BUG: Clip corr edge cases between -1.0 and 1.0

[j-hendricks]

Closes #61120

Clips correlation coefficient in DataFrame.corr() between -1.0 and 1.0

Adds test_corr_within_bounds to ensure coefficient within bounds

• closes BUG: .corr() values significantly higher than 1 #61120 (Replace xxxx with the GitHub issue number)
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.

[mroeschke]

Thanks, does nancorr_spearman also need this change?

[j-hendricks]

I do not think nancorr_spearman requires this change because it computes the divisor by first ranking the raw data rather than using the raw data itself like nancorr. This results in a stable value for the divisor. In the case of y = [1.35951, 1.3595100000000007], the divisor equals 0.5 for nancorr_spearman but equals almost 0 for nancorr.

[mroeschke]

Thanks could you add a whatsnew note to v3.0.0.rst?

[j-hendricks]

Added a whatnew note under "Notable Bug Fixes"

[mroeschke]

A single line entry under the Numeric section would be more appropriate

[mroeschke]

Thanks again @j-hendricks

[TomAugspurger]

@j-hendricks I'm seeing different behavior, depending on whether missing values are present. Can you confirm whether the following behavior is expected?

At 83979d6

In [50]: x = pd.DataFrame({"A": [1, 2, None, 4], "B": [2, 4, None, 9]})

In [51]: x.cov()
Out[51]:
     A    B
A  1.0  1.0
B  1.0  1.0

In [52]: x.dropna().cov()
Out[52]:
          A     B
A  2.333333   5.5
B  5.500000  13.0

In [53]: pd.__git_version__
Out[53]: '83979d6a0c5a223bac2af8ef706c5ff8d432bcca'

With 2.2.3:

In [67]: x = pd.DataFrame({"A": [1, 2, None, 4], "B": [2, 4, None, 9]})

In [68]: x.cov()
Out[68]:
          A     B
A  2.333333   5.5
B  5.500000  13.0

In [69]: x.dropna().cov()
Out[69]:
          A     B
A  2.333333   5.5
B  5.500000  13.0

In [70]: pd.__version__
Out[70]: '2.2.3'

Depending on my digging in dask/dask#11857, there might be some more differences, but this seemed to be the largest.

[mroeschke]

It appears this clipping should have only happened if cov=False. @j-hendricks do you mind opening a follow up PR with this fix?