BUG: std with array_manager and NaT results

[rhshadrach]

When a reduction results in NaT, the array manager reduction assumes the output dtype is the same as the input dtype. This is not correct for std (and from what I can tell, only std is incorrect).

df = pd.DataFrame({'a': ['2022-01-01', '2022-01-02', pd.NaT, '2022-01-03']})
df['a'] = pd.to_datetime(df['a'])

result = df.std(skipna=True)
print(result)
# a   1 days
# dtype: timedelta64[ns]

result2 = df.std(skipna=False)
print(result2)
# a   NaT
# dtype: datetime64[ns]

[jbrockmendel]

@rhshadrach im working on a branch that implements keepdims that would fix this. is there an extant test for this somewhere?

[jbrockmendel]

Looks like an xfail in test_std_datetime64_with_nat

[topper-123]

Just checked and this is not fixed by #52788 ATM so probably std needs some dtype info. I' pretty sure this is fixable after #52788, so can be done in a follow-up.

[jbrockmendel]

df.std() now raises ValueError with ArrayManager

[rhshadrach]

The ArrayManager is now deprecated. Closing.