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I have a numpy array. I want to create a new array which is the average over every consecutive triplet of elements. So the new array will be a third of the size as the original.

As an example:

 np.array([1,2,3,1,2,3,1,2,3])

should return the array:

 np.array([2,2,2])

Can anyone suggest an efficient way of doing this? I'm drawing blanks.

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3 Answers 3

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157

If your array arr has a length divisible by 3:

np.mean(arr.reshape(-1, 3), axis=1)

Reshaping to a higher dimensional array and then performing some form of reduce operation on one of the additional dimensions is a staple of numpy programming.

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  • 19
    Jaime - thank you, that is a very elegant way of doing things. Do you have any advice for where one can read about these so-called 'staples of numpy programming'?
    – user1654183
    Commented Apr 14, 2013 at 21:55
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    if arr length is not divisible by 3, you can do something like: arr = np.nanmean(np.pad(arr.astype(float), (0, 3 - arr.size%3), mode='constant', constant_values=np.NaN).reshape(-1, 3), axis=1)
    – plong0
    Commented Jul 31, 2017 at 10:01
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    That padding comment by @plong0 helped me, but to make it general so that it works even if your array is also divisible by 3, I had to add another mod to the padding sizes: ( 0, ((3 - arr.size%3) % 3) ), or something like ( 0, 0 if arr.size % 3 == 0 else 3 - arr.size % 3 )
    – Scott Staniewicz
    Commented Oct 4, 2018 at 17:32
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    For an array not necessarily divisible by 3, I used np.mean(arr[:(len(arr)//3)*3].reshape(-1,3), axis=1) which seems a lot simpler to me. I believe this will work for python2 and python3
    – Chris
    Commented Dec 17, 2018 at 10:01
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    @Chris That is not the same, because it simply discard the data in the last group (if it is not a group of 3), whereas the solutions above also work on the remainder group.
    – bluenote10
    Commented Sep 15, 2019 at 12:26
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For googlers looking for a simple generalisation for arrays with multiple dimensions: the function block_reduce in the scikit-image module (link to docs).

It has a very simple interface to downsample arrays by applying a function such as numpy.mean, but can also use others (maximum, median, ...). The downsampling can be done by different factors for different axes by supplying a tuple with different sizes for the blocks. Here's an example with a 2D array; downsampling only axis 1 by 5 using the mean:

import numpy as np
from skimage.measure import block_reduce

arr = np.stack((np.arange(1,20), np.arange(20,39)))

# array([[ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
#        [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]])

arr_reduced = block_reduce(arr, block_size=(1,5), func=np.mean, cval=np.mean(arr))

# array([[ 3. ,  8. , 13. , 17.8],
#        [22. , 27. , 32. , 33. ]])

As it was discussed in the comments to the other answer: if the array in the reduced dimension is not divisible by block size, padding values are provided by the argument cval (0 by default).

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To apply the accepted answer to 2D array for each column/feature:

arr.reshape(-1, downsample_ratio, arr.shape[1]).mean(axis = 1)
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