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.
np.dot() won't give give you the desired output , unless you involve extra step(s) that would probably include reshaping. Here's one vectorized approach using np.einsum to do it one shot without any extra memory overhead -
Final_Product = np.einsum('ijk,lk->lij',A,Combinations)
For completeness, here's with np.dot and reshaping as discussed earlier -
M,N,R = A.shape
Final_Product = A.reshape(-1,R).dot(Combinations.T).T.reshape(-1,M,N)
Runtime tests and verify output -
In [138]: # Inputs ( smaller version of those listed in question )
...: A = np.random.uniform(0,1, (374, 138, 3))
...: Combinations = np.random.randint(0,3, (30,3))
...:
In [139]: %timeit np.array([ np.sum( A*cb, axis=2) for cb in Combinations])
1 loops, best of 3: 324 ms per loop
In [140]: %timeit np.einsum('ijk,lk->lij',A,Combinations)
10 loops, best of 3: 32 ms per loop
In [141]: M,N,R = A.shape
In [142]: %timeit A.reshape(-1,R).dot(Combinations.T).T.reshape(-1,M,N)
100 loops, best of 3: 15.6 ms per loop
In [143]: Final_Product =np.array([np.sum( A*cb, axis=2) for cb in Combinations])
...: Final_Product2 = np.einsum('ijk,lk->lij',A,Combinations)
...: M,N,R = A.shape
...: Final_Product3 = A.reshape(-1,R).dot(Combinations.T).T.reshape(-1,M,N)
...:
In [144]: print np.allclose(Final_Product,Final_Product2)
True
In [145]: print np.allclose(Final_Product,Final_Product3)
True
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.
