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
1006413760,I_kwDOAMm_X847_KfA,5815,Inconsistent dropping of `DatetimeIndex.freq` attribute from `DataArray`s index.,4806678,closed,0,,,7,2021-09-24T12:28:27Z,2023-08-23T13:41:17Z,2023-08-23T13:41:17Z,CONTRIBUTOR,,,,"<!-- Please include a self-contained copy-pastable example that generates the issue if possible.

Please be concise with code posted. See guidelines below on how to provide a good bug report:

- Craft Minimal Bug Reports: http://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports
- Minimal Complete Verifiable Examples: https://stackoverflow.com/help/mcve

Bug reports that follow these guidelines are easier to diagnose, and so are often handled much more quickly.
-->

**What happened**:

Indexing on `DataArray`s sometimes produce inconsistent behaviors on `DataArray`s indexed with a `DatetimeIndex`.
There are cases (see code below) where copied versions of the array obtained with `DataArray.copy()` loose the index's `freq` attribute when calling `isel()`, whereas copied versions obtained using `DataArray.sortby()` do not.

**What you expected to happen**:

I would expect the `freq` not to be dropped from the axis when indexing the `DataArray`. Or at least, if it is dropped, it should _always_ be dropped, and not depend on how the `DataArray` has been obtained (i.e., it should not depend on whether it's a `copy()` of another array).

**Minimal Complete Verifiable Example**:

```python
import xarray as xr
import pandas as pd
import numpy as np
from pandas.tseries.frequencies import to_offset

freq = to_offset('MS')
time_index = pd.DatetimeIndex([pd.Timestamp('20130101') + i * freq for i in range(10)])

xa_orig = xr.DataArray(np.random.randn(10), 
                       dims=('time'), 
                       coords={'time': time_index})

xa_copy = xa_orig.copy()

xa_sorted = xa_orig.sortby('time')

# Set freq on all DataArrays:
xa_orig.get_index('time').freq = freq
xa_copy.get_index('time').freq = freq
xa_sorted.get_index('time').freq = freq

# Print to confirm the freq is set correctly:
print(xa_orig.get_index('time').freq)
print(xa_copy.get_index('time').freq)
print(xa_sorted.get_index('time').freq)
```

Output (OK - as expected)
```
> <MonthBegin>
> <MonthBegin>
> <MonthBegin>
```

Now, try some indexing using `isel()` on slices:
```python
print(xa_orig.isel({'time': slice(0, 5, None)}).get_index('time').freq)
print(xa_copy.isel({'time': slice(0, 5, None)}).get_index('time').freq)  # freq is dropped!
print(xa_sorted.isel({'time': slice(0, 5, None)}).get_index('time').freq)
```

Output (Not as expected: `freq` is dropped inconsistently, only on the _copied_ DataArray)
```
> <MonthBegin>
> None
> <MonthBegin>
```

Now, try the same using `isel()` on lists:
```python
print(xa_orig.isel({'time': [0, 1, 2, 3, 4]}).get_index('time').freq)
print(xa_copy.isel({'time': [0, 1, 2, 3, 4]}).get_index('time').freq)
print(xa_sorted.isel({'time': [0, 1, 2, 3, 4]}).get_index('time').freq)
```

Output (Not as expected: `freq` always dropped)
```
> None
> None
> None
```

**Anything else we need to know?**:

**Environment**:

<details><summary>Output of <tt>xr.show_versions()</tt></summary>

INSTALLED VERSIONS
------------------
commit: None
python: 3.8.5 (default, Sep  4 2020, 02:22:02) 
[Clang 10.0.0 ]
python-bits: 64
OS: Darwin
OS-release: 20.5.0
machine: x86_64
processor: i386
byteorder: little
LC_ALL: None
LANG: None
LOCALE: (None, 'UTF-8')
libhdf5: None
libnetcdf: None

xarray: 0.19.0
pandas: 1.2.3
numpy: 1.19.5
scipy: 1.6.2
netCDF4: None
pydap: None
h5netcdf: None
h5py: None
Nio: None
zarr: None
cftime: None
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: None
dask: None
distributed: None
matplotlib: 3.4.1
cartopy: None
seaborn: None
numbagg: None
pint: None
setuptools: 49.6.0.post20200814
pip: 21.1.3
conda: None
pytest: None
IPython: 7.22.0
sphinx: 3.2.1


</details>
","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/5815/reactions"", ""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,completed,13221727,issue
1128304139,I_kwDOAMm_X85DQI4L,6256,Indexing a RangeIndexed' DataArray with a RangeIndex returns a deprecated Int64Index,4806678,open,0,,,2,2022-02-09T09:55:06Z,2022-02-21T21:28:57Z,,CONTRIBUTOR,,,,"### What happened?

