code: def _contract_component(ring, tensor_tree, sum_dims, target_dims):
      """
      Contract out ``sum_dims - target_dims`` in a tree of tensors in-place, via
      message passing. This reduces all tensors down to a single tensor in the
      minimum plate context.
  
      This function should be deterministic.
      This function has side-effects: it modifies ``tensor_tree``.
  
      :param pyro.ops.rings.Ring ring: an algebraic ring defining tensor
          operations.
      :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 set target_dims: An subset of ``sum_dims`` that should be preserved
          in the result.
      :return: a pair ``(ordinal, tensor)``
      :rtype: tuple of frozenset and torch.Tensor
      """
      # Group sum dims by ordinal.
      dim_to_ordinal = {}
      for t, terms in tensor_tree.items():
          for term in terms:
              for dim in sum_dims.intersection(term._pyro_dims):
                  dim_to_ordinal[dim] = dim_to_ordinal.get(dim, t) & t
      dims_tree = defaultdict(set)
      for dim, t in dim_to_ordinal.items():
          dims_tree[t].add(dim)
  
      # Recursively combine terms in different plate contexts.
      local_terms = []
      local_dims = target_dims.copy()
      local_ordinal = frozenset()
      min_ordinal = frozenset.intersection(*tensor_tree)
      while any(dims_tree.values()):
          # Arbitrarily deterministically choose a leaf.
          leaf = max(tensor_tree, key=len)
          leaf_terms = tensor_tree.pop(leaf)
          leaf_dims = dims_tree.pop(leaf, set())
  
          # Split terms at the current ordinal into connected components.
          for terms, dims in _partition_terms(
              ring, leaf_terms, leaf_dims
          ):
              # Eliminate sum dims via a sumproduct contraction.
              term = ring.sumproduct(terms, dims - local_dims)
  
              # Eliminate extra plate dims via product contractions.
              if leaf == min_ordinal:
                  parent = leaf
              else:
                  pending_dims = sum_dims.intersection(term._pyro_dims)
                  parent = frozenset.union(
                      *(
                          t
                          for t, d in dims_tree.items()
                          if d & pending_dims
                      )
                  )
                  _check_tree_structure(parent, leaf)
                  contract_frames = leaf - parent
                  contract_dims = dims & local_dims
                  if contract_dims:
                      term, local_term = ring.global_local(
                          term, contract_dims, contract_frames
                      )
                      local_terms.append(local_term)
                      local_dims |= sum_dims.intersection(
                          local_term._pyro_dims
                      )
                      local_ordinal |= leaf
                  else:
                      term = ring.product(term, contract_frames)
              tensor_tree.setdefault(parent, []).append(term)
  
      # Extract single tensor at root ordinal.
      assert len(tensor_tree) == 1
      ordinal, (term,) = tensor_tree.popitem()
      assert ordinal == min_ordinal
  
      # Perform optional localizing pass.
      if local_terms:
          assert target_dims
          local_terms.append(term)
          term = ring.sumproduct(local_terms, local_dims - target_dims)
          ordinal |= local_ordinal
  
      return ordinal, term
  
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 4 for calling a global function with example usage: _contract_component(ring, tensor_tree, sum_dims, target_dims) and returns: ordinal,  term