Interpolation

import os
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d
os.chdir(r'D:\data\scripts\wordpress\ex50')
os.getcwd()
A,nu,k=10,4,2

def f(x,A,nu,k):
    return A*np.exp(-k*x)*np.cos(2*np.pi*nu*x)

xmax,nx=0.5,8
x=np.linspace(0,xmax,nx)
y=f(x,A,nu,k)
f_nearest=interp1d(x,y,kind='nearest')
f_linear =interp1d(x,y)
f_cubic =interp1d(x,y,kind='cubic')
x2=np.linspace(0,xmax,100)
plt.plot(x,y,'o',label='datapoints')
plt.plot(x2,f(x2,A,nu,k),label='exact')
plt.plot(x2,f_nearest(x2),label='nearest')
plt.plot(x2, f_linear(x2), label='linear')
plt.plot(x2, f_cubic(x2), label='cubic')
plt.legend()
plt.show()
plt.tight_layout()
plt.savefig("example50.png", dpi=100)
plt.show()
plt.close()