[Consistency] Default axes in linalg.diagonal and linalg.trace.

[lezcano]

The functions linalg.trace and linalg.diagonal have as default axis1=0, axis2=1.

This goes against the rest of the documentation, in which a batch of matrices is defined as a tensor with shape (..., M, N).

It would be more consistent with the rest of the API to have axis1=-2, axis2=-1 to handle batches of matrices correctly by default.

[leofang]

Wouldn't it be better to just remove axis1 and axis2 entirely and always use the last two axes? This makes it more consistent with other linalg APIs, and is mathematically more intuitive. Users who need to compute trace/diagonal along arbitrary two axes can always swap the axes (related: #228) first before calling the API.

[lezcano]

At least in PyTorch, it would be as efficient to transpose the diagonals to the back and then call diagonal than it would be calling it with this API. Now, this API may be convenient for some applications? That I do not know. I have never used diagonal with anything other than -2, -1, but my experience is very biased towards working with matrices.

[leofang]

In CuPy it's also as efficient, given that transpose/swapaxes only return views (with different strides). I guess this suggests for both PyTorch and CuPy (and likely NumPy) removing axis1/axis2 is safe. 🙂

[rgommers]

trace is not heavily used (there's no data in https://github.com/data-apis/python-record-api, and a search in SciPy seems to confirm it's not used there at all). I suspect when it is used, it's indeed with -2, -1.

Wouldn't it be better to just remove axis1 and axis2 entirely and always use the last two axes? This makes it more consistent with other linalg APIs, and is mathematically more intuitive.

+1 makes sense to me

[rgommers]

Fixed by gh-241, which removes the keywords. Thanks @lezcano and @leofang