code: def contract_to_tensor(
      tensor_tree,
      sum_dims,
      target_ordinal=None,
      target_dims=None,
      cache=None,
      ring=None,
  ):
      """
      Contract out ``sum_dims`` in a tree of tensors, via message
      passing. This reduces all terms down to a single tensor in the plate
      context specified by ``target_ordinal``, optionally preserving sum
      dimensions ``target_dims``.
  
      This function should be deterministic and free of side effects.
  
      :param OrderedDict tensor_tree: a dictionary mapping ordinals to lists of
          tensors. An ordinal is a frozenset of ``CondIndepStack`` frames.
      :param set sum_dims: the complete set of sum-contractions dimensions
          (indexed from the right). This is needed to distinguish sum-contraction
          dimensions from product-contraction dimensions.
      :param frozenset target_ordinal: An optional ordinal to which the result
          will be contracted or broadcasted.
      :param set target_dims: An optional subset of ``sum_dims`` that should be
          preserved in the result.
      :param dict cache: an optional :func:`~opt_einsum.shared_intermediates`
          cache.
      :param pyro.ops.rings.Ring ring: an optional algebraic ring defining tensor
          operations.
      :returns: a single tensor
      :rtype: torch.Tensor
      """
      if target_ordinal is None:
          target_ordinal = frozenset()
      if target_dims is None:
          target_dims = set()
      assert isinstance(tensor_tree, OrderedDict)
      assert isinstance(sum_dims, set)
      assert isinstance(target_ordinal, frozenset)
      assert isinstance(target_dims, set) and target_dims <= sum_dims
      if ring is None:
          ring = LogRing(cache)
  
      ordinals = {
          term: t for t, terms in tensor_tree.items() for term in terms
      }
      all_terms = [
          term for terms in tensor_tree.values() for term in terms
      ]
      contracted_terms = []
  
      # Split this tensor tree into connected components.
      modulo_total = bool(target_dims)
      for terms, dims in _partition_terms(ring, all_terms, sum_dims):
          if modulo_total and dims.isdisjoint(target_dims):
              continue
          component = OrderedDict()
          for term in terms:
              component.setdefault(ordinals[term], []).append(term)
  
          # Contract this connected component down to a single tensor.
          ordinal, term = _contract_component(
              ring, component, dims, target_dims & dims
          )
          _check_plates_are_sensible(
              target_dims.intersection(term._pyro_dims),
              ordinal - target_ordinal,
          )
  
          # Eliminate extra plate dims via product contractions.
          contract_frames = ordinal - target_ordinal
          if contract_frames:
              assert not sum_dims.intersection(term._pyro_dims)
              term = ring.product(term, contract_frames)
  
          contracted_terms.append(term)
  
      # Combine contracted tensors via product, then broadcast.
      term = ring.sumproduct(contracted_terms, set())
      assert sum_dims.intersection(term._pyro_dims) <= target_dims
      return ring.broadcast(term, target_ordinal)
  
imports: import itertools
  import warnings
  from collections import OrderedDict, defaultdict
  import opt_einsum
  import torch
  from opt_einsum import shared_intermediates
  from pyro.ops.rings import BACKEND_TO_RING, LogRing
  from pyro.util import ignore_jit_warnings
label_desc: Use image node_id 6 for calling a global function with example usage: contract_to_tensor(tensor_tree, sum_dims, target_ordinal, target_dims, cache, ring) and returns: ring