Is there a way to speed up this smoothing operation in python?

Question

I'm doing smoothing of some sequential integer data that I have in a list. My smoothing method is to replace each number with the mean of that number and its neighbors. I'm currently doing that with this code:

from statistics import mean
smoothednums = [mean(nums[:2])] + [mean(nums[i-1:i+2]) for i in range(1,len(nums))]

This has significantly increased the runtime of my script. Is there a better way to do this operation?

Possible duplicate of [Weighted smoothing of a 1D array - Python](https://stackoverflow.com/questions/35234680/weighted-smoothing-of-a-1d-array-python) — mkrieger1, Jun 12 '19 at 20:59
How big is the list and how much is “significantly increased”? — Ry-, Jun 12 '19 at 21:00

score 2 · Accepted Answer · answered Jun 12 '19 at 21:17

2

https://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html

You are describing convolution with a uniform (box) filter:

smoothednums = np.convolve(nums, [1/3, 1/3, 1/3]);

For larger windows, you might consider looking at the summed area table algorithm which is O(1) in window size:

Efficient summed Area Table Calculation with Numpy

answered Jun 12 '19 at 21:17

Alex Taylor

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Thanks. For future readers, the mode='same' parameter is required to get the same result as my original code. The default parameter will give different results. – Colin Jun 12 '19 at 21:32

score 0 · Answer 2 · answered Jun 12 '19 at 21:08

You can avoid all slicing and copying by adding and subtracting 1/3 of each value. (Floating point error makes this not exactly equivalent to your original, but it should be close enough in normal cases.) I don’t know if it ends up faster, but it seems worth a shot:

window_mean = mean(nums[:3])
smoothednums = [mean(nums[:2]), window_mean]

for i in range(2, len(nums) - 1):
    window_mean -= nums[i - 2] / 3
    window_mean += nums[i + 1] / 3
    smoothednums.append(window_mean)

smoothednums.append(mean(nums[-2:]))

Is there a way to speed up this smoothing operation in python?

2 Answers2