def Integrals(expressions, quadrature_multiindex, argument_multiindices, parameters):
"""Constructs an integral representation for each GEM integrand
expression.
:arg expressions: integrand multiplied with quadrature weight;
multi-root GEM expression DAG
:arg quadrature_multiindex: quadrature multiindex (tuple)
:arg argument_multiindices: tuple of argument multiindices,
one multiindex for each argument
:arg parameters: parameters dictionary
:returns: list of integral representations
"""
# Rewrite: a / b => a * (1 / b)
expressions = replace_division(expressions)
# Unroll
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
expressions = unroll_indexsum(expressions, predicate=predicate)
expressions = [index_sum(e, quadrature_multiindex) for e in expressions]
argument_indices = tuple(chain(*argument_multiindices))
return [Integral(e, quadrature_multiindex, argument_indices) for e in expressions]
def Integrals(expressions, quadrature_multiindex, argument_multiindices, parameters):
"""Constructs an integral representation for each GEM integrand
expression.
:arg expressions: integrand multiplied with quadrature weight;
multi-root GEM expression DAG
:arg quadrature_multiindex: quadrature multiindex (tuple)
:arg argument_multiindices: tuple of argument multiindices,
one multiindex for each argument
:arg parameters: parameters dictionary
:returns: list of integral representations
"""
# Unroll
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
expressions = unroll_indexsum(expressions, predicate=predicate)
# Choose GEM expression as the integral representation
expressions = [index_sum(e, quadrature_multiindex) for e in expressions]
expressions = replace_delta(expressions)
expressions = remove_componenttensors(expressions)
expressions = replace_division(expressions)
argument_indices = tuple(itertools.chain(*argument_multiindices))
return optimise_expressions(expressions, argument_indices)
def Integrals(expressions, quadrature_multiindex, argument_multiindices,
parameters):
"""Constructs an integral representation for each GEM integrand
expression.
:arg expressions: integrand multiplied with quadrature weight;
multi-root GEM expression DAG
:arg quadrature_multiindex: quadrature multiindex (tuple)
:arg argument_multiindices: tuple of argument multiindices,
one multiindex for each argument
:arg parameters: parameters dictionary
:returns: list of integral representations
"""
# Unroll
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
expressions = unroll_indexsum(expressions, predicate=predicate)
# Integral representation: just a GEM expression
return replace_division(
[index_sum(e, quadrature_multiindex) for e in expressions])
def test_replace_div():
i = Index()
A = Variable('A', ())
B = Variable('B', (6,))
Bi = Indexed(B, (i,))
d = Division(Bi, A)
result, = replace_division([d])
expected = Product(Bi, Division(Literal(1.0), A))
assert result == expected