[BUG] cuDF covariance does not agree with pandas when ddof=N

[bdice]

In PR #9889, @isVoid observed that cudf and pandas handle covariance calculations differently when N == ddof. Here is a minimal example showing a few differences in behavior with ddof. This is a bug because cudf should give the same results as pandas. The bug affects both df.cov() and df.groupby(...).cov(). Note that this is not related to the pandas bug 45814 which was also found during #9889 (not directly linked here because it is not related) regarding ddof with missing data, because no data is missing here.

import pandas as pd
import cudf

pdf = pd.DataFrame({"i": [0, 0], "a": [0, 1]})
gdf = cudf.from_pandas(pdf)
print("pandas cov")
print(pdf.cov(ddof=2))
print("cudf cov")
print(gdf.cov(ddof=2))
print("pandas groupby cov")
print(pdf.groupby("i").cov(ddof=2))
print("cudf groupby cov")
print(gdf.groupby("i").cov(ddof=2))

Results (warnings not shown):

pandas cov                                                                                                                                                                                    
    i    a
i NaN  NaN
a NaN  inf

cudf cov
     i    a
i  0.0  0.0
a  0.0  0.5

pandas groupby cov
       a
i       
0 a  inf

cudf groupby cov
        a
i        
0 a  <NA>

Notice that cudf isn't self-consistent between df.cov() and df.groupby(...).cov() in its results for a.

Originally posted by @bdice in #9889 (comment)

[isVoid]

This was accidentally closed because my comment here: #9889 (review)

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[github-actions]

This issue has been labeled inactive-90d due to no recent activity in the past 90 days. Please close this issue if no further response or action is needed. Otherwise, please respond with a comment indicating any updates or changes to the original issue and/or confirm this issue still needs to be addressed.