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).
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```

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