python中黄金分割法实现方法

本文实例讲述了python中黄金分割法实现方法。分享给大家供大家参考。具体实现方法如下：

    ''' a,b = bracket(f,xStart,h)
      Finds the brackets (a,b) of a minimum point of the
      user-supplied scalar function f(x).
      The search starts downhill from xStart with a step
      length h.
      x,fMin = search(f,a,b,tol=1.0e-6)
      Golden section method for determining x that minimizes
      the user-supplied scalar function f(x).
      The minimum must be bracketed in (a,b).
    '''    
    from math import log, ceil
    def bracket(f,x1,h):
      c = 1.618033989 
      f1 = f(x1)
      x2 = x1 + h; f2 = f(x2)
     # Determine downhill direction and change sign of h if needed
      if f2 > f1:
        h = -h
        x2 = x1 + h; f2 = f(x2)
       # Check if minimum between x1 - h and x1 + h
        if f2 > f1: return x2,x1 - h 
     # Search loop
      for i in range (100):  
        h = c*h
        x3 = x2 + h; f3 = f(x3)
        if f3 > f2: return x1,x3
        x1 = x2; x2 = x3
        f1 = f2; f2 = f3
      print "Bracket did not find a mimimum"    
    def search(f,a,b,tol=1.0e-9):
      nIter = int(ceil(-2.078087*log(tol/abs(b-a)))) # Eq. (10.4)
      R = 0.618033989
      C = 1.0 - R
     # First telescoping
      x1 = R*a + C*b; x2 = C*a + R*b
      f1 = f(x1); f2 = f(x2)
     # Main loop
      for i in range(nIter):
        if f1 > f2:
          a = x1
          x1 = x2; f1 = f2
          x2 = C*a + R*b; f2 = f(x2)
        else:
          b = x2
          x2 = x1; f2 = f1
          x1 = R*a + C*b; f1 = f(x1)
      if f1 < f2: return x1,f1
      else: return x2,f2

希望本文所述对大家的Python程序设计有所帮助。