Numpy sum of values in subarrays between pairs of indices

Question

Suppose I have an array A. I have a series of index pairs (a1, b1), (a2, b2) ... (an, bn)

I want to obtain all the sums of the elements between those pairs. i.e.

sum(A[a1:b1]), sum(A[a2:b2]), sum(A[a3:b3]) ...

In terms of run-time, what's the most efficient way of doing this?

Thanks!

Answer 1

Assuming your index pairs are stored in a NumPy array indices of shape (n, 2) and n is fairly large, it is probably best to avoid any Python loop:

c = numpy.r_[0, A.cumsum()][indices]
sums = c[:,1] - c[:,0]

Answer 2

Here's another way:

a = np.random.rand(3000)
indices = np.array([[0,3], [9,20], [5,30], [9,33]])
sums = np.add.reduceat(a, indices.ravel())[::2]

assert np.all(sums == np.array([a[i:j].sum() for i,j in indices]))

The cumsum one above is probably more efficient if there are many indices.