id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
303130664,MDU6SXNzdWUzMDMxMzA2NjQ=,1973,question: dataset variables as coordinates,10928117,closed,0,,,1,2018-03-07T14:57:19Z,2019-01-13T21:00:29Z,2019-01-13T21:00:29Z,NONE,,,,"#### Problem description

Let's consider two datasets, ``ds1`` and ``ds2`` with dummy data.

```python
import xarray as xr
import numpy as np

x = np.linspace(0, 1, 10)
da1 = xr.concat([xr.DataArray(x**2, coords={'x': x, 'a': 0}, dims='x'),
                 xr.DataArray(x**2+1, coords={'x': x+1, 'a': 1}, dims='x')],
                dim='a')

ds1 = da1.to_dataset(name='y')

ds2 = xr.concat([xr.Dataset({'x': ('n', x), 'y': ('n', x**2)}, coords={'n': range(10), 'a': 0}),
                 xr.Dataset({'x': ('n', x+1), 'y': ('n', x**2+1)}, coords={'n': range(10), 'a': 1})],
                dim='a')
```
These two datasets represents in principle the same data, stored in two different ways.

```python
>>> ds1.y
<xarray.DataArray 'y' (a: 2, x: 19)>
array([[ 0.      ,  0.012346,  0.049383,  0.111111,  0.197531,  0.308642,
         0.444444,  0.604938,  0.790123,  1.      ,       nan,       nan,
              nan,       nan,       nan,       nan,       nan,       nan,
              nan],
       [      nan,       nan,       nan,       nan,       nan,       nan,
              nan,       nan,       nan,  1.      ,  1.012346,  1.049383,
         1.111111,  1.197531,  1.308642,  1.444444,  1.604938,  1.790123,  2.      ]])
Coordinates:
  * x        (x) float64 0.0 0.1111 0.2222 0.3333 0.4444 0.5556 0.6667 ...
  * a        (a) int64 0 1
```
```python
>>> ds2.x
<xarray.DataArray 'x' (a: 2, n: 10)>
array([[ 0.      ,  0.111111,  0.222222,  0.333333,  0.444444,  0.555556,
         0.666667,  0.777778,  0.888889,  1.      ],
       [ 1.      ,  1.111111,  1.222222,  1.333333,  1.444444,  1.555556,
         1.666667,  1.777778,  1.888889,  2.      ]])
Coordinates:
  * n        (n) int64 0 1 2 3 4 5 6 7 8 9
  * a        (a) int64 0 1
```
```python
>>> ds2.y
<xarray.DataArray 'y' (a: 2, n: 10)>
array([[ 0.      ,  0.012346,  0.049383,  0.111111,  0.197531,  0.308642,
         0.444444,  0.604938,  0.790123,  1.      ],
       [ 1.      ,  1.012346,  1.049383,  1.111111,  1.197531,  1.308642,
         1.444444,  1.604938,  1.790123,  2.      ]])
Coordinates:
  * n        (n) int64 0 1 2 3 4 5 6 7 8 9
  * a        (a) int64 0 1
```


#### Question
Is there a straightforward way to reshape ``ds2`` to look like ``ds1``? 
In this dummy data it is clear that ``y = y(x)`` and first structure is more obvious to start with.

Second structure however is more natural when ``x`` and ``y`` could be some separately calculated quantities depending on parameter ``a``, that one would like to explore as ``y(x)``.

#### Output of ``xr.show_versions()``

<details>
# Paste the output here xr.show_versions() here
INSTALLED VERSIONS
------------------
commit: None
python: 3.6.4.final.0
python-bits: 64
OS: Linux
OS-release: 4.13.16-100.fc25.x86_64
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_GB.UTF-8
LOCALE: en_GB.UTF-8

xarray: 0.10.1
pandas: 0.22.0
numpy: 1.13.3
scipy: 0.19.1
netCDF4: None
h5netcdf: None
h5py: None
Nio: None
zarr: None
bottleneck: None
cyordereddict: None
dask: None
distributed: None
matplotlib: 2.1.2
cartopy: None
seaborn: None
setuptools: 38.5.1
pip: 9.0.1
conda: None
pytest: 3.4.1
IPython: 6.1.0
sphinx: None
</details>
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