Arithmetic doesn't broadcast when MultiIndex has the same data, different names

[gedkins]

Code Sample

import pandas as pd

index_st = pd.MultiIndex.from_tuples([(1,1),(1,2),(2,1),(2,2)], names=['second','third'])
index_ft1 = pd.MultiIndex.from_tuples([(1,1),(1,2),(2,1),(2,2)], names=['first','third'])
index_ft2 = pd.MultiIndex.from_tuples([(1,1),(2,1),(1,2),(2,2)], names=['first','third'])

st = pd.DataFrame([1,2,3,4], index=index_st, columns=['val'])
ft1 = pd.DataFrame([10,20,30,40], index=index_ft1, columns=['val'])
ft2 = pd.DataFrame([10,30,20,40], index=index_ft2, columns=['val'])

print(st.add(ft1))
print(st.add(ft2))

Problem description

The calculation of ft1 doesn't broadcast as expected. Instead, it treats the differently-named indexed columns as identical and performs a component-wise addition.

The calculation of ft2 is as expected.

ft1 and ft2 having different index columns is definitely not expected.

Output That I See

              val
second third
1      1       11
       2       22
2      1       33
       2       44
                    val
third second first
1     1      1       11
             2       31
      2      1       13
             2       33
2     1      1       22
             2       42
      2      1       24
             2       44

Expected Output

The expected output of the two calculations should be the same, possibly with the rows returned in a different order.

                    val
third second first
1     1      1       11
             2       31
      2      1       13
             2       33
2     1      1       22
             2       42
      2      1       24
             2       44

                    val
third second first
1     1      1       11
             2       31
      2      1       13
             2       33
2     1      1       22
             2       42
      2      1       24
             2       44

Where the problem lies

The problem appears to be in MultiIndex.equals

This is called by NDFrame. _indexed_same, which is called by _align_method_FRAME

The problem is that MultiIndex.equals doesn't check the names, and so reports indices as equal when they're not. This in turn means the non-broadcasting case is taken, when it should broadcast.

Output of pd.show_versions()

INSTALLED VERSIONS

commit : ae79bb2
python : 3.8.0.final.0
python-bits : 64
OS : Linux
OS-release : 4.19.76-linuxkit
Version : #1 SMP Thu Oct 17 19:31:58 UTC 2019
machine : x86_64
processor :
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.1.0.dev0+725.gae79bb23c
numpy : 1.18.1
pytz : 2019.3
dateutil : 2.8.1
pip : 19.3.1
setuptools : 41.6.0
Cython : 0.29.15
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : None
fastparquet : None
gcsfs : None
matplotlib : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pytables : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
numba : None

See also (I haven't checked if these are related, but they "sound similar")

#20565
#5645
#19606

[emilyjia]

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