Lecture 2 Linear Model Linear Model

参考资料

1. 一句话解释numpy.meshgrid()
2. matplotlib教程之——Custom profiles and drawing styles（rcParams和style）
3. python中zip()函数的用法
4. matplotlib之plot()详解
5. matplotlib 3D绘图警告

课堂练习

实现线性模型y=wx的平面图

import numpy as np
import matplotlib.pyplot as plt

#保存数据集,The same index is a sample
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

#Feedforward of the model
def forward(x):
    return x * w

#损失函数
def loss(x, y):
    y_pred = forward(x)         #According to the feedforward requirementy_hat
    return (y_pred - y) ** 2    #计算损失


# 穷举法
w_list = []     #权重
mse_list = []   #The loss value corresponding to the weight
for w in np.arange(0.0, 4.1, 0.1):
    print("w=", w)
    l_sum = 0
    #从x_data, y_data取出x_val, y_val
    for x_val, y_val in zip(x_data, y_data):
        y_pred_val = forward(x_val)
        loss_val = loss(x_val, y_val)
        l_sum += loss_val
        print('x_val==', x_val, 'y_val==',y_val, 'y_pred_val==',y_pred_val,'loss_val==', loss_val)
    print('MSE=', l_sum / 3)
    w_list.append(w)
    mse_list.append(l_sum / 3)

#调用画图
plt.plot(w_list, mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
plt.show()

pattern trace

课后练习

实现线性模型（y=wx+b）并输出loss的3D图像
There are several issues that need to be addressed here

1.w,b的取值

in previous class practice,只需要取一个w,因此可以用for循环取值.Correction is required in the exercises after classw,bTwo values ​​for value operation,因此要使用meshgrid函数

一句话解释numpy.meshgrid()

2.Images cannot be displayed in Chinese

Add in front

from pylab import * mpl.rcParams[‘font.sans-serif’] = [‘SimHei’]

3.matplotlib 3D绘图警告

matplotlib 3D绘图警告
Code for homework exercises：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from pylab import *
mpl.rcParams['font.sans-serif'] = ['SimHei']
#Here the function is set to y=3x+2
x_data = [1.0,2.0,3.0]
y_data = [5.0,8.0,11.0]

def forward(x):
    return x * w + b

def loss(x,y):
    y_pred = forward(x)
    return (y_pred-y)*(y_pred-y)

mse_list = []
W=np.arange(0.0,4.1,0.1)
B=np.arange(0.0,4.1,0.1)

w,b=np.meshgrid(W,B)
# print("w==",w)
# print('b==',b)

l_sum = 0
for x_val, y_val in zip(x_data, y_data):
    y_pred_val = forward(x_val)
    loss_val = loss(x_val, y_val)
    print('x_val==', x_val,'\ny_val==', y_val,'\ny_pred_val==', y_pred_val, '\nloss_val==',loss_val)
    l_sum += loss_val

fig = plt.figure()
ax = Axes3D(fig,auto_add_to_figure=False)
fig.add_axes(ax)
ax.plot_surface(w, b, l_sum/3)
ax.set_xlabel("权重 W")
ax.set_ylabel("偏置项 B")
ax.set_zlabel("损失值")
plt.show()

3D图：