# plot the error polynomial on [a,b]

import numpy as np
import matplotlib.pyplot as plt
from chebyshev import chebyshev

a = -1
b =  1


# points for visualization
Xf = np.linspace(a,b,100)

fs = 24 #font size



for N in range(2,101,5):
    # interpolation points
    Xb = np.linspace(-1,1,N)
    #Xb = chebyshev(-1,1,N)
    
    # form the polynomial
    # (x-x1)*(x-x2)*...*(x-xN)
    p = lambda x: np.prod(x-Xb)
    # evaluate at the visualization points
    pf = [p(x) for x in Xf]
    maxpf = max(np.abs(pf))
    
    # visualize
    plt.clf()
    plt.plot(Xf,pf,'-', Xb,np.zeros_like(Xb),'x', linewidth=3,markeredgewidth=3,markersize=10)
    plt.xlabel('x',fontsize=fs)
    plt.ylabel('y',fontsize=fs) 
    plt.axis([a, b,-maxpf,maxpf])
    plt.grid(True)
    plt.title('Interpolation using %3d points' % (N), fontsize=fs)
    plt.show(block=False)
    plt.draw()
    # wait for a key press
    _ = input("Press [enter] to continue.")