python - Why does indexing numpy arrays with brackets and commas differ in behavior?

Question

I tend to index numpy arrays (matrices) with brackets, but I've noticed when I want to slice an array (matrix) I must use the comma notation. Why is this? For example,

>>> x = numpy.array([[1, 2], [3, 4], [5, 6]])
>>> x
array([[1, 2],
       [3, 4],
       [5, 6]])
>>> x[1][1]
4                 # expected behavior
>>> x[1,1]
4                 # expected behavior
>>> x[:][1]
array([3, 4])     # huh?
>>> x[:,1]
array([2, 4, 6])  # expected behavior

Answer 1

This:

x[:, 1]

means "take all indices of x along the first axis, but only index 1 along the second".

This:

x[:][1]

means "take all indices of x along the first axis (so all of x), then take index 1 along the first axis of the result". You're applying the 1 to the wrong axis.

x[1][2] and x[1, 2] are only equivalent because indexing an array with an integer shifts all remaining axes towards the front of the shape, so the first axis of x[1] is the second axis of x. This doesn't generalize at all; you should almost always use commas instead of multiple indexing steps.