How Can I Efficiently Calculate the Cumulative Sum of a Numerical List?

How to Efficiently Compute the Cumulative Sum of Numbers in a List

When processing numerical data, it's often necessary to calculate the cumulative sum of numbers in a list. Here, we provide a comprehensive solution and address an issue raised by a user who attempted to manually sum the elements of a list.

For example, given time_interval = [4, 6, 12], the user aims to compute [4, 4 6, 4 6 12] to obtain the cumulative sum t = [4, 10, 22].

Manual Approach:

The user initially tried a manual approach by iterating over the list and accumulating the sums:

t1 = time_interval[0]
t2 = time_interval[1] + t1
t3 = time_interval[2] + t2
print(t1, t2, t3)  # -> 4 10 22

This approach, however, requires explicit iteration and may become tedious for larger lists.

Numpy Implementation:

If you frequently perform numerical operations on arrays, numpy is a highly recommended library that provides a built-in function for cumulative summation: cumsum. Using numpy, the cumulative sum can be computed efficiently:

import numpy as np

a = [4, 6, 12]

np.cumsum(a)
#array([4, 10, 22])

Performance Comparison:

Numpy often outperforms pure python implementations for such numerical operations. A comparison between numpy's cumsum and the user's manual accumulation function (accumu) demonstrates the difference:

In [136]: timeit list(accumu(range(1000)))
10000 loops, best of 3: 161 us per loop

In [137]: timeit list(accumu(xrange(1000)))
10000 loops, best of 3: 147 us per loop

In [138]: timeit np.cumsum(np.arange(1000))
100000 loops, best of 3: 10.1 us per loop

While numpy may introduce a dependency, its efficiency may justify its use if you frequently perform similar numerical operations.

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