issues: 134359597

[Edited for more clarity]

First of all, I find the MultiIndex very useful and I'm looking forward to see the TODOs in #719 implemented in the next releases, especially the three first ones in the list!

Apart from these issues, I think that some other aspects may be improved, notably regarding data selection. Or maybe I've not correctly understood how to deal with multi-index and data selection...

To illustrate this, I use some fake spectral data with two discontinuous bands of different length / resolution:

``` In [1]: import pandas as pd

In [2]: import xarray as xr

In [3]: band = np.array(['foo', 'foo', 'bar', 'bar', 'bar'])

In [4]: wavenumber = np.array([4050.2, 4050.3, 4100.1, 4100.3, 4100.5])

In [5]: spectrum = np.array([1.7e-4, 1.4e-4, 1.2e-4, 1.0e-4, 8.5e-5])

In [6]: s = pd.Series(spectrum, index=[band, wavenumber])

In [7]: s.index.names = ('band', 'wavenumber')

In [8]: da = xr.DataArray(s, dims='band_wavenumber')

In [9]: da Out[9]: <xarray.DataArray (band_wavenumber: 5)> array([ 1.70000000e-04, 1.40000000e-04, 1.20000000e-04, 1.00000000e-04, 8.50000000e-05]) Coordinates: * band_wavenumber (band_wavenumber) object ('foo', 4050.2) ... ```

I extract the band 'bar' using sel:

``` In [10]: da_bar = da.sel(band_wavenumber='bar')

In [11]: da_bar Out[11]: <xarray.DataArray (band_wavenumber: 3)> array([ 1.20000000e-04, 1.00000000e-04, 8.50000000e-05]) Coordinates: * band_wavenumber (band_wavenumber) object ('bar', 4100.1) ... ```

It selects the data the way I want, although using the dimension name is confusing in this case. It would be nice if we can also use the MultiIndex names as arguments of the sel method, even though I don't know if it is easy to implement.

Futhermore, da_bar still has the 'band_wavenumber' dimension and the 'band' index-level, but it is not very useful anymore. Ideally, I'd rather like to obtain a DataArray object with a 'wavenumber' dimension / coordinate and the 'bar' band name dropped from the multi-index, i.e., something would require automatic index-level removal and/or automatic unstack when selecting data.

Extracting the band 'bar' from the pandas Series object gives something closer to what I need (see below), but using pandas is not an option as my spectral data involves other dimensions (e.g., time, scans, iterations...) not shown here for simplicity.

``` In [12]: s_bar = s.loc['bar']

In [13]: s_bar Out[13]: wavenumber 4100.1 0.000120 4100.3 0.000100 4100.5 0.000085 dtype: float64 ```

The problem is also that the unstacked DataArray object resulting from the selection has the same dimensions and size than the original, unstacked DataArray object. The only difference is that unselected values are replaced by nan.

``` In [13]: da.unstack('band_wavenumber') Out[13]: <xarray.DataArray (band: 2, wavenumber: 5)> array([[ nan, nan, 1.20000000e-04, 1.00000000e-04, 8.50000000e-05], [ 1.70000000e-04, 1.40000000e-04, nan, nan, nan]]) Coordinates: * band (band) object 'bar' 'foo' * wavenumber (wavenumber) float64 4.05e+03 4.05e+03 4.1e+03 4.1e+03 4.1e+03

In [14]: da_bar.unstack('band_wavenumber') Out[14]: <xarray.DataArray (band: 2, wavenumber: 5)> array([[ nan, nan, 1.20000000e-04, 1.00000000e-04, 8.50000000e-05], [ nan, nan, nan, nan, nan]]) Coordinates: * band (band) object 'bar' 'foo' * wavenumber (wavenumber) float64 4.05e+03 4.05e+03 4.1e+03 4.1e+03 4.1e+03 ```