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
930918574,MDExOlB1bGxSZXF1ZXN0Njc4NTA3NDMw,5540,Cache some properties,14371165,open,0,,,4,2021-06-27T12:22:16Z,2022-07-10T14:34:34Z,,MEMBER,,1,pydata/xarray/pulls/5540,"Cache some small properties that are rather slow to calculate but doesn't change that often.

Questions that needs to be resolved:

- [ ] Can these properties change during the lifetime of the class? If so the cache needs to be reset when that happens.


<!-- Feel free to remove check-list items aren't relevant to your change -->

- [ ] Related to #3514
- [ ] Tests added
- [ ] Passes `pre-commit run --all-files`
- [ ] User visible changes (including notable bug fixes) are documented in `whats-new.rst`
- [ ] New functions/methods are listed in `api.rst`


Notes
* Mixin classes makes it difficult to cache properties. For example `ndim` in `NdimSizeLenMixin` cannot be easily be replaced with `cache_readonly`.","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/5540/reactions"", ""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,,13221727,pull
597785475,MDU6SXNzdWU1OTc3ODU0NzU=,3962,"Interpolation - Support extrapolation method ""clip""",14371165,open,0,,,4,2020-04-10T09:07:13Z,2022-05-02T13:42:24Z,,MEMBER,,,,"Hello, 

I would like an option in `da.interp() `that instead of returning NaNs during extrapolation returns the data corresponding to the end of the breakpoint data set range. 

One way to do this is to limit the new coordinates to the array coordinates minimum and maximum value, I did a simple example with this solution down below. 
I think this is a rather safe way as we are just modifying the inputs to all the various interpolation classes that xarray is using at the moment. 
But it does look a little weird when printing the extrapolated value, the coordinates shows the limited value instead of the requested coordinates. Maybe this can be handled elegantly somewhere in the source code?


MATLAB uses this quite frequently in their interpolation functions:
* https://mathworks.com/help/simulink/ug/methods-for-estimating-missing-points.html
* https://mathworks.com/help/simulink/slref/2dlookuptable.html

#### MCVE Code Sample
<!-- In order for the maintainers to efficiently understand and prioritize issues, we ask you post a ""Minimal, Complete and Verifiable Example"" (MCVE): http://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports -->

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


def interp(da, coords, extrapolation='clip'):
    """"""
    Linear interpolation that clips the inputs to the coords min and max value.

    Parameters
    ----------
    da : DataArray
        DataArray to interpolate.
    coords : dict
        Coordinates for the interpolated value.
    """"""
    if extrapolation == 'clip':
        for k, v in da.coords.items():
            coords[k] = np.maximum(coords[k], np.min(v.values))
            coords[k] = np.minimum(coords[k], np.max(v.values))

    return da.interp(coords)


# Create coordinates:
x = np.linspace(1000, 6000, 4)
y = np.linspace(100, 1200, 3)

# Create data:
X = np.meshgrid(*[x, y], indexing='ij')
data = X[0] * X[1]

# Create DataArray:
da = xr.DataArray(data=data, coords=[('x', x), ('y', y)], name='data')

# Attempt to extrapolate:
datai = interp(da, {'x': 7000, 'y': 375})
```

#### Expected Output
````python
print(datai)
<xarray.DataArray 'data' ()>
array(2250000.)
Coordinates:
    x        float64 6e+03
    y        float64 375.0
````

#### Versions

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

INSTALLED VERSIONS
------------------
commit: None
python: 3.7.7 (default, Mar 23 2020, 23:19:08) [MSC v.1916 64 bit (AMD64)]
python-bits: 64
OS: Windows
OS-release: 10
machine: AMD64
processor: Intel64 Family 6 Model 58 Stepping 9, GenuineIntel
byteorder: little
LC_ALL: None
LANG: en
LOCALE: None.None
libhdf5: 1.10.4
libnetcdf: None

xarray: 0.15.0
pandas: 1.0.3
numpy: 1.18.1
scipy: 1.4.1
netCDF4: None
pydap: None
h5netcdf: None
h5py: 2.10.0
Nio: None
zarr: None
cftime: None
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: 1.3.2
dask: 2.13.0
distributed: 2.13.0
matplotlib: 3.1.3
cartopy: None
seaborn: 0.10.0
numbagg: None
setuptools: 46.1.3.post20200330
pip: 20.0.2
conda: 4.8.3
pytest: 5.4.1
IPython: 7.13.0
sphinx: 2.4.4


</details>
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