import matplotlib.pyplot as plt
import numpy as np
from math import *


def coeffs(X,Y):
    n = len(X)-1
    diff_div=[[0 for _ in xrange(n+1)] for _ in xrange(n+1)]
    for i in xrange(n+1):
        diff_div[i][0] = Y[i]
    for j in xrange(1,n+1):
        for i in xrange(n-j+1):
            r = float(diff_div[i+1][j-1]-diff_div[i][j-1])/(X[i+j]-X[i])
            diff_div[i][j] = r
    print diff_div
    return diff_div[0]


print "TP 2.1 ............"


def forloop(list):
    r = 1
    for x in list:
        r *= x
    return r


def construit_pol(X,Y):
    d = coeffs(X,Y)
    n = len(X)-1
    return lambda x : sum([d[i]*forloop([x - X[j] for j in xrange(i)]) for i in xrange(n+1)])


"""
print "tp 2.1....."
X = [10,25,60]
Y = [2.3, 8, 24.6]
p = construit_pol(X,Y)
Yp =[p(x) for x in X]

print p(15)
print p(40)
print p(100)


x=np.linspace(10,100,100)
plt.plot(x,p(x))  
plt.ylabel('temps d\'execution')
plt.xlabel("taille des donnees")
plt.show()



"""

print "tp 2.2....."
X1 = [-1+0.25*i for i in xrange(9)]
Y1 = [e**x for x in X1]
p1 = construit_pol(X1,Y1)


X2 = [cos(pi/2*(float(2*i+1)/9)) for i in xrange(9)]
Y2 = [e**x for x in X2]
p2 = construit_pol(X2,Y2)



e1 = lambda x : abs(p1(x) - e**x)
e2 = lambda x : abs(p2(x) - e**x)
x=np.linspace(-1,1,1000)

plt.plot(x,e1(x))  
plt.plot(x,e2(x))  

plt.ylabel('exp')
plt.xlabel("x")
plt.show()