code: def to_hetero_with_bases(
      module: Module,
      metadata: Metadata,
      num_bases: int,
      in_channels: Optional[Dict[str, int]] = None,
      input_map: Optional[Dict[str, str]] = None,
      debug: bool = False,
  ) -> GraphModule:
      r"""Converts a homogeneous GNN model into its heterogeneous equivalent
      via the basis-decomposition technique introduced in the
      `"Modeling Relational Data with Graph Convolutional Networks"
      <https://arxiv.org/abs/1703.06103>`_ paper.
  
      For this, the heterogeneous graph is mapped to a typed homogeneous graph,
      in which its feature representations are aligned and grouped to a single
      representation.
      All GNN layers inside the model will then perform message passing via
      basis-decomposition regularization.
      This transformation is especially useful in highly multi-relational data,
      such that the number of parameters no longer depend on the number of
      relations of the input graph:
  
      .. code-block:: python
  
          import torch
          from torch_geometric.nn import SAGEConv, to_hetero_with_bases
  
          class GNN(torch.nn.Module):
              def __init__(self):
                  super().__init__()
                  self.conv1 = SAGEConv((16, 16), 32)
                  self.conv2 = SAGEConv((32, 32), 32)
  
              def forward(self, x, edge_index):
                  x = self.conv1(x, edge_index).relu()
                  x = self.conv2(x, edge_index).relu()
                  return x
  
          model = GNN()
  
          node_types = ['paper', 'author']
          edge_types = [
              ('paper', 'cites', 'paper'),
              ('paper', 'written_by', 'author'),
              ('author', 'writes', 'paper'),
          ]
          metadata = (node_types, edge_types)
  
          model = to_hetero_with_bases(model, metadata, num_bases=3,
                                       in_channels={'x': 16})
          model(x_dict, edge_index_dict)
  
      where :obj:`x_dict` and :obj:`edge_index_dict` denote dictionaries that
      hold node features and edge connectivity information for each node type and
      edge type, respectively.
      In case :obj:`in_channels` is given for a specific input argument, its
      heterogeneous feature information is first aligned to the given
      dimensionality.
  
      The below illustration shows the original computation graph of the
      homogeneous model on the left, and the newly obtained computation graph of
      the regularized heterogeneous model on the right:
  
      .. figure:: ../_figures/to_hetero_with_bases.svg
        :align: center
        :width: 90%
  
        Transforming a model via :func:`to_hetero_with_bases`.
  
      Here, each :class:`~torch_geometric.nn.conv.MessagePassing` instance
      :math:`f_{\theta}^{(\ell)}` is duplicated :obj:`num_bases` times and
      stored in a set :math:`\{ f_{\theta}^{(\ell, b)} : b \in \{ 1, \ldots, B \}
      \}` (one instance for each basis in
      :obj:`num_bases`), and message passing in layer :math:`\ell` is performed
      via
  
      .. math::
  
          \mathbf{h}^{(\ell)}_v = \sum_{r \in \mathcal{R}} \sum_{b=1}^B
          f_{\theta}^{(\ell, b)} ( \mathbf{h}^{(\ell - 1)}_v, \{
          a^{(\ell)}_{r, b} \cdot \mathbf{h}^{(\ell - 1)}_w :
          w \in \mathcal{N}^{(r)}(v) \}),
  
      where :math:`\mathcal{N}^{(r)}(v)` denotes the neighborhood of :math:`v \in
      \mathcal{V}` under relation :math:`r \in \mathcal{R}`.
      Notably, only the trainable basis coefficients :math:`a^{(\ell)}_{r, b}`
      depend on the relations in :math:`\mathcal{R}`.
  
      Args:
          module (torch.nn.Module): The homogeneous model to transform.
          metadata (Tuple[List[str], List[Tuple[str, str, str]]]): The metadata
              of the heterogeneous graph, *i.e.* its node and edge types given
              by a list of strings and a list of string triplets, respectively.
              See :meth:`torch_geometric.data.HeteroData.metadata` for more
              information.
          num_bases (int): The number of bases to use.
          in_channels (Dict[str, int], optional): A dictionary holding
              information about the desired input feature dimensionality of
              input arguments of :obj:`module.forward`.
              In case :obj:`in_channels` is given for a specific input argument,
              its heterogeneous feature information is first aligned to the given
              dimensionality.
              This allows handling of node and edge features with varying feature
              dimensionality across different types. (default: :obj:`None`)
          input_map (Dict[str, str], optional): A dictionary holding information
              about the type of input arguments of :obj:`module.forward`.
              For example, in case :obj:`arg` is a node-level argument, then
              :obj:`input_map['arg'] = 'node'`, and
              :obj:`input_map['arg'] = 'edge'` otherwise.
              In case :obj:`input_map` is not further specified, will try to
              automatically determine the correct type of input arguments.
              (default: :obj:`None`)
          debug (bool, optional): If set to :obj:`True`, will perform
              transformation in debug mode. (default: :obj:`False`)
      """
      transformer = ToHeteroWithBasesTransformer(
          module, metadata, num_bases, in_channels, input_map, debug
      )
      return transformer.transform()
  
imports: import copy
  import warnings
  from typing import Any, Dict, List, Optional, Union
  import torch
  from torch import Tensor
  from torch.nn import Module, Parameter
  from torch_geometric.nn.conv import MessagePassing
  from torch_geometric.nn.dense import Linear
  from torch_geometric.nn.fx import Transformer
  from torch_geometric.typing import EdgeType, Metadata, NodeType, SparseTensor
  from torch_geometric.utils.hetero import get_unused_node_types
label_desc: Use image node_id 1 for calling a global function with example usage: to_hetero_with_bases(module, metadata, num_bases, in_channels, input_map, debug) and returns: transformer