Inconsistent advanced indexing in NumPy

Question

Why are the following indexing forms produce differently shaped outputs?

a = np.zeros((5, 5, 5, 5))
print(a[:, :, [1, 2], [3, 4]].shape)
# (5, 5, 2)

print(a[:, :, 1:3, [3, 4]].shape)
#(5, 5, 2, 2)

Almost certain I'm missing something obvious.

Answer 1

[1, 2], [3, 4] doesn't mean "select indices 1 and 2 in one dimension and 3 and 4 in another". It means "select the pairs of indices (1, 3) and (2, 4)".

Your first expression select all elements at locations of the form a, b, c, d where a and b can be any index and c and d must be either the pair (1, 3) or the pair (2, 4).

Your second expression selects all elements at locations of the form a, b, c, d where a and b can be any index, c must be in the half-open range [1, 3), and d must be either 3 or 4. Unlike the first one, c and d are allowed to be (2, 3) or (1, 4).

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Note that using both basic and advanced indexing in the same indexing expression (which mostly means mixing : and advanced indexing) has unintuitive effects on the order of the axes of the result. It's best to avoid mixing them.