Better ordering of coords in repr

[jsignell]

Update coords order in repr based off @ianhi's suggestions in #11039. This undoes a bunch of the docstring changes that came in on #10778 but the order feels more intuitive to me with this PR. All of the original issues are still improved:

Examples

From #712:

In [1]: from collections import *
   ...: import numpy as np
   ...: import xarray as xr
   ...: 
   ...: d1 = xr.DataArray(np.empty((2, 2)), coords=OrderedDict([("foo", [0, 1]), ("bar", [0, 1])]))
   ...: d2 = xr.DataArray(np.empty((2, 2)), coords=OrderedDict([("bar", [0, 1]), ("foo", [0, 1])]))
   ...: 
   ...: ds = xr.Dataset({"d1": d1, "d2": d2})
   ...: 
   ...: print(ds.d1)
<xarray.DataArray 'd1' (foo: 2, bar: 2)> Size: 32B
array([[8.66714752e-277, 9.89251937e-046],
       [4.12632174e+106, 5.37987067e-002]])
Coordinates:
  * foo      (foo) int64 16B 0 1
  * bar      (bar) int64 16B 0 1

In [2]: print(ds.d2)
<xarray.DataArray 'd2' (bar: 2, foo: 2)> Size: 32B
array([[ 8.66714752e-277, -9.89251937e-046],
       [-4.12632174e+106, -5.37987067e-002]])
Coordinates:
  * bar      (bar) int64 16B 0 1
  * foo      (foo) int64 16B 0 1

From #4515

In [1]: import xarray as xr
   ...: import numpy as np
   ...: 
   ...: ds = xr.Dataset()
   ...: ds.coords["as"] = 10
   ...: ds["var"] = xr.DataArray(np.ones((10,)), dims="x", coords={"x": np.arange(10)})
   ...: ds
Out[1]: 
<xarray.Dataset> Size: 168B
Dimensions:  (x: 10)
Coordinates:
  * x        (x) int64 80B 0 1 2 3 4 5 6 7 8 9
    as       int64 8B 10
Data variables:
    var      (x) float64 80B 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

From #11039

In [1]: import numpy as np
   ...: import xarray as xr
   ...: 
   ...: ds = xr.Dataset(
   ...:     {"data": (("a", "b", "c"), np.random.rand(3, 3, 3))},
   ...:     coords={"a": [0, 1, 2], "b": [0, 1, 2], "c": [3, 2, 1]},
   ...: )
   ...: 
   ...: ds = ds.assign_coords({"a_1":('a', [5,6,7])})
   ...: ds = ds.assign_coords({"b_1":('b', [5,6,7])})
   ...: ds = ds.assign_coords({"c_1":('c', [5,6,7])})
   ...: print(ds)
<xarray.Dataset> Size: 360B
Dimensions:  (a: 3, b: 3, c: 3)
Coordinates:
  * a        (a) int64 24B 0 1 2
    a_1      (a) int64 24B 5 6 7
  * b        (b) int64 24B 0 1 2
    b_1      (b) int64 24B 5 6 7
  * c        (c) int64 24B 3 2 1
    c_1      (c) int64 24B 5 6 7
Data variables:
    data     (a, b, c) float64 216B 0.9063 0.6277 0.8161 ... 0.7899 0.1621 0.247

In [1]: import pandas as pd
   ...: import xarray as xr
   ...: 
   ...: midx = pd.MultiIndex.from_product([["a", "b"], [1, 2]], names=("foo", "bar"))
   ...: ds = xr.Dataset(coords=xr.Coordinates.from_pandas_multiindex(midx, "x"))
   ...: ds.assign_coords(y=[1, 2])
Out[1]: 
<xarray.Dataset> Size: 112B
Dimensions:  (x: 4, y: 2)
Coordinates:
  * x        (x) object 32B MultiIndex
  * foo      (x) object 32B 'a' 'a' 'b' 'b'
  * bar      (x) int64 32B 1 2 1 2
  * y        (y) int64 16B 1 2
Data variables:
    *empty*

• Closes Ordering of Coords in Repr #11039
• Tests updated
• User visible changes (including notable bug fixes) are documented in whats-new.rst

[jsignell]

I switched this to look at dims in reverse order because this feels like the right order:

        >>> import numpy as np
        >>> import xarray as xr
        >>> temperature = np.arange(25).reshape(5, 5)
        >>> pressure = np.arange(50, 75).reshape(5, 5)
        >>> da = xr.DataArray(
        ...     data=temperature,
        ...     dims=["x", "y"],
        ...     coords=dict(
        ...         lon=("x", np.arange(10, 15)),
        ...         lat=("y", np.arange(20, 25)),
        ...         Pressure=(["x", "y"], pressure),
        ...     ),
        ...     name="Temperature",
        ... )
        >>> da
        <xarray.DataArray 'Temperature' (x: 5, y: 5)> Size: 200B
        array([[ 0,  1,  2,  3,  4],
               [ 5,  6,  7,  8,  9],
               [10, 11, 12, 13, 14],
               [15, 16, 17, 18, 19],
               [20, 21, 22, 23, 24]])
        Coordinates:
            lon       (x) int64 40B 10 11 12 13 14
            lat       (y) int64 40B 20 21 22 23 24
            Pressure  (x, y) int64 200B 50 51 52 53 54 55 56 57 ... 68 69 70 71 72 73 74
        Dimensions without coordinates: x, y

[ianhi]

nice! thanks for this. I left one comment about the comments but otherwise seems good by me

[jsignell]

Just checked GenericMappingTools/pygmt#4143 since that was linked as fallout from the original coord ordering PR. It looks like they had a simple case (all dimension coordinates) so the repr should be the same with the PR in as it was after #10778. No change needed on that library