Bug in broadcasting with multi-indexes

[dcherian]

What happened?

import numpy as np
import xarray as xr

ds = xr.Dataset(
    {"foo": (("x", "y", "z"), np.ones((3, 4, 2)))},
    {"x": ["a", "b", "c"], "y": [1, 2, 3, 4]},
)
expected = ds.sum("z")
stacked = ds.stack(space=["x", "y"])

broadcasted, _ = xr.broadcast(stacked, stacked.space)

stacked.sum("z").unstack("space")  # works
broadcasted.sum("z").unstack("space")  # error

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [13], in <module>
     10 broadcasted, _ = xr.broadcast(stacked, stacked.space)
     11 stacked.sum("z").unstack("space")
---> 12 broadcasted.sum("z").unstack("space")

File ~/work/python/xarray/xarray/core/dataset.py:4332, in Dataset.unstack(self, dim, fill_value, sparse)
   4330     non_multi_dims = set(dims) - set(stacked_indexes)
   4331     if non_multi_dims:
-> 4332         raise ValueError(
   4333             "cannot unstack dimensions that do not "
   4334             f"have exactly one multi-index: {tuple(non_multi_dims)}"
   4335         )
   4337 result = self.copy(deep=False)
   4339 # we want to avoid allocating an object-dtype ndarray for a MultiIndex,
   4340 # so we can't just access self.variables[v].data for every variable.
   4341 # We only check the non-index variables.
   4342 # https://github.com/pydata/xarray/issues/5902

ValueError: cannot unstack dimensions that do not have exactly one multi-index: ('space',)

What did you expect to happen?

This should work.

Minimal Complete Verifiable Example

No response

Relevant log output

No response

Anything else we need to know?

No response

Environment

xarray main after the flexible indexes refactor

[benbovy]

Probably because we still need some internal refactoring in xr.broadcast (added in #6293).

broadcasted.xindexes
# Indexes:
# space: <xarray.core.indexes.PandasMultiIndex object at 0x163e5c6d0>
# y: <xarray.core.indexes.PandasMultiIndex object at 0x163e5c510>
# x: <xarray.core.indexes.PandasMultiIndex object at 0x163e5c510>

space and x / y should all have identical PandasMultiIndex objects but they don't.