f(x)=10x^6 -72x^5 +165x^4 -120x^3 +72
with the estimation error less than 0.01,where x is defined the real line.
這個其實是最佳化作業一，當時還在學 Python ，所以就順手用 Python 做作業了。
就把它貼在這邊吧，不然這邊好久沒有新東西了，我都在做作業...
其實還蠻想貼類神經的作業呢 ... BPNN, LVQ, CPN, SOM, ART, ...
不過這些是分組作業的，所以得尊重趴呢，(時間都耗在這上面阿...)
廢話不多說了，直接來貼 code
#-*- coding:UTF-8 -*-
def f(x):
return 10*x**6 - 72*x**5 + 165*x**4 -120*x**3 + 72
global result #儲存最大最小值
result = []
def findminInterval(x0,d):
x = [] # 儲存全部的x值
x.append(x0) #x0
d = d #step-size
n = 0
global x_down #需要找的下界
global x_up #需要找的上界
t = [f(x[0]-d), f(x[0]), f(x[0]+d)] #儲存f(x0)的值
print "x%d = %d" %(n,x[0])
print "d = ", d
print "f(x%d - d) = %f" %(n, t[0])
print "f(x%d) = %f" %(n, t[1])
print "f(x%d + d) = %f" %(n, t[2])
#判斷一開始的大小
if t[0] == max(t) and t[2] == min(t):
print "f(x%d - d) >= f(x%d) >= f(x%d + d)" %(n,n,n)
state = True
while state:
beforevalue = f(x[n])
x.append(x[n] + d*(2**n))
n = n + 1
print "x%d = %f" %(n,x[n])
nowvalue = f(x[n])
if nowvalue < beforevalue:
print "f(%f) = %f < f(x%d)" %(x[n],nowvalue,n-1)
else:
print "f(%f) = %f > f(x%d)" %(x[n],nowvalue,n-1)
print "x = ", x
if len(x) > 2:
x_down = x[n-2]
x_up = x[n]
else:
x_down = x[0]-d
x_up = x[0]+d
state = False #找到最小值所在之區間，跳出迴圈
elif t[0] == min(t) and t[2] == max(t):
print "f(x%d - d) <= f(x%d) <= f(x%d + d)" %(n,n,n)
state = True
while state:
beforevalue = f(x[n])
x.append((x[n] - d*(2**n)))
n = n + 1
print "x%d = %f" %(n,x[n])
nowvalue = f(x[n])
if nowvalue < beforevalue:
print "f(%f) = %f < f(x%d)" %(x[n],nowvalue,n-1)
else:
print "f(%f) = %f > f(x%d)" %(x[n],nowvalue,n-1)
print "x = ", x
if len(x) > 2:
x_down = x[n]
x_up = x[n-2]
else:
x_down = x[0]-d
x_up = x[0]+d
state = False #找到最小值所在之區間，跳出迴圈
elif t[1] == min(t):
print "f(x%d - d) >= f(x%d) <= f(x%d + d)" %(n,n,n)
print "x%d = %f" %(n,x[n])
x_down = x[0] - d
x_up = x[0] + d
elif t[1] == max(t):
print "f(x%d - d) <= f(x%d) >= f(x%d + d)" %(n,n,n)
print "x%d = %f" %(n,x[n])
print "It must have maximum in the interval!"
x_down = x[0] - d
x_up = x[0] + d
else:
print "It may have some problem!!!"
print "%f <= x* <= %f" %(x_down,x_up)
def findmaxInterval(x0,d):
x = [] # 儲存全部的x值
x.append(x0) #x0
d = d #step-size
n = 0
global x_down #需要找的下界
global x_up #需要找的上界
t = [f(x[0]-d), f(x[0]), f(x[0]+d)] #儲存f(x0)的值
print "x%d = %f" %(n,x[0])
print "d = ", d
print "f(x%d - d) = %f" %(n, t[0])
print "f(x%d) = %f" %(n, t[1])
print "f(x%d + d) = %f" %(n, t[2])
#判斷一開始的大小
if t[0] == max(t) and t[2] == min(t):
print "f(x%d - d) >= f(x%d) >= f(x%d + d)" %(n,n,n)
state = True
while state:
beforevalue = f(x[n])
x.append(x[n] - d*(2**n))
n = n + 1
print "x%d = %f" %(n,x[n])
nowvalue = f(x[n])
if nowvalue > beforevalue:
print "f(%f) = %f > f(x%d)" %(x[n],nowvalue,n-1)
else:
print "f(%f) = %f < f(x%d)" %(x[n],nowvalue,n-1)
print "x = ", x
if len(x) > 2:
x_down = x[n]
x_up = x[n-2]
else:
x_down = x[0]-d
x_up = x[0]+d
state = False #找到最大值所在之區間，跳出迴圈
elif t[0] == min(t) and t[2] == max(t):
print "f(x%d - d) <= f(x%d) <= f(x%d + d)" %(n,n,n)
state = True
while state:
beforevalue = f(x[n])
x.append((x[n] + d*(2**n)))
n = n + 1
print "x%d = %f" %(n,x[n])
nowvalue = f(x[n])
if nowvalue > beforevalue:
print "f(%f) = %f > f(x%d)" %(x[n],nowvalue,n-1)
else:
print "f(%f) = %f < f(x%d)" %(x[n],nowvalue,n-1)
print "x = ", x
if len(x) > 2:
x_down = x[n-2]
x_up = x[n]
else:
x_down = x[0]-d
x_up = x[0]+d
state = False #找到最大值所在之區間，跳出迴圈
elif t[1] == min(t):
print "f(x%d - d) >= f(x%d) <= f(x%d + d)" %(n,n,n)
print "x%d = %f" %(n,x[n])
print "It must have minima value!!"
