[SPARK-46976][PS] Implement DataFrameGroupBy.corr

[zhengruifeng]

What changes were proposed in this pull request?

Implement DataFrameGroupBy.corr

Why are the changes needed?

for pandas parity
https://pandas.pydata.org/docs/reference/api/pandas.core.groupby.DataFrameGroupBy.corr.html

Does this PR introduce any user-facing change?

yes

In [5]: pdf = pd.DataFrame({'A': [0, 0, 0, 1, 1, 2], 'B': [-1, 2, 3, 5, 6, 0], 'C': [4, 6, 5, 1, 3, 0]}, columns=['A', 'B', 'C'])

In [6]: pdf.groupby("A").corr()
Out[6]: 
            B         C
A                      
0 B  1.000000  0.720577
  C  0.720577  1.000000
1 B  1.000000  1.000000
  C  1.000000  1.000000
2 B       NaN       NaN
  C       NaN       NaN

In [7]: psdf = ps.from_pandas(pdf)

In [8]: psdf.groupby("A").corr()
                                                                                
            B         C
A                      
0 B  1.000000  0.720577
  C  0.720577  1.000000
1 B  1.000000  1.000000
  C  1.000000  1.000000
2 B       NaN       NaN
  C       NaN       NaN

How was this patch tested?

added tests

Was this patch authored or co-authored using generative AI tooling?

no

[xinrong-meng]

typo: df

[zhengruifeng]

thanks

[xinrong-meng]

LGTM after fixing the typo in doctest, thanks!

[zhengruifeng]

thanks for the reviews
merged to master