import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D

#f(w1,w2) = w1^2 + w2^2 + 2*w1*w2 + 500
def targetFunction(W): #目標(biāo)函數(shù)
 w1,w2 = W
 return w1 ** 2 + w2**2 + 2*w1*w2+500

def gradientFunction(W): #梯度函數(shù)：分別對w1,w2求偏導(dǎo)
 w1,w2 = W
 w1_grad = 2*w1+2*w2
 w2_grad = 2*w2 + 2*w1
 return np.array([w1_grad,w2_grad])

def batch_gradient_distance(targetFunc,gradientFunc,init_W,learning_rate = 0.01,tolerance = 0.0000001): #核心算法
 W = init_W
 target_value = targetFunc(W)
 counts = 0 #用于計算次數(shù)
 while counts<5000:
 gradient = gradientFunc(W)
 next_W = W-gradient*learning_rate
 next_target_value = targetFunc(next_W)
 if abs(next_target_value-target_value) <tolerance:
 print("此結(jié)果經(jīng)過了", counts, "次循環(huán)")
 return next_W
 else:
 W,target_value = next_W,next_target_value
 counts += 1
 else:
 print("沒有取到極值點")


if __name__ == '__main__':
 np.random.seed(0) #保證每次運行隨機出來的結(jié)果一致
 init_W = np.array([np.random.random(),np.random.random()]) #隨機初始的w1,w2
 w1,w2 = batch_gradient_distance(targetFunction,gradientFunction,init_W)
 print(w1,w2)
 #畫圖
 x1=np.arange(-10,11,1) #為了繪制函數(shù)的原圖像
 x2=np.arange(-10,11,1)

 x1, x2 = np.meshgrid(x1, x2) # meshgrid :3D坐標(biāo)系

 z=x1**2 + x2**2 + 2*x1*x2+500

 fig = plt.figure()
 ax = Axes3D(fig)
 ax.plot_surface(x1, x2, z) #繪制3D坐標(biāo)系中的函數(shù)圖像
 ax.scatter(w1,w2, targetFunction([w1,w2]), s=50, c='red') #繪制已經(jīng)找到的極值點
 ax.legend() #使坐標(biāo)系為網(wǎng)格狀

 plt.show() #顯示