Extraploation with 'nearest' method in Python

Question

I'm looking to find the Python equivalent of the following Matlab statement:

vq interp1(x,y, xq,'nearest','extrap')

It looks as if interp(xq, x, y) works perfectly for linear interpolation/extrapolation.

I also looked at

F = scipy.interpolate.interp1d(x, y, kind='nearest')

which works perfectly for the nearest method, but will not perform extrapolation.

Is there anything else I've overlooked? Thanks.

Answer 1

For linear interpolation that will extrapolate using nearest interpolation, use numpy.interp. It does this by default.

For example:

yi = np.interp(xi, x, y)

Otherwise, if you just want nearest interpolation everywhere, as you describe, you can do it in the short, but inefficient way: (you can make this a one-liner, if you want)

def nearest_interp(xi, x, y):
    idx = np.abs(x - xi[:,None])
    return y[idx.argmin(axis=1)]

Or in a more efficient way using searchsorted:

def fast_nearest_interp(xi, x, y):
    """Assumes that x is monotonically increasing!!."""
    # Shift x points to centers
    spacing = np.diff(x) / 2
    x = x + np.hstack([spacing, spacing[-1]])
    # Append the last point in y twice for ease of use
    y = np.hstack([y, y[-1]])
    return y[np.searchsorted(x, xi)]

To illustrate the difference between numpy.interp and the nearest interpolation examples above:

import numpy as np
import matplotlib.pyplot as plt

def main():
    x = np.array([0.1, 0.3, 1.9])
    y = np.array([4, -9, 1])
    xi = np.linspace(-1, 3, 200)

    fig, axes = plt.subplots(nrows=2, sharex=True, sharey=True)
    for ax in axes:
        ax.margins(0.05)
        ax.plot(x, y, 'ro')

    axes[0].plot(xi, np.interp(xi, x, y), color='blue')
    axes[1].plot(xi, nearest_interp(xi, x, y), color='green')

    kwargs = dict(x=0.95, y=0.9, ha='right', va='top')
    axes[0].set_title("Numpy's $interp$ function", **kwargs)
    axes[1].set_title('Nearest Interpolation', **kwargs)

    plt.show()

def nearest_interp(xi, x, y):
    idx = np.abs(x - xi[:,None])
    return y[idx.argmin(axis=1)]

main()

Answer 2

In later versions of SciPy (at least v0.19.1+), scipy.interpolate.interp1d has the option fill_value = “extrapolate”.

For example:

import pandas as pd
>>> s = pd.Series([1, 2, 3])
Out[1]: 
0    1
1    2
2    3
dtype: int64

>>> t = pd.concat([s, pd.Series(index=s.index + 0.1)]).sort_index()
Out[2]: 
0.0    1.0
0.1    NaN
1.0    2.0
1.1    NaN
2.0    3.0
2.1    NaN
dtype: float64

>>> t.interpolate(method='nearest')
Out[3]: 
0.0    1.0
0.1    1.0
1.0    2.0
1.1    2.0
2.0    3.0
2.1    NaN
dtype: float64

>>> t.interpolate(method='nearest', fill_value='extrapolate')
Out[4]: 
0.0    1.0
0.1    1.0
1.0    2.0
1.1    2.0
2.0    3.0
2.1    3.0
dtype: float64