issue_comments

I am late for the party (but still only have time to write a short comment). I am a big fan of MultiIndex and like @shoyer 's idea.

ds.sel(multi=list_of_pairs) can probably be replaced by ds.sel(x=..., y=...), but how about reindex along MultiIndex? I have encountered its use cases several times. I also think it would be nice to have MultiIndex as a variable.

@shoyer, thank you for detailing.

I am thinking how can we establish the following selecting-concatenating behavior with MultiIndex(-like) coordinate with our new Indexes machinary, xr.concat([da.isel(x=i) for i in range(len(da['x':))], dim='x') Personally, I think it would be nice if we could recover the original Index structue. We may need to track Indexes object even when the corresponding dimension becomes one dimensional? But scalar index sounds strange...

Or, we may give up to restore the original coordinate structure during the above action, but stil keep them as ordinary coodinates.

Thanks for the details. (Sorry for my late responce. It took a long for me to understand what does it look like.)

I am wondering what the advantageous cases which are realized with this Index concept are. As far as my understanding is correct,

1. It will enable more flexible indexing, e.g. more than one Indexes are associated with one dimension and we can select from these coordinate values very flexibly.
2. It will naturally integrate more advanced Indexes such as KDTree

Are they correct?

Probably the most elegant rule would again be to check all indexed variables for exact matches.

That sounds reasonable.

In principle, this data model would allow for two mostly equivalent indexing schemes: MultiIndex[time, space] vs two indexes Index[time] and Index[space].

I like the latter one, as it is easier to understand even for non-pandas users.

What does the actual implementation look like? xr.Dataset.indexes will be an OrderedDict that maps from variable's name to its associated dimension? Actual instance of Index will be one of xr.Dataset.variables?

@shoyer, could you add more details of this idea? I think I do not yet fully understand the practical difference between dim and index.

1. Use cases of the independent Index and dims Would it be general cases where dimension and index are independent? (It is the case only for MultiIndex and KDtree)?

2. MultiIndex implementation In MultiIndex case, will a xarray object store a MultiIndex object and also the level variables as Variable objects (there will be some duplicates)? If indexes[dim] returns multiple Variables, which realizes a MultiIndex-like structure without pd.MultiIndex, indexes would be very different from dim, because a single dimension can have multiple indexes.

I think we currently assume variables[dim] is an Index. Does your proposal means that Dataset will keep an additional attribute indexes, and indexes[dim] gives a pd.Index (or pd.MultiIndex, KDTree)?

It sounds a much cleaner data model.

I'm using MultiIndex a lot, but I noticed that it is just a workaround to index along multiple kinds of coordinate.

Consider the following example, ```python In [1]: import numpy as np ...: import xarray as xr ...: da = xr.DataArray(np.arange(5), dims=['x'], ...: coords={'experiment': ('x', [0, 0, 0, 1, 1]), ...: 'time': ('x', [0.0, 0.1, 0.2, 0.0, 0.15])}) ...:

In [2]: da Out[2]: <xarray.DataArray (x: 5)> array([0, 1, 2, 3, 4]) Coordinates: experiment (x) int64 0 0 0 1 1 time (x) float64 0.0 0.1 0.2 0.0 0.15 Dimensions without coordinates: x

```

I want to do something like this python da.sel(experiment=0).sel(time=0.1) but it cannot. MultiIndexing enables this,

python In [2]: da = da.set_index(exp_time=['experiment', 'time']) ...: da ...: Out[2]: <xarray.DataArray (x: 5)> array([0, 1, 2, 3, 4]) Coordinates: * exp_time (exp_time) MultiIndex - experiment (exp_time) int64 0 0 0 1 1 - time (exp_time) float64 0.0 0.1 0.2 0.0 0.15 Dimensions without coordinates: x

If we could make a selection from a non-index coordinate, MultiIndex is not necessary for this case.

I think there should be other important usecases of MultiIndex. I would be happy if anyone could list them in this issue.