Let's revisit Runge's example from Chapter 2, Interpolation and Approximation, where we computed a Lagrange interpolation of Runge's function using eleven equally spaced nodes in the interval from -5 to 5:
In [1]: import numpy as np, matplotlib.pyplot as plt; \ ...: from scipy.interpolate import BarycentricInterpolator In [2]: def f(t): return 1. / (1. + t**2) In [3]: nodes = np.linspace(-5, 5, 11); \ ...: domain = np.linspace(-5, 5, 128); \ ...: interpolant = BarycentricInterpolator(nodes, f(nodes)) In [4]: plt.figure(); \ ...: plt.subplot(121); \ ...: plt.plot(domain, f(domain), 'r-', label='original'); \ ...: plt.plot(nodes, f(nodes), 'ro', label='nodes'); \ ...: plt.plot(domain, interpolant1(domain), 'b--', ...: label='interpolant'); \ ...: plt.legend(loc=9); \ ...: plt.subplot(122); \ ...: plt.plot(domain, np.abs(f(domain)-interpolant1(domain))); \ ...: plt.title('error or interpolation'); \ ...: plt.show()
