\(\newcommand{L}[1]{\| #1 \|}\newcommand{VL}[1]{\L{ \vec{#1} }}\newcommand{R}[1]{\operatorname{Re}\,(#1)}\newcommand{I}[1]{\operatorname{Im}\, (#1)}\)

numpy.tranpose for swapping axes

Numpy allows you to swap axes without costing anything in memory, and very little in time.

The obvious axis swap is a 2D array transpose:

>>> import numpy as np
>>> arr = np.arange(10).reshape((5, 2))
>>> arr
array([[0, 1],
       [2, 3],
       [4, 5],
       [6, 7],
       [8, 9]])

>>> arr.T
array([[0, 2, 4, 6, 8],
       [1, 3, 5, 7, 9]])

The transpose method - and the np.tranpose function does the same thing as the .T attribute above:

>>> arr.transpose()
array([[0, 2, 4, 6, 8],
       [1, 3, 5, 7, 9]])

The advantage of transpose over the .T attribute is that is allows you to move axes into any arbitrary order.

For example, let’s say you had a 3D array:

>>> arr = np.arange(24).reshape((2, 3, 4))
>>> arr
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]],
<BLANKLINE>
       [[12, 13, 14, 15],
        [16, 17, 18, 19],
        [20, 21, 22, 23]]])

>>> arr.shape
(2, 3, 4)

>>> arr[:, :, 0]
array([[ 0,  4,  8],
       [12, 16, 20]])

transpose allows you to re-order these axes as you like. For example, maybe you wanted to take the current last axis, and make it the first axis. You pass transpose the order of the axes that you want:

>>> new_arr = arr.transpose(2, 0, 1)

>>> new_arr
array([[[ 0,  4,  8],
        [12, 16, 20]],
<BLANKLINE>
       [[ 1,  5,  9],
        [13, 17, 21]],
<BLANKLINE>
       [[ 2,  6, 10],
        [14, 18, 22]],
<BLANKLINE>
       [[ 3,  7, 11],
        [15, 19, 23]]])

>>> new_arr.shape
(4, 2, 3)

>>> new_arr[0, :, :]
array([[ 0,  4,  8],
       [12, 16, 20]])

Notice that the contents of the axis has not changed, just the position. new_arr[i, :, :] is the same as arr[:, :, i] for any i.