Source code for apache_beam.transforms.combiners

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"""A library of basic combiner PTransform subclasses."""

# pytype: skip-file

import copy
import heapq
import itertools
import operator
import random
from typing import Any
from typing import Dict
from typing import Iterable
from typing import List
from typing import Set
from typing import Tuple
from typing import TypeVar
from typing import Union

from apache_beam import typehints
from apache_beam.transforms import core
from apache_beam.transforms import cy_combiners
from apache_beam.transforms import ptransform
from apache_beam.transforms import window
from apache_beam.transforms.display import DisplayDataItem
from apache_beam.typehints import with_input_types
from apache_beam.typehints import with_output_types
from apache_beam.utils.timestamp import Duration
from apache_beam.utils.timestamp import Timestamp

__all__ = [
    'Count', 'Mean', 'Sample', 'Top', 'ToDict', 'ToList', 'ToSet', 'Latest'
]

# Type variables
T = TypeVar('T')
K = TypeVar('K')
V = TypeVar('V')
TimestampType = Union[int, float, Timestamp, Duration]


class CombinerWithoutDefaults(ptransform.PTransform):
  """Super class to inherit without_defaults to built-in Combiners."""
  def __init__(self, has_defaults=True):
    super().__init__()
    self.has_defaults = has_defaults

  def with_defaults(self, has_defaults=True):
    new = copy.copy(self)
    new.has_defaults = has_defaults
    return new

  def without_defaults(self):
    return self.with_defaults(False)


[docs]class Mean(object): """Combiners for computing arithmetic means of elements."""
[docs] class Globally(CombinerWithoutDefaults): """combiners.Mean.Globally computes the arithmetic mean of the elements."""
[docs] def expand(self, pcoll): if self.has_defaults: return pcoll | core.CombineGlobally(MeanCombineFn()) else: return pcoll | core.CombineGlobally(MeanCombineFn()).without_defaults()
[docs] class PerKey(ptransform.PTransform): """combiners.Mean.PerKey finds the means of the values for each key."""
[docs] def expand(self, pcoll): return pcoll | core.CombinePerKey(MeanCombineFn())
# TODO(laolu): This type signature is overly restrictive. This should be # more general. @with_input_types(Union[float, int]) @with_output_types(float) class MeanCombineFn(core.CombineFn): """CombineFn for computing an arithmetic mean.""" def create_accumulator(self): return (0, 0) def add_input(self, sum_count, element): (sum_, count) = sum_count return sum_ + element, count + 1 def merge_accumulators(self, accumulators): sums, counts = zip(*accumulators) return sum(sums), sum(counts) def extract_output(self, sum_count): (sum_, count) = sum_count if count == 0: return float('NaN') return sum_ / float(count) def for_input_type(self, input_type): if input_type is int: return cy_combiners.MeanInt64Fn() elif input_type is float: return cy_combiners.MeanFloatFn() return self
[docs]class Count(object): """Combiners for counting elements."""
[docs] class Globally(CombinerWithoutDefaults): """combiners.Count.Globally counts the total number of elements."""
[docs] def expand(self, pcoll): if self.has_defaults: return pcoll | core.CombineGlobally(CountCombineFn()) else: return pcoll | core.CombineGlobally(CountCombineFn()).without_defaults()
[docs] class PerKey(ptransform.PTransform): """combiners.Count.PerKey counts how many elements each unique key has."""
[docs] def expand(self, pcoll): return pcoll | core.CombinePerKey(CountCombineFn())
[docs] class PerElement(ptransform.PTransform): """combiners.Count.PerElement counts how many times each element occurs."""
