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。