Double Summation in Python

Question

I am trying to write a code to conduct a double summation (see pic)

enter image description here

in which; M is the subjects, N is the Trials, Yijt is the measured wave form data (3d array)

so far I have; Given Y is the data arranged as Y[subjects, trials, time]

# ranges:
I = len(Y)
J = len(Y[0])

Y_i_vals = 0

for i in range(M):
    for j in range(N):
        Y_i_vals = Y_i_vals +Y[i][j]
Yt = (1.0/(M*N)) * Y_i_vals

this doesnt seem the most effective way to do this, nor am i certain it is giving the correct result.

Do you know [list comprehension](http://docs.python.org/2/tutorial/datastructures.html#list-comprehensions)? That would be much faster. Or in that case, try to use [sum](http://docs.python.org/2/library/functions.html#sum) — Paco, Oct 09 '13 at 14:29

YXD · Accepted Answer · 2013-10-09T15:03:42.850

9

If you're using numpy just do

np.mean(Y)

Also, it's good to add sample input and expected output data to your question.

If you want means for each t you can do np.mean(np.mean(a, axis=0), axis=0), or as noted by @ophion you can shorten this to np.mean(a, axis=(0, 1)) in newer (1.71 and on) versions of NumPy.

edited Oct 09 '13 at 15:03

answered Oct 09 '13 at 14:33

YXD

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This would compute the mean over all 3 dimensions, where the desire is to generate separate means over *M* and *N* for each *t*. (Unless *Y* in the code really represents a slice for a specific *t*.) – chepner Oct 09 '13 at 14:38
Updated. Adding expected input and output would make it much clearer! – YXD Oct 09 '13 at 14:39
2

In numpy 1.7.1 you can simplify this to `np.mean(a, axis=(0,1))` – Daniel Oct 09 '13 at 14:56
@Ophion nice, I didn't know that – YXD Oct 09 '13 at 15:02

score 1 · Answer 2 · answered Oct 10 '17 at 18:23

1

To add a more general answer to your question:

You can code a double summation with the help of python list comprehension.

Yt = (1.0/(M*N)) * sum([Y[i][j] for i in range(M) for j in range(N)])

answered Oct 10 '17 at 18:23

Axel

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Andreas K. · Answer 3 · 2019-12-11T12:00:06.730

1

When it comes to simple double summations like in your case, it's nice to use numpy's einsum:

np.einsum('tij -> t', Y) / (M*N)

edited Dec 11 '19 at 12:00

answered Dec 11 '19 at 11:49

Andreas K.

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Double Summation in Python

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