[docs] def expand(self, pcoll): paired_with_void_type = typehints.Tuple[pcoll.element_type, Any] output_type = typehints.KV[pcoll.element_type, int] return ( pcoll | ( '%s:PairWithVoid' % self.label >> core.Map( lambda x: (x, None)).with_output_types(paired_with_void_type)) | core.CombinePerKey(CountCombineFn()).with_output_types(output_type))
@with_input_types(Any) @with_output_types(int) class CountCombineFn(core.CombineFn): """CombineFn for computing PCollection size.""" def create_accumulator(self): return 0 def add_input(self, accumulator, element): return accumulator + 1 def add_inputs(self, accumulator, elements): return accumulator + len(list(elements)) def merge_accumulators(self, accumulators): return sum(accumulators) def extract_output(self, accumulator): return accumulator
[docs]class Top(object): """Combiners for obtaining extremal elements.""" # pylint: disable=no-self-argument
[docs] @with_input_types(T) @with_output_types(List[T]) class Of(CombinerWithoutDefaults): """Obtain a list of the compare-most N elements in a PCollection. This transform will retrieve the n greatest elements in the PCollection to which it is applied, where "greatest" is determined by the comparator function supplied as the compare argument. """ def __init__(self, n, key=None, reverse=False): """Creates a global Top operation. The arguments 'key' and 'reverse' may be passed as keyword arguments, and have the same meaning as for Python's sort functions. Args: n: number of elements to extract from pcoll. key: (optional) a mapping of elements to a comparable key, similar to the key argument of Python's sorting methods. reverse: (optional) whether to order things smallest to largest, rather than largest to smallest """ super().__init__() self._n = n self._key = key self._reverse = reverse
[docs] def default_label(self): return 'Top(%d)' % self._n
[docs] def expand(self, pcoll): if pcoll.windowing.is_default(): # This is a more efficient global algorithm. top_per_bundle = pcoll | core.ParDo( _TopPerBundle(self._n, self._key, self._reverse)) # If pcoll is empty, we can't guarantee that top_per_bundle # won't be empty, so inject at least one empty accumulator # so that downstream is guaranteed to produce non-empty output. empty_bundle = ( pcoll.pipeline | core.Create([(None, [])]).with_output_types( top_per_bundle.element_type)) return ((top_per_bundle, empty_bundle) | core.Flatten() | core.GroupByKey() | core.ParDo( _MergeTopPerBundle(self._n, self._key, self._reverse))) else: if self.has_defaults: return pcoll | core.CombineGlobally( TopCombineFn(self._n, self._key, self._reverse)) else: return pcoll | core.CombineGlobally( TopCombineFn(self._n, self._key, self._reverse)).without_defaults()
[docs] @with_input_types(Tuple[K, V]) @with_output_types(Tuple[K, List[V]]) class PerKey(ptransform.PTransform): """Identifies the compare-most N elements associated with each key. This transform will produce a PCollection mapping unique keys in the input PCollection to the n greatest elements with which they are associated, where "greatest" is determined by the comparator function supplied as the compare argument in the initializer. """ def __init__(self, n, key=None, reverse=False): """Creates a per-key Top operation. The arguments 'key' and 'reverse' may be passed as keyword arguments, and have the same meaning as for Python's sort functions. Args: n: number of elements to extract from pcoll. key: (optional) a mapping of elements to a comparable key, similar to the key argument of Python's sorting methods. reverse: (optional) whether to order things smallest to largest, rather than largest to smallest """ self._n = n self._key = key self._reverse = reverse
[docs] def default_label(self): return 'TopPerKey(%d)' % self._n
[docs] def expand(self, pcoll): """Expands the transform. Raises TypeCheckError: If the output type of the input PCollection is not compatible with Tuple[A, B]. Args: pcoll: PCollection to process Returns: the PCollection containing the result. """ return pcoll | core.CombinePerKey( TopCombineFn(self._n, self._key, self._reverse))
[docs] @staticmethod @ptransform.ptransform_fn def Largest(pcoll, n, has_defaults=True): """Obtain a list of the greatest N elements in a PCollection.""" if has_defaults: return pcoll | Top.Of(n) else: return pcoll | Top.Of(n).without_defaults()
[docs] @staticmethod @ptransform.ptransform_fn def Smallest(pcoll, n, has_defaults=True): """Obtain a list of the least N elements in a PCollection.""" if has_defaults: return pcoll | Top.Of(n, reverse=True) else: return pcoll | Top.Of(n, reverse=True).without_defaults()
