text: #https://github.com/ctr4si/Hyperbolic-VAE-with-Ranking-Loss
  import argparse
  import torch
  import torch.utils.data
  from torch import nn, optim
  from torch.autograd import Variable
  from torch.nn import functional as F
  from torchvision import datasets, transforms
  from torchvision.utils import save_image
  import matplotlib
  
  matplotlib.use('Agg')
  import matplotlib.pyplot as plt
  import numpy as np
  import os
  
  dir_path = os.path.dirname(os.path.realpath(__file__))
  os.chdir(dir_path)
  
  parser = argparse.ArgumentParser(description='VAE MNIST Example')
  parser.add_argument('--batch-size', type=int, default=16, metavar='N',
                      help='input batch size for training (default: 128)')
  parser.add_argument('--epochs', type=int, default=10, metavar='N',
                      help='number of epochs to train (default: 10)')
  parser.add_argument('--no-cuda', action='store_true', default=False,
                      help='enables CUDA training')
  parser.add_argument('--seed', type=int, default=1, metavar='S',
                      help='random seed (default: 1)')
  parser.add_argument('--log-interval', type=int, default=10, metavar='N',
                      help='how many batches to wait before logging training status')
  args = parser.parse_args()
  
  args.cuda = (not args.no_cuda) and torch.cuda.is_available()
  
  torch.manual_seed(args.seed)
  if args.cuda:
      torch.cuda.manual_seed(args.seed)
  EPS = 1e-5
  
  kwargs = {'num_workers': 1, 'pin_memory': True} if args.cuda else {}
  train_loader = torch.utils.data.DataLoader(
      datasets.MNIST('../data', train=True, download=True,
                     transform=transforms.ToTensor()),
      batch_size=args.batch_size, shuffle=True, **kwargs)
  test_loader = torch.utils.data.DataLoader(
      datasets.MNIST('../data', train=False, transform=transforms.ToTensor()),
      batch_size=args.batch_size, shuffle=False, **kwargs)
  
  
  class encoder(nn.Module):
      def __init__(self):
          super(encoder, self).__init__()
  
          self.fc1 = nn.Linear(784, 400)
          self.fc21 = nn.Linear(400, 5)
          self.fc22 = nn.Linear(400, 5)
  
          self.relu = nn.ReLU()
          self.sigmoid = nn.Sigmoid()
  
      def encode(self, x):
          h1 = self.relu(self.fc1(x))
          return self.fc21(h1), self.fc22(h1)
  
      def reparameterize(self, mu, logvar):
          std = logvar.mul(0.5).exp_()
          eps = Variable(std.data.new(std.size()).normal_())
          return eps.mul(std).add_(mu), mu, logvar
  
      def forward(self, x):
          mu, logvar = self.encode(x.view(-1, 784))
          return self.reparameterize(mu, logvar)
  
  
  class decoder(nn.Module):
      def __init__(self):
          super(decoder, self).__init__()
  
          self.fc3 = nn.Linear(5, 400)
          self.fc4 = nn.Linear(400, 784)
  
          self.relu = nn.ReLU()
          self.sigmoid = nn.Sigmoid()
  
      def decode(self, z):
          h3 = self.relu(self.fc3(z))
          return self.sigmoid(self.fc4(h3))
  
      def forward(self, z):
          return self.decode(z)
  
  
  enc_ = encoder()
  dec_ = decoder()
  
  if args.cuda:
      enc_.cuda()
      dec_.cuda()
  
  
  def loss_function(recon_x, x, mu, logvar):
      BCE = F.binary_cross_entropy(recon_x, x.view(-1, 784))
  
