测试1(y=3∗x1−4∗x2y=3*x_{1}-4*x_{2}y=3∗x1​−4∗x2​),lr=1e-2

%matplotlib inline
import torch
import numpy as np
torch.manual_seed(1)
from torch.nn import Linear
from torch.autograd import Variable
import torch.nn as nn
import random
np.random.seed(1)
random.seed(1)   #每次运行的结果都一样
torch.manual_seed(1) import torch
import matplotlib.pyplot as plt# x1 = torch.unsqueeze(torch.linspace(-1, 1, 200), dim=1)
# x2 = torch.unsqueeze(torch.linspace(-2, 2, 200), dim=1)
#x3 = torch.unsqueeze(torch.linspace(-2, 2, 100), dim=1)x1=torch.randn(200,1)
x2=torch.randn(200,1)y = 3*x1 -4*x2# # 画图
# plt.scatter(x.data.numpy(), y.data.numpy())
# plt.show()
# import numpy as np
# import matplotlib.pyplot as plt
# from mpl_toolkits import mplot3d# ax = plt.axes(projection='3d')
# ax.scatter3D(x1.data.numpy(), x2.data.numpy(),y.data.numpy())
# print(x1.size())
# print(x2.size())
# print(y.size())
#torch.cat((x1,x2),dim=1)#保持
class Net(nn.Module):#这里是大写的Moduledef __init__(self):super(Net,self).__init__()self.Linear=nn.Linear(2,1)#把线性层赋值给自己的属性def forward(self,x):#forward()是有两个参数的x=self.Linear(x)return x
model=Net()#网络
print(model)
criter=torch.nn.MSELoss()#损失函数#optimizer = torch.optim.SGD(model.parameters(), lr=1e-2)#优化器optimizer=torch.optim.Adam(model.parameters(),lr=1e-2)
#还需要一个DataGenerator()
num_epochs=1000
for i in range(num_epochs):#向前传播input=Variable(torch.cat((x1,x2),dim=1))target=Variable(y)out=model(input)#loss=criter(out,target)##向后传播optimizer.zero_grad()#梯度清0loss.backward()#反向传播optimizer.step()#更新梯度print("epoch=%d,loss=%.6f"%(i,loss.item()))
#model.eval()
print(model)
parm={}
for name,parameters in model.named_parameters():print(name,':',parameters.size())parm[name]=parameters.detach().numpy()
print(parm)

结果如下

可以看到这个结果是准确的，但是一定要注意迭代的次数不能太少，且学习率不能太低，否则不容易收敛到真值，从而怀疑是不是自己代码写错了

测试2(y=3∗x1−4∗x2y=3*x_{1}-4*x_{2}y=3∗x1​−4∗x2​,lr=1e-3)

%matplotlib inline
import torch
import numpy as np
torch.manual_seed(1)
from torch.nn import Linear
from torch.autograd import Variable
import torch.nn as nn
import random
np.random.seed(1)
random.seed(1)   #每次运行的结果都一样
torch.manual_seed(1) import torch
import matplotlib.pyplot as plt# x1 = torch.unsqueeze(torch.linspace(-1, 1, 200), dim=1)
# x2 = torch.unsqueeze(torch.linspace(-2, 2, 200), dim=1)
#x3 = torch.unsqueeze(torch.linspace(-2, 2, 100), dim=1)x1=torch.randn(200,1)
x2=torch.randn(200,1)y = 3*x1 -4*x2# # 画图
# plt.scatter(x.data.numpy(), y.data.numpy())
# plt.show()
# import numpy as np
# import matplotlib.pyplot as plt
# from mpl_toolkits import mplot3d# ax = plt.axes(projection='3d')
# ax.scatter3D(x1.data.numpy(), x2.data.numpy(),y.data.numpy())
# print(x1.size())
# print(x2.size())
# print(y.size())
#torch.cat((x1,x2),dim=1)#保持
class Net(nn.Module):#这里是大写的Moduledef __init__(self):super(Net,self).__init__()self.Linear=nn.Linear(2,1)#把线性层赋值给自己的属性def forward(self,x):#forward()是有两个参数的x=self.Linear(x)return x
model=Net()#网络
print(model)
criter=torch.nn.MSELoss()#损失函数#optimizer = torch.optim.SGD(model.parameters(), lr=1e-2)#优化器optimizer=torch.optim.Adam(model.parameters(),lr=1e-3)
#还需要一个DataGenerator()
num_epochs=1000
for i in range(num_epochs):#向前传播input=Variable(torch.cat((x1,x2),dim=1))target=Variable(y)out=model(input)#loss=criter(out,target)##向后传播optimizer.zero_grad()#梯度清0loss.backward()#反向传播optimizer.step()#更新梯度print("epoch=%d,loss=%.6f"%(i,loss.item()))
#model.eval()
print(model)
parm={}
for name,parameters in model.named_parameters():print(name,':',parameters.size())parm[name]=parameters.detach().numpy()
print(parm)
## 如果学习率过低，收敛很慢

