Obtaining cumulative product for a list elements

Question

I tried to calculate the cumulative products for my list elements as below. In my list, each element is two-dimensional list:

import numpy as np

Orig_list = [[[1,2,3], [4,5,6], [7,8,9]], [[11,3,4], [22, 4, 5], [22, 5, 1]], [[7,6,7], [2,5,6], [4,6,7]], [[234, 56, 22], [44, 66, 33], [44, 66, 33]]]

Result_list = [np.nan] * 4
Result_list[0] = Orig_list[0]
for i in range(1, len(Result_list)):
  Result_list[i] = (np.array(Result_list[i - 1]) @ np.array(Orig_list[i])).tolist()

The above works, but I am looking for cleaner and faster implementation as my original list is fairly big and each element is also a large two-dimensional list.

Is there anything like a more direct cumulative product function/method for above calculation?

@furas If I understand correctly, cumprod produces elementwise multiplication. However, OP asks for matrix-matrix multiplication (the inputs are 3×3 matrices which are not to be accumulated with an element-wise product but with a matrix-matrix product, which is why they use the @ operator). — simon
– simon, Commented Oct 21 at 13:33
@simon I was going to ask OP for showing result which OP gets - to see if this "cumulative product" produces normal cumprod :). Meanwhile I run this code and now I see it needs something different. So pandas.DataFrame.cumprod (and numpy.cumprod) seems useless for this. — furas
– furas, Commented Oct 21 at 13:37
@furas You can see their desired result from Result_list after their for loop (which produces, as mentioned, the desired result, but which, being a loopy solution, they want to avoid) — simon
– simon, Commented Oct 21 at 13:38
@simon without running code I don't see what this code is really doing. But meanwhile I ran it and saw it :) — furas
– furas, Commented Oct 21 at 13:41

mozway · Accepted Answer · 2025-10-21 13:45:49Z

3

You could use itertools.accumulate:

from itertools import accumulate

out = np.array(list(accumulate(Orig_list, np.dot)))

Output:

array([[[      1,       2,       3],
        [      4,       5,       6],
        [      7,       8,       9]],

       [[    121,      26,      17],
        [    286,      62,      47],
        [    451,      98,      77]],

       [[    967,     958,    1122],
        [   2314,    2308,    2703],
        [   3661,    3658,    4284]],

       [[ 317798,  191432,   89914],
        [ 761960,  460310,  216271],
        [1206122,  729188,  342628]]])

If you only care about the final result, go with numpy.linalg.multi_dot:

out = np.linalg.multi_dot(Orig_list)

Output:

array([[ 317798,  191432,   89914],
       [ 761960,  460310,  216271],
       [1206122,  729188,  342628]])

answered Oct 21 at 13:45

mozway

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