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





def f(x):
    return cos(x)-x

def fp(x):
    return -sin(x)-1




def  iteration_dichotomie(a,b,m,epsilon,f):
    def maj_test(xn,xnm1):
        return f(xn) != 0 and abs(xnm1-xn) > epsilon  
    xnm1 = a 
    xn= a
    X=[]
    n = 1
    an= a
    bn=b
    test = True
    while n <= m and test:
        xnm1 = xn
        xn=float(an+bn)/2
        test = maj_test(xn,xnm1)
        X +=[xn]
        if f(an)*f(xn)<=0 : 
            bn=xn
        else :
            an=xn
        n +=1
    return (n,X)

def  iteration_newton(x0,m,epsilon,f,fp):
    def maj_test(xn,xnm1):
        return f(xn) != 0 and abs(xnm1-xn) > epsilon  
    n=0;
    test= f(x0) != 0
    xn=x0
    X=[x0]
    while n < m and test:
        qn=fp(xn)
        xnm1=xn
        xn= xn-f(xn)/qn
        X += [xn]
        n=n+1
        test= maj_test(xn,xnm1)

#f(x) !=0 and n<m  and abs(x-xm1)>epsilon
    return (n,X)


def  iteration_corde(a,b,x0,m,epsilon,f):
    def maj_test(xn,xnm1):
        return f(xn) != 0 and abs(xnm1-xn) > epsilon  
    n=0;
    q=float(f(b)-f(a))/(b-a)
    test= f(x0) != 0
    xn=x0
    X=[x0]
    while n < m and test:
        xnm1=xn
        xn= xn-f(xn)/q
        X += [xn]
        n=n+1
        test= maj_test(xn,xnm1)

#f(x) !=0 and n<m  and abs(x-xm1)>epsilon
    return (n,X)

"""def  iteration_newton(x0,m,epsilon,f,fp):
    n=0;
    delta=float(1)/fp(x0)
    test= f(x0) != 0
    x=x0
    X=[x0]
    while(test):
        xm1=x
        x= x-delta*f(x)
        delta=float(1)/fp(x)
        X += [x]
        n=n+1
        test= not (f(x)==0 or n>=m  or abs(x-xm1)<=epsilon)
    return (n,X)
"""

def  iteration_lagrange(x0,x1,m,epsilon,f):
    n=0;
    delta=float(x1-x0)/(f(x1)-f(x0))
    test= f(x0) != 0
    x=x1
    X=[x1]
    while(test):
        xm1=x
        x= x-delta*f(x)
        delta=float(x-xm1)/(f(x)-f(xm1))
        X += [x]
        n=n+1
        test= not (f(x)==0 or n>=m  or abs(x-xm1)<=epsilon)
    return (n,X)


def main():
    print "TP 3.1 ............ dichotomie"
    print iteration_dichotomie(0,pi/2,200,0.00000001,f)

    
    print "TP 3.1 ............ corde"
    print iteration_corde(0,pi/2,0,200,0.00000001,f)


    print "TP 3.1 ............ newton"
    print iteration_newton(0,200,0.00000001,f,fp)


    print "TP 3.1 ............ lagrange"
    print iteration_lagrange(0,pi/2,200,0.00000001,f)
    

if __name__ == '__main__':
    main()