Shapes of numpy arrays

Question

Been working with numpy for a while now. Just when I think I have arrays figured out, though, it throws me another curve. For instance, I construct the 3D array pltz, and

Answer 1

You should tell us the lenth of gridset2 and the shape of pltz.

But I've deduced from the documentation that user2357112 gave us that

len(gridset2) == 17
pltz.shape[1] == 160

http://docs.scipy.org/doc/numpy-1.10.0/reference/arrays.indexing.html#combining-advanced-and-basic-indexing

• The advanced indexes are separated by a slice, ellipsis or newaxis. For example x[arr1, :, arr2].
• The advanced indexes are all next to each other. For example x[..., arr1, arr2, :] but not x[arr1, :, 1] since 1 is an advanced index in this regard.

In the first case, the dimensions resulting from the advanced indexing operation come first in the result array, and the subspace dimensions after that. In the second case, the dimensions from the advanced indexing operations are inserted into the result array at the same spot as they were in the initial array

>>> pltz[10,:,gridset2].shape
(17, 160)

This is the first case in the quote, a slice in the middle. gridset2 is advanced indexing (e.g. [1,2,3,...]). It is put first; the [10,:] subspace is placed after.

 >>> pltz[10][:,gridset2].shape
 (160, 17)

with pltz[10], the new array (a view) is 2d `(160,N)'. It now puts the size 17 dim last, the 2nd case in the documentation.

Answer 2

Since your indexing expression has both a : and a list in it, NumPy needs to apply both the basic and advanced indexing rules, and the way they interact is kind of weird. The relevant documentation is here, and you should consult it if you want to know the full details. I'll focus on the part that causes this shape mismatch.

When all components of the indexing expression that use advanced indexing are next to each other, dimensions of the result coming from advanced indexing are placed into the result in the position of the dimensions they replace. Advanced indexing components are array-likes, such as arrays, lists, and scalars; scalars can also be used in basic indexing, but for this purpose, they're considered advanced. Thus, if arr.shape == (10, 20, 30) and ind.shape = (2, 3, 4), then

arr[:, ind, :].shape == (10, 2, 3, 4, 30)

Your first expression falls into this case.

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On the other hand, if components of the indexing expression that use advanced indexing are separated by components that use basic indexing, there is no unambiguous place to insert the advanced indexing dimensions. For example, with

arr[ind, :, ind]

the result needs to have dimensions of length 2, 3, 4, and 20, and there's no good place to stick the 20.

When advanced indexing components are separated by basic indexing components, NumPy sticks all dimensions resulting from advanced indexing at the start of the result array. Basic indexing components are :, ..., and np.newaxis (None). Your second expression falls into this case.

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Since your second expression has advanced indexing components separated by basic indexing components and your first expression doesn't, your two expressions use different indexing rules. To avoid this, you could separate the basic indexing and advanced indexing into two stages, or you could replace the basic indexing with equivalent advanced indexing. Whatever you do, I recommend putting an explanatory comment above such code.