issue_comments: 238050009

This is very exciting to see!

A few thoughts on implementation:

Instead of always creating a dictionary of level coordinates, I would add an attribute level_names to Coordinate, which would default to None and be set to a tuple of MultiIndex.names if a Coordinate is created from a MultiIndex. This would make make checking for multi-index levels very cheap, even if we do need to iterate through every coordinate to find them.

It's much cheaper to call .get_level_values() after slicing a MultiIndex than before, e.g.,

``` In [12]: idx = pd.MultiIndex.from_product([np.linspace(0, 1, num=500), np.arange(1000)])

In [13]: %timeit idx.get_level_values(0)[:10] 1000 loops, best of 3: 1.28 ms per loop

In [14]: %timeit idx[:10].get_level_values(0) 10000 loops, best of 3: 101 µs per loop ```

It's even more extreme for larger indexes. If possible, we should use something closer to this approach when formatting coordinates.

However, it is not possible anymore to mix level indexers and non-dict dimension indexers, e.g., da.sel(x='a', level_2=1) doesn't work but da.sel(x={'level_1': 'a'}, level_2=1) does, which is already quite flexible though.

I would actually be happy to disallow both, which might be even easy. It seems like a fine rule to say that you cannot call .sel on both a level and the dimension name at the same time. Actually, if we check uniqueness of level names at Dataset/DataArray creation (which is a good idea!), there is not much need for level indexing with a dictionary at all.