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.

Answer 1

If you have a lot of index pairs and your array is long then caching might be an option. I'd try a recursive approach like

CACHE = {}
def mysum(a, b):
    if (a, b) in CACHE:
        return CACHE[(a, b)]

    if a >= b:
        return 0

    s = A[a] + mysum(a+1, b)
    CACHE[(a, b)] = s
    return s

Not checked for correctness or efficiency, though. Decreasing the upper index b could be used as well.