code: def _compute_model_factors(model_trace, guide_trace):
      # y depends on x iff ordering[x] <= ordering[y]
      # TODO refine this coarse dependency ordering using time.
      ordering = {
          name: _find_ordinal(trace, site)
          for trace in (model_trace, guide_trace)
          for name, site in trace.nodes.items()
          if site["type"] == "sample"
      }
  
      # Collect model sites that may have been enumerated in the model.
      cost_sites = OrderedDict()
      enum_sites = OrderedDict()
      enum_dims = set()
      non_enum_dims = set().union(*ordering.values())
      for name, site in model_trace.nodes.items():
          if site["type"] == "sample":
              if name in guide_trace.nodes:
                  cost_sites.setdefault(ordering[name], []).append(site)
                  non_enum_dims.update(
                      guide_trace.nodes[name]["packed"][
                          "log_prob"
                      ]._pyro_dims
                  )
              elif site["infer"].get("_enumerate_dim") is None:
                  cost_sites.setdefault(ordering[name], []).append(site)
              else:
                  enum_sites.setdefault(ordering[name], []).append(site)
                  enum_dims.update(
                      site["packed"]["log_prob"]._pyro_dims
                  )
      enum_dims -= non_enum_dims
      log_factors = OrderedDict()
      scale = 1
      if not enum_sites:
          marginal_costs = OrderedDict(
              (t, [site["packed"]["log_prob"] for site in sites_t])
              for t, sites_t in cost_sites.items()
          )
          return marginal_costs, log_factors, ordering, enum_dims, scale
      _check_model_guide_enumeration_constraint(enum_sites, guide_trace)
  
      # Marginalize out all variables that have been enumerated in the model.
      marginal_costs = OrderedDict()
      scales = []
      for t, sites_t in cost_sites.items():
          for site in sites_t:
              if enum_dims.isdisjoint(
                  site["packed"]["log_prob"]._pyro_dims
              ):
                  # For sites that do not depend on an enumerated variable, proceed as usual.
                  marginal_costs.setdefault(t, []).append(
                      site["packed"]["log_prob"]
                  )
              else:
                  # For sites that depend on an enumerated variable, we need to apply
                  # the mask inside- and the scale outside- of the log expectation.
                  if "masked_log_prob" not in site["packed"]:
                      site["packed"][
                          "masked_log_prob"
                      ] = packed.scale_and_mask(
                          site["packed"]["unscaled_log_prob"],
                          mask=site["packed"]["mask"],
                      )
                  cost = site["packed"]["masked_log_prob"]
                  log_factors.setdefault(t, []).append(cost)
                  scales.append(site["scale"])
      for t, sites_t in enum_sites.items():
          # TODO refine this coarse dependency ordering using time and tensor shapes.
          for site in sites_t:
              logprob = site["packed"]["unscaled_log_prob"]
              log_factors.setdefault(t, []).append(logprob)
              scales.append(site["scale"])
      scale = _get_common_scale(scales)
      return marginal_costs, log_factors, ordering, enum_dims, scale
  
imports: import queue
  import warnings
  import weakref
  from collections import OrderedDict
  import torch
  from opt_einsum import shared_intermediates
  import pyro
  import pyro.distributions
  import pyro.ops.jit
  import pyro.poutine
  from pyro.distributions.util import is_identically_zero
  from pyro.infer.elbo import ELBO
  from pyro.infer.enum import get_importance_trace, iter_discrete_escape, iter_discrete_extend
  from pyro.infer.util import Dice, is_validation_enabled
  from pyro.ops import packed
  from pyro.ops.contract import contract_tensor_tree, contract_to_tensor
  from pyro.ops.rings import SampleRing
  from pyro.poutine.enum_messenger import EnumMessenger
  from pyro.util import check_traceenum_requirements, ignore_jit_warnings, warn_if_nan
label_desc: Use image node_id 5 for calling a global function with example usage: _compute_model_factors(model_trace, guide_trace) and returns: marginal_costs,  log_factors,  ordering,  enum_dims,  scale, marginal_costs,  log_factors,  ordering,  enum_dims,  scale