def preprocess_expression(expression, complex_mode=False,
do_apply_restrictions=False):
"""Imitates the compute_form_data processing pipeline.
:arg complex_mode: Are we in complex UFL mode?
:arg do_apply_restrictions: Propogate restrictions to terminals?
Useful, for example, to preprocess non-scalar expressions, which
are not and cannot be forms.
"""
if complex_mode:
expression = do_comparison_check(expression)
else:
expression = remove_complex_nodes(expression)
expression = apply_algebra_lowering(expression)
expression = apply_derivatives(expression)
expression = apply_function_pullbacks(expression)
expression = apply_geometry_lowering(expression, preserve_geometry_types)
expression = apply_derivatives(expression)
expression = apply_geometry_lowering(expression, preserve_geometry_types)
expression = apply_derivatives(expression)
if not complex_mode:
expression = remove_complex_nodes(expression)
if do_apply_restrictions:
expression = apply_restrictions(expression)
return expression
def test_comparison_checker(self):
cell = triangle
element = FiniteElement("Lagrange", cell, 1)
u = TrialFunction(element)
v = TestFunction(element)
a = conditional(ge(abs(u), imag(v)), u, v)
b = conditional(le(sqrt(abs(u)), imag(v)), as_ufl(1), as_ufl(1j))
c = conditional(gt(abs(u), pow(imag(v), 0.5)), sin(u), cos(v))
d = conditional(lt(as_ufl(-1), as_ufl(1)), u, v)
e = max_value(as_ufl(0), real(u))
f = min_value(sin(u), cos(v))
g = min_value(sin(pow(u, 3)), cos(abs(v)))
assert do_comparison_check(a) == conditional(ge(real(abs(u)), real(imag(v))), u, v)
with pytest.raises(ComplexComparisonError):
b = do_comparison_check(b)
with pytest.raises(ComplexComparisonError):
c = do_comparison_check(c)
assert do_comparison_check(d) == conditional(lt(real(as_ufl(-1)), real(as_ufl(1))), u, v)
assert do_comparison_check(e) == max_value(real(as_ufl(0)), real(real(u)))
assert do_comparison_check(f) == min_value(real(sin(u)), real(cos(v)))
assert do_comparison_check(g) == min_value(real(sin(pow(u, 3))), real(cos(abs(v))))
def compute_form_data(form,
# Default arguments configured to behave the way old FFC expects it:
do_apply_function_pullbacks=False,
do_apply_integral_scaling=False,
do_apply_geometry_lowering=False,
preserve_geometry_types=(),
do_apply_default_restrictions=True,
do_apply_restrictions=True,
do_estimate_degrees=True,
complex_mode=False,
):
# TODO: Move this to the constructor instead
self = FormData()
# --- Store untouched form for reference.
# The user of FormData may get original arguments,
# original coefficients, and form signature from this object.
# But be aware that the set of original coefficients are not
# the same as the ones used in the final UFC form.
# See 'reduced_coefficients' below.
self.original_form = form
# --- Pass form integrands through some symbolic manipulation
# Note: Default behaviour here will process form the way that is
# currently expected by vanilla FFC
# Check that the form does not try to compare complex quantities:
# if the quantites being compared are 'provably' real, wrap them
# with Real, otherwise throw an error.
if complex_mode:
form = do_comparison_check(form)
# Lower abstractions for tensor-algebra types into index notation,
# reducing the number of operators later algorithms and form
# compilers need to handle
form = apply_algebra_lowering(form)
# After lowering to index notation, remove any complex nodes that
# have been introduced but are not wanted when working in real mode,
# allowing for purely real forms to be written
if not complex_mode:
form = remove_complex_nodes(form)
# Apply differentiation before function pullbacks, because for
# example coefficient derivatives are more complicated to derive
# after coefficients are rewritten, and in particular for
# user-defined coefficient relations it just gets too messy
form = apply_derivatives(form)
# strip the coordinate derivatives away from the integral as they
# interfere with the integral grouping
(form, coordinate_derivatives) = strip_coordinate_derivatives(form)
