Numpy and scipy have been the core of a huge amount of my optimisations. The first question I try and ask is

"Could this be solved with matrix multiplications and summing?"

Often the answer is "yes" and allows you to group a huge amount of calculations all together, and use the heavily optimised code available numpy/scipy.

I recently swapped out something that was running at about 100 rows calculated/second to about half a million in about 0.2s.