1 #coding:utf-8
 2 import numpy as np
 3 import matplotlib.pyplot as plt
 4 #定义梯度下降法
 5 def gd(x_start,step,g):
 6     x=x_start
 7     for i in range(20):
 8         grad=g(x)
 9         x-=grad*step  #x=x-grad*step
10         print('[epoch {0} ] grad={1}, x={2}'.format(i,grad, x))
11         if abs(grad) < 1e-6:
12             break;
13     return x
14         #解释
15 #定义待优化函数
16 def f(x):
17     return x*x-2*x+1
18 #定义待优化函数的导数
19 def g(x):
20     return 2*x-2
21 #可视化待优化函数
22 x=np.linspace(-5,7,100)
23 y=f(x)
24 plt.plot(x,y)
25 plt.show()
26 #实现梯度下降法
27 gd(5,0.1,g)
28
29 #print('{0} {1} {2}'.format('epoch', 'grad','x'))
30 #epoch grad x

[epoch 0 ] grad=8, x=4.2    #epoch0, grad=2*5-2=8, x=5-grad*0.1=4.2
[epoch 1 ] grad=6.4, x=3.56   #epoch1, grad=2*4.2-2=6.4, x=4.2-grad*0.1=3.56
[epoch 2 ] grad=5.12, x=3.048
[epoch 3 ] grad=4.096, x=2.6384
[epoch 4 ] grad=3.2767999999999997, x=2.31072
[epoch 5 ] grad=2.6214399999999998, x=2.0485759999999997
[epoch 6 ] grad=2.0971519999999995, x=1.8388607999999997
[epoch 7 ] grad=1.6777215999999995, x=1.6710886399999998
[epoch 8 ] grad=1.3421772799999996, x=1.536870912
[epoch 9 ] grad=1.0737418239999998, x=1.4294967295999998
[epoch 10 ] grad=0.8589934591999997, x=1.34359738368
[epoch 11 ] grad=0.6871947673599998, x=1.274877906944
[epoch 12 ] grad=0.5497558138879999, x=1.2199023255552
[epoch 13 ] grad=0.4398046511103999, x=1.17592186044416
[epoch 14 ] grad=0.35184372088831983, x=1.1407374883553278
[epoch 15 ] grad=0.2814749767106557, x=1.1125899906842622
[epoch 16 ] grad=0.22517998136852446, x=1.0900719925474098
[epoch 17 ] grad=0.18014398509481966, x=1.0720575940379278
[epoch 18 ] grad=0.14411518807585555, x=1.0576460752303423
[epoch 19 ] grad=0.11529215046068453, x=1.0461168601842739