# --- Group form integrals
# TODO: Refactor this, it's rather opaque what this does
# TODO: Is self.original_form.ufl_domains() right here?
# It will matter when we start including 'num_domains' in ufc form.
form = group_form_integrals(form, self.original_form.ufl_domains())
# attach coordinate derivatives again
form = attach_coordinate_derivatives(form, coordinate_derivatives)
# Estimate polynomial degree of integrands now, before applying
# any pullbacks and geometric lowering. Otherwise quad degrees
# blow up horrifically.
if do_estimate_degrees:
form = attach_estimated_degrees(form)
if do_apply_function_pullbacks:
# Rewrite coefficients and arguments in terms of their
# reference cell values with Piola transforms and symmetry
# transforms injected where needed.
# Decision: Not supporting grad(dolfin.Expression) without a
# Domain. Current dolfin works if Expression has a
# cell but this should be changed to a mesh.
form = apply_function_pullbacks(form)
# Scale integrals to reference cell frames
if do_apply_integral_scaling:
form = apply_integral_scaling(form)
# Apply default restriction to fully continuous terminals
if do_apply_default_restrictions:
form = apply_default_restrictions(form)
# Lower abstractions for geometric quantities into a smaller set
# of quantities, allowing the form compiler to deal with a smaller
# set of types and treating geometric quantities like any other
# expressions w.r.t. loop-invariant code motion etc.
if do_apply_geometry_lowering:
form = apply_geometry_lowering(form, preserve_geometry_types)
# Apply differentiation again, because the algorithms above can
# generate new derivatives or rewrite expressions inside
# derivatives
if do_apply_function_pullbacks or do_apply_geometry_lowering:
form = apply_derivatives(form)
# Neverending story: apply_derivatives introduces new Jinvs,
# which needs more geometry lowering
if do_apply_geometry_lowering:
form = apply_geometry_lowering(form, preserve_geometry_types)
# Lower derivatives that may have appeared
form = apply_derivatives(form)
form = apply_coordinate_derivatives(form)
# Propagate restrictions to terminals
if do_apply_restrictions:
form = apply_restrictions(form)
# --- Group integrals into IntegralData objects
# Most of the heavy lifting is done above in group_form_integrals.
self.integral_data = build_integral_data(form.integrals())
# --- Create replacements for arguments and coefficients
# Figure out which form coefficients each integral should enable
for itg_data in self.integral_data:
itg_coeffs = set()
# Get all coefficients in integrand
for itg in itg_data.integrals:
itg_coeffs.update(extract_coefficients(itg.integrand()))
# Store with IntegralData object
itg_data.integral_coefficients = itg_coeffs
# Figure out which coefficients from the original form are
# actually used in any integral (Differentiation may reduce the
# set of coefficients w.r.t. the original form)
reduced_coefficients_set = set()
for itg_data in self.integral_data:
reduced_coefficients_set.update(itg_data.integral_coefficients)
self.reduced_coefficients = sorted(reduced_coefficients_set,
key=lambda c: c.count())
self.num_coefficients = len(self.reduced_coefficients)
self.original_coefficient_positions = [i for i, c in enumerate(self.original_form.coefficients())
if c in self.reduced_coefficients]
# Store back into integral data which form coefficients are used
# by each integral
for itg_data in self.integral_data:
itg_data.enabled_coefficients = [bool(coeff in itg_data.integral_coefficients)
for coeff in self.reduced_coefficients]
# --- Collect some trivial data
# Get rank of form from argument list (assuming not a mixed arity form)
self.rank = len(self.original_form.arguments())
# Extract common geometric dimension (topological is not common!)
self.geometric_dimension = self.original_form.integrals()[0].ufl_domain().geometric_dimension()
