Why is the print result of 3d arrays different from the mental visualisation of the same in python?

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I am learning machine learning and I don't have much coding experience. While trying to understand 3d arrays, I was instructed to visualise a 2x4x3 array to be: 2x4x3

But when I create a random array with the same shape using:

X = np.random.randint(10, size=(2, 4, 3))
print(X)

the output is

[[[6 1 0]
  [6 6 5]
  [2 7 0]
  [5 4 3]]

 [[7 8 2]
  [9 1 2]
  [2 0 1]
  [8 0 9]]]

This looks like 4x3x2 to me.

Am I wrong in understanding 2x4x3 as the image given above? Why is python printing 3d arrays like this? And finally if my mental visualisation is correct, how are the generated random values arranged in the image?

reshape multidimensional-array numpy arrays python
2 Answers

MATLAB/Octave does display this 3d array as 3 blocks of (2,4) matrices

>> reshape(1:24,2, 4, 3)
ans =

ans(:,:,1) =

   1   3   5   7
   2   4   6   8

ans(:,:,2) =

    9   11   13   15
   10   12   14   16

ans(:,:,3) =

   17   19   21   23
   18   20   22   24

But here the trailing dimension is the outermost. This called column major or Fortran convention. Notice how the values increase, going down the column.

But in numpy the leading dimension is outer most. Values increase across the rows. This is a row-major or C ordering

In [22]: np.arange(1,25).reshape(2,4,3)                                         
Out[22]: 
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]]])

This dimension ordering matches the nesting in the list equivalent:

In [24]: np.arange(1,25).reshape(2,4,3).tolist()                                
Out[24]: 
[[[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]],
 [[13, 14, 15], [16, 17, 18], [19, 20, 21], [22, 23, 24]]]

The meaning of the dimensions comes from the application and user, not from Python/numpy. Images are often (height, width, channels). Computationally it may be convenient to keep the 3 (or 4) elements of a channel for one pixel together, that is, make it that dimension last. So your (2,4,3) could be thought of as a (2,4) image with 3 colors (rgb). The normal numpy print isn't the best for visualizing that.

But if the image is (400, 600, 3) shape, we don't want a 'print' of the array. We want a plot or image display, a picture, that renders that last dimension as colors.

user_9019250

It is 2×4×3. The first dimension is the outermost one. We see that the outer list (see the outer square brackets), has two elements:

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

 [[7, 8, 2],
  [9, 1, 2],
  [2, 0, 1],
  [8, 0, 9]]]

Each of these items has the same dimensions: a 4×3 matrix. Indeed, if take a look at the first item of the list, we have:

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

here there are four rows, and if we take a look at the first row for example, we see a collection with three elements:

[6, 1, 0]
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