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 compute_integrand_scaling_factor(integral):
"""Change integrand geometry to the right representations."""
domain = integral.ufl_domain()
integral_type = integral.integral_type()
# co = CellOrientation(domain)
weight = QuadratureWeight(domain)
tdim = domain.topological_dimension()
# gdim = domain.geometric_dimension()
# Polynomial degree of integrand scaling
degree = 0
if integral_type == "cell":
detJ = JacobianDeterminant(domain)
degree = estimate_total_polynomial_degree(
apply_geometry_lowering(detJ))
# Despite the abs, |detJ| is polynomial except for
# self-intersecting cells, where we have other problems.
scale = abs(detJ) * weight
elif integral_type.startswith("exterior_facet"):
if tdim > 1:
# Scaling integral by facet jacobian determinant and
# quadrature weight
detFJ = FacetJacobianDeterminant(domain)
degree = estimate_total_polynomial_degree(
apply_geometry_lowering(detFJ))
scale = detFJ * weight
else:
# No need to scale 'integral' over a vertex
scale = 1
elif integral_type.startswith("interior_facet"):
if tdim > 1:
# Scaling integral by facet jacobian determinant from one
# side and quadrature weight
detFJ = FacetJacobianDeterminant(domain)
degree = estimate_total_polynomial_degree(
apply_geometry_lowering(detFJ))
scale = detFJ('+') * weight
else:
# No need to scale 'integral' over a vertex
scale = 1
elif integral_type in custom_integral_types:
# Scaling with custom weight, which includes eventual volume
# scaling
scale = weight
elif integral_type in point_integral_types:
# No need to scale 'integral' over a point
scale = 1
else:
error("Unknown integral type {}, don't know how to scale.".format(
integral_type))
return scale, degree
def compute_integrand_scaling_factor(integral):
"""Change integrand geometry to the right representations."""
domain = integral.ufl_domain()
integral_type = integral.integral_type()
# co = CellOrientation(domain)
weight = QuadratureWeight(domain)
tdim = domain.topological_dimension()
# gdim = domain.geometric_dimension()
# Polynomial degree of integrand scaling
degree = 0
if integral_type == "cell":
detJ = JacobianDeterminant(domain)
degree = estimate_total_polynomial_degree(apply_geometry_lowering(detJ))
# Despite the abs, |detJ| is polynomial except for
# self-intersecting cells, where we have other problems.
scale = abs(detJ) * weight
elif integral_type.startswith("exterior_facet"):
if tdim > 1:
# Scaling integral by facet jacobian determinant and
# quadrature weight
detFJ = FacetJacobianDeterminant(domain)
degree = estimate_total_polynomial_degree(apply_geometry_lowering(detFJ))
scale = detFJ * weight
else:
# No need to scale 'integral' over a vertex
scale = 1
elif integral_type.startswith("interior_facet"):
if tdim > 1:
# Scaling integral by facet jacobian determinant from one
# side and quadrature weight
detFJ = FacetJacobianDeterminant(domain)
degree = estimate_total_polynomial_degree(apply_geometry_lowering(detFJ))
scale = detFJ('+') * weight
else:
# No need to scale 'integral' over a vertex
scale = 1
elif integral_type in custom_integral_types:
# Scaling with custom weight, which includes eventual volume
# scaling
scale = weight
elif integral_type in point_integral_types:
# No need to scale 'integral' over a point
scale = 1
else:
error("Unknown integral type {}, don't know how to scale.".format(integral_type))
return scale, degree
def preprocess_expression(expression):
"""Imitates the compute_form_data processing pipeline.
Useful, for example, to preprocess non-scalar expressions, which
are not and cannot be forms.
"""
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)
return expression
def preprocess_expression(expression):
"""Imitates the compute_form_data processing pipeline.
Useful, for example, to preprocess non-scalar expressions, which
are not and cannot be forms.