# --- Build mapping from old incomplete element objects to new
# well defined elements. This is to support the Expression
# construct in dolfin which subclasses Coefficient but doesn't
# provide an element, and the Constant construct that doesn't
# provide the domain that a Coefficient is supposed to have. A
# future design iteration in UFL/UFC/FFC/DOLFIN may allow removal
# of this mapping with the introduction of UFL types for
# Expression-like functions that can be evaluated in quadrature
# points.
self.element_replace_map = _compute_element_mapping(self.original_form)
# Mappings from elements and coefficients that reside in form to
# objects with canonical numbering as well as completed cells and
# elements
renumbered_coefficients, function_replace_map = \
_build_coefficient_replace_map(self.reduced_coefficients,
self.element_replace_map)
self.function_replace_map = function_replace_map
# --- Store various lists of elements and sub elements (adds
# members to self)
_compute_form_data_elements(self,
self.original_form.arguments(),
renumbered_coefficients,
self.original_form.ufl_domains())
# --- Store number of domains for integral types
# TODO: Group this by domain first. For now keep a backwards
# compatible data structure.
self.max_subdomain_ids = _compute_max_subdomain_ids(self.integral_data)
# --- Checks
_check_elements(self)
_check_facet_geometry(self.integral_data)
# TODO: This is a very expensive check... Replace with something
# faster!
preprocessed_form = reconstruct_form_from_integral_data(self.integral_data)
# If in real mode, remove complex nodes entirely.
if not complex_mode:
preprocessed_form = remove_complex_nodes(preprocessed_form)
check_form_arity(preprocessed_form, self.original_form.arguments(), complex_mode) # Currently testing how fast this is
# TODO: This member is used by unit tests, change the tests to
# remove this!
self.preprocessed_form = preprocessed_form
return self
def compute_form_data(
form,
# Default arguments configured to behave the way old FFC expects it:
do_apply_function_pullbacks=False,
do_apply_integral_scaling=False,
do_apply_geometry_lowering=False,
preserve_geometry_types=(),
do_apply_default_restrictions=True,
do_apply_restrictions=True,
do_estimate_degrees=True,
do_append_everywhere_integrals=True,
complex_mode=False,
):
# TODO: Move this to the constructor instead
self = FormData()
# --- Store untouched form for reference.
# The user of FormData may get original arguments,
# original coefficients, and form signature from this object.
# But be aware that the set of original coefficients are not
# the same as the ones used in the final UFC form.
# See 'reduced_coefficients' below.
self.original_form = form
# --- Pass form integrands through some symbolic manipulation
# Note: Default behaviour here will process form the way that is
# currently expected by vanilla FFC
# Check that the form does not try to compare complex quantities:
# if the quantites being compared are 'provably' real, wrap them
# with Real, otherwise throw an error.
if complex_mode:
form = do_comparison_check(form)
# Lower abstractions for tensor-algebra types into index notation,
# reducing the number of operators later algorithms and form
# compilers need to handle
form = apply_algebra_lowering(form)
# After lowering to index notation, remove any complex nodes that
# have been introduced but are not wanted when working in real mode,
# allowing for purely real forms to be written
if not complex_mode:
form = remove_complex_nodes(form)
# Apply differentiation before function pullbacks, because for
# example coefficient derivatives are more complicated to derive
# after coefficients are rewritten, and in particular for
# user-defined coefficient relations it just gets too messy
form = apply_derivatives(form)
# --- Group form integrals
# TODO: Refactor this, it's rather opaque what this does
# TODO: Is self.original_form.ufl_domains() right here?
# It will matter when we start including 'num_domains' in ufc form.
form = group_form_integrals(
form,
self.original_form.ufl_domains(),
do_append_everywhere_integrals=do_append_everywhere_integrals)
# Estimate polynomial degree of integrands now, before applying
# any pullbacks and geometric lowering. Otherwise quad degrees
# blow up horrifically.
if do_estimate_degrees:
form = attach_estimated_degrees(form)
if do_apply_function_pullbacks:
