[人工智能]人工神经网络实验课三

实验一：Pass
实验二：
效果图：
学习率a = 0.9

学习率a = 0.1:

# -*- coding: utf-8 -*-
# @Time    : 2022/3/21 16:36
# @Author  : sido
# @FileName: 实验二.py
# @Software: PyCharm
'''
f(x) = w^2
the derivative of f(x): f`(x) = 2*w
Initilize w = 1, a = 0.4
'''

import matplotlib.pyplot as plt
import numpy as np

# -------------超参数-----------
k = 4
w = [1]
a = 0.9

# ----------梯度下降，更新w-----------
for i in range(k):
    w.append(w[-1] - a * 2 * w[-1])

# -------------绘制图像------------
plt.ion()  # 打开交互模式
x = np.linspace(-1, 1, 30)
plt.plot(x, np.square(x))
for i in range(0, len(w)-1):
    plt.plot(w[i:i+2], np.square(w[i:i+2]), 'r-o')
    print(w[i], '---->', w[i+1])
    plt.pause(2)
plt.ioff()  # 关闭交互模式
print("绘制图像完成！")
plt.waitforbuttonpress()  # 等待键盘输入退出

实验三：
学习率 a = 0.1：

学习率 a = 0.9：

# -*- coding: utf-8 -*-
# @Time    : 2022/3/21 17:51
# @Author  : sido
# @FileName: 实验三.py
# @Software: PyCharm
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
'''
f(W) = w1^2 + w2^2 
W = (1, 3)
a = 0.1
'''
# --------------------------------------------------超参数---------------------------------------------------------
w = np.array([[1, 3]])
a = 0.1
k = 20

# -------------------------------------------------梯度下降，更新参数-------------------------------------------------
for i in range(k):
    w = np.concatenate((w, np.array([[w[-1][0] - a * 2 * w[-1][0], w[-1][1] - a * 2 * w[-1][1]]])), axis=0)

# -------------------------------------------------绘制图像---------------------------------------------------------
w1 = np.linspace(-3, 3, 20)
w2 = np.linspace(-3, 3, 20)
plt.ion()
x, y = np.meshgrid(w1, w2)  # 生成网格点坐标矩阵
fig = plt.figure()
ax = plt.gca(projection='3d')
ax.set_zlabel('Z', fontdict={'size': 15, 'color': 'red'})
ax.set_ylabel('Y', fontdict={'size': 15, 'color': 'blue'})
ax.set_xlabel('X', fontdict={'size': 15, 'color': 'green'})
ax.plot_surface(x, y, np.square(x)+np.square(y), alpha = 0.5)
print(w)
for i in range(len(w) - 10):
    ax.plot(w[i:i+2, 0], w[i:i+2, 1], [sum(np.square(w[i])), sum(np.square(w[i+1]))], 'r-o')
    print('x: ', w[i:i+2, 0], ' ---> y: ', w[i:i+2, 1],' ----> z: ',  [sum(np.square(w[i])), sum(np.square(w[i+1]))])
    plt.pause(0.5)
plt.ioff()
def press(event):  # 监控键盘输入
    if event.key == "escape":
        plt.close()
fig.canvas.mpl_connect('key_press_event', press)
# plt.waitforbuttonpress()  # 只要接受到键盘或者鼠标输入就退出
plt.show()