"""File:     bisect1.py
   Purpose:  Find a root of a function given initial guesses that
             bracket a root -- i.e., one is larger, the other is
             smaller

   Run:      python bisect1.py

   Input:    maximum error tolerance (float)
             maximum number of iterations (int)
             value less than root (float)
             value greater than root (float)
"""

#----------------------------------------------------------------------
def f(x):
   """Function whose roots are +/- sqrt(2)
   """
   return x*x - 2

#----------------------------------------------------------------------
def bisect(lo, hi, tol, max_iter):

   est = (hi + lo)/2.0
   iter = 1;
   err_bd = (hi-lo)/2.0
   while err_bd > tol and iter < max_iter:
      if f(est) == 0:
         break
      elif f(est)*f(hi) > 0:
         hi = est
      else:
         lo = est
      est = (hi + lo)/2.0
      iter = iter + 1;
      err_bd = (hi-lo)/2.0
#     print "iter =", iter, ", est =", est
   
   print "The number of iterations was", iter
   print "The error in the estimate", est, "is less than or equal to", err_bd
   if err_bd > tol:
      return None
   else:
      return est

#----------------------------------------------------------------------
# Program starts here
tol = float(raw_input("Enter the maximum tolerance\n   "))
max_iter = int(raw_input("Enter the maximum number of iterations\n   "))

lo = float(raw_input("Enter a value < the zero of f\n   "))
hi = float(raw_input("Enter a value > the zero of f\n   "))
while f(lo)*f(hi) > 0:
   print "Enter values for which the product f(lo)*f(hi) < 0"
   lo = float(raw_input("Enter a value < the zero of f\n   "))
   hi = float(raw_input("Enter a value > the zero of f\n   "))

est = bisect(lo, hi, tol, max_iter)

if est == None:
   print "The iteration failed to converge"
else:
   print "The iteration converged"
   print "The estimate is", est
   print "f(", est, ") = ", f(est)