x_down = x[0] - d
x_up = x[0] + d
elif t[1] == max(t):
print "f(x%d - d) <= f(x%d) >= f(x%d + d)" %(n,n,n)
print "x%d = %f" %(n,x[n])
x_down = x[0] - d
x_up = x[0] + d
else:
print "It may have some problem!!!"
print "%f <= x* <= %f" %(x_down,x_up)
def findmin(xdown, xup):
a = xdown # 下界
b = xup # 上界
global xm
state = True
while state:
L = b - a
xm = (a + b)*0.5
x1 = a + 0.25*L
x2 = b - 0.25*L
print "*"*50
print "a = %f" %a
print "b = %f" %b
print "L = %f" %L
print "xm = %f" %xm
print "x1 = %f" %x1
print "x2 = %f" %x2
t = [f(xm), f(x1), f(x2)] #暫存計算結果
if t[1] > t[0] and t[2] > t[0]:
print "f(%f) = %f > f(%f) = %f" %(x1, t[1], xm, t[0])
print "f(%f) = %f > f(%f) = %f" %(x2, t[2], xm, t[0])
a = x1
b = x2
elif t[1] < t[0] and t[2] > t[0]:
print "f(%f) = %f < f(%f) = %f" %(x1, t[1], xm, t[0])
print "f(%f) = %f > f(%f) = %f" %(x2, t[2], xm, t[0])
b = xm
elif t[1] > t[0] and t[2] < t[0]:
print "f(%f) = %f > f(%f) = %f" %(x1, t[1], xm, t[0])
print "f(%f) = %f < f(%f) = %f" %(x2, t[2], xm, t[0])
a = xm
else:
print "f(%f) = %f <= f(%f) = %f" %(x1, t[1], xm, t[0])
print "f(%f) = %f <= f(%f) = %f" %(x2, t[2], xm, t[0])
print "You must try to find the maximum."
state = False
if b - a < 0.01:
print "The minima must be %f" %xm
result.append("The minima must be %f" %xm) #將最小值結果加入結果串中
state = False
def findmax(xdown, xup):
a = xdown # 下界
b = xup # 上界
global xm
state = True
while state:
L = b - a
xm = (a + b)*0.5
x1 = a + 0.25*L
x2 = b - 0.25*L
print "*"*50
print "a = %f" %a
print "b = %f" %b
print "L = %f" %L
print "xm = %f" %xm
print "x1 = %f" %x1
print "x2 = %f" %x2
t = [f(xm), f(x1), f(x2)] #暫存計算結果
if t[1] < t[0] and t[2] < t[0]:
print "f(%f) = %f < f(%f) = %f" %(x1, t[1], xm, t[0])
print "f(%f) = %f < f(%f) = %f" %(x2, t[2], xm, t[0])
a = x1
b = x2
elif t[1] < t[0] and t[2] > t[0]:
print "f(%f) = %f < f(%f) = %f" %(x1, t[1], xm, t[0])
print "f(%f) = %f > f(%f) = %f" %(x2, t[2], xm, t[0])
a = xm
elif t[1] > t[0] and t[2] < t[0]:
print "f(%f) = %f > f(%f) = %f" %(x1, t[1], xm, t[0])
print "f(%f) = %f < f(%f) = %f" %(x2, t[2], xm, t[0])
b = xm
else:
print "f(%f) = %f >= f(%f) = %f" %(x1, t[1], xm, t[0])
print "f(%f) = %f >= f(%f) = %f" %(x2, t[2], xm, t[0])
print "You must try to find the minima."
state = False
if b - a < 0.01:
print "The maximum must be %f" %xm
result.append("The maximum must be %f" %xm) #將最大值結果加入結果串中
state = False
def main():
findminInterval(0,0.001)
findmin(x_down, x_up)
state = True
while state:
try:
findmaxInterval(xm+0.1,0.001)
findmax(x_down, x_up)
findminInterval(xm+0.1,0.001)
findmin(x_down, x_up)
except OverflowError:
print "It may have no other max or min interval."
state = False
print "*"*50
#print result
print "Use region elimination methods to estimate the two minima and one maximum of the function"
print "f(x)=10x^6-72x^5+165x^4-120x^3+72"
print "with the estimation error less than 0.01, where x is defined on the real line."
print "The result is:"
n = 0
while n < len(result):
print result[n]
n = n + 1
print "*"*50
if __name__ == "__main__":
main()
raw_input("Please
這東西我就不解釋了，實在不是很好解釋...
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