结果如下

可以看到这里没有收敛的，

测试3($y=3\ast x+4$一元线性回归）

%matplotlib inline
import torch
import numpy as np
torch.manual_seed(1)
from torch.nn import Linear
from torch.autograd import Variable
import torch.nn as nn
import random
np.random.seed(1)
random.seed(1)   #每次运行的结果都一样
torch.manual_seed(1) import torch
import matplotlib.pyplot as pltx1=torch.randn(200,1)y = 3*x1 +4# # 画图
# plt.scatter(x.data.numpy(), y.data.numpy())
# plt.show()
# import numpy as np
# import matplotlib.pyplot as plt
# from mpl_toolkits import mplot3d# ax = plt.axes(projection='3d')
# ax.scatter3D(x1.data.numpy(), x2.data.numpy(),y.data.numpy())
# print(x1.size())
# print(x2.size())
# print(y.size())
#torch.cat((x1,x2),dim=1)#保持
class Net(nn.Module):#这里是大写的Moduledef __init__(self):super(Net,self).__init__()self.Linear=nn.Linear(1,1)#把线性层赋值给自己的属性def forward(self,x):#forward()是有两个参数的x=self.Linear(x)return x
model=Net()#网络
print(model)
criter=torch.nn.MSELoss()#损失函数#optimizer = torch.optim.SGD(model.parameters(), lr=1e-2)#优化器optimizer=torch.optim.Adam(model.parameters(),lr=1e-2)
#还需要一个DataGenerator()
num_epochs=1000
for i in range(num_epochs):#向前传播input=Variable(x1)target=Variable(y)out=model(input)#loss=criter(out,target)##向后传播optimizer.zero_grad()#梯度清0loss.backward()#反向传播optimizer.step()#更新梯度print("epoch=%d,loss=%.6f"%(i,loss.item()))
#model.eval()
print(model)
parm={}
for name,parameters in model.named_parameters():print(name,':',parameters.size())parm[name]=parameters.detach().numpy()
print(parm)

