# min_search.py  note: smaller h did not give better result
#                      smaller t, tolerance, if it converges, better
#                      searches xi to +infinity

def f(x):
  return (x-5)**4 # minimum at x=5

def optMinSearch(f, xi, h, t=1.0e-9):
  ssx = xi
  x = xi
  fx = f(x)
  sx = x
  x += h
  fxn = f(x)
  n = 0

  while abs(fxn-fx) > t :
    while fx > fxn:
      n += 1
      fx = fxn
      ssx = sx
      sx = x
      x += h
      fxn = f(x)
    
    xx = x
    h = h / 2
    x = ssx
    fx = f(x)
    sx = x
    x += h
    fxn = f(x)
    n += 1  
    
  return x, fxn, n, sx, xx

h = 0.1
print "min of (x-5)**4, h=", h
xmin, fmin, n, sx, xx = optMinSearch(f, -2.0, h)
print "xmin=",xmin
print "fmin=",fmin
print "n=", n, ", sx=", sx, ", xx=", xx
print " "

h = 0.01
print "min of (x-5)**4, h=", h
xmin, fmin, n, sx, xx = optMinSearch(f, -2.0, h)
print "xmin=",xmin
print "fmin=",fmin
print "n=", n, ", sx=", sx, ", xx=", xx
print " "

h = 2.0
print "min of (x-5)**4, h=", h
xmin, fmin, n, sx, xx = optMinSearch(f, -2.0, h, 1.0e-15)
print "xmin=",xmin
print "fmin=",fmin
print "n=", n, ", sx=", sx, ", xx=", xx
print " "