两个变量（可支持多自变量）的简单梯度下降

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 from mpl_toolkits.mplot3d.axes3d import Axes3D
 4 
 5 #   公式 f(x,y) = 2x^2+6y^2+6xy+x+4y+8
 6 def targetFunc(x,y):
 7     return 2*(x**2)+6*y**2+6*x*y+x+4*y+8
 8 
 9 #   偏导
10 #   f‘x(x,y)=4x+6y+1
11 #   f‘y(x,y)=12y+6x+4
12 def derivativeFunc(x,y):
13     rx = 4*x+6*y+1
14     ry = 12*y+6*x+4
15     return (rx,ry)
16 
17 def linerFunc(initPoint:tuple,targetFunc,derivativeFunc,step = 0.01,limitValue = 0.00000001,timeout=1000000,ax:Axes3D = None):
18     count = 1
19     initPoint = np.array(initPoint)
20     ro,do = targetFunc(*initPoint),np.array(derivativeFunc(*initPoint))
21     if ax !=None:
22         ax.scatter(*initPoint,ro,c=‘r‘)
23 
24     newPoint = initPoint-do*step
25     rn,dn = targetFunc(*newPoint),np.array(derivativeFunc(*newPoint))
26 
27     diff = np.abs(np.array(do-dn))
28 
29     while (diff > limitValue).any() and count < timeout:
30         # print(initPoint)
31         initPoint = newPoint
32         ro, do = targetFunc(*initPoint), np.array(derivativeFunc(*initPoint))
33 
34         newPoint = np.where(np.abs(do*step) >= limitValue,initPoint-do*step,initPoint)
35         rn, dn = targetFunc(*newPoint), np.array(derivativeFunc(*newPoint))
36         diff = np.abs(np.array(do - dn))
37 
38         if ax != None:
39             ax.scatter(*initPoint, ro, c=‘r‘)
40         count+=1
41         pass
42     print("最终运算次数为 : {0}".format(count))
43     return rn,newPoint
44     pass
45 
46 
47 if __name__=="__main__":
48     x,y = np.linspace(-200,200,1000),np.linspace(-200,200,1000)
49     x,y = np.meshgrid(x,y)
50     fxy=targetFunc(x,y)
51 
52     fig = plt.figure()
53     ax = Axes3D(fig)
54 
55     # ax.plot_surface(x, y, fxy)
56     limitValue,limitPoint = linerFunc((20,20),targetFunc,derivativeFunc,ax=ax)
57     print("该函数在({0},{1})处有驻点，值为{2}".format(limitPoint[0],limitPoint[1],limitValue))
58     ax.legend()
59 
60 
61     plt.show()
62 
63 
64 
65     pass