def test_partition_terms(inputs, dims, expected_num_components):
ring = LogRing()
symbol_to_size = dict(zip('abc', [2, 3, 4]))
shapes = [tuple(symbol_to_size[s] for s in input_) for input_ in inputs]
tensors = [torch.randn(shape) for shape in shapes]
for input_, tensor in zip(inputs, tensors):
tensor._pyro_dims = input_
components = list(_partition_terms(ring, tensors, dims))
# Check that result is a partition.
expected_terms = sorted(tensors, key=id)
actual_terms = sorted((x for c in components for x in c[0]), key=id)
assert actual_terms == expected_terms
assert dims == set.union(set(), *(c[1] for c in components))
# Check that the partition is not too coarse.
assert len(components) == expected_num_components
# Check that partition is not too fine.
component_dict = {x: i for i, (terms, _) in enumerate(components) for x in terms}
for x in tensors:
for y in tensors:
if x is not y:
if dims.intersection(x._pyro_dims, y._pyro_dims):
assert component_dict[x] == component_dict[y]
def contract_tensor_tree(tensor_tree, sum_dims, cache=None, ring=None):
"""
Contract out ``sum_dims`` in a tree of tensors via message passing.
This partially contracts out plate dimensions.
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 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 contracted version of ``tensor_tree``
:rtype: OrderedDict
"""
assert isinstance(tensor_tree, OrderedDict)
assert isinstance(sum_dims, set)
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_tree = OrderedDict()
# Split this tensor tree into connected components.
for terms, dims in _partition_terms(ring, all_terms, sum_dims):
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, set())
contracted_tree.setdefault(ordinal, []).append(term)
return contracted_tree
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_batch_dims_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)