结果如下

测试4 $y=3\ast x+4$ 使用dataloader-batch_size=32

%matplotlib inline
import torch
import numpy as np
torch.manual_seed(1)
from torch.nn import Linear
from torch.autograd import Variable
from torch.utils.data import DataLoader, Dataset,TensorDataset
import torch.nn as nn
import random
np.random.seed(1)
random.seed(1)   #每次运行的结果都一样
torch.manual_seed(1) import torch
import matplotlib.pyplot as pltx1=torch.randn(200,1)y = 3*x1 +4# # 画图
# plt.scatter(x.data.numpy(), y.data.numpy())
# plt.show()
# import numpy as np
# import matplotlib.pyplot as plt
# from mpl_toolkits import mplot3d# ax = plt.axes(projection='3d')
# ax.scatter3D(x1.data.numpy(), x2.data.numpy(),y.data.numpy())
# print(x1.size())
# print(x2.size())
# print(y.size())
#torch.cat((x1,x2),dim=1)#保持
class Net(nn.Module):#这里是大写的Moduledef __init__(self):super(Net,self).__init__()self.Linear=nn.Linear(1,1)#把线性层赋值给自己的属性def forward(self,x):#forward()是有两个参数的x=self.Linear(x)return x
model=Net()#网络
print(model)
criter=torch.nn.MSELoss()#损失函数dataset = TensorDataset(torch.FloatTensor(x1),torch.FloatTensor(y))dataloader = DataLoader(dataset,batch_size = 32)#optimizer = torch.optim.SGD(model.parameters(), lr=1e-2)#优化器optimizer=torch.optim.Adam(model.parameters(),lr=1e-3)
#还需要一个DataGenerator()
num_epochs=1000
for epoch in range(num_epochs):#向前传播mse_loss=0for idx,(input_x,target_y) in enumerate(dataloader):input=Variable(input_x)target=Variable(target_y)out=model(input)#loss=criter(out,target)#mse_loss += loss.item()#向后传播optimizer.zero_grad()#梯度清0loss.backward()#反向传播optimizer.step()#更新梯度print("epoch={},mse loss ={}".format(epoch,mse_loss/len(dataloader)))
model.eval()
print(model)
parm={}
for name,parameters in model.named_parameters():print(name,':',parameters.size())parm[name]=parameters.detach().numpy()
print(parm)

可以看到使用batch_size进行训练时，也是可以得到准确的结果的

测试5($y=3\ast x1-4\ast x2+2.30$ dataloader,batch_size=32)

%matplotlib inline
import torch
import numpy as np
torch.manual_seed(1)
from torch.nn import Linear
from torch.autograd import Variable
from torch.utils.data import DataLoader, Dataset,TensorDataset
import torch.nn as nn
import random
np.random.seed(1)
random.seed(1)   #每次运行的结果都一样
torch.manual_seed(1) import torch
import matplotlib.pyplot as plt# x1 = torch.unsqueeze(torch.linspace(-1, 1, 200), dim=1)
# x2 = torch.unsqueeze(torch.linspace(-2, 2, 200), dim=1)
#x3 = torch.unsqueeze(torch.linspace(-2, 2, 100), dim=1)x1=torch.randn(200,1)
x2=torch.randn(200,1)y = 3*x1 -4*x2 + 2.30class Net(nn.Module):#这里是大写的Moduledef __init__(self):super(Net,self).__init__()self.Linear=nn.Linear(2,1)#把线性层赋值给自己的属性def forward(self,x):#forward()是有两个参数的x=self.Linear(x)return x
model=Net()#网络
print(model)
criter=torch.nn.MSELoss()#损失函数#optimizer = torch.optim.SGD(model.parameters(), lr=1e-2)#优化器optimizer=torch.optim.Adam(model.parameters(),lr=1e-2)
dataset = TensorDataset(torch.FloatTensor(x1),torch.FloatTensor(x2),torch.FloatTensor(y))
dataloader = DataLoader(dataset,batch_size = 32)#还需要一个DataGenerator()
num_epochs=1000
for epoch in range(num_epochs):mse_loss=0for idx,(input_x1,input_x2,target_y) in enumerate(dataloader):#向前传播input=Variable(torch.cat((input_x1,input_x2),dim=1))target=Variable(target_y)out=model(input)#loss=criter(out,target)#mse_loss += loss.item()#向后传播optimizer.zero_grad()#梯度清0loss.backward()#反向传播optimizer.step()#更新梯度print("epoch={},mse loss ={}".format(epoch,mse_loss/len(dataloader)))
#model.eval()
print(model)
parm={}
for name,parameters in model.named_parameters():print(name,':',parameters.size())parm[name]=parameters.detach().numpy()
print(parm)