# polynomial interpolation 
# on uniformly distributed points

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

# poits for vizualization
Xf = np.linspace(-1,1,500)
fs = 24 #font size

f = lambda x: np.cos(np.pi/2*x)
#f = lambda x: np.exp(-1./np.maximum(0.25-x**2,0.0))/np.exp(-4)
#f = lambda x: 1/(1+10*x**2)

plt.plot(Xf,f(Xf),'--',linewidth=3,markeredgewidth=3,markersize=10)
plt.grid(True)
plt.xlabel('x',fontsize=fs)
plt.ylabel('y',fontsize=fs)
plt.axis([-1, 1,-0.5,1.5])
plt.title('Function f',fontsize=fs)
plt.show(block=False)
# wait for a key press
_ = input("Press [enter] to continue.")

for N in range(2,101,5):
    # interpolation points
    Xb = np.linspace(-1,1,N)
    #Xb = chebyshev(-1,1,N) 
    Yb = f(Xb)
    # calculate coefficients with Newton's divided differences
    c = newtdd(Xb,Yb)
    # evaluate the interpolating polynomial
    Yf= nest(c,Xf,Xb)
    
    # vizualize
    plt.clf()
    plt.plot(Xf,f(Xf),'--',Xf,Yf,'-',Xb,Yb,'x',linewidth=3,markeredgewidth=3,markersize=10)
    plt.grid(True)
    plt.xlabel('x',fontsize=fs)
    plt.ylabel('y',fontsize=fs)
    plt.axis([-1, 1,-0.5,1.5])
    plt.title('Interpolation using %3d points' % (N),fontsize=fs)
    plt.draw()
    plt.show(block=False)
    # wait for a key press
    _ = input("Press [enter] to continue.")