【PyTorch基础教程1】线性模型（学不会来打我啊）
文章目录
- 一、线性模型
- 二、绘图工具
- 三、作业
- Reference
一、线性模型
不要小看简单线性模型哈哈，虽然这讲我们还没正式用到pytorch，但是用到的前向传播、损失函数、两种绘loss图等方法在后面是很常用的。
对下面的代码说明：
zip函数可以将x_data和y_data组合元组列表，在for循环中每次遍历就是对于列表中的每个元组。- 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。
# -*- coding: utf-8 -*-
"""
Created on Tue Oct 12 14:30:13 2021
@author: 86493
"""
import numpy as np
import matplotlib.pyplot as plt
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
def forward(x):
return x * w
def loss(x, y):
y_pred = forward(x)
return (y_pred - y) * (y_pred - y)
# 保存权重
w_list = []
# 保存权重的损失函数值
mse_list = []
# 穷举w值对应的损失函数MSE
for w in np.arange(0.0, 4.1, 0.1):
print('w = ', w)
loss_sum = 0
for x_val, y_val in zip(x_data, y_data):
# 为了打印y预测值，其实loss里也计算了
y_pred_val = forward(x_val)
loss_val = loss(x_val, y_val)
loss_sum += loss_val
print('\t', x_val, y_val,
y_pred_val, loss_val)
print('MSE = ', loss_sum / 3)
print('='*60)
w_list.append(w)
mse_list.append(loss_sum / 3)
# 绘loss变化图，横坐标是w，纵坐标是loss
plt.plot(w_list, mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
plt.show()
刚才对应的打印结果为：
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
============================================================
二、绘图工具
在深度学习中，我们一般没有打印上面这种loss图（一般横坐标为epoch，而上面这种图可以用于检测最优超参数是多少），下图这里loss虽然随着epoch增大而减少，但是在开发集上的效果却可能是先减小后增大的，所以应该找中间这个画竖线的点。
PS：可以学习模型训练可视化visdom工具，训练还要注意存盘的问题（如防止要训练7天，但在第6天报错了）。
画图除了用matplotlib.pyplot，还经常使用pandas的dataframe.plot，如下：
# 增加loss折线图
import pandas as pd
df = pd.DataFrame(columns = ["Loss"]) # columns列名
df.index.name = "Epoch"
for epoch in range(1, 201):
loss = train()
#df.loc[epoch] = loss.item()
df.loc[epoch] = loss.item()
df.plot()
上面这种loss图也是最典型的.
三、作业
实现线性模型（ y = w x + b y=wx+b y=wx+b）并输出loss的3D图像。
# -*- coding: utf-8 -*-
"""
Created on Tue Oct 12 17:04:46 2021
@author: 86493
"""
import numpy as np
import matplotlib.pyplot as plt;
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
# 线性模型,多了个b
def forward(x,w,b):
return x * w + b
# 损失函数，此处没变
def loss(x, y, w, b):
y_pred = forward(x, w, b)
return (y_pred - y) * (y_pred - y)
# 单独写出mse函数，为了计算不同w和b情况下对应的mse
def mse(w,b):
l_sum = 0
for x_val, y_val in zip(x_data, y_data):
y_pred_val = forward(x_val,w,b)
loss_val = loss(x_val, y_val,w,b)
l_sum += loss_val
print('\t', x_val, y_val, y_pred_val, loss_val)
print('MSE=', l_sum / 3)
return l_sum/3
#迭代取值，计算每个w取值下的x，y，y_pred,loss_val
mse_list = []
# 画图
# 1.定义网格化数据
b_list=np.arange(-30,30,0.1)
w_list=np.arange(-30,30,0.1);
# 2.生成网格化数据
xx, yy = np.meshgrid(b_list, w_list, sparse=False, indexing='xy')
# 3.每个点的对应高度
zz=mse(xx,yy)
fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(xx, yy, zz,
rstride=1, # rows stride 指定行的跨度为1，只能是int
cstride=1, # columns stride 指定列的跨度为1
cmap=cm.viridis) # 设置曲面的颜色
plt.show()
Reference
[1] 3D图绘制：https://matplotlib.org/stable/tutorials/toolkits/mplot3d.html
[2] https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid
[3] Matplotlib3D作图-plot_surface(), .contourf(), plt.colorbar()
[4]【matplotlib】如何进行颜色设置选择cmap
[5] https://blog.csdn.net/Pin_BOY/article/details/119707358
[6] http://biranda.top/archives/page/2/