On Thu, Jul 17, 2008 at 03:16, StÃ©fan van der Walt <stefan@sun.ac.za> wrote:

Hi Robert

2008/7/17 Robert Kern <robert.kern@gmail.com>:

In [42]: smallcube = cube[idx_i,idx_j,idx_k]

Fantastic -- a good way to warm up the brain-circuit in the morning! Is there an easy-to-remember rule that predicts the output shape of the operation above? I'm trying to imaging how the output would change if I altered the dimensions of idx_i or idx_j, but it's hard.

Like I said, they all get broadcasted against each other. The final output is the shape of the broadcasted index arrays and takes values found by iterating in parallel over those broadcasted index arrays.

It looks like you can do all sorts of interesting things by manipulation the indices. For example, if I take

In [137]: x = np.arange(12).reshape((3,4))

I can produce either

In [138]: x[np.array([[0,1]]), np.array([[1, 2]])] Out[138]: array([[1, 6]])

or

In [140]: x[np.array([[0],[1]]), np.array([[1], [2]])] Out[140]: array([[1], [6]])

and even

In [141]: x[np.array([[0],[1]]), np.array([[1, 2]])] Out[141]: array([[1, 2], [5, 6]])

or its transpose

In [143]: x[np.array([[0,1]]), np.array([[1], [2]])] Out[143]: array([[1, 5], [2, 6]])

Is it possible to separate the indexing in order to understand it better? My thinking was

cube_i = cube[idx_i,:,:].squeeze() cube_j = cube_i[:,idx_j,:].squeeze() cube_k = cube_j[:,:,idx_k].squeeze()

Not sure what would happen if the original array had single dimensions, though.

You'd have a problem. So the way fancy indexing interacts with slices is a bit tricky, and this is why we couldn't use the nicer syntax of cube[:,:,idx_k]. All axes with fancy indices are collected together. Their index arrays are broadcasted and iterated over. *For each iterate*, all of the slices are collected, and those sliced axes are *added* to the output array. If you had used fancy indexing on all of the axes, then the iterate would be a scalar value pulled from the original array. If you mix fancy indexing and slices, the iterate is the *array* formed by the remaining slices. So if idx_k is shaped (ni,nj,3), for example, cube[:,:,idx_k] will have the shape (ni,nj,ni,nj,3). So smallcube[:,:,i,j,k]==cube[:,:,idx_k[i,j,k]]. Is that clear, or am I obfuscating the subject more?

Back to the original problem:

In [127]: idx_i.shape Out[127]: (10, 1, 1)

In [128]: idx_j.shape Out[128]: (1, 15, 1)

In [129]: idx_k.shape Out[129]: (10, 15, 7)

For the constant slice case, I guess idx_k also have been (1, 1, 7)?

The construction of the cube could probably be done using only

cube.flat = np.arange(nk)

Yes, but only due to a weird feature of assigning to .flat. If the RHS is too short, it gets repeated. Since the last axis is contiguous, repeating arange(nk) happily coincides with the desired result of cube[i,j] == arange(nk) for all i,j. This won't check the size, though. If I give it cube.flat=np.arange(nk+1), it will repeat that array just fine, although it doesn't line up. cube[:,:,:]=np.arange(nk), on the other hand broadcasts the RHS to the shape of cube, then does the assignment. If the RHS cannot be broadcasted to the right shape (in this case because it is not the same length as the final axis of the LHS), an error is raised. I find the reuse of the broadcasting concept to be more memorable, and robust over the (mostly) ad hoc use of plain repetition with .flat. -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco