BUG: Unexpected KeyError in transform() with dict-like func argument

[sfo]

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Reproducible Example

import pandas as pd

pd.DataFrame({'foo': [2,4,6], 'bar': [1,2,3]}).transform(
    {
        'foo': lambda x: x+2,
        'bar': lambda x: x*2
    },
    axis="columns"
)

Issue Description

The code raises KeyError: "Column(s) ['bar', 'foo'] do not exist" even though the columns are present, evidently.

Expected Behavior

Transform the columns according to the dict-like argument of the tranform() function and return a new data frame, without raising an error.

Installed Versions

INSTALLED VERSIONS

commit : d9cdd2e
python : 3.11.9.final.0
python-bits : 64
OS : Linux
OS-release : 6.8.7-200.fc39.x86_64
Version : #1 SMP PREEMPT_DYNAMIC Wed Apr 17 19:35:11 UTC 2024
machine : x86_64
processor :
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.2
numpy : 1.24.2
pytz : 2022.7.1
dateutil : 2.8.2
setuptools : 67.1.0
pip : 24.0
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.9.2
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.10.0
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.11.2
bottleneck : None
dataframe-api-compat : None
fastparquet : 2023.2.0
fsspec : 2023.1.0
gcsfs : None
matplotlib : 3.6.3
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.1
pandas_gbq : None
pyarrow : 16.0.0
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.10.0
sqlalchemy : 2.0.24
tables : None
tabulate : None
xarray : 2023.2.0
xlrd : 2.0.1
zstandard : None
tzdata : 2024.1
qtpy : 2.3.0
pyqt5 : None

[Aloqeely]

You can pass axis="index" to apply the function to each column (I'm not quite sure what that means) per the doc at https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.transform.html

But I will admit this is a little confusing, I don't know why the error message says Column(s) [...] do not exist, the error message should be improved.
And I also find the docs to be a little inconsistent when it comes to the axis parameter, some docs say axis="index" will compute row-wise, and some say apply on each column, the only issue related issue I could found is #43128

[rhshadrach]

But I will admit this is a little confusing, I don't know why the error message says Column(s) [...] do not exist, the error message should be improved.

Agreed.

And I also find the docs to be a little inconsistent when it comes to the axis parameter, some docs say axis="index" will compute row-wise, and some say apply on each column, the only issue related issue I could found is #43128

Best to see the context, but I believe row-wise is meant as "down the rows", which is the same as applying to each column.

[luke396]

take