"""File:     newton.py
   Purpose:  Implement Newton's method to approximately solve f(x) = 0

   Run:      python newton.py

   Input:    tol:  approximate solution must be within tol of the 
             actual solution
             max_iter:  program should make no more than this many
             passes through the while loop in the newton function
             guess:  the initial guess at a solution
   Output:   Number of iterations
             Whether the method converged
             If it converges, the approx solution and the value
             of the function at the approx solution.
"""

#----------------------------------------------------------------------
def f(x):
   """Solutions to f(x) = 0 are +/- sqrt(2)"""
   return x*x - 2


def f_prime(x):
   """Derivative of f(x)"""
   return 2*x

#----------------------------------------------------------------------
def newton(g, tol, max_iter):
   
   if (f_prime(g) == 0):
      print "f'(", g ,") = 0 after 0 iterations"
      return None
   new_g = g - f(g)/f_prime(g)
   err_bd = abs(new_g - g)
   iters = 1
   while err_bd > tol and iters < max_iter:
      g = new_g
      if (f_prime(g) == 0):
         print "f'(", g ,") = 0 after", iters, "iterations"
         return None
      new_g = g - f(g)/f_prime(g)
      err_bd = abs(new_g - g)
      iters = iters + 1

   print "The method completed", iters, "iterations"
   if err_bd <= tol:
      return new_g
   else:
      return None


#----------------------------------------------------------------------
# main
tol = float(raw_input("What's the maximum acceptable error?\n   "))
max_iter = int(raw_input("What's the maximum number of passes?\n   "))
guess = float(raw_input("What's the initial guess?\n   "))

est = newton(guess, tol, max_iter)

if est == None:
   print "The method failed"
else:
   print "The method converged"
   print "The approximate solution to f(x) = 0 is", est
   print "f(", est, ") =", f(est)