How to make scipy.interpolate give an extrapolated result beyond the input range?

You can take a look at InterpolatedUnivariateSpline

Here an example using it:

import matplotlib.pyplot as pltimport numpy as npfrom scipy.interpolate import InterpolatedUnivariateSpline# given valuesxi = np.array([0.2, 0.5, 0.7, 0.9])yi = np.array([0.3, -0.1, 0.2, 0.1])# positions to inter/extrapolatex = np.linspace(0, 1, 50)# spline order: 1 linear, 2 quadratic, 3 cubic ... order = 1# do inter/extrapolations = InterpolatedUnivariateSpline(xi, yi, k=order)y = s(x)# example showing the interpolation for linear, quadratic and cubic interpolationplt.figure()plt.plot(xi, yi)for order in range(1, 4):    s = InterpolatedUnivariateSpline(xi, yi, k=order)    y = s(x)    plt.plot(x, y)plt.show()

As of SciPy version 0.17.0, there is a new option for scipy.interpolate.interp1d that allows extrapolation. Simply set fill_value='extrapolate' in the call. Modifying your code in this way gives:

import numpy as npfrom scipy import interpolatex = np.arange(0,10)y = np.exp(-x/3.0)f = interpolate.interp1d(x, y, fill_value='extrapolate')print f(9)print f(11)

and the output is:

0.04978706836790.010394302658

1. Constant extrapolation

You can use interp function from scipy, it extrapolates left and right values as constant beyond the range:

>>> from scipy import interp, arange, exp>>> x = arange(0,10)>>> y = exp(-x/3.0)>>> interp([9,10], x, y)array([ 0.04978707,  0.04978707])

2. Linear (or other custom) extrapolation

You can write a wrapper around an interpolation function which takes care of linear extrapolation. For example:

from scipy.interpolate import interp1dfrom scipy import arange, array, expdef extrap1d(interpolator):    xs = interpolator.x    ys = interpolator.y    def pointwise(x):        if x < xs[0]:            return ys[0]+(x-xs[0])*(ys[1]-ys[0])/(xs[1]-xs[0])        elif x > xs[-1]:            return ys[-1]+(x-xs[-1])*(ys[-1]-ys[-2])/(xs[-1]-xs[-2])        else:            return interpolator(x)    def ufunclike(xs):        return array(list(map(pointwise, array(xs))))    return ufunclike

extrap1d takes an interpolation function and returns a function which can also extrapolate. And you can use it like this:

x = arange(0,10)y = exp(-x/3.0)f_i = interp1d(x, y)f_x = extrap1d(f_i)print f_x([9,10])

Output:

[ 0.04978707  0.03009069]