PyTorch 深度学习实践 第2讲

PyTorch 深度学习实践 第2讲
第2讲 linear_model 源代码

B站 刘二大人 ，传送门 PyTorch深度学习实践——线性模型

代码说明：

1、函数forward()中，有一个变量w。这个变量最终的值是从for循环中传入的。
2、for循环中，使用了np.arange。若对numpy不太熟悉，传送门Numpy数据计算从入门到实战
3、python中zip()函数的用法

import numpy as np
import matplotlib.pyplot as plt
 #数据集
x_data = [1.0, 2.0, 3.0]  # 输入的x
y_data = [2.0, 4.0, 6.0] # 输出的y
 
# 定义模型（前馈forward）
def forward(x):
    return x*w  # y_hat = x * w
 
 #定义损失函数
def loss(x, y):
    y_pred = forward(x) # y_hat = x * w
    return (y_pred - y)**2  # loss = (y_hat - y) ^ 2 = (x * w - y) ^ 2
    # 模型算出来的值和真实值之间的误差
 
 #存放权重和权重损失值对应的列表
 # 保存图像中x轴（权重）和y轴（损失）的值
# 穷举法
w_list = []
mse_list = []
#np.arange(0.0, 4.1, 0.1) w取值为0-4，间隔为0.1
for w in np.arange(0.0, 4.1, 0.1):
    print("w=", w)
    l_sum = 0
    # 把数据集里的数据取出来拼成x_val和y_val
    for x_val, y_val in zip(x_data, y_data):   # zip(x_data, y_data) zip函数：打包为元组的列表 # 结果：[(1.0, 2.0), (2.0, 4.0), (3.0, 6.0)]
        y_pred_val = forward(x_val)   # 计算 y_hat
        loss_val = loss(x_val, y_val)  # 计算 损失loss
        l_sum += loss_val  # 损失值求和
        print('\t', x_val, y_val, y_pred_val, loss_val)   # 输出x值、y值、y_hat和每组数据的损失值
    print('MSE=', l_sum/3)  # 求平均平方误差MSE（平均损失值，每组数据的损失值之和÷总数）
    
    w_list.append(w)   # 将每0.1存入列表中，作为x轴
    mse_list.append(l_sum/3)  # 对每个x轴上的值算整个数据集的平均平方误差MSE（平均损失值）
    
print(np.where(mse_matrix==np.min(mse_matrix))) #找到mse最小值的索引
# print(mse_matrix[5][20])
# print(w_matrix[5][20])
# print(b_matrix[5][20])

# 画出（x轴为权重，y轴为损失值）图像    
plt.plot(w_list,mse_list)  # x轴值、y轴值的列表
plt.ylabel('Loss')  # y轴名称
plt.xlabel('w')  # x轴名称
plt.show()    # 展示不同权重处的平均平方误差MSE（平均损失值）

#绘制三维图
fig = plt.figure()
ax = fig.gca(projection='3d')
plt.xlabel('w')
plt.ylabel('b')
ax.plot_surface(w_matrix, b_matrix, mse_matrix,rstride=1, cstride=1, cmap=cm.coolwarm,linewidth=0, antialiased=False)
plt.show()