[docs] @staticmethod @ptransform.ptransform_fn def LargestPerKey(pcoll, n): """Identifies the N greatest elements associated with each key.""" return pcoll | Top.PerKey(n)
[docs] @staticmethod @ptransform.ptransform_fn def SmallestPerKey(pcoll, n, reverse=True): """Identifies the N least elements associated with each key.""" return pcoll | Top.PerKey(n, reverse=True)
@with_input_types(T) @with_output_types(Tuple[None, List[T]]) class _TopPerBundle(core.DoFn): def __init__(self, n, key, reverse): self._n = n self._compare = operator.gt if reverse else None self._key = key def start_bundle(self): self._heap = [] def process(self, element): if self._compare or self._key: element = cy_combiners.ComparableValue(element, self._compare, self._key) if len(self._heap) < self._n: heapq.heappush(self._heap, element) else: heapq.heappushpop(self._heap, element) def finish_bundle(self): # Though sorting here results in more total work, this allows us to # skip most elements in the reducer. # Essentially, given s map bundles, we are trading about O(sn) compares in # the (single) reducer for O(sn log n) compares across all mappers. self._heap.sort() # Unwrap to avoid serialization via pickle. if self._compare or self._key: yield window.GlobalWindows.windowed_value( (None, [wrapper.value for wrapper in self._heap])) else: yield window.GlobalWindows.windowed_value((None, self._heap)) @with_input_types(Tuple[None, Iterable[List[T]]]) @with_output_types(List[T]) class _MergeTopPerBundle(core.DoFn): def __init__(self, n, key, reverse): self._n = n self._compare = operator.gt if reverse else None self._key = key def process(self, key_and_bundles): _, bundles = key_and_bundles def push(hp, e): if len(hp) < self._n: heapq.heappush(hp, e) return False elif e < hp[0]: # Because _TopPerBundle returns sorted lists, all other elements # will also be smaller. return True else: heapq.heappushpop(hp, e) return False if self._compare or self._key: heapc = [] # type: List[cy_combiners.ComparableValue] for bundle in bundles: if not heapc: heapc = [ cy_combiners.ComparableValue(element, self._compare, self._key) for element in bundle ] continue for element in reversed(bundle): if push(heapc, cy_combiners.ComparableValue(element, self._compare, self._key)): break heapc.sort() yield [wrapper.value for wrapper in reversed(heapc)] else: heap = [] for bundle in bundles: if not heap: heap = bundle continue for element in reversed(bundle): if push(heap, element): break heap.sort() yield heap[::-1] @with_input_types(T) @with_output_types(List[T]) class TopCombineFn(core.CombineFn): """CombineFn doing the combining for all of the Top transforms. This CombineFn uses a key or comparison operator to rank the elements. Args: key: (optional) a mapping of elements to a comparable key, similar to the key argument of Python's sorting methods. reverse: (optional) whether to order things smallest to largest, rather than largest to smallest """ def __init__(self, n, key=None, reverse=False): self._n = n self._compare = operator.gt if reverse else operator.lt self._key = key def _hydrated_heap(self, heap): if heap: first = heap[0] if isinstance(first, cy_combiners.ComparableValue): if first.requires_hydration: for comparable in heap: assert comparable.requires_hydration comparable.hydrate(self._compare, self._key) assert not comparable.requires_hydration return heap else: return heap else: return [ cy_combiners.ComparableValue(element, self._compare, self._key) for element in heap ] else: return heap def display_data(self): return { 'n': self._n, 'compare': DisplayDataItem( self._compare.__name__ if hasattr(self._compare, '__name__') else self._compare.__class__.__name__).drop_if_none() } # The accumulator type is a tuple # (bool, Union[List[T], List[ComparableValue[T]]) # where the boolean indicates whether the second slot contains a List of T # (False) or List of ComparableValue[T] (True). In either case, the List # maintains heap invariance. When the contents of the List are # ComparableValue[T] they either all 'requires_hydration' or none do. # This accumulator representation allows us to minimize the data encoding # overheads. Creation of ComparableValues is elided for performance reasons # when there is no need for complicated comparison functions. def create_accumulator(self, *args, **kwargs): return (False, []) def add_input(self, accumulator, element, *args, **kwargs): # Caching to avoid paying the price of variadic expansion of args / kwargs # when it's not needed (for the 'if' case below). holds_comparables, heap = accumulator if self._compare is not operator.lt or self._key: heap = self._hydrated_heap(heap) holds_comparables = True else: assert not holds_comparables comparable = ( cy_combiners.ComparableValue(element, self._compare, self._key) if holds_comparables else element) if len(heap) < self._n: heapq.heappush(heap, comparable) else: heapq.heappushpop(heap, comparable) return (holds_comparables, heap) def merge_accumulators(self, accumulators, *args, **kwargs): result_heap = None holds_comparables = None for accumulator in accumulators: holds_comparables, heap = accumulator if self._compare is not operator.lt or self._key: heap = self._hydrated_heap(heap) holds_comparables = True else: assert not holds_comparables if result_heap is None: result_heap = heap else: for comparable in heap: _, result_heap = self.add_input( (holds_comparables, result_heap), comparable.value if holds_comparables else comparable) assert result_heap is not None and holds_comparables is not None return (holds_comparables, result_heap) def compact(self, accumulator, *args, **kwargs): holds_comparables, heap = accumulator # Unwrap to avoid serialization via pickle. if holds_comparables: return (False, [comparable.value for comparable in heap]) else: return accumulator def extract_output(self, accumulator, *args, **kwargs): holds_comparables, heap = accumulator if self._compare is not operator.lt or self._key: if not holds_comparables: heap = self._hydrated_heap(heap) holds_comparables = True else: assert not holds_comparables assert len(heap) <= self._n heap.sort(reverse=True) return [ comparable.value if holds_comparables else comparable for comparable in heap ] class Largest(TopCombineFn): def default_label(self): return 'Largest(%s)' % self._n class Smallest(TopCombineFn): def __init__(self, n): super().__init__(n, reverse=True) def default_label(self): return 'Smallest(%s)' % self._n
[docs]class Sample(object): """Combiners for sampling n elements without replacement.""" # pylint: disable=no-self-argument
[docs] @with_input_types(T) @with_output_types(List[T]) class FixedSizeGlobally(CombinerWithoutDefaults): """Sample n elements from the input PCollection without replacement.""" def __init__(self, n): super().__init__() self._n = n
[docs] def expand(self, pcoll): if self.has_defaults: return pcoll | core.CombineGlobally(SampleCombineFn(self._n)) else: return pcoll | core.CombineGlobally(SampleCombineFn( self._n)).without_defaults()
[docs] def display_data(self): return {'n': self._n}
[docs] def default_label(self): return 'FixedSizeGlobally(%d)' % self._n
[docs] @with_input_types(Tuple[K, V]) @with_output_types(Tuple[K, List[V]]) class FixedSizePerKey(ptransform.PTransform): """Sample n elements associated with each key without replacement.""" def __init__(self, n): self._n = n
[docs] def expand(self, pcoll): return pcoll | core.CombinePerKey(SampleCombineFn(self._n))
[docs] def display_data(self): return {'n': self._n}
[docs] def default_label(self): return 'FixedSizePerKey(%d)' % self._n
@with_input_types(T) @with_output_types(List[T]) class SampleCombineFn(core.CombineFn): """CombineFn for all Sample transforms.""" def __init__(self, n): super().__init__() # Most of this combiner's work is done by a TopCombineFn. We could just # subclass TopCombineFn to make this class, but since sampling is not # really a kind of Top operation, we use a TopCombineFn instance as a # helper instead. self._top_combiner = TopCombineFn(n) def setup(self): self._top_combiner.setup() def create_accumulator(self): return self._top_combiner.create_accumulator() def add_input(self, heap, element): # Before passing elements to the Top combiner, we pair them with random # numbers. The elements with the n largest random number "keys" will be # selected for the output. return self._top_combiner.add_input(heap, (random.random(), element)) def merge_accumulators(self, heaps): return self._top_combiner.merge_accumulators(heaps) def compact(self, heap): return self._top_combiner.compact(heap) def extract_output(self, heap): # Here we strip off the random number keys we added in add_input. return [e for _, e in self._top_combiner.extract_output(heap)] def teardown(self): self._top_combiner.teardown() class _TupleCombineFnBase(core.CombineFn): def __init__(self, *combiners, merge_accumulators_batch_size=None): self._combiners = [core.CombineFn.maybe_from_callable(c) for c in combiners] self._named_combiners = combiners # If the `merge_accumulators_batch_size` value is not specified, we chose a # bounded default that is inversely proportional to the number of # accumulators in merged tuples. num_combiners = max(1, len(combiners)) self._merge_accumulators_batch_size = ( merge_accumulators_batch_size or max(10, 1000 // num_combiners)) def display_data(self): combiners = [ c.