text: #!/usr/bin/env python3
  # -*- coding: utf-8 -*-
  
  # Copyright 2019 Shigeki Karita
  #  Apache 2.0  (http://www.apache.org/licenses/LICENSE-2.0)
  
  """Positonal Encoding Module."""
  
  import math
  
  import torch
  
  
  def _pre_hook(
      state_dict,
      prefix,
      local_metadata,
      strict,
      missing_keys,
      unexpected_keys,
      error_msgs,
  ):
      """Perform pre-hook in load_state_dict for backward compatibility.
  
      Note:
          We saved self.pe until v.0.5.2 but we have omitted it later.
          Therefore, we remove the item "pe" from `state_dict` for backward compatibility.
  
      """
      k = prefix + "pe"
      if k in state_dict:
          state_dict.pop(k)
  
  
  class PositionalEncoding(torch.nn.Module):
      """Positional encoding.
  
      :param int d_model: embedding dim
      :param float dropout_rate: dropout rate
      :param int max_len: maximum input length
  
      """
  
      def __init__(self, d_model, dropout_rate, max_len=5000):
          """Construct an PositionalEncoding object."""
          super(PositionalEncoding, self).__init__()
          self.d_model = d_model
          self.xscale = math.sqrt(self.d_model)
          self.dropout = torch.nn.Dropout(p=dropout_rate)
          self.pe = None
          self.extend_pe(torch.tensor(0.0).expand(1, max_len))
          self._register_load_state_dict_pre_hook(_pre_hook)
  
      def extend_pe(self, x):
          """Reset the positional encodings."""
          if self.pe is not None:
              if self.pe.size(1) >= x.size(1):
                  if self.pe.dtype != x.dtype or self.pe.device != x.device:
                      self.pe = self.pe.to(dtype=x.dtype, device=x.device)
                  return
          pe = torch.zeros(x.size(1), self.d_model)
          position = torch.arange(0, x.size(1), dtype=torch.float32).unsqueeze(1)
          div_term = torch.exp(
              torch.arange(0, self.d_model, 2, dtype=torch.float32)
              * -(math.log(10000.0) / self.d_model)
          )
          pe[:, 0::2] = torch.sin(position * div_term)
          pe[:, 1::2] = torch.cos(position * div_term)
          pe = pe.unsqueeze(0)
          self.pe = pe.to(device=x.device, dtype=x.dtype)
  
      def forward(self, x: torch.Tensor):
          """Add positional encoding.
  
          Args:
              x (torch.Tensor): Input. Its shape is (batch, time, ...)
  
          Returns:
              torch.Tensor: Encoded tensor. Its shape is (batch, time, ...)
  
          """
          self.extend_pe(x)
          x = x * self.xscale + self.pe[:, : x.size(1)]
          return self.dropout(x)
  
      def forward_one_step(self, x: torch.Tensor, i=0):
          """Add positional encoding.
  
          Args:
              x (torch.Tensor): Input. Its shape is (batch, time, ...)
  
          Returns:
              torch.Tensor: Encoded tensor. Its shape is (batch, time, ...)
  
          """
          self.extend_pe(x)
          x = x * self.xscale + self.pe[:, i: i+x.size(1)]
          return self.dropout(x)
  
  class PositionalEncodingChunk(torch.nn.Module):
      """Positional encoding.
  
      :param int d_model: embedding dim
      :param float dropout_rate: dropout rate
      :param int max_len: maximum input length
  
      """
  
      def __init__(self, d_model, dropout_rate, max_len=5000):
          """Construct an PositionalEncoding object."""
          super(PositionalEncodingChunk, self).__init__()
          self.d_model = d_model
          self.xscale = math.sqrt(self.d_model)
          self.dropout = torch.nn.Dropout(p=dropout_rate)
          self.pe = None
          self.extend_pe(torch.tensor(0.0).expand(1,1, max_len))
          self._register_load_state_dict_pre_hook(_pre_hook)
  
      def extend_pe(self, x):
          """Reset the positional encodings."""
          if self.pe is not None:
              if self.pe.size(1) >= x.size(2):
                  if self.pe.dtype != x.dtype or self.pe.device != x.device:
                      self.pe = self.pe.to(dtype=x.dtype, device=x.device)
                  return
          pe = torch.zeros(x.size(2), self.d_model)
          position = torch.arange(0, x.size(2), dtype=torch.float32).unsqueeze(1)
          div_term = torch.exp(
              torch.arange(0, self.d_model, 2, dtype=torch.float32)
              * -(math.log(10000.0) / self.d_model)
          )
          pe[:, 0::2] = torch.sin(position * div_term)
          pe[:, 1::2] = torch.cos(position * div_term)
          pe = pe.unsqueeze(0)
          self.pe = pe.to(device=x.device, dtype=x.dtype)
  
      def forward(self, x: torch.Tensor):
          """Add positional encoding.
  
          Args:
              x (torch.Tensor): Input. Its shape is (batch, time, ...)
  
          Returns:
              torch.Tensor: Encoded tensor. Its shape is (batch, time, ...)
  
          """
          self.extend_pe(x)
          x = x * self.xscale + self.pe[:, : x.size(2)].unsqueeze(1)
          return self.dropout(x)
  
  class ScaledPositionalEncoding(PositionalEncoding):
      """Scaled positional encoding module.
  
      See also: Sec. 3.2  https://arxiv.org/pdf/1809.08895.pdf
  
      """
  
      def __init__(self, d_model, dropout_rate, max_len=5000):
          """Initialize class.
  
          :param int d_model: embedding dim
          :param float dropout_rate: dropout rate
          :param int max_len: maximum input length
  
          """
          super().__init__(d_model=d_model, dropout_rate=dropout_rate, max_len=max_len)
          self.alpha = torch.nn.Parameter(torch.tensor(1.0))
  
      def reset_parameters(self):
          """Reset parameters."""
          self.alpha.data = torch.tensor(1.0)
  
      def forward(self, x):
          """Add positional encoding.
  
          Args:
              x (torch.Tensor): Input. Its shape is (batch, time, ...)
  
          Returns:
              torch.Tensor: Encoded tensor. Its shape is (batch, time, ...)
  
          """
          self.extend_pe(x)
          x = x + self.alpha * self.pe[:, : x.size(1)]
          return self.dropout(x)
  