输出结果：

w =  0.0
	 1.0 2.0 0.0 4.0
	 2.0 4.0 0.0 16.0
	 3.0 6.0 0.0 36.0
MSE =  18.666666666666668
w =  0.1
	 1.0 2.0 0.1 3.61
	 2.0 4.0 0.2 14.44
	 3.0 6.0 0.30000000000000004 32.49
MSE =  16.846666666666668
w =  0.2
	 1.0 2.0 0.2 3.24
	 2.0 4.0 0.4 12.96
	 3.0 6.0 0.6000000000000001 29.160000000000004
MSE =  15.120000000000003
w =  0.30000000000000004
	 1.0 2.0 0.30000000000000004 2.8899999999999997
	 2.0 4.0 0.6000000000000001 11.559999999999999
	 3.0 6.0 0.9000000000000001 26.009999999999998
MSE =  13.486666666666665
w =  0.4
	 1.0 2.0 0.4 2.5600000000000005
	 2.0 4.0 0.8 10.240000000000002
	 3.0 6.0 1.2000000000000002 23.04
MSE =  11.946666666666667
w =  0.5
	 1.0 2.0 0.5 2.25
	 2.0 4.0 1.0 9.0
	 3.0 6.0 1.5 20.25
MSE =  10.5
w =  0.6000000000000001
	 1.0 2.0 0.6000000000000001 1.9599999999999997
	 2.0 4.0 1.2000000000000002 7.839999999999999
	 3.0 6.0 1.8000000000000003 17.639999999999993
MSE =  9.146666666666663
w =  0.7000000000000001
	 1.0 2.0 0.7000000000000001 1.6899999999999995
	 2.0 4.0 1.4000000000000001 6.759999999999998
	 3.0 6.0 2.1 15.209999999999999
MSE =  7.886666666666666
w =  0.8
	 1.0 2.0 0.8 1.44
	 2.0 4.0 1.6 5.76
	 3.0 6.0 2.4000000000000004 12.959999999999997
MSE =  6.719999999999999
w =  0.9
	 1.0 2.0 0.9 1.2100000000000002
	 2.0 4.0 1.8 4.840000000000001
	 3.0 6.0 2.7 10.889999999999999
MSE =  5.646666666666666
w =  1.0
	 1.0 2.0 1.0 1.0
	 2.0 4.0 2.0 4.0
	 3.0 6.0 3.0 9.0
MSE =  4.666666666666667
w =  1.1
	 1.0 2.0 1.1 0.8099999999999998
	 2.0 4.0 2.2 3.2399999999999993
	 3.0 6.0 3.3000000000000003 7.289999999999998
MSE =  3.779999999999999
w =  1.2000000000000002
	 1.0 2.0 1.2000000000000002 0.6399999999999997
	 2.0 4.0 2.4000000000000004 2.5599999999999987
	 3.0 6.0 3.6000000000000005 5.759999999999997
MSE =  2.986666666666665
w =  1.3
	 1.0 2.0 1.3 0.48999999999999994
	 2.0 4.0 2.6 1.9599999999999997
	 3.0 6.0 3.9000000000000004 4.409999999999998
MSE =  2.2866666666666657
w =  1.4000000000000001
	 1.0 2.0 1.4000000000000001 0.3599999999999998
	 2.0 4.0 2.8000000000000003 1.4399999999999993
	 3.0 6.0 4.2 3.2399999999999993
MSE =  1.6799999999999995
w =  1.5
	 1.0 2.0 1.5 0.25
	 2.0 4.0 3.0 1.0
	 3.0 6.0 4.5 2.25
MSE =  1.1666666666666667
w =  1.6
	 1.0 2.0 1.6 0.15999999999999992
	 2.0 4.0 3.2 0.6399999999999997
	 3.0 6.0 4.800000000000001 1.4399999999999984
MSE =  0.746666666666666
w =  1.7000000000000002
	 1.0 2.0 1.7000000000000002 0.0899999999999999
	 2.0 4.0 3.4000000000000004 0.3599999999999996
	 3.0 6.0 5.1000000000000005 0.809999999999999
MSE =  0.4199999999999995
w =  1.8
	 1.0 2.0 1.8 0.03999999999999998
	 2.0 4.0 3.6 0.15999999999999992
	 3.0 6.0 5.4 0.3599999999999996
MSE =  0.1866666666666665
w =  1.9000000000000001
	 1.0 2.0 1.9000000000000001 0.009999999999999974
	 2.0 4.0 3.8000000000000003 0.0399999999999999
	 3.0 6.0 5.7 0.0899999999999999
MSE =  0.046666666666666586
w =  2.0
	 1.0 2.0 2.0 0.0
	 2.0 4.0 4.0 0.0
	 3.0 6.0 6.0 0.0
MSE =  0.0
w =  2.1
	 1.0 2.0 2.1 0.010000000000000018
	 2.0 4.0 4.2 0.04000000000000007
	 3.0 6.0 6.300000000000001 0.09000000000000043
MSE =  0.046666666666666835
w =  2.2
	 1.0 2.0 2.2 0.04000000000000007
	 2.0 4.0 4.4 0.16000000000000028
	 3.0 6.0 6.6000000000000005 0.36000000000000065
MSE =  0.18666666666666698
w =  2.3000000000000003
	 1.0 2.0 2.3000000000000003 0.09000000000000016
	 2.0 4.0 4.6000000000000005 0.36000000000000065
	 3.0 6.0 6.9 0.8100000000000006
MSE =  0.42000000000000054
w =  2.4000000000000004
	 1.0 2.0 2.4000000000000004 0.16000000000000028
	 2.0 4.0 4.800000000000001 0.6400000000000011
	 3.0 6.0 7.200000000000001 1.4400000000000026
MSE =  0.7466666666666679
w =  2.5
	 1.0 2.0 2.5 0.25
	 2.0 4.0 5.0 1.0
	 3.0 6.0 7.5 2.25
MSE =  1.1666666666666667
w =  2.6
	 1.0 2.0 2.6 0.3600000000000001
	 2.0 4.0 5.2 1.4400000000000004
	 3.0 6.0 7.800000000000001 3.2400000000000024
MSE =  1.6800000000000008
w =  2.7
	 1.0 2.0 2.7 0.49000000000000027
	 2.0 4.0 5.4 1.960000000000001
	 3.0 6.0 8.100000000000001 4.410000000000006
MSE =  2.2866666666666693
w =  2.8000000000000003
	 1.0 2.0 2.8000000000000003 0.6400000000000005
	 2.0 4.0 5.6000000000000005 2.560000000000002
	 3.0 6.0 8.4 5.760000000000002
MSE =  2.986666666666668
w =  2.9000000000000004
	 1.0 2.0 2.9000000000000004 0.8100000000000006
	 2.0 4.0 5.800000000000001 3.2400000000000024
	 3.0 6.0 8.700000000000001 7.290000000000005
MSE =  3.780000000000003
w =  3.0
	 1.0 2.0 3.0 1.0
	 2.0 4.0 6.0 4.0
	 3.0 6.0 9.0 9.0
MSE =  4.666666666666667
w =  3.1
	 1.0 2.0 3.1 1.2100000000000002
	 2.0 4.0 6.2 4.840000000000001
	 3.0 6.0 9.3 10.890000000000004
MSE =  5.646666666666668
w =  3.2
	 1.0 2.0 3.2 1.4400000000000004
	 2.0 4.0 6.4 5.760000000000002
	 3.0 6.0 9.600000000000001 12.96000000000001
MSE =  6.720000000000003
w =  3.3000000000000003
	 1.0 2.0 3.3000000000000003 1.6900000000000006
	 2.0 4.0 6.6000000000000005 6.7600000000000025
	 3.0 6.0 9.9 15.210000000000003
MSE =  7.886666666666668
w =  3.4000000000000004
	 1.0 2.0 3.4000000000000004 1.960000000000001
	 2.0 4.0 6.800000000000001 7.840000000000004
	 3.0 6.0 10.200000000000001 17.640000000000008
MSE =  9.14666666666667
w =  3.5
	 1.0 2.0 3.5 2.25
	 2.0 4.0 7.0 9.0
	 3.0 6.0 10.5 20.25
MSE =  10.5
w =  3.6
	 1.0 2.0 3.6 2.5600000000000005
	 2.0 4.0 7.2 10.240000000000002
	 3.0 6.0 10.8 23.040000000000006
MSE =  11.94666666666667
w =  3.7
	 1.0 2.0 3.7 2.8900000000000006
	 2.0 4.0 7.4 11.560000000000002
	 3.0 6.0 11.100000000000001 26.010000000000016
MSE =  13.486666666666673
w =  3.8000000000000003
	 1.0 2.0 3.8000000000000003 3.240000000000001
	 2.0 4.0 7.6000000000000005 12.960000000000004
	 3.0 6.0 11.4 29.160000000000004
MSE =  15.120000000000005
w =  3.9000000000000004
	 1.0 2.0 3.9000000000000004 3.610000000000001
	 2.0 4.0 7.800000000000001 14.440000000000005
	 3.0 6.0 11.700000000000001 32.49000000000001
MSE =  16.84666666666667
w =  4.0
	 1.0 2.0 4.0 4.0
	 2.0 4.0 8.0 16.0
	 3.0 6.0 12.0 36.0
MSE =  18.666666666666668