__name__ if hasattr(c, '__name__') else c.__class__.__name__ for c in self._named_combiners ] return { 'combiners': str(combiners), 'merge_accumulators_batch_size': self._merge_accumulators_batch_size } def setup(self, *args, **kwargs): for c in self._combiners: c.setup(*args, **kwargs) def create_accumulator(self, *args, **kwargs): return [c.create_accumulator(*args, **kwargs) for c in self._combiners] def merge_accumulators(self, accumulators, *args, **kwargs): # Make sure that `accumulators` is an iterator (so that the position is # remembered). accumulators = iter(accumulators) result = next(accumulators) while True: # Load accumulators into memory and merge in batches to decrease peak # memory usage. accumulators_batch = [result] + list( itertools.islice(accumulators, self._merge_accumulators_batch_size)) if len(accumulators_batch) == 1: break result = [ c.merge_accumulators(a, *args, **kwargs) for c, a in zip(self._combiners, zip(*accumulators_batch)) ] return result def compact(self, accumulator, *args, **kwargs): return [ c.compact(a, *args, **kwargs) for c, a in zip(self._combiners, accumulator) ] def extract_output(self, accumulator, *args, **kwargs): return tuple( c.extract_output(a, *args, **kwargs) for c, a in zip(self._combiners, accumulator)) def teardown(self, *args, **kwargs): for c in reversed(self._combiners): c.teardown(*args, **kwargs) class TupleCombineFn(_TupleCombineFnBase): """A combiner for combining tuples via a tuple of combiners. Takes as input a tuple of N CombineFns and combines N-tuples by combining the k-th element of each tuple with the k-th CombineFn, outputting a new N-tuple of combined values. """ def add_input(self, accumulator, element, *args, **kwargs): return [ c.add_input(a, e, *args, **kwargs) for c, a, e in zip(self._combiners, accumulator, element) ] def with_common_input(self): return SingleInputTupleCombineFn(*self._combiners) class SingleInputTupleCombineFn(_TupleCombineFnBase): """A combiner for combining a single value via a tuple of combiners. Takes as input a tuple of N CombineFns and combines elements by applying each CombineFn to each input, producing an N-tuple of the outputs corresponding to each of the N CombineFn's outputs. """ def add_input(self, accumulator, element, *args, **kwargs): return [ c.add_input(a, element, *args, **kwargs) for c, a in zip(self._combiners, accumulator) ]
[docs]@with_input_types(T) @with_output_types(List[T]) class ToList(CombinerWithoutDefaults): """A global CombineFn that condenses a PCollection into a single list."""
[docs] def expand(self, pcoll): if self.has_defaults: return pcoll | self.label >> core.CombineGlobally(ToListCombineFn()) else: return pcoll | self.label >> core.CombineGlobally( ToListCombineFn()).without_defaults()
@with_input_types(T) @with_output_types(List[T]) class ToListCombineFn(core.CombineFn): """CombineFn for to_list.""" def create_accumulator(self): return [] def add_input(self, accumulator, element): accumulator.append(element) return accumulator def merge_accumulators(self, accumulators): return sum(accumulators, []) def extract_output(self, accumulator): return accumulator
[docs]@with_input_types(Tuple[K, V]) @with_output_types(Dict[K, V]) class ToDict(CombinerWithoutDefaults): """A global CombineFn that condenses a PCollection into a single dict. PCollections should consist of 2-tuples, notionally (key, value) pairs. If multiple values are associated with the same key, only one of the values will be present in the resulting dict. """
[docs] def expand(self, pcoll): if self.has_defaults: return pcoll | self.label >> core.CombineGlobally(ToDictCombineFn()) else: return pcoll | self.label >> core.CombineGlobally( ToDictCombineFn()).without_defaults()
@with_input_types(Tuple[K, V]) @with_output_types(Dict[K, V]) class ToDictCombineFn(core.CombineFn): """CombineFn for to_dict.""" def create_accumulator(self): return {} def add_input(self, accumulator, element): key, value = element accumulator[key] = value return accumulator def merge_accumulators(self, accumulators): result = {} for a in accumulators: result.update(a) return result def extract_output(self, accumulator): return accumulator
[docs]@with_input_types(T) @with_output_types(Set[T]) class ToSet(CombinerWithoutDefaults): """A global CombineFn that condenses a PCollection into a set."""
