Interpolation - Support extrapolation method "clip"

[Illviljan]

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

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

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

Versions

Output of `xr.show_versions()`

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

[dcherian]

Scipy will do this for you if you ask it to:

da.interp(x=7000, y=375, method="linear", kwargs=dict(fill_value=None))

See #3956 .

[Illviljan]

Nice find! The documentation doesn't explain that at all currently.

But that solution doesn't work for 1d DataArrays. You have to use this kwargs instead:

kwargs = dict(fill_value=(np.min(da.data), np.max(da.data)))

So it still isn't as convenient as I would like it to be. The wrapper function can now be simplified to this however:

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':
        if len(da.coords) > 1:
            kwargs = dict(fill_value=None)
        else:
            kwargs = dict(fill_value=(np.min(da.data), np.max(da.data)))
    return da.interp(coords, kwargs=kwargs)


# Create coordinates:
x = np.linspace(1000, 6000, 4)
y = np.linspace(100, 1200, 3)
z = np.linspace(1, 2, 2)

# Create 1D DataArray:
da1 = xr.DataArray(data=2*x, coords=[('x', x)])

# Create 2D DataArray:
X = np.meshgrid(*[x, y], indexing='ij')
data = X[0] * X[1]
da2 = xr.DataArray(data=data, coords=[('x', x), ('y', y)])

# Create 3D DataArray:
X = np.meshgrid(*[x, y, z], indexing='ij')
data = X[0] * X[1] * X[2]
da3 = xr.DataArray(data=data, coords=[('x', x), ('y', y), ('z', z)])

# Attempt to extrapolate:
print(interp(da1, {'x': 7000}))
print(interp(da2, {'x': 7000, 'y': 375}))
print(interp(da3, {'x': 7000, 'y': 375, 'z': 1}))

[dcherian]

As noted in #3956 fill_value="extrapolate" is what we need for 1D.

xarray could use the same interpolation function for both 1d and nd.

Not sure if there's a big performance gain. @jhamman implemented these interpolators originally AFAIK. Perhaps he remembers why we use both.

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