rolling().sum() is numerically unstable #7128
Description
What happened?
On an input array like
array([0. , 0. , 0. , 0.57392103, 0.57392103,
0.57392103, 0.57392103, 0.57392103, 0.57392103, 0.57392103,
0.57392103, 0.57392103, 0. , 0.57392103, 0.57392103,
0.57392103, 0.57392103, 0.57392103, 0.57392103, 2.29551022,
2.29551022, 2.29551022, 2.29551022, 2.29551022, 2.29551022,
2.29551022, 2.29551022, 2.29551022, 2.29551022, 2.29551022,
2.29551022, 2.29551022, 2.29551022, 0.57383408, 0.57383408,
0.57383408, 0.57383408, 0.57383408, 0.57383408, 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ])
that has all positive values, and then zeros, computing the rolling sum (or mean) leads to negative values
mydata.rolling(t=3, min_periods=1).sum().values[0,0,:]
array([-3.33066907e-14, -3.33066907e-14, -3.33066907e-14, 5.73921029e-01,
2.14784206e+00, 1.72176309e+00, 1.72176309e+00, 1.72176309e+00,
1.72176309e+00, 1.72176309e+00, 1.72176309e+00, 1.72176309e+00,
1.14784206e+00, 1.14784206e+00, 1.14784206e+00, 1.72176309e+00,
1.72176309e+00, 1.72176309e+00, 1.72176309e+00, 3.44335228e+00,
5.16494146e+00, 6.88653065e+00, 6.88653065e+00, 6.88653065e+00,
6.88653065e+00, 6.88653065e+00, 6.88653065e+00, 6.88653065e+00,
6.88653065e+00, 6.88653065e+00, 6.88653065e+00, 6.88653065e+00,
6.88653065e+00, 5.16485452e+00, 3.44317838e+00, 1.72150224e+00,
1.72150224e+00, 1.72150224e+00, 1.72150224e+00, 1.14766816e+00,
5.73834081e-01, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14,
-3.35287353e-14, -3.35287353e-14, -3.35287353e-14, -3.35287353e-14])
Both arrays have dtype = float64.
The issue aggravates as the rolling window increases.
What did you expect to happen?
the rolling calculation could be more numerically precise by keeping track for instance of the Kahan compensation term.
https://en.wikipedia.org/wiki/Kahan_summation_algorithm
MVCE confirmation
- Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
- Complete example — the example is self-contained, including all data and the text of any traceback.
- Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
- [X ] New issue — a search of GitHub Issues suggests this is not a duplicate.
Environment
this is reproducible across xarray versions, but mine is 2022.09.0.