code: def to_dense_batch(
      x: Tensor,
      batch: Optional[Tensor] = None,
      fill_value: float = 0.0,
      max_num_nodes: Optional[int] = None,
      batch_size: Optional[int] = None,
  ) -> Tuple[Tensor, Tensor]:
      r"""Given a sparse batch of node features
      :math:`\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times F}` (with
      :math:`N_i` indicating the number of nodes in graph :math:`i`), creates a
      dense node feature tensor
      :math:`\mathbf{X} \in \mathbb{R}^{B \times N_{\max} \times F}` (with
      :math:`N_{\max} = \max_i^B N_i`).
      In addition, a mask of shape :math:`\mathbf{M} \in \{ 0, 1 \}^{B \times
      N_{\max}}` is returned, holding information about the existence of
      fake-nodes in the dense representation.
  
      Args:
          x (Tensor): Node feature matrix
              :math:`\mathbf{X} \in \mathbb{R}^{(N_1 + \ldots + N_B) \times F}`.
          batch (LongTensor, optional): Batch vector
              :math:`\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N`, which assigns each
              node to a specific example. Must be ordered. (default: :obj:`None`)
          fill_value (float, optional): The value for invalid entries in the
              resulting dense output tensor. (default: :obj:`0`)
          max_num_nodes (int, optional): The size of the output node dimension.
              (default: :obj:`None`)
          batch_size (int, optional): The batch size. (default: :obj:`None`)
  
      :rtype: (:class:`Tensor`, :class:`BoolTensor`)
  
      Examples:
          >>> x = torch.arange(12).view(6, 2)
          >>> x
          tensor([[ 0,  1],
                  [ 2,  3],
                  [ 4,  5],
                  [ 6,  7],
                  [ 8,  9],
                  [10, 11]])
  
          >>> out, mask = to_dense_batch(x)
          >>> mask
          tensor([[True, True, True, True, True, True]])
  
          >>> batch = torch.tensor([0, 0, 1, 2, 2, 2])
          >>> out, mask = to_dense_batch(x, batch)
          >>> out
          tensor([[[ 0,  1],
                  [ 2,  3],
                  [ 0,  0]],
                  [[ 4,  5],
                  [ 0,  0],
                  [ 0,  0]],
                  [[ 6,  7],
                  [ 8,  9],
                  [10, 11]]])
          >>> mask
          tensor([[ True,  True, False],
                  [ True, False, False],
                  [ True,  True,  True]])
  
          >>> out, mask = to_dense_batch(x, batch, max_num_nodes=4)
          >>> out
          tensor([[[ 0,  1],
                  [ 2,  3],
                  [ 0,  0],
                  [ 0,  0]],
                  [[ 4,  5],
                  [ 0,  0],
                  [ 0,  0],
                  [ 0,  0]],
                  [[ 6,  7],
                  [ 8,  9],
                  [10, 11],
                  [ 0,  0]]])
  
          >>> mask
          tensor([[ True,  True, False, False],
                  [ True, False, False, False],
                  [ True,  True,  True, False]])
      """
      if batch is None and max_num_nodes is None:
          mask = torch.ones(
              1, x.size(0), dtype=torch.bool, device=x.device
          )
          return x.unsqueeze(0), mask
  
      if batch is None:
          batch = x.new_zeros(x.size(0), dtype=torch.long)
  
      if batch_size is None:
          batch_size = int(batch.max()) + 1
  
      num_nodes = scatter(
          batch.new_ones(x.size(0)),
          batch,
          dim=0,
          dim_size=batch_size,
          reduce="sum",
      )
      cum_nodes = cumsum(num_nodes)
  
      filter_nodes = False
      dynamic_shapes_disabled = is_experimental_mode_enabled(
          "disable_dynamic_shapes"
      )
  
      if max_num_nodes is None:
          max_num_nodes = int(num_nodes.max())
      elif (
          not dynamic_shapes_disabled
          and num_nodes.max() > max_num_nodes
      ):
          filter_nodes = True
  
      tmp = (
          torch.arange(batch.size(0), device=x.device)
          - cum_nodes[batch]
      )
      idx = tmp + (batch * max_num_nodes)
      if filter_nodes:
          mask = tmp < max_num_nodes
          x, idx = x[mask], idx[mask]
  
      size = [batch_size * max_num_nodes] + list(x.size())[1:]
      out = torch.as_tensor(fill_value, device=x.device)
      out = out.to(x.dtype).repeat(size)
      out[idx] = x
      out = out.view([batch_size, max_num_nodes] + list(x.size())[1:])
  
      mask = torch.zeros(
          batch_size * max_num_nodes, dtype=torch.bool, device=x.device
      )
      mask[idx] = 1
      mask = mask.view(batch_size, max_num_nodes)
  
      return out, mask
  
imports: from typing import Optional, Tuple
  import torch
  from torch import Tensor
  from torch_geometric.experimental import disable_dynamic_shapes, is_experimental_mode_enabled
  from torch_geometric.utils import cumsum, scatter
label_desc: Use image node_id 1 for calling a global function with example usage: to_dense_batch(x, batch, fill_value, max_num_nodes, batch_size) and returns: out,  mask, x,  mask