Numpy [...,None]

The slice of [..., None] consists of two "shortcuts":

The ellipsis literal component:

The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is a rank 5 array (i.e., it has 5 axes), then

• x[1,2,...] is equivalent to x[1,2,:,:,:],
• x[...,3] to x[:,:,:,:,3] and
• x[4,...,5,:] to x[4,:,:,5,:].

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The None component:

numpy.newaxis

The newaxis object can be used in all slicing operations to create an axis of length one. newaxis is an alias for ‘None’, and ‘None’ can be used in place of this with the same result.

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So, arr[..., None] takes an array of dimension N and "adds" a dimension "at the end" for a resulting array of dimension N+1.

Example:

import numpy as npx = np.array([[1,2,3],[4,5,6]])print(x.shape)          # (2, 3)y = x[...,None]print(y.shape)          # (2, 3, 1)z = x[:,:,np.newaxis]print(z.shape)          # (2, 3, 1)a = np.expand_dims(x, axis=-1)print(a.shape)          # (2, 3, 1)print((y == z).all())   # Trueprint((y == a).all())   # True

Consider this code:

np.ones(shape=(2,3))[...,None].shape 

As you see the 'None' phrase change the (2,3) matrix to a (2,3,1) tensor. As a matter of fact it put the matrix in the LAST index of the tensor.

If you use

np.ones(shape=(2,3))[None, ...].shape

it put the matrix in the FIRST‌ index of the tensor