code: def optimize_for_inference(
      model: torch.nn.Module,
      pass_config: Optional[Dict[str, Any]] = None,
      tracer: Type[fx.Tracer] = fx.Tracer,
  ) -> torch.nn.Module:
      """
      Performs a set of optimization passes to optimize a model for the
      purposes of inference. Specifically, the passes that are run are:
      1. Conv/BN fusion
      2. Dropout removal
      3. MKL layout optimizations
  
      The third optimization takes a function `use_mkl_heuristic` that's used
      to determine whether a subgraph should be explicitly run in MKL layout.
  
      Note: As FX does not currently handle aliasing, this pass currently
      assumes nothing aliases. If that isn't true, use at your own risk.
      """
      default_pass_config = {
          "conv_bn_fuse": True,
          "remove_dropout": True,
          "mkldnn_layout_optimize": {"heuristic": use_mkl_length},
      }
      if pass_config is None:
          pass_config = {}
      default_pass_config.update(pass_config)
  
      if default_pass_config["conv_bn_fuse"]:
          model = fuse(model)
      if default_pass_config["remove_dropout"]:
          model = remove_dropout(model)
      if default_pass_config["mkldnn_layout_optimize"] is False:
          return model
      if not isinstance(
          default_pass_config["mkldnn_layout_optimize"], dict
      ):
          raise RuntimeError(
              "mkldnn_layout_optimize config is not a dict"
          )
      if (
          "heuristic"
          not in default_pass_config["mkldnn_layout_optimize"]
      ):
          raise RuntimeError(
              "Heuristic not found in mkldnn_layout_optimize config"
          )
      use_mkl_heuristic = default_pass_config["mkldnn_layout_optimize"][
          "heuristic"
      ]
  
      cur_tracer = tracer()
      fx_graph = cur_tracer.trace(copy.deepcopy(model))
      fx_model = fx.GraphModule(cur_tracer.root, fx_graph)
      modules: Dict[str, nn.Module] = dict(model.named_modules())
  
      class MklSupport(Enum):
          NO = 1
          YES = 2
          UNKNOWN = 3
  
      # Inserts to_mkldnn and to_dense around every node we want to be a MKLDNN node.
      # If the op is in `mkldnn_supported` then we always treat it as a MKLDNN node.
      # However, if it's in `mkldnn_supported_unknown`, then we only treat it as
      # a MKLDNN node if its inputs are MKLDNN nodes.
      for node in list(fx_graph.nodes):
          supports_mkldnn = MklSupport.NO
          if node.op == "call_module":
              cur_module = modules[node.target]
              if type(cur_module) in mkldnn_supported:
                  supports_mkldnn = MklSupport.YES
                  sample_parameter = next(cur_module.parameters(), None)
                  if sample_parameter is not None:
                      assert (
                          sample_parameter.dtype == torch.float
                      ), "this pass is only for torch.float modules"
                      assert sample_parameter.device == torch.device(
                          "cpu"
                      ), "this pass is only for CPU modules"
          elif node.op == "call_function":
              if node.target in mkldnn_supported:
                  supports_mkldnn = MklSupport.YES
              elif node.target in mkldnn_supported_unknown:
                  supports_mkldnn = MklSupport.UNKNOWN
  
          if supports_mkldnn != MklSupport.NO:
              if supports_mkldnn == MklSupport.UNKNOWN:
                  if not any(
                      arg.target == "to_dense" for arg in node.args
                  ):
                      continue
              with fx_graph.inserting_before(node):
                  mkldnn_args = fx.map_arg(
                      node.args,
                      lambda n: fx_graph.call_method("to_mkldnn", (n,)),
                  )
  
              node.args = cast(Tuple[fx.node.Argument], mkldnn_args)
  
              with fx_graph.inserting_after(node):
                  dense_x = fx_graph.create_node(
                      "call_method", "to_dense", (node,)
                  )
                  node.replace_all_uses_with(dense_x)
                  dense_x.args = (node,)
  
      # Does pre-conversion of all modules into MKLDNN (when possible)
      old_modules = modules_to_mkldnn(list(fx_graph.nodes), modules)
      fx_graph.old_modules = old_modules  # type: ignore[attr-defined]
  
