent of system size, but there are O(log 8 (N )) scales to process for each atom, so this step also has O(N log 8 (N )) scaling.