BUG: Series.corr() returns nan for identical Series objects of length 1

[jackgoldsmith4]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd
s = pd.Series([2])
s.corr(s)

Issue Description

This should return 1.0 because the Series object is being compared to itself. However, this returns nan.

Expected Behavior

Returning 1.0 is expected because the Series object is being compared to itself.

Installed Versions

INSTALLED VERSIONS

commit : 8e522eb
python : 3.8.13.final.0
python-bits : 64
OS : Linux
OS-release : 5.10.47-linuxkit
Version : #1 SMP Sat Jul 3 21:51:47 UTC 2021
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : C.UTF-8
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.5.0.dev0+823.g8e522ebd43
numpy : 1.22.4
pytz : 2022.1
dateutil : 2.8.2
setuptools : 62.3.2
pip : 22.0.4
Cython : 0.29.30
pytest : 7.1.2
hypothesis : 6.46.9
sphinx : 4.5.0
blosc : None
feather : None
xlsxwriter : 3.0.3
lxml.etree : 4.8.0
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 3.0.3
IPython : 8.3.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : 1.3.4
brotli :
fastparquet : 0.8.1
fsspec : 2021.11.0
gcsfs : 2021.11.0
matplotlib : 3.5.2
numba : 0.53.1
numexpr : 2.8.0
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : 8.0.0
pyreadstat : 1.1.6
pyxlsb : None
s3fs : 2021.11.0
scipy : 1.8.1
snappy :
sqlalchemy : 1.4.36
tables : 3.7.0
tabulate : 0.8.9
xarray : 2022.3.0
xlrd : 2.0.1
xlwt : 1.3.0
zstandard : None

[simonjayhawkins]

Thanks @jackgoldsmith4 for the report.

The nan result occurs with a Series of any length series of non varying values, not just with length 1.

from #20954

In general, the correlation between two Series is not defined when one Series does not have varying values, like e.g. s_a or s_c, as the denominator of the correlation function is evaluated to zero, resulting in a by-zero-division.

and #20954 (comment) gives a more detailed explanation.

[jackgoldsmith4]

@simonjayhawkins I understand, thanks for clarifying that for me! Unless you think it would be useful to add to the docs for this function, I can go ahead and close this

[simonjayhawkins]

Unless you think it would be useful to add to the docs for this function, I can go ahead and close this

I think the more common issue with the correlation implementation actually calculating the correlation function for identical series is rounding error.

s = pd.Series([1] * 100 + [1.1])
s.corr(s)  # 0.9999999999999998

I don't see anything about that in the docs and if this constant series issue was considered as less common would be happy to close this issue without a doc fix.

I'll remove the bug label, add a doc label and can leave open for now (with the closing candidate label) to see what others think.

[mroeschke]

I think it would be worth adding an example to the docs of a constant valued series returning nan

[fbourgey]

take

[fbourgey]

In the function scipy.stats.pearsonr function, a ConstantInputWarning is raised if an input is a constant array and np.nan is returned too.