Radial basis functions can be used for smoothing/interpolating scattered
data in n-dimensions, but should be used with caution for extrapolation
outside of the observed data range.
This example compares the usage of the Rbf and UnivariateSpline classes
from the scipy.interpolate module.
import numpy as np
from scipy.interpolate import Rbf, InterpolatedUnivariateSpline
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
# setup data
x = np.linspace(0, 10, 9)
y = np.sin(x)
xi = np.linspace(0, 10, 101)
# use fitpack2 method
ius = InterpolatedUnivariateSpline(x, y)
yi = ius(xi)
plt.subplot(2, 1, 1)
plt.plot(x, y, 'bo')
plt.plot(xi, yi, 'g')
plt.plot(xi, np.sin(xi), 'r')
plt.title('Interpolation using univariate spline')
# use RBF method
rbf = Rbf(x, y)
fi = rbf(xi)
plt.subplot(2, 1, 2)
plt.plot(x, y, 'bo')
plt.plot(xi, fi, 'g')
plt.plot(xi, np.sin(xi), 'r')
plt.title('Interpolation using RBF - multiquadrics')
plt.tight_layout()
plt.savefig('rbf1d.png')
# 2-d tests - setup scattered data
x = np.random.rand(100)*4.0-2.0
y = np.random.rand(100)*4.0-2.0
z = x*np.exp(-x**2-y**2)
ti = np.linspace(-2.0, 2.0, 100)
XI, YI = np.meshgrid(ti, ti)
# use RBF
rbf = Rbf(x, y, z, epsilon=2)
ZI = rbf(XI, YI)
# plot the result
n = plt.normalize(-2., 2.)
plt.subplot(1, 1, 1)
plt.pcolor(XI, YI, ZI, cmap=cm.jet)
plt.scatter(x, y, 100, z, cmap=cm.jet)
plt.title('RBF interpolation - multiquadrics')
plt.xlim(-2, 2)
plt.ylim(-2, 2)
plt.colorbar()
plt.savefig('rbf2d.png')