# Rewrite coefficients and arguments in terms of their
# reference cell values with Piola transforms and symmetry
# transforms injected where needed.
# Decision: Not supporting grad(dolfin.Expression) without a
# Domain. Current dolfin works if Expression has a
# cell but this should be changed to a mesh.
form = apply_function_pullbacks(form)
# Scale integrals to reference cell frames
if do_apply_integral_scaling:
form = apply_integral_scaling(form)
# Apply default restriction to fully continuous terminals
if do_apply_default_restrictions:
form = apply_default_restrictions(form)
# Lower abstractions for geometric quantities into a smaller set
# of quantities, allowing the form compiler to deal with a smaller
# set of types and treating geometric quantities like any other
# expressions w.r.t. loop-invariant code motion etc.
if do_apply_geometry_lowering:
form = apply_geometry_lowering(form, preserve_geometry_types)
# Apply differentiation again, because the algorithms above can
# generate new derivatives or rewrite expressions inside
# derivatives
if do_apply_function_pullbacks or do_apply_geometry_lowering:
form = apply_derivatives(form)
# Neverending story: apply_derivatives introduces new Jinvs,
# which needs more geometry lowering
if do_apply_geometry_lowering:
form = apply_geometry_lowering(form, preserve_geometry_types)
# Lower derivatives that may have appeared
form = apply_derivatives(form)
form = apply_coordinate_derivatives(form)
# Propagate restrictions to terminals
if do_apply_restrictions:
form = apply_restrictions(form)
# --- Group integrals into IntegralData objects
# Most of the heavy lifting is done above in group_form_integrals.
self.integral_data = build_integral_data(form.integrals())
# --- Create replacements for arguments and coefficients
# Figure out which form coefficients each integral should enable
for itg_data in self.integral_data:
itg_coeffs = set()
# Get all coefficients in integrand
for itg in itg_data.integrals:
itg_coeffs.update(extract_coefficients(itg.integrand()))
# Store with IntegralData object
itg_data.integral_coefficients = itg_coeffs
# Figure out which coefficients from the original form are
# actually used in any integral (Differentiation may reduce the
# set of coefficients w.r.t. the original form)
reduced_coefficients_set = set()
for itg_data in self.integral_data:
reduced_coefficients_set.update(itg_data.integral_coefficients)
self.reduced_coefficients = sorted(reduced_coefficients_set,
key=lambda c: c.count())
self.num_coefficients = len(self.reduced_coefficients)
self.original_coefficient_positions = [
i for i, c in enumerate(self.original_form.coefficients())
if c in self.reduced_coefficients
]
# Store back into integral data which form coefficients are used
# by each integral
for itg_data in self.integral_data:
itg_data.enabled_coefficients = [
bool(coeff in itg_data.integral_coefficients)
for coeff in self.reduced_coefficients
]
# --- Collect some trivial data
# Get rank of form from argument list (assuming not a mixed arity form)
self.rank = len(self.original_form.arguments())
# Extract common geometric dimension (topological is not common!)
self.geometric_dimension = self.original_form.integrals()[0].ufl_domain(
).geometric_dimension()
# --- Build mapping from old incomplete element objects to new
# well defined elements. This is to support the Expression
# construct in dolfin which subclasses Coefficient but doesn't
# provide an element, and the Constant construct that doesn't
# provide the domain that a Coefficient is supposed to have. A
# future design iteration in UFL/UFC/FFC/DOLFIN may allow removal
# of this mapping with the introduction of UFL types for
# Expression-like functions that can be evaluated in quadrature
# points.
self.element_replace_map = _compute_element_mapping(self.original_form)
# Mappings from elements and coefficients that reside in form to
# objects with canonical numbering as well as completed cells and
# elements
renumbered_coefficients, function_replace_map = \
_build_coefficient_replace_map(self.reduced_coefficients,
self.element_replace_map)
self.function_replace_map = function_replace_map
# --- Store various lists of elements and sub elements (adds
# members to self)
_compute_form_data_elements(self, self.original_form.arguments(),
renumbered_coefficients,
self.original_form.ufl_domains())
# --- Store number of domains for integral types
# TODO: Group this by domain first. For now keep a backwards
# compatible data structure.
self.max_subdomain_ids = _compute_max_subdomain_ids(self.integral_data)
# --- Checks
_check_elements(self)
_check_facet_geometry(self.integral_data)
# TODO: This is a very expensive check... Replace with something
# faster!
preprocessed_form = reconstruct_form_from_integral_data(self.integral_data)
# If in real mode, remove complex nodes entirely.
if not complex_mode:
preprocessed_form = remove_complex_nodes(preprocessed_form)
check_form_arity(preprocessed_form, self.original_form.arguments(),
complex_mode) # Currently testing how fast this is
# TODO: This member is used by unit tests, change the tests to
# remove this!
self.preprocessed_form = preprocessed_form
return self