text: import math
  
  import torch
  import torch.nn as nn
  
  
  class PositionalEncoding(nn.Module):
  
      def __init__(self, d_model, dropout=0.1, max_len=5000):
          super(PositionalEncoding, self).__init__()
          self.dropout = nn.Dropout(p=dropout)
  
          pe = torch.zeros(max_len, d_model)
          position = torch.arange(0, max_len, dtype=torch.float).unsqueeze(1)
          div_term = torch.exp(torch.arange(0, d_model, 2).float() * (-math.log(10000.0) / d_model))
          pe[:, 0::2] = torch.sin(position * div_term)
          pe[:, 1::2] = torch.cos(position * div_term)
          pe = pe.unsqueeze(0).transpose(0, 1)
          self.register_buffer('pe', pe)
  
      def forward(self, x):
          x = x + self.pe[:x.size(0), :]
          return self.dropout(x)
  
  