      # optimizes all a -> to_dense -> to_mkldnn -> b patterns into a -> b
      for node in fx_graph.nodes:
          if node.op == "call_method" and node.target == "to_dense":
              prv_node = node.args[0]
              users = list(node.users)
              for user in users:
                  if (
                      user.op == "call_method"
                      and user.target == "to_mkldnn"
                  ):
                      user.replace_all_uses_with(prv_node)
                      fx_graph.erase_node(user)
              if len(node.users) == 0:
                  fx_graph.erase_node(node)
  
      num_nodes = len(fx_graph.nodes)
      uf = UnionFind(num_nodes)
  
      def get_color(n):
          if hasattr(
              n, "color"
          ):  # Current node is part of a MKL subgraph
              return uf.find(n.color)
          if hasattr(
              n, "start_color"
          ):  # Current node is input to MKL subgraph
              return uf.find(n.start_color)
          return None
  
      # This code is to find each MKLDNN subgraph. Each MKLDNN subgraph consists
      # of input nodes (which are only `to_mkldnn` calls), output nodes
      # (`to_dense` calls), and intermediate nodes, which are run entirely on
      # MKLDNN layout tensors.
      #
      # Specifically, this code does a flood fill on a directed acyclic graph
      # (DAG), starting from each possible "start node" (i.e: `to_mkldnn` nodes).
      # If every node only had one input, this would be sufficient. However, in
      # the case that a node has multiple inputs coming from different start
      # nodes (i.e. colors), we need to join these 2 colors into 1. That's done
      # using a Disjoint Set Union.
      for cur_idx, node in enumerate(fx_graph.nodes):
          if node.op == "call_method" and node.target == "to_mkldnn":
              node.start_color = cur_idx
              uf.make_set(cur_idx)
          elif node.op == "call_method" and node.target == "to_dense":
              assert get_color(node.args[0]) is not None
              node.end_color = get_color(node.args[0])
          else:
              cur_colors = [
                  get_color(i)
                  for i in node.all_input_nodes
                  if isinstance(i, fx.Node)
                  if get_color(i) is not None
              ]
  
              if len(cur_colors) == 0:
                  continue
              assert not any(i is None for i in cur_colors)
              cur_colors = sorted(cur_colors)
              node.color = cur_colors[0]
              for other_color in cur_colors[1:]:
                  uf.join(cur_colors[0], other_color)
  
      mkldnn_graphs: Dict[int, MklSubgraph] = defaultdict(
          lambda: MklSubgraph(fx_graph)
      )
      for node in fx_graph.nodes:
          if hasattr(node, "color"):
              mkldnn_graphs[uf.find(node.color)].nodes.append(node)
          if hasattr(node, "start_color"):
              mkldnn_graphs[
                  uf.find(node.start_color)
              ].start_nodes.append(node)
          if hasattr(node, "end_color"):
              mkldnn_graphs[uf.find(node.end_color)].end_nodes.append(
                  node
              )
  
      # Now that we have all the subgraphs, we need to decide which MKLDNN
      # subgraphs we actually want to keep in MKLDNN.
      for graph in mkldnn_graphs.values():
          if not use_mkl_heuristic(graph):
              for node in graph.start_nodes + graph.end_nodes:
                  prv = node.args[0]
                  node.replace_all_uses_with(prv)
                  fx_graph.erase_node(node)
              reset_modules(graph.nodes, modules, old_modules)
  
      mkldnn_conversions = 0
      for node in fx_graph.nodes:
          if node.target == "to_mkldnn" or node.target == "to_dense":
              mkldnn_conversions += 1
  
      logging.getLogger(__name__).info(
          f"mkldnn conversions: {mkldnn_conversions}"
      )
      fx_graph.lint()
      result = fx.GraphModule(model, fx_graph)
      return result
  
imports: import torch.fx
  from torch.fx.node import Argument, Target
  from torch.nn.utils.fusion import fuse_conv_bn_eval
  from typing import Type, Dict, Any, Tuple, Iterable, Optional, List, cast
  import torch
  import torch.nn
  import torch.nn.functional
  from torch.fx.passes.shape_prop import ShapeProp
  import copy
  from collections import defaultdict
  import torch.utils.mkldnn
  import operator
  import time
  import logging
  from enum import Enum
label_desc: Use image node_id 11 for calling a global function with example usage: optimize_for_inference(model, pass_config, tracer) and returns: result, model, None, uf, uf