import torch

 import torch.utils.data as Data

 import torch.nn.functional as F

 import matplotlib.pyplot as plt

 import torch.optim

 # torch.manual_seed(1)    # reproducible

 LR = 0.01

 BATCH_SIZE = 32

 EPOCH = 12

 # fake dataset

 x = torch.unsqueeze(torch.linspace(-1, 1, 1000), dim=1)

 y = x.pow(2) + 0.1*torch.normal(torch.zeros(*x.size()))

 # plot dataset

 plt.scatter(x.numpy(), y.numpy())

 plt.show()

 # put dateset into torch dataset

 torch_dataset = Data.TensorDataset(x, y)

 loader = Data.DataLoader(dataset=torch_dataset, batch_size=BATCH_SIZE, shuffle=True, num_workers=2,)

 # default network

 class Net(torch.nn.Module):

     def __init__(self):

         super(Net, self).__init__()

         self.hidden = torch.nn.Linear(1, 20)   # hidden layer

         self.predict = torch.nn.Linear(20, 1)   # output layer

     def forward(self, x):

         x = F.relu(self.hidden(x))      # activation function for hidden layer

         x = self.predict(x)             # linear output

         return x

 if __name__ == '__main__':

     # different nets

     net_SGD         = Net()

     net_Momentum    = Net()

     net_RMSprop     = Net()

     net_Adam        = Net()

     nets = [net_SGD, net_Momentum, net_RMSprop, net_Adam]

     # different optimizers

     opt_SGD         = torch.optim.SGD(net_SGD.parameters(), lr=LR)

     opt_Momentum    = torch.optim.SGD(net_Momentum.parameters(), lr=LR, momentum=0.8)

     opt_RMSprop     = torch.optim.RMSprop(net_RMSprop.parameters(), lr=LR, alpha=0.9)

     opt_Adam        = torch.optim.Adam(net_Adam.parameters(), lr=LR, betas=(0.9, 0.99))

     optimizers = [opt_SGD, opt_Momentum, opt_RMSprop, opt_Adam]

     loss_func = torch.nn.MSELoss()

     losses_his = [[], [], [], []]   # record loss

     # training

     for epoch in range(EPOCH):

         print('Epoch: ', epoch)

         for step, (b_x, b_y) in enumerate(loader):          # for each training step

             for net, opt, l_his in zip(nets, optimizers, losses_his):

                 output = net(b_x)              # get output for every net

                 loss = loss_func(output, b_y)  # compute loss for every net

                 opt.zero_grad()                # clear gradients for next train

                 loss.backward()                # backpropagation, compute gradients

                 opt.step()                     # apply gradients

                 l_his.append(loss.data.numpy())     # loss recoder

     labels = ['SGD', 'Momentum', 'RMSprop', 'Adam']

     for i, l_his in enumerate(losses_his):

         plt.plot(l_his, label=labels[i])

     plt.legend(loc='best')

     plt.xlabel('Steps')

     plt.ylabel('Loss')

     plt.ylim((0, 0.2))

     plt.show()