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Showing content from https://github.com/pydata/xarray/issues/688 below:

Keep attrs & Add a 'keep_coords' argument to Dataset.apply · Issue #688 · pydata/xarray · GitHub

Generally this isn't a problem, since the coords are carried over by the resulting DataArrays:

In [11]:

ds = xray.Dataset({
        'a':pd.DataFrame(pd.np.random.rand(10,3)),
        'b':pd.Series(pd.np.random.rand(10))
    })
ds.coords['c'] = pd.Series(pd.np.random.rand(10))
ds
Out[11]:
<xray.Dataset>
Dimensions:  (dim_0: 10, dim_1: 3)
Coordinates:
  * dim_0    (dim_0) int64 0 1 2 3 4 5 6 7 8 9
  * dim_1    (dim_1) int64 0 1 2
    c        (dim_0) float64 0.9318 0.2899 0.3853 0.6235 0.9436 0.7928 ...
Data variables:
    a        (dim_0, dim_1) float64 0.5707 0.9485 0.3541 0.5987 0.406 0.7992 ...
    b        (dim_0) float64 0.4106 0.2316 0.5804 0.6393 0.5715 0.6463 ...
In [12]:

ds.apply(lambda x: x*2)
Out[12]:
<xray.Dataset>
Dimensions:  (dim_0: 10, dim_1: 3)
Coordinates:
    c        (dim_0) float64 0.9318 0.2899 0.3853 0.6235 0.9436 0.7928 ...
  * dim_0    (dim_0) int64 0 1 2 3 4 5 6 7 8 9
  * dim_1    (dim_1) int64 0 1 2
Data variables:
    a        (dim_0, dim_1) float64 1.141 1.897 0.7081 1.197 0.812 1.598 ...
    b        (dim_0) float64 0.8212 0.4631 1.161 1.279 1.143 1.293 0.3507 ...

But if there's an operation that removes the coords from the DataArrays, the coords are not there on the result (notice c below).
Should the Dataset retain them? Either always or with a keep_coords argument, similar to keep_attrs.

In [13]:

ds = xray.Dataset({
        'a':pd.DataFrame(pd.np.random.rand(10,3)),
        'b':pd.Series(pd.np.random.rand(10))
    })
ds.coords['c'] = pd.Series(pd.np.random.rand(10))
ds
Out[13]:
<xray.Dataset>
Dimensions:  (dim_0: 10, dim_1: 3)
Coordinates:
  * dim_0    (dim_0) int64 0 1 2 3 4 5 6 7 8 9
  * dim_1    (dim_1) int64 0 1 2
    c        (dim_0) float64 0.4121 0.2507 0.6326 0.4031 0.6169 0.441 0.1146 ...
Data variables:
    a        (dim_0, dim_1) float64 0.4813 0.2479 0.5158 0.2787 0.06672 ...
    b        (dim_0) float64 0.2638 0.5788 0.6591 0.7174 0.3645 0.5655 ...
In [14]:

ds.apply(lambda x: x.to_pandas()*2)
Out[14]:
<xray.Dataset>
Dimensions:  (dim_0: 10, dim_1: 3)
Coordinates:
  * dim_0    (dim_0) int64 0 1 2 3 4 5 6 7 8 9
  * dim_1    (dim_1) int64 0 1 2
Data variables:
    a        (dim_0, dim_1) float64 0.9627 0.4957 1.032 0.5574 0.1334 0.8289 ...
    b        (dim_0) float64 0.5275 1.158 1.318 1.435 0.7291 1.131 0.1903 ...

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