1. Implementation steps
1. Prepare data
x_data = torch.tensor([[1.0],[2.0],[3.0]])
y_data = torch.tensor([[2.0],[4.0],[6.0]])
2. Design model
class LinearModel(torch.nn.Module):
def __init__(self):
super(LinearModel,self).__init__()
self.linear = torch.nn.Linear(1,1)
def forward(self, x):
y_pred = self.linear(x)
return y_pred
model = LinearModel()
3. Construct the loss function and optimizer
criterion = torch.nn.MSELoss(reduction='sum')
optimizer = torch.optim.SGD(model.parameters(),lr=0.01)
4. Training process
epoch_list = []
loss_list = []
w_list = []
b_list = []
for epoch in range(1000):
y_pred = model(x_data) # 计算预测值
loss = criterion(y_pred, y_data) # 计算损失
print(epoch,loss)
epoch_list.append(epoch)
loss_list.append(loss.data.item())
w_list.append(model.linear.weight.item())
b_list.append(model.linear.bias.item())
optimizer.zero_grad() # 梯度归零
loss.backward() # 反向传播
optimizer.step() # 更新
5. Result display
Show the final weights and biases:
# 输出权重和偏置
print('w = ',model.linear.weight.item())
print('b = ',model.linear.bias.item())
The result is:
w = 1.9998501539230347
b = 0.0003405189490877092
Model test:
# 测试模型
x_test = torch.tensor([[4.0]])
y_test = model(x_test)
print('y_pred = ',y_test.data)
y_pred = tensor([[7.9997]])
Plot the 2D curve of the loss value as a function of the number of iterations and the 3D scatterplot of the loss as the weight and bias change:
# 二维曲线图
plt.plot(epoch_list,loss_list,'b')
plt.xlabel('epoch')
plt.ylabel('loss')
plt.show()
# 三维散点图
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(w_list,b_list,loss_list,c='r')
#设置坐标轴
ax.set_xlabel('weight')
ax.set_ylabel('bias')
ax.set_zlabel('loss')
plt.show()
The result is shown below:
