Numerical Analysis

import Spline
import Lagrange
import numpy as np
import matplotlib as mpl
mpl.use("TkAgg")
import matplotlib.pylab as plt
plt.ion()

#runMode = 'error'
runMode = 'normal'

#Function setup
x = lambda n: np.linspace(-1,1,n)
f = lambda x: np.cos(np.sin(np.pi*x))
n = 5
E=200
data = zip(x(n),f(x(n)))

#Function in solid black line
if runMode == 'normal':
    plt.plot(x(E),f(x(E)),'k')

#Cubic Splines in red dashed line
splines,xn = Spline.Splines(data)
SX,SY = Spline.splinesToPlot(splines,xn,E)
if runMode == 'normal':
    plt.plot(SX,SY,'r--')
else:
    eSY = [abs(SY[i]-f(X)) for i,X in enumerate(SX)]
    plt.semilogy(SX,eSY,'r--')

#Langrange Polynomial in solid blue line
LX=x(E)
LY = Lagrange.LagrangeInterp(data, LX)
if runMode == 'normal':
    plt.plot(LX,LY,'b')
else:
    eLY = [abs(LY[i]-f(X)) for i,X in enumerate(LX)]
    plt.semilogy(LX,eLY,'b')