问题描述
我有一个函数,我想找到它的最大值和最小值.我的职能是这样:
I have a function and I would like to find its maximum and minimum values. My function is this:
def function(x, y):
exp = (math.pow(x, 2) + math.pow(y, 2)) * -1
return math.exp(exp) * math.cos(x * y) * math.sin(x * y)
我有一个x [-1,1]和y [-1,1]的间隔.我想找到一种方法来限制此间隔,以发现此函数的最大值和最小值.
I have an interval for x [-1, 1] and y [-1, 1]. I would like to find a way, limited to this interval, to discover the max and min values of this function.
推荐答案
例如,使用scipy
的 fmin
(其中包含Nelder-Mead算法的实现),您可以尝试以下操作:
Using, for instance, scipy
's fmin
(which contains an implementation of the Nelder-Mead algorithm), you can try this:
import numpy as np
from scipy.optimize import fmin
import math
def f(x):
exp = (math.pow(x[0], 2) + math.pow(x[1], 2)) * -1
return math.exp(exp) * math.cos(x[0] * x[1]) * math.sin(x[0] * x[1])
fmin(f,np.array([0,0]))
将产生以下输出:
Optimization terminated successfully.
Current function value: -0.161198
Iterations: 60
Function evaluations: 113
array([ 0.62665701, -0.62663095])
请记住:
1)和scipy
,您需要将您的函数转换为接受数组的函数(在上面的示例中,我演示了如何做到这一点);
1) with scipy
you need to convert your function into a function accepting an array (I showed how to do it in the example above);
2)fmin
像它的大多数对一样,使用迭代算法,因此您必须提供一个起点(在我的示例中,我提供了(0,0)
).您可以提供不同的起点来获得不同的最小值/最大值.
2) fmin
uses, like most of its pairs, an iterative algorithm, therefore you must provide a starting point (in my example, I provided (0,0)
). You can provide different starting points to obtain different minima/maxima.
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