issue_comments

Over in https://github.com/pydata/xarray/issues/7344#issuecomment-1336299057 @shoyer

That said -- we could also switch to smarter NumPy based algorithms to implement most moving window calculations, e.g,. using np.nancumsum for moving window means.

After some digging, this would involve using "summed area tables" which have been generalized to nD, and can be used to compute all our built-in reductions (except median). Basically we'd store the summed area table (repeated np.cumsum) and then calculate reductions using binary ops (mostly subtraction) on those tables.

This would be an intermediate level project but we could implement it incrementally (start with sum for example). One downside is the potential for floating point inaccuracies because we're taking differences of potentially large numbers.

cc @aulemahal

This is already done for counts, correct? Here:

https://github.com/pydata/xarray/blob/1597e3a91eaf96626725987d23bbda2a80d2bae7/xarray/core/rolling.py#L370-L382

This should work for most of the reductions (and is a bit similar to what is done in weighted for mean and sum):

• [x] count: isnull() -> rolling -> sum
• [x] argmax: fillna(-inf) -> rolling -> argmax
• [x] argmin: fillna(inf) -> rolling -> argmin
• [x] max: fillna(-inf) -> rolling -> max (not sure about this one, need to be careful with the dtype)
• [x] min: fillna(inf) -> rolling -> min (dito)
• [x] mean: fillna(0) -> rolling -> sum / count (ensure nan if count == 0)
• [x] prod: fillna(1) -> rolling -> prod
• [x] sum: fillna(0) -> rolling -> sum
• [ ] var: fillna(0) -> rolling -> possible (?) but a bit more involved
• [ ] std: sqrt(var)
• [ ] median: probably not possible

I think this should not be too difficult, the thing is that rolling itself is already quite complicated

I just saw that numpy 1.20 introduces stride_tricks.sliding_window_view. I have not looked at this yet. Just leaving this here for reference.

https://numpy.org/devdocs/reference/generated/numpy.lib.stride_tricks.sliding_window_view.html#numpy.lib.stride_tricks.sliding_window_view

https://numpy.org/devdocs/release/1.20.0-notes.html#sliding-window-view-provides-a-sliding-window-view-for-numpy-arrays

https://github.com/numpy/numpy/pull/17394

@mathause Oh, I missed this issue. Yes, this is implemented only for count.

the thing is that rolling itself is already quite complicated

Agreed. We need to clean this up.

One possible option would be to drop support of bottleneck. This does not work for nd-rolling and if we implement the nd-nanreduce, the speed should be comparable with bottleneck.