BUG: Concat 2 dataframes with different `PeriodIndex` raises an exception when using `keys` parameter

[corralien]

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

q_period = pd.period_range('2022-1-1', '2022-12-31', freq='Q')
y_period = pd.period_range('2019-1-1', '2023-1-1', freq='Y')

q_df = pd.DataFrame([range(len(q_period))], columns=q_period)
y_df = pd.DataFrame([range(len(y_period))], columns=y_period)

df1 = pd.concat([q_df, y_df], axis=1)
df2 = pd.concat([q_df, y_df], keys=['Quarterly', 'Yearly'], axis=1)

Issue Description

When using keys parameter on pd.concat, this code raises IncompatibleFrequency exception but it's not the case if you don't specify keys because both period indexes are converted to a simple Index of Period instances.

---------------------------------------------------------------------------
IncompatibleFrequency                     Traceback (most recent call last)
<ipython-input-91-9d5cb81992f8> in <cell line: 8>()
      6 
      7 df1 = pd.concat([q_df, y_df], axis=1)
----> 8 df2 = pd.concat([q_df, y_df], keys=['Quarterly', 'Yearly'], axis=1)

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/util/_decorators.py in wrapper(*args, **kwargs)
    329                     stacklevel=find_stack_level(),
    330                 )
--> 331             return func(*args, **kwargs)
    332 
    333         # error: "Callable[[VarArg(Any), KwArg(Any)], Any]" has no

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/reshape/concat.py in concat(objs, axis, join, ignore_index, keys, levels, names, verify_integrity, sort, copy)
    366     1   3   4
    367     """
--> 368     op = _Concatenator(
    369         objs,
    370         axis=axis,

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/reshape/concat.py in __init__(self, objs, axis, join, keys, levels, names, ignore_index, verify_integrity, copy, sort)
    561         self.copy = copy
    562 
--> 563         self.new_axes = self._get_new_axes()
    564 
    565     def get_result(self):

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/reshape/concat.py in _get_new_axes(self)
    631     def _get_new_axes(self) -> list[Index]:
    632         ndim = self._get_result_dim()
--> 633         return [
    634             self._get_concat_axis if i == self.bm_axis else self._get_comb_axis(i)
    635             for i in range(ndim)

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/reshape/concat.py in <listcomp>(.0)
    632         ndim = self._get_result_dim()
    633         return [
--> 634             self._get_concat_axis if i == self.bm_axis else self._get_comb_axis(i)
    635             for i in range(ndim)
    636         ]

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/_libs/properties.pyx in pandas._libs.properties.CachedProperty.__get__()

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/reshape/concat.py in _get_concat_axis(self)
    691             concat_axis = _concat_indexes(indexes)
    692         else:
--> 693             concat_axis = _make_concat_multiindex(
    694                 indexes, self.keys, self.levels, self.names
    695             )

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/reshape/concat.py in _make_concat_multiindex(indexes, keys, levels, names)
    762             codes_list.extend(concat_index.codes)
    763         else:
--> 764             codes, categories = factorize_from_iterable(concat_index)
    765             levels.append(categories)
    766             codes_list.append(codes)

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/arrays/categorical.py in factorize_from_iterable(values)
   2978         # but only the resulting categories, the order of which is independent
   2979         # from ordered. Set ordered to False as default. See GH #15457
-> 2980         cat = Categorical(values, ordered=False)
   2981         categories = cat.categories
   2982         codes = cat.codes

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/arrays/categorical.py in __init__(self, values, categories, ordered, dtype, fastpath, copy)
    439         if dtype.categories is None:
    440             try:
--> 441                 codes, categories = factorize(values, sort=True)
    442             except TypeError as err:
    443                 codes, categories = factorize(values, sort=False)

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/algorithms.py in factorize(values, sort, na_sentinel, use_na_sentinel, size_hint)
    830             # TODO: Can remove when na_sentinel=na_sentinel as in TODO above
    831             na_sentinel = -1
--> 832         uniques, codes = safe_sort(
    833             uniques, codes, na_sentinel=na_sentinel, assume_unique=True, verify=False
    834         )

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/core/algorithms.py in safe_sort(values, codes, na_sentinel, assume_unique, verify)
   1868     else:
   1869         try:
-> 1870             sorter = values.argsort()
   1871             if is_mi:
   1872                 # Operate on original object instead of casted array (MultiIndex)

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/_libs/tslibs/period.pyx in pandas._libs.tslibs.period._Period.__richcmp__()

~/devel/stackoverflow/venv/lib/python3.9/site-packages/pandas/_libs/tslibs/period.pyx in pandas._libs.tslibs.period.PeriodMixin._require_matching_freq()

IncompatibleFrequency: Input has different freq=Q-DEC from Period(freq=A-DEC)

Expected Behavior

I don't except anything just to understand the behavior. I answered to this SO question. In my original answer, I use pd.concat with keys to create a MultiIndex. As it doesn't work as expected, I downcast the Period instances to string.

Maybe instead of raising an exception, convert as Index (like if I don't use keys parameter) and raises a UserWarning or RuntimeWarning about the incompatibility of PeriodIndex?

(You are doing a great job with Pandas, thank you so much!)

Installed Versions

INSTALLED VERSIONS

commit : 2e218d1
python : 3.9.16.final.0
python-bits : 64
OS : Linux
OS-release : 6.1.7-arch1-1
Version : #1 SMP PREEMPT_DYNAMIC Wed, 18 Jan 2023 19:54:38 +0000
machine : x86_64
processor :
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.5.3
numpy : 1.21.5
pytz : 2022.1
dateutil : 2.8.2
setuptools : 65.6.3
pip : 22.3.1
Cython : 0.29.30
pytest : 7.2.0
hypothesis : None
sphinx : 5.0.1
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.7.1
html5lib : 1.1
pymysql : 1.0.2
psycopg2 : 2.9.3
jinja2 : 3.1.2
IPython : 7.34.0
pandas_datareader: 0.10.0
bs4 : 4.10.0
bottleneck : None
brotli : 1.0.9
fastparquet : None
fsspec : 2022.01.0
gcsfs : None
matplotlib : 3.5.2
numba : 0.55.1
numexpr : 2.8.3
odfpy : None
openpyxl : 3.1.0
pandas_gbq : None
pyarrow : 6.0.1
pyreadstat : None
pyxlsb : 1.0.8
s3fs : None
scipy : 1.7.1
snappy : None
sqlalchemy : 1.4.25
tables : 3.8.0
tabulate : 0.8.9
xarray : 0.20.1
xlrd : 2.0.1
xlwt : None
zstandard : 0.19.0
tzdata : None

[topper-123]

The issue is that it is trying to do a factorize with sort=True:

>>> p1 = pd.Period('2022Q1', 'Q-DEC')
>>> p2 = pd.Period('2019', 'A-DEC')
>>> arr = np.array([p1, p2], dtype=object)
>>> pd.factorize(arr, sort=True)
IncompatibleFrequency: Input has different freq=Q-DEC from Period(freq=A-DEC)
>>> pd.factorize(arr, sort=False)
(array([0, 1]),
 array([Period('2022Q1', 'Q-DEC'), Period('2019', 'A-DEC')], dtype=object))

My guess is that the call to factorize shouldn't sort here, but investigations welcome.