      # see Appendix B from VAE paper:
      # Kingma and Welling. Auto-Encoding Variational Bayes. ICLR, 2014
      # https://arxiv.org/abs/1312.6114
      # 0.5 * sum(1 + log(sigma^2) - mu^2 - sigma^2)
      KLD = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())
      # Normalise by same number of elements as in reconstruction
      KLD /= args.batch_size * 784
  
      return BCE + KLD
  
  
  def proj(params):
      paramsy = params.clone()
      t_val = (params.norm(p=2, dim=1) ** 2 + 1).sqrt()
      for i in range(args.batch_size):
          paramsy[i] = params[i] / (1 + t_val[i])
      return paramsy
  
  
  def arcosh(x):
      return torch.log(x + torch.sqrt(x ** 2 - 1))
  
  
  def distance(u, v):
      uu = u.norm() ** 2
      vv = v.norm() ** 2
      u0 = (uu + 1)
      v0 = (vv + 1)
      d = arcosh(u0.sqrt() * v0.sqrt() - torch.dot(u, v))
      return d.clamp(min=EPS)
  
  
  
  def punisher(z, label):
      same_family = 0
      diff_family = 0
      for i, latent_1 in enumerate(z):
          for j, latent_2 in enumerate(z):
              if i >= j:
                  continue
              elif label[i] == label[j]:
                  same_family += torch.exp(-distance(latent_1, latent_2))
              else:
                  diff_family += torch.exp(-distance(latent_1, latent_2))
  
      return -torch.log(same_family) + torch.log(diff_family)
  
  
  optimizer_enc = optim.Adam(enc_.parameters(), lr=1e-3)
  optimizer_dec = optim.Adam(dec_.parameters(), lr=1e-3)
  
  
  def train(epoch):
      enc_.train()
      dec_.train()
      train_loss = 0
      logvar_sum = 0
      skipit = 0
      for batch_idx, (data, label) in enumerate(train_loader):
          go_skip=False
          data = Variable(data)
          if args.cuda:
              data = data.cuda()
          optimizer_enc.zero_grad()
          optimizer_dec.zero_grad()
          z, mu, logvar = enc_(data)
          recon_batch = dec_(z)
          loss = loss_function(recon_batch, data, mu, logvar)+0.1 * punisher(z, label)
          loss.backward()
  
          for i, ass in enumerate(enc_.parameters()):
              if ass.grad is None:
                  continue
              elif np.isnan(((ass.grad).data).numpy()).any():
                  go_skip=True
  
          if (not go_skip):
              train_loss += loss.data[0]
              logvar_sum += logvar.data[0]
              optimizer_enc.step()
              optimizer_dec.step()
          else:
              optimizer_enc.zero_grad()
              optimizer_dec.zero_grad()
              skipit+=1
          if batch_idx % args.log_interval == 0:
              print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                  epoch, batch_idx * len(data), len(train_loader.dataset),
                  100. * batch_idx / len(train_loader),
                  loss.data[0] / len(data)))
              print('Skip number : '+str(skipit))
              skipit=0
  
      print('====> Epoch: ' + str(epoch) + ' Average loss: ' + str(
          train_loss / len(train_loader.dataset)))
      print('====> Epoch: ' + str(epoch) + ' Average logvar: ' + str(
          logvar_sum / len(train_loader.dataset)))
      print(('====> Epoch: {} Average loss: {:.4f}').format(
          epoch, train_loss / len(train_loader.dataset)))
  
  
  def test(epoch):
      enc_.eval()
      dec_.eval()
      test_loss = 0
      for i, (data, label) in enumerate(test_loader):
          if args.cuda:
              data = data.cuda()
          data = Variable(data, volatile=True)
          z, mu, logvar = enc_(data)
          recon_batch = dec_(z)
          test_loss += loss_function(recon_batch, data, mu, logvar).data[0]
          test_loss += 0.1 * punisher(z, label).data[0]
          if i == 0:
              n = min(data.size(0), 8)
              comparison = torch.cat([data[:n],
                                      recon_batch.view(args.batch_size, 1, 28, 28)[:n]])
              save_image(comparison.data.cpu(),
                         'results_hyp/reconstruction_d5_' + str(epoch) + '.png', nrow=n)
  
      test_loss /= len(test_loader.dataset)
  
      print('<-------------TEST LOSS------------->')
      print(test_loss)
  
  
  
  for epoch in range(1, args.epochs + 1):
      train(epoch)
      test(epoch)
  