# -*- coding: utf-8 -*-
"""
Created on Thu Dec 18 10:50:10 2014

@author: grivet

Exercice 5-1b : Résolution d'une équation non-linéaire
par regula falsi
"""

from pylab import *

TOL = 1E-6
def  fn(x):
    return x - 0.2*sin(x) - 0.5
    
xg = float(input("abscisse gauche: ")) 
xd = float(input("abscisse droite: "))
fg = fn(xg); fd = fn(xd)
fm = (fg+fd)/2.0

while abs(fm) > TOL:
    xm = xg - fg*(xg-xd)/(fg-fd)
    fm = fn(xm)
    if fm*fg < 0:
        xd = xm; fd = fm
    else:
        xg = xm; fg = fm
        
xm = xg - fg*(xd-xg)/(fd-fg);
print  ("\n racine: %12.6f valeur de la fonction! %12.6f\n" %(xm,  fn(xm)))