python中黄金分割法实现方法

''' 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 = 1.6180339 
 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 = 0.6180339
 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

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