from toolz.itertoolz import partition_all
from toolz.compatibility import reduce, map
from toolz.utils import no_default
[docs]def fold(binop, seq, default=no_default, map=map, chunksize=128, combine=None):
Reduce without guarantee of ordered reduction.
``binop`` - associative operator. The associative property allows us to
leverage a parallel map to perform reductions in parallel.
``seq`` - a sequence to be aggregated
``default`` - an identity element like 0 for ``add`` or 1 for mul
``map`` - an implementation of ``map``. This may be parallel and
determines how work is distributed.
``chunksize`` - Number of elements of ``seq`` that should be handled
within a single function call
``combine`` - Binary operator to combine two intermediate results.
If ``binop`` is of type (total, item) -> total
then ``combine`` is of type (total, total) -> total
Defaults to ``binop`` for common case of operators like add
Fold chunks up the collection into blocks of size ``chunksize`` and then
feeds each of these to calls to ``reduce``. This work is distributed
with a call to ``map``, gathered back and then refolded to finish the
computation. In this way ``fold`` specifies only how to chunk up data but
leaves the distribution of this work to an externally provided ``map``
function. This function can be sequential or rely on multithreading,
multiprocessing, or even distributed solutions.
If ``map`` intends to serialize functions it should be prepared to accept
and serialize lambdas. Note that the standard ``pickle`` module fails
>>> # Provide a parallel map to accomplish a parallel sum
>>> from operator import add
>>> fold(add, [1, 2, 3, 4], chunksize=2, map=map)
if combine is None:
combine = binop
chunks = partition_all(chunksize, seq)
# Evaluate sequence in chunks via map
if default == no_default:
results = map(lambda chunk: reduce(binop, chunk), chunks)
results = map(lambda chunk: reduce(binop, chunk, default), chunks)
results = list(results) # TODO: Support complete laziness
if len(results) == 1: # Return completed result
else: # Recurse to reaggregate intermediate results
return fold(combine, results, map=map, chunksize=chunksize)