# L-15 MCS 275 Mon 15 Feb 2010 : bisection.py

# If f(a)*f(b) < 0 for some continuous function,
# then there is a root r: f(r) = 0, a <= r <= b.

def bisect(f,a,b):
   """
   If (a,b) contains a root of f,
   the on return is a smaller (a,b)
   containing a root of f.
   The string f is a function in x.
   """
   m = (a + b)/2
   x = a; fa = eval(f)
   x = m; fm = eval(f)
   if fm*fa < 0:
      return (a,m)
   else:
      return (m,b)

def main():
   """
   Applies the bisection method to find a
   root of some function.
   """
   f = raw_input('Give function in x : ')
   while True:
      a = float(input('give left bound a : '))
      b = float(input('give right bound b : '))
      x = a; fa = eval(f)
      x = b; fb = eval(f)
      if fa*fb >= 0:
         print 'f(a) = ', fa, ', f(b) = ', fb
         print 'please try again'
      else:
         break
   print 'a =', a, ', b = ', b
   while True:
      (a,b) = bisect(f,a,b)
      print 'a =', a, ', b = ', b
      ans = raw_input('continue ? ')
      if ans != 'y': break

main()