python - Vectorize large NumPy multiplication

Question

I am interested in calculating a large NumPy array. I have a large array A which contains a bunch of numbers. I want to calculate the sum of different combinations of these numbers. The structure of the data is as follows:

A = np.random.uniform(0,1, (3743, 1388, 3))
Combinations = np.random.randint(0,3, (306,3))
Final_Product = np.array([  np.sum( A*cb, axis=2)  for cb in Combinations])

My question is if there is a more elegant and memory efficient way to calculate this? I find it frustrating to work with np.dot() when a 3-D array is involved.

If it helps, the shape of Final_Product ideally should be (3743, 306, 1388). Currently Final_Product is of the shape (306, 3743, 1388), so I can just reshape to get there.

Answer 1

Instead of dot you could use tensordot. Your current method is equivalent to:

np.tensordot(A, Combinations, [2, 1]).transpose(2, 0, 1)

Note the transpose at the end to put the axes in the correct order.

Like dot, the tensordot function can call down to the fast BLAS/LAPACK libraries (if you have them installed) and so should be perform well for large arrays.