What's the best way to downsample a numpy array?

Reshape to split the last two axes into two more, such that the latter split ones are of lengths equal to the block sizes, giving us a 5D array and then use mean along the third and fifth axes -

BSZ = (8,8)
m,n = a.shape[1:]
out = a.reshape(N,m//BSZ[0],BSZ[0],n//BSZ[1],BSZ[1]).mean(axis=(2,4))

Sample run on smaller array with smaller block-size (2,2) -

1) Inputs :

In [271]: N = 2

In [272]: a = np.random.randint(0,9,(N,6,6))

In [273]: a
Out[273]: 
array([[[3, 1, 8, 7, 8, 2],
        [0, 6, 2, 6, 8, 2],
        [2, 1, 1, 0, 0, 1],
        [8, 3, 0, 2, 8, 0],
        [4, 7, 2, 6, 6, 7],
        [5, 5, 1, 7, 2, 7]],

       [[0, 0, 8, 1, 7, 6],
        [8, 6, 5, 8, 4, 0],
        [0, 3, 7, 7, 6, 1],
        [7, 1, 7, 6, 3, 6],
        [7, 6, 4, 6, 4, 5],
        [4, 2, 0, 2, 6, 2]]])

2) Get few output values for manual verification :

In [274]: a[0,:2,:2].mean()
Out[274]: 2.5

In [275]: a[0,:2,2:4].mean()
Out[275]: 5.75

In [276]: a[0,:2,4:6].mean()
Out[276]: 5.0

In [277]: a[0,2:4,:2].mean()
Out[277]: 3.5

3) Use proposed approach and manually verify :

In [278]: BSZ = (2,2)

In [279]: m,n = a.shape[1:]

In [280]: a.reshape(N,m//BSZ[0],BSZ[0],n//BSZ[1],BSZ[1]).mean(axis=(2,4))
Out[280]: 
array([[[ 2.5 ,  5.75,  5.  ],
        [ 3.5 ,  0.75,  2.25],
        [ 5.25,  4.  ,  5.5 ]],

       [[ 3.5 ,  5.5 ,  4.25],
        [ 2.75,  6.75,  4.  ],
        [ 4.75,  3.  ,  4.25]]])

There is a neat solution in form of 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. 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. ]])