# -*- coding: utf-8 -*-
"""
Created on Wed Dec 17 12:05:23 2014

@author: grivet

Listing 5.1 : Méthode de dichotomie ou de bissection 
pour résoudre une équation non-linéaire

"""

from pylab import *

NITMAX = 20;TOL = 1E-2

def fn(x):
    return x**2 - cos(x)

nit = 0
xg = float(input("valeur à gauche: " ))
xd = float(input("valeur à droite: "))
fg = fn(xg); fd = fn(xd)
print ('xg: %8.4f  fg! %8.4f  xd! %8.4f  fd: %8.4f' %(xg,fg,xd,fd))
while (nit < NITMAX) & (abs(xd - xg) > TOL):
    xm = 0.5*(xg+xd);
    fm = fn(xm); 
    if fm*fg < 0:
        xd = xm; fd = fm;
    else:
        xg = xm; fg = fm;   
    print ("%d  %10.6f  %10.6f" %(nit,xg,xd))
    nit = nit+1
print ('\n racine: ', 0.5*(xg+xd))