[docs] def expand(self, pcoll): if self.has_defaults: return pcoll | self.label >> core.CombineGlobally(ToSetCombineFn()) else: return pcoll | self.label >> core.CombineGlobally( ToSetCombineFn()).without_defaults()
@with_input_types(T) @with_output_types(Set[T]) class ToSetCombineFn(core.CombineFn): """CombineFn for ToSet.""" def create_accumulator(self): return set() def add_input(self, accumulator, element): accumulator.add(element) return accumulator def merge_accumulators(self, accumulators): return set.union(*accumulators) def extract_output(self, accumulator): return accumulator class _CurriedFn(core.CombineFn): """Wrapped CombineFn with extra arguments.""" def __init__(self, fn, args, kwargs): self.fn = fn self.args = args self.kwargs = kwargs def setup(self): self.fn.setup(*self.args, **self.kwargs) def create_accumulator(self): return self.fn.create_accumulator(*self.args, **self.kwargs) def add_input(self, accumulator, element): return self.fn.add_input(accumulator, element, *self.args, **self.kwargs) def merge_accumulators(self, accumulators): return self.fn.merge_accumulators(accumulators, *self.args, **self.kwargs) def compact(self, accumulator): return self.fn.compact(accumulator, *self.args, **self.kwargs) def extract_output(self, accumulator): return self.fn.extract_output(accumulator, *self.args, **self.kwargs) def teardown(self): self.fn.teardown(*self.args, **self.kwargs) def apply(self, elements): return self.fn.apply(elements, *self.args, **self.kwargs) def curry_combine_fn(fn, args, kwargs): if not args and not kwargs: return fn else: return _CurriedFn(fn, args, kwargs) class PhasedCombineFnExecutor(object): """Executor for phases of combine operations.""" def __init__(self, phase, fn, args, kwargs): self.combine_fn = curry_combine_fn(fn, args, kwargs) if phase == 'all': self.apply = self.full_combine elif phase == 'add': self.apply = self.add_only elif phase == 'merge': self.apply = self.merge_only elif phase == 'extract': self.apply = self.extract_only elif phase == 'convert': self.apply = self.convert_to_accumulator else: raise ValueError('Unexpected phase: %s' % phase) def full_combine(self, elements): return self.combine_fn.apply(elements) def add_only(self, elements): return self.combine_fn.add_inputs( self.combine_fn.create_accumulator(), elements) def merge_only(self, accumulators): return self.combine_fn.merge_accumulators(accumulators) def extract_only(self, accumulator): return self.combine_fn.extract_output(accumulator) def convert_to_accumulator(self, element): return self.combine_fn.add_input( self.combine_fn.create_accumulator(), element)
[docs]class Latest(object): """Combiners for computing the latest element"""
[docs] @with_input_types(T) @with_output_types(T) class Globally(CombinerWithoutDefaults): """Compute the element with the latest timestamp from a PCollection."""
[docs] @staticmethod def add_timestamp(element, timestamp=core.DoFn.TimestampParam): return [(element, timestamp)]
[docs] def expand(self, pcoll): if self.has_defaults: return ( pcoll | core.ParDo(self.add_timestamp).with_output_types( Tuple[T, TimestampType]) | core.CombineGlobally(LatestCombineFn())) else: return ( pcoll | core.ParDo(self.add_timestamp).with_output_types( Tuple[T, TimestampType]) | core.CombineGlobally(LatestCombineFn()).without_defaults())
[docs] @with_input_types(Tuple[K, V]) @with_output_types(Tuple[K, V]) class PerKey(ptransform.PTransform): """Compute elements with the latest timestamp for each key from a keyed PCollection"""
[docs] @staticmethod def add_timestamp(element, timestamp=core.DoFn.TimestampParam): key, value = element return [(key, (value, timestamp))]
[docs] def expand(self, pcoll): return ( pcoll | core.ParDo(self.add_timestamp).with_output_types( Tuple[K, Tuple[T, TimestampType]]) | core.CombinePerKey(LatestCombineFn()))
@with_input_types(Tuple[T, TimestampType]) @with_output_types(T) class LatestCombineFn(core.CombineFn): """CombineFn to get the element with the latest timestamp from a PCollection.""" def create_accumulator(self): return (None, window.MIN_TIMESTAMP) def add_input(self, accumulator, element): if accumulator[1] > element[1]: return accumulator else: return element def merge_accumulators(self, accumulators): result = self.create_accumulator() for accumulator in accumulators: result = self.add_input(result, accumulator) return result def extract_output(self, accumulator): return accumulator[0]