NumPy Array Reshaped but how to change axis for pooling?

Question

I have a 8x8 matrix as follows:

[[ 0.3  0.3  0.3  0.3  0.3  0.5  0.1 -0.1]
 [ 0.1  0.1 -0.1  0.3  0.3 -0.1 -0.1 -0.5]
 [-0.1  0.1  0.3 -0.1  0.3 -0.1 -0.1 -0.1]
 [-0.1  0.1  0.5  0.3 -0.3 -0.1 -0.3 -0.1]
 [ 0.5  0.1 -0.1  0.1 -0.1 -0.1 -0.3 -0.5]
 [ 0.1 -0.1 -0.3 -0.5 -0.5 -0.1 -0.1 -0.3]
 [-0.5 -0.3 -0.3 -0.3 -0.1 -0.5 -0.1 -0.3]
 [-0.3 -0.3 -0.3 -0.3 -0.1 -0.1 -0.5 -0.3]]

My window is 2x2. What I am trying to do is get four numbers together (up and down numbers) for pooling. Sample output looks like this:

    [[0.3 0.3
      0.1 0.1]

      [0.3 0.3
      -0.1 0.3]
       .......
       .......
      [-0.1 -0.3
       -0.5 -0.3]]

What I using is print arr.reshape(16,2,2) What i can't understand is how to setup axis for this requirement. My output is:

[[[ 0.3  0.3]
  [ 0.3  0.3]]

 [[ 0.3  0.1]
  [ 0.5 -0.1]]

 [[ 0.1 -0.1]
  [ 0.1  0.3]]

 [[ 0.3 -0.1]
  [-0.1 -0.5]]

 [[-0.1  0.3]
  [ 0.1 -0.1]]

 [[ 0.3 -0.1]
  [-0.1 -0.1]]

 [[-0.1  0.5]
  [ 0.1  0.3]]

 [[-0.3 -0.3]
  [-0.1 -0.1]]

 [[ 0.5 -0.1]
  [ 0.1  0.1]]

 [[-0.1 -0.3]
  [-0.1 -0.5]]

 [[ 0.1 -0.3]
  [-0.1 -0.5]]

 [[-0.5 -0.1]
  [-0.1 -0.3]]

 [[-0.5 -0.3]
  [-0.3 -0.3]]

 [[-0.1 -0.1]
  [-0.5 -0.3]]

 [[-0.3 -0.3]
  [-0.3 -0.3]]

 [[-0.1 -0.5]
  [-0.1 -0.3]]]

Please explain how would axis be applied on this type of situation. Or if their is a better way to get max-pooling do mention.

Note: All of this is for max-pooling. I am using NumPy, SciPy on python.

Answer 1

Reshape splitting each of the two axes into two each such that the latter of the split axes is of the same length as the block size. This would give us a 4D array. Then, perform maximum finding along those latter axes, which would be the second and fourth axes in that 4D array.

Thus, simply do -

m,n = a.shape
out = a.reshape(m//2,2,n//2,2).max(axis=(1,3))

Sample run -

In [50]: a
Out[50]: 
array([[87, 96, 46, 97, 25, 22, 13, 16],
       [65, 62, 68, 87, 52, 80, 26, 82],
       [27, 82, 50, 20, 11, 14, 94, 23],
       [86, 44, 17, 97, 17, 57, 76, 42],
       [47, 85, 30, 61, 55, 87, 11, 35],
       [36, 11, 29, 45, 16, 54, 40, 77],
       [38, 87, 94, 77, 53, 20, 46, 18],
       [86, 50, 17, 23, 91, 23, 25, 11]])

In [51]: m,n = a.shape

In [52]: a.reshape(m//2,2,n//2,2).max(axis=(1,3))
Out[52]: 
array([[96, 97, 80, 82],
       [86, 97, 57, 94],
       [85, 61, 87, 77],
       [87, 94, 91, 46]])