Difficulty understanding .moveaxis in Numpy

[leea2024]

I am having difficulties understanding .moveaxis in Numpy.

I first create an array by using a=np.arange(24).reshape(2,3,4). The system will first fill up axis 2 with 0 1 2 3, then move along axis 1 to the next row. When the first 'page' is done, the system move along axis 0. The following is obtained.

Output:
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]],

       [[12, 13, 14, 15],
        [16, 17, 18, 19],
        [20, 21, 22, 23]]])

If I input b = np.swapaxes(a,0,2); b now, the system should fill up axis 0 first, then axis 1 and finally axis 2. The following is obtained.

Output:
array([[[ 0, 12],
        [ 4, 16],
        [ 8, 20]],

       [[ 1, 13],
        [ 5, 17],
        [ 9, 21]],

       [[ 2, 14],
        [ 6, 18],
        [10, 22]],

       [[ 3, 15],
        [ 7, 19],
        [11, 23]]])

This is understandable as axis 1 is preserved, so we can still see columns like 0 4 8 and 1 5 9 after swapping the axes.

But I don't really understand how .moveaxis works. If I input b = np.moveaxis(a,0,2); b, the following is obtained.

Output:
array([[[ 0, 12],
        [ 1, 13],
        [ 2, 14],
        [ 3, 15]],

       [[ 4, 16],
        [ 5, 17],
        [ 6, 18],
        [ 7, 19]],

       [[ 8, 20],
        [ 9, 21],
        [10, 22],
        [11, 23]]])

I know that the .moveaxis function is meant to 'move axis 0 to a new position while the other axes remain the same order', but what is the meaning of that? I understand that the result should be an array with shape (3, 4, 2), but why would the system go down the first column in the first place then move on to the second page? If axis 0 is now moved to the last place, shouldn't the system fill up the array along axis 0 first?

[Gribouillis]

Let us call the original axes A B C instead of 0, 1, 2. Initially

• moving along axis A changes page: 0 -> 12 (slow axis)
  
• moving along axis B changes row: 0 -> 4
  
• moving along axis C changes element: 0 -> 1 (fast axis)
  

In array b after the moveaxis operation, the axes are now in the order B C A so

• page changes along axis B: 0 -> 4 (now the slow axis)
  
• row changes along axis C: 0 -> 1
  
• element changes along axis A: 0-> 12 (now the fast axis)
  

I hope it helps.

An experiment

>>> import numpy as np
>>> a=np.arange(24).reshape(2,3,4)
>>> b = np.moveaxis(a, 0, 2)
>>> for i in range(2):
...     for j in range(3):
...         for k in range(4):
...             assert a[i][j][k] == b[j][k][i]
... 
>>> 

[leea2024]

Let us call the original axes A B C instead of 0, 1, 2. Initially

• moving along axis A changes page: 0 -> 12 (slow axis)
  
• moving along axis B changes row: 0 -> 4
  
• moving along axis C changes element: 0 -> 1 (fast axis)
  

In array b after the moveaxis operation, the axes are now in the order B C A so

• page changes along axis B: 0 -> 4 (now the slow axis)
  
• row changes along axis C: 0 -> 1
  
• element changes along axis A: 0-> 12 (now the fast axis)
  

I hope it helps.

An experiment

>>> import numpy as np
>>> a=np.arange(24).reshape(2,3,4)
>>> b = np.moveaxis(a, 0, 2)
>>> for i in range(2):
...     for j in range(3):
...         for k in range(4):
...             assert a[i][j][k] == b[j][k][i]
... 
>>> 

This is very clear. Thank you for your explanation!