sum through specific values in an array

Question

I have an array of data-points, for example:

[10, 9, 8, 7, 6, 5, 4, 3, 2, 1]

and I need to perform the following sum on the values:

However, the problem is that I need to perform this sum on each value > i. For example, using the last 3 values in the set the sum would be:

and so on up to 10. If i run something like:

import numpy as np

x = np.array([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])
alpha = 1/np.log(2) 

for i in x:
    y = sum(x**(alpha)*np.log(x))
print (y)

It returns a single value of y = 247.7827060452275, whereas I need an array of values. I think I need to reverse the order of the data to achieve what I want but I'm having trouble visualising the problem (hope I explained it properly) as a whole so any suggestions would be much appreciated.

Just get rid of the for loop and the sum. It's simply y = x**(alpha)*np.log(x) or perhaps y = x**(alpha)*np.log(x).cumsum() — roganjosh
– roganjosh, Commented May 25, 2020 at 12:14
Thanks, I thought I had already tried that but it seems I decided to just overcomplicate things! — Tyr
– Tyr, Commented May 25, 2020 at 12:19
Why do you need/expect an array of output values? You are summing over x, a one-dimensional array, and thus you end up with a scalar. Is the formula written incorrectly? Should i=1 be a variable instead, like i=j, and j runs from 1 to 10? That is what I gather from your example code. — 9769953
– 9769953, Commented May 25, 2020 at 12:29
@AmitaiIrron I'm not convinced that it adds anything to the SO repository of knowledge since it fixes a single case that isn't expressed clearly in a title. Feel free to take the approach in my comment and post as an answer, though. — roganjosh
– roganjosh, Commented May 25, 2020 at 13:01

Amitai Irron · Accepted Answer · 2020-05-25 14:36:27Z

1

The following computes all the partial sums of the grand sum in your formula

import numpy as np

# Generate numpy array [1, 10]
x = np.arange(1, 11)
alpha = 1 / np.log(2)
# Compute parts of the sum
parts = x ** alpha * np.log(x)
# Compute all partial sums
part_sums = np.cumsum(parts)
print(part_sums)

You really do not any explicit loop, or a non-numpy operation (like sum()) here. numpy takes care of all your needs.

answered May 25, 2020 at 14:36

Amitai Irron

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