First, apology if this is not actually a bug - I'm not too sure of what the intended behaviour should be. But I find this counter-intuitive.

When indexing a `DataArray` that is indexed using a `RangeIndex`, the resulting index is an `Int64Index`:
```python
my_da.get_index('time')
>>> RangeIndex(start=0, stop=100, step=1, name='time')

a = my_da.sel({'time': pd.RangeIndex(0,2)})
a.get_index('time')
>>> Int64Index([0, 1], dtype='int64', name='time')
```

Setting the index to the desired `RangeIndex` using `assign_coords()` then works. But I find it a bit problematic that `sel()` returns an `Int64Index` even when used with a `RangeIndex`. Also because `Int64Index` has been recently deprecated in Pandas 1.4.

### What did you expect to happen?

I would have expected the resulting `DataArray` to be indexed with the same `RangeIndex` used in `sel()`.

### Minimal Complete Verifiable Example

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

my_da = xr.DataArray(np.random.rand(100,),
                     dims=('time'),
                     coords={'time': pd.RangeIndex(0, 100)})

print(my_da.get_index('time'))
a = my_da.sel({'time': pd.RangeIndex(0,2)})
print(a.get_index('time'))
```


### Relevant log output

```python
RangeIndex(start=0, stop=100, step=1, name='time')
Int64Index([0, 1], dtype='int64', name='time')
```


### Anything else we need to know?

_No response_

### Environment

INSTALLED VERSIONS
------------------
commit: None
python: 3.8.5 (default, Sep  4 2020, 02:22:02) 
[Clang 10.0.0 ]
python-bits: 64
OS: Darwin
OS-release: 20.6.0
machine: x86_64
processor: i386
byteorder: little
LC_ALL: None
LANG: None
LOCALE: (None, 'UTF-8')
libhdf5: None
libnetcdf: None

xarray: 0.20.2
pandas: 1.4.0
numpy: 1.22.1
scipy: 1.7.3
netCDF4: None
pydap: None
h5netcdf: None
h5py: None
Nio: None
zarr: None
cftime: None
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: None
dask: None
distributed: None
matplotlib: 3.5.1
cartopy: None
seaborn: None
numbagg: None
fsspec: 2021.11.1
cupy: None
pint: None
sparse: None
setuptools: 59.5.0
pip: 21.3.1
conda: None
pytest: 6.2.5
IPython: 8.0.1
sphinx: 4.3.2","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/6256/reactions"", ""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,,13221727,issue
919798222,MDU6SXNzdWU5MTk3OTgyMjI=,5466,`DataArray.sortby()` discards `freq` component of `DatetimeIndex`,4806678,open,0,,,0,2021-06-13T13:22:04Z,2021-06-13T13:22:20Z,,CONTRIBUTOR,,,,"**What happened**:

Calling `sortby()` on a `DataArray` indexed with a `pd.DatetimeIndex` discards the underlying `freq` component of the `pd.DatetimeIndex`.

**What you expected to happen**:

The `freq` component should probably be kept.

**Minimal Complete Verifiable Example**:

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

ar = xr.DataArray(np.random.randn(4, 2), 
                  dims=('time', 'component'), 
                  coords={'time': pd.date_range('20130101', '20130104'),
                          'component': ['a', 'b']})

print(ar.get_index('time'))

ar_sorted = ar.sortby('time')

print(ar_sorted.get_index('time'))
```

Output for the above snippet (note how the `freq` becomes `None`):
```
DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04'], dtype='datetime64[ns]', name='time', freq='D')
DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04'], dtype='datetime64[ns]', name='time', freq=None)
```

**Anything else we need to know?**:

**Environment**:

<details><summary>Output of <tt>xr.show_versions()</tt></summary>

INSTALLED VERSIONS
------------------
commit: None
python: 3.8.10 (default, May 19 2021, 11:01:55) 
[Clang 10.0.0 ]
python-bits: 64
OS: Darwin
OS-release: 20.3.0
machine: x86_64
processor: i386
byteorder: little
LC_ALL: None
LANG: None
LOCALE: (None, 'UTF-8')
libhdf5: 1.10.6
libnetcdf: 4.7.4

xarray: 0.18.2
pandas: 1.2.3
numpy: 1.19.5
scipy: 1.6.2
netCDF4: 1.5.6
pydap: None
h5netcdf: None
h5py: None
Nio: None
zarr: None
cftime: 1.5.0
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: 1.3.2
dask: 2021.05.1
distributed: 2021.05.1
matplotlib: 3.4.1
cartopy: None
seaborn: None
numbagg: None
pint: None
setuptools: 52.0.0.post20210125
pip: 21.1.1
conda: None
pytest: None
IPython: 7.22.0
sphinx: None


</details>
","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/5466/reactions"", ""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,,13221727,issue