[Scientific / technical calculation by Python] 3rd order spline interpolation, scipy
Perform third-order spline interpolation using the interp1d method ** of ** scipy.interpolate.
Contents
Example: Consider $ y = 1 / (1 + x ^ 2) $. Sample and interpolate the 11-point data set $ (x_i, y_i) $. This function does not work with Lagrange interpolation (see Qiita article).
from scipy.interpolate import interp1d
import numpy as np
import matplotlib.pyplot as plt
x =np.linspace(-5,5,num=11)
y = 1.0/(1.0+x**2)
f_line = interp1d(x, y)
f_CS = interp1d(x, y, kind='cubic') #Execute 3rd spline interpolation!
#for plot
xnew =np.linspace(-5,5,num=51)
plt.plot(x, y, 'o', xnew, f_CS(xnew), '-')
plt.legend(['Raw data','Lagrange', 'Cubic spline'], loc='best')
plt.xlim([-6, 6])
plt.ylim([0, 1.4])
plt.show()
result
11 data points sampled by blue. The orange line is spline interpolated.
[Addendum]
As shown in the figure below, Lagrange polynomial does not interpolate this function well.
11 data points sampled by blue. The orange line is spline-interpolated and the green line is Lagrange-interpolated, causing unnatural vibration near both ends.