在第二节中的线性模型中，求解w的最优值（使得MSE最小的w）问题。
从图中可以看出：w=2时，MSE最小。（即最优）

前面mse的计算没有特别说明的，采用最小平方误差判别（MSE），对线性可分数据集和非线性可分数据集进行分类
注意使用plot_surface绘制三维图时，要求mse必须是二维数据，开始的思路是先用列表存储w,b和mse的值，再使用meshgrid()创建W和B，最后将mse转换为二维数据，但是这个过程中由于W和B是由生成的列表转化而来，不仅矩阵很大，而且数据的排列顺序发生变化，导致mse矩阵的生成比较麻烦(这里应该有好方法)，因此想到先将w和b也转化为二维，采用meshgrid()函数，直接用其中的值计算mse矩阵。（这里处理的比较笨，但还是能够完成任务的。）

W = np.arange(0, 4.1, 0.1)
B = np.arange(-0.5, 0.6, 0.1)
w_matrix, b_matrix = np.meshgrid(W, B)
mse_matrix = np.zeros([w_matrix.shape[0], w_matrix.shape[1]])

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D		# 3D绘图工具包

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

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(-2.0, 2.1, 0.1)
[w, b] = np.meshgrid(W, B)      # [X, Y] = np.meshgrid(x, y) 函数用两个坐标轴上的点在平面上画网格。

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)
    l_sum += loss_val
    print('\t', x_val, y_val, y_pred_val, loss_val)

fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(w, b, l_sum / 3, cmap='rainbow')    # 画曲面图---Axes3D.plot_surface(X, Y, Z)
ax.set_title('Cost Value')
ax.set_xlabel('w')
ax.set_ylabel('b')
ax.set_zlabel('loss')
plt.show()

本节课最后留的作业：https://blog.csdn.net/bit452/article/details/109627469

传送门 第二讲–线性模型（作业）