num_train,num_test = 10,10
num_features = 200
true_w = torch.ones((num_features,1),dtype=torch.float32) * 0.01
true_b = torch.tensor(0.5)
samples = torch.normal(0,1,(num_train+num_test,num_features))
noise = torch.normal(0,0.01,(num_train+num_test,1))
labels = samples.matmul(true_w) + true_b + noise
train_samples, train_labels= samples[:num_train],labels[:num_train]
test_samples, test_labels = samples[num_train:],labels[num_train:]

def loss_function(predict,label,w,lambd):
 loss = (predict - label) ** 2
 loss = loss.mean() + lambd * (w**2).mean()
 return loss

def semilogy(x_val,y_val,x_label,y_label,x2_val,y2_val,legend):
 plt.figure(figsize=(3,3))
 plt.xlabel(x_label)
 plt.ylabel(y_label)
 plt.semilogy(x_val,y_val)
 if x2_val and y2_val:
  plt.semilogy(x2_val,y2_val)
  plt.legend(legend)
 plt.show()

def fit_and_plot(train_samples,train_labels,test_samples,test_labels,num_epoch,lambd):
 w = torch.normal(0,1,(train_samples.shape[-1],1),requires_grad=True)
 b = torch.tensor(0.,requires_grad=True)
 optimizer = torch.optim.Adam([w,b],lr=0.05)
 train_loss = []
 test_loss = []
 for epoch in range(num_epoch):
  predict = train_samples.matmul(w) + b
  epoch_train_loss = loss_function(predict,train_labels,w,lambd)
  optimizer.zero_grad()
  epoch_train_loss.backward()
  optimizer.step()
  test_predict = test_sapmles.matmul(w) + b
  epoch_test_loss = loss_function(test_predict,test_labels,w,lambd)
  train_loss.append(epoch_train_loss.item())
  test_loss.append(epoch_test_loss.item())
 semilogy(range(1,num_epoch+1),train_loss,'epoch','loss',range(1,num_epoch+1),test_loss,['train','test'])