content: # ------------------------------------------------------------------------
  # UP-DETR
  # Copyright (c) Tencent, Inc. and its affiliates. All Rights Reserved.
  # ------------------------------------------------------------------------
  # Modified from DETR (https://github.com/facebookresearch/detr)
  # Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved
  # ------------------------------------------------------------------------
  """
  Various positional encodings for the transformer.
  """
  import math
  import torch
  from torch import nn
  
  from util.misc import NestedTensor
  
  
  class PositionEmbeddingSine(nn.Module):
      """
      This is a more standard version of the position embedding, very similar to the one
      used by the Attention is all you need paper, generalized to work on images.
      """
      def __init__(self, num_pos_feats=64, temperature=10000, normalize=False, scale=None):
          super().__init__()
          self.num_pos_feats = num_pos_feats
          self.temperature = temperature
          self.normalize = normalize
          if scale is not None and normalize is False:
              raise ValueError("normalize should be True if scale is passed")
          if scale is None:
              scale = 2 * math.pi
          self.scale = scale
  
      def forward(self, tensor_list: NestedTensor):
          x = tensor_list.tensors
          mask = tensor_list.mask
          assert mask is not None
          not_mask = ~mask
          y_embed = not_mask.cumsum(1, dtype=torch.float32)
          x_embed = not_mask.cumsum(2, dtype=torch.float32)
          if self.normalize:
              eps = 1e-6
              y_embed = y_embed / (y_embed[:, -1:, :] + eps) * self.scale
              x_embed = x_embed / (x_embed[:, :, -1:] + eps) * self.scale
  
          dim_t = torch.arange(self.num_pos_feats, dtype=torch.float32, device=x.device)
          dim_t = self.temperature ** (2 * (dim_t // 2) / self.num_pos_feats)
  
          pos_x = x_embed[:, :, :, None] / dim_t
          pos_y = y_embed[:, :, :, None] / dim_t
          pos_x = torch.stack((pos_x[:, :, :, 0::2].sin(), pos_x[:, :, :, 1::2].cos()), dim=4).flatten(3)
          pos_y = torch.stack((pos_y[:, :, :, 0::2].sin(), pos_y[:, :, :, 1::2].cos()), dim=4).flatten(3)
          pos = torch.cat((pos_y, pos_x), dim=3).permute(0, 3, 1, 2)
          return pos
  
  
  class PositionEmbeddingLearned(nn.Module):
      """
      Absolute pos embedding, learned.
      """
      def __init__(self, num_pos_feats=256):
          super().__init__()
          self.row_embed = nn.Embedding(50, num_pos_feats)
          self.col_embed = nn.Embedding(50, num_pos_feats)
          self.reset_parameters()
  
      def reset_parameters(self):
          nn.init.uniform_(self.row_embed.weight)
          nn.init.uniform_(self.col_embed.weight)
  
      def forward(self, tensor_list: NestedTensor):
          x = tensor_list.tensors
          h, w = x.shape[-2:]
          i = torch.arange(w, device=x.device)
          j = torch.arange(h, device=x.device)
          x_emb = self.col_embed(i)
          y_emb = self.row_embed(j)
          pos = torch.cat([
              x_emb.unsqueeze(0).repeat(h, 1, 1),
              y_emb.unsqueeze(1).repeat(1, w, 1),
          ], dim=-1).permute(2, 0, 1).unsqueeze(0).repeat(x.shape[0], 1, 1, 1)
          return pos
  
  
  def build_position_encoding(args):
      N_steps = args.hidden_dim // 2
      if args.position_embedding in ('v2', 'sine'):
          # TODO find a better way of exposing other arguments
          position_embedding = PositionEmbeddingSine(N_steps, normalize=True)
      elif args.position_embedding in ('v3', 'learned'):
          position_embedding = PositionEmbeddingLearned(N_steps)
      else:
          raise ValueError(f"not supported {args.position_embedding}")
  
      return position_embedding
  