def product(*args, **kwargs):
"""Product of multiple :py:class:`MonomialSum`s"""
rename_map = kwargs.pop('rename_map', None)
if rename_map is None:
rename_map = make_rename_map()
if kwargs:
raise ValueError("Unrecognised keyword argument: " + kwargs.pop())
result = MonomialSum()
for monomials in product(*args):
renamer = make_renamer(rename_map)
sum_indices = []
atomics = []
rest = one
for s, a, r in monomials:
s_, applier = renamer(s)
sum_indices.extend(s_)
atomics.extend(map(applier, a))
rest = Product(applier(r), rest)
result.add(sum_indices, atomics, rest)
return result
def product(*args, **kwargs):
"""Product of multiple :py:class:`MonomialSum`s"""
rename_map = kwargs.pop('rename_map', None)
if rename_map is None:
rename_map = make_rename_map()
if kwargs:
raise ValueError("Unrecognised keyword argument: " + kwargs.pop())
result = MonomialSum()
for monomials in product(*args):
renamer = make_renamer(rename_map)
sum_indices = []
atomics = []
rest = one
for s, a, r in monomials:
s_, applier = renamer(s)
sum_indices.extend(s_)
atomics.extend(map(applier, a))
rest = Product(applier(r), rest)
result.add(sum_indices, atomics, rest)
return result
def collect_monomials(expressions, classifier):
"""Refactorises expressions into a sum-of-products form, using
distributivity rules (i.e. a*(b + c) -> a*b + a*c). Expansion
proceeds until all "compound" expressions are broken up.
:arg expressions: GEM expressions to refactorise
:arg classifier: a function that can classify any GEM expression
as ``ATOMIC``, ``COMPOUND``, or ``OTHER``. This
classification drives the factorisation.
:returns: list of :py:class:`MonomialSum`s
:raises FactorisationError: Failed to break up some "compound"
expressions with expansion.
"""
# Get ComponentTensors out of the way
expressions = remove_componenttensors(expressions)
# Get ListTensors out of the way
must_unroll = [] # indices to unroll
for node in traversal(expressions):
if isinstance(node, Indexed):
child, = node.children
if isinstance(child, ListTensor) and classifier(node) == COMPOUND:
must_unroll.extend(node.multiindex)
if must_unroll:
must_unroll = set(must_unroll)
expressions = unroll_indexsum(expressions,
predicate=lambda i: i in must_unroll)
expressions = remove_componenttensors(expressions)
# Expand Conditional nodes which are COMPOUND
conditional_predicate = lambda node: classifier(node) == COMPOUND
expressions = expand_conditional(expressions, conditional_predicate)
# Finally, refactorise expressions
mapper = Memoizer(_collect_monomials)
mapper.classifier = classifier
mapper.rename_map = make_rename_map()
return list(map(mapper, expressions))
def collect_monomials(expressions, classifier):
"""Refactorises expressions into a sum-of-products form, using
distributivity rules (i.e. a*(b + c) -> a*b + a*c). Expansion
proceeds until all "compound" expressions are broken up.
:arg expressions: GEM expressions to refactorise
:arg classifier: a function that can classify any GEM expression
as ``ATOMIC``, ``COMPOUND``, or ``OTHER``. This
classification drives the factorisation.
:returns: list of :py:class:`MonomialSum`s
:raises FactorisationError: Failed to break up some "compound"
expressions with expansion.
"""
# Get ComponentTensors out of the way
expressions = remove_componenttensors(expressions)
# Get ListTensors out of the way
must_unroll = [] # indices to unroll
for node in traversal(expressions):
if isinstance(node, Indexed):
child, = node.children
if isinstance(child, ListTensor) and classifier(node) == COMPOUND:
must_unroll.extend(node.multiindex)
if must_unroll:
must_unroll = set(must_unroll)
expressions = unroll_indexsum(expressions,
predicate=lambda i: i in must_unroll)
expressions = remove_componenttensors(expressions)
# Expand Conditional nodes which are COMPOUND
conditional_predicate = lambda node: classifier(node) == COMPOUND
expressions = expand_conditional(expressions, conditional_predicate)
# Finally, refactorise expressions
mapper = Memoizer(_collect_monomials)
mapper.classifier = classifier
mapper.rename_map = make_rename_map()
return list(map(mapper, expressions))