BUG: indexing with `at` and Multi-index gives unexpected error

[lschwetlick]

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Reproducible Example

import pandas as pd

qwe = pd.DataFrame({"b":[3,4,5], "n":[5,4,3], "a":[3,4,5], "c":[5,4,3]})
qwe.columns = pd.MultiIndex.from_tuples([("A", "b"),("A", "n"),("B", "a"),("B", "c")])
qwe["q"] = "asd"
# demo of getter error
print(f" 'loc' getter works fine for qwe.at[0, ('A', 'n')] {qwe.loc[0, ('A', 'n')]}")
print(f" 'at' getter works fine for qwe.at[0, ('A', 'n')] {qwe.at[0, ('A', 'n')]}")
print(f" 'loc' getter works fine for qwe.loc[0, 'q'] {qwe.loc[0, 'q']}")
print(f" 'at' getter doesnt work for qwe.at[0, 'q'] {qwe.at[0, 'q']}")
#demo of setter error
qwe.at[0, ("A", "n")] = 6 # Works fine!
qwe.at[0, "q"] = 6 # Works fine!
qwe.at[0, "q"] = [9,8,7] # Error

Issue Description

Given a dataframe with a multiindex, I can index individual cells using at. I would expect the indexing to work analogously to loc. I have encountered some related errors:

1. getting an individual cell with at doesn't work when the second level of the multi-index is empty. This is okay to do in loc. i.e. qwe.at[0, 'q'] for getting does not work is the second level of q is empty, but for qwe.loc[0, 'q'] it works.
2. The same kind of indexing using at for setting does not produce an error when setting a scalar, i.e. qwe.at[0, 'q']=5 is ok
3. The same kind of indexing using at for setting does produce an error when setting a list, i.e. qwe.at[0, 'q']=[1,2,3] is not ok

Expected Behavior

I would expect at to work analogously to loc for indexing and for the getters and setters to either both work or both not work. I would also expect to be able to insert lists into a cell, even when the dataframe has a multiindex.

Installed Versions

INSTALLED VERSIONS

commit : 87cfe4e38bafe7300a6003a1d18bd80f3f77c763 python : 3.10.3.final.0 python-bits : 64 OS : Darwin OS-release : 21.4.0 Version : Darwin Kernel Version 21.4.0: Fri Mar 18 00:45:05 PDT 2022; root:xnu-8020.101.4~15/RELEASE_X86_64 machine : x86_64 processor : i386 byteorder : little LC_ALL : en_US.UTF-8 LANG : None LOCALE : en_US.UTF-8

pandas : 1.5.0 numpy : 1.22.4 pytz : 2022.1 dateutil : 2.8.2 setuptools : 58.1.0 pip : 22.1.2 Cython : None pytest : 7.1.2 hypothesis : None sphinx : None blosc : None feather : None xlsxwriter : None lxml.etree : None html5lib : None pymysql : None psycopg2 : None jinja2 : None IPython : 8.4.0 pandas_datareader: None bs4 : None bottleneck : None brotli : None fastparquet : None fsspec : None gcsfs : None matplotlib : 3.5.2 numba : 0.55.2 numexpr : None odfpy : None openpyxl : None pandas_gbq : None pyarrow : None pyreadstat : None pyxlsb : None s3fs : None scipy : 1.8.1 snappy : None sqlalchemy : None tables : None tabulate : None xarray : 2022.3.0 xlrd : None xlwt : None zstandard : None tzdata : None

Clear Cell Output Convert to Markdown Cell Delete Cell Add Cell Above Add Cell Below Visibility Input Output Extended Output Parameterized Cell 1 ​

Clear Cell Output Convert to Markdown Cell Delete Cell Add Cell Above Add Cell Below Visibility Input Output Extended Output Parameterized Cell 1 ​ ​

[phofl]

Hi, thanks for your report. Can you please produce the initial df without concat? Hard to see what's going on here

[lschwetlick]

@phofl I did it with pd.MultiIndex.from_tuples. Is that better? I also fixed some details in the description.

[lschwetlick]

Doing it, I also noticed the following, possibly related, difference between implicitly and explicitly setting the multi index. In the implicit version the name of the unused index is an empty string. When setting it explicitely it is NaN.

qwe = pd.DataFrame({"b":[3,4,5], "n":[5,4,3], "a":[3,4,5], "c":[5,4,3]})
qwe.columns = pd.MultiIndex.from_tuples([("A", "b"),("A", "n"),("B", "a"),("B", "c")])
qwe["q"] = "asd"
qwe.columns

->

MultiIndex([('A', 'b'),
            ('A', 'n'),
            ('B', 'a'),
            ('B', 'c'),
            ('q',  '')],
           )

and

qwe = pd.DataFrame({"b":[3,4,5], "n":[5,4,3], "a":[3,4,5], "c":[5,4,3], "q":"asd"})
qwe.columns = pd.MultiIndex.from_tuples([("A", "b"),("A", "n"),("B", "a"),("B", "c"), ("q")])
qwe["q"] = "asd"
qwe.columns

->

MultiIndex([('A', 'b'),
            ('A', 'n'),
            ('B', 'a'),
            ('B', 'c'),
            ('q', nan)],
           )