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

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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.

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