BUG: MultiIndex level not sorted (as desired) after making it a CategoricalIndex

[d-s-dc]

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

months = ['January','February','March','April','May','June','July','August','September','October','November','December']
df = pd.DataFrame({'col' : np.arange(1,25,1)},\
                  index = pd.MultiIndex.from_product([months, [1,2]], names = ['idx_1', 'idx_2'])).sort_index()
cidx = pd.CategoricalIndex(df.index.get_level_values(0).unique(), months, ordered = True)
df.index = df.index.set_levels(cidx, level = 0)
df = df.sort_index(level = 0)
display(df)

Issue Description

I wanted to sort the months at MultiIndex level0 according to real life scenario. So I used CategoricalIndex and assigned it to the level0 of the MultiIndex. What I expected after sort_index was that the level0 would be sorted using the order defined in the CategoricalIndex.
But even after making them as CategoricalIndex they are not sorted as expected.

Expected Behavior

What I wanted is that months should be sorted according to the given order in CategoricalIndex

The expected behaviour can be produced by this code as follows

display(df.reindex(months, level = 0))

Installed Versions

INSTALLED VERSIONS

commit : 4bfe3d0
python : 3.9.12.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19044
machine : AMD64
processor : Intel64 Family 6 Model 142 Stepping 9, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United States.1252

pandas : 1.4.2
numpy : 1.21.5
pytz : 2022.1
dateutil : 2.8.2
pip : 21.2.4
setuptools : 61.2.0
Cython : 0.29.30
pytest : 7.1.2
hypothesis : None
sphinx : 4.4.0
blosc : None
feather : None
xlsxwriter : 3.0.3
lxml.etree : 4.8.0
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 2.11.3
IPython : 8.3.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : 1.3.4
brotli :
fastparquet : None
fsspec : 2022.3.0
gcsfs : None
markupsafe : 2.0.1
matplotlib : 3.5.1
numba : 0.55.1
numexpr : 2.8.3
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.7.3
snappy :
sqlalchemy : 1.4.32
tables : 3.6.1
tabulate : 0.8.9
xarray : 0.20.1
xlrd : 2.0.1
xlwt : None
zstandard : None

[simonjayhawkins]

can confirm that works as intended for regular Index and data columns.

There is another issue where a level of a MultiIndex appears to be not sorted. Maybe related. see #21136 (comment)

contributions and PRs to fix welcome.

[GYHHAHA]

take

[GYHHAHA]

When you use set_levels, pandas directly change the old level to a new one without aligning the original data value. Is this the desired result? @d-s-dc

[d-s-dc]

Sorry for the late reply.
Yeah it's fine that the old level is directly changed. My problem is when I call sort_index command. Since I set the level using categorical index, I want the order to be as defined in categorical index.

[d-s-dc]

I've found another thing. Basically, the problem seems when the multi-index is already sorted in lexicographical order. If somehow that ordering is removed then the sorting works according to categorical index.

Currently,

df.sort_index(level=0)

which doesn't work and the idx1 is lexicographically sorted.

But if we remove the lexicographical sorting somehow, like below

df.sort_index(level=1)

and then sort level 0, the sorting works according to categorical indexing.

df.sort_index(level=1).sort_index(level=0)

All thanks to this answer on stackoverflow.

[NA-Dev]

Just wasted a lot of time dealing with this bug. +1 to users who want this fixed.

[tehunter]

Any progress on this @GYHHAHA? I'm encountering this bug too and it's was very hard to pin down the issue. Fortunately this workaround worked for me as well:

But if we remove the lexicographical sorting somehow, like below

df.sort_index(level=1)

and then sort level 0, the sorting works according to categorical indexing.

df.sort_index(level=1).sort_index(level=0)

All thanks to this answer on stackoverflow.