"""
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)
return expression
def test_index_simplification_reference_grad(self):
mesh = Mesh(VectorElement("P", quadrilateral, 1))
i, = indices(1)
A = as_tensor(Indexed(Jacobian(mesh), MultiIndex((i, i))), (i,))
expr = apply_derivatives(apply_geometry_lowering(
apply_algebra_lowering(A[0])))
assert expr == ReferenceGrad(SpatialCoordinate(mesh))[0, 0]
assert expr.ufl_free_indices == ()
assert expr.ufl_shape == ()
def change_integrand_geometry_representation(integrand, scale, integral_type):
"""Change integrand geometry to the right representations."""
integrand = apply_function_pullbacks(integrand)
integrand = change_to_reference_grad(integrand)
integrand = integrand * scale
if integral_type == "quadrature":
physical_coordinates_known = True
else:
physical_coordinates_known = False
integrand = apply_geometry_lowering(integrand, physical_coordinates_known)
return integrand
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,
):
# 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
# 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)
# 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())
# 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)
# 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)
check_form_arity(
preprocessed_form,
self.original_form.arguments()) # 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 compile_ufl_kernel(expression, to_pts, to_element, fs):
import collections
from ufl.algorithms.apply_function_pullbacks import apply_function_pullbacks
from ufl.algorithms.apply_algebra_lowering import apply_algebra_lowering
from ufl.algorithms.apply_derivatives import apply_derivatives
from ufl.algorithms.apply_geometry_lowering import apply_geometry_lowering
from ufl.algorithms import extract_arguments, extract_coefficients
from gem import gem, impero_utils
from tsfc import fem, ufl_utils
from tsfc.coffee import generate as generate_coffee
from tsfc.kernel_interface import (KernelBuilderBase,
needs_cell_orientations,
cell_orientations_coffee_arg)
# Imitate the compute_form_data processing pipeline
#
# Unfortunately, we cannot call compute_form_data here, since
# we only have an expression, not a form
expression = apply_algebra_lowering(expression)
expression = apply_derivatives(expression)
expression = apply_function_pullbacks(expression)
expression = apply_geometry_lowering(expression)
expression = apply_derivatives(expression)
expression = apply_geometry_lowering(expression)
expression = apply_derivatives(expression)
# Replace coordinates (if any)
if expression.ufl_domain():
assert fs.mesh() == expression.ufl_domain()
expression = ufl_utils.replace_coordinates(expression, fs.mesh().coordinates)
if extract_arguments(expression):
return ValueError("Cannot interpolate UFL expression with Arguments!")
builder = KernelBuilderBase()
args = []
coefficients = extract_coefficients(expression)
for i, coefficient in enumerate(coefficients):
args.append(builder.coefficient(coefficient, "w_%d" % i))
point_index = gem.Index(name='p')
ir = fem.process('cell', fs.mesh().ufl_cell(), to_pts, None,
point_index, (), expression,
builder.coefficient_mapper,
collections.defaultdict(gem.Index))
assert len(ir) == 1
# Deal with non-scalar expressions
tensor_indices = ()
if fs.shape:
tensor_indices = tuple(gem.Index() for s in fs.shape)
ir = [gem.Indexed(ir[0], tensor_indices)]
# Build kernel body
return_var = gem.Variable('A', (len(to_pts),) + fs.shape)
return_expr = gem.Indexed(return_var, (point_index,) + tensor_indices)
impero_c = impero_utils.compile_gem([return_expr], ir, [point_index])
body = generate_coffee(impero_c, index_names={point_index: 'p'})
oriented = needs_cell_orientations(ir)
if oriented:
args.insert(0, cell_orientations_coffee_arg)
# Build kernel
args.insert(0, ast.Decl("double", ast.Symbol('A', rank=(len(to_pts),) + fs.shape)))
kernel_code = builder.construct_kernel("expression_kernel", args, body)
return op2.Kernel(kernel_code, kernel_code.name), oriented, coefficients
def compile_ufl_kernel(expression, to_pts, to_element, fs):
import collections
from ufl.algorithms.apply_function_pullbacks import apply_function_pullbacks
from ufl.algorithms.apply_algebra_lowering import apply_algebra_lowering
from ufl.algorithms.apply_derivatives import apply_derivatives
from ufl.algorithms.apply_geometry_lowering import apply_geometry_lowering
from ufl.algorithms import extract_arguments, extract_coefficients
from gem import gem, impero_utils
from tsfc import fem, ufl_utils
from tsfc.coffee import generate as generate_coffee
from tsfc.kernel_interface import (KernelBuilderBase,
needs_cell_orientations,
cell_orientations_coffee_arg)
# Imitate the compute_form_data processing pipeline
#
# Unfortunately, we cannot call compute_form_data here, since
# we only have an expression, not a form
expression = apply_algebra_lowering(expression)
expression = apply_derivatives(expression)
expression = apply_function_pullbacks(expression)
expression = apply_geometry_lowering(expression)
expression = apply_derivatives(expression)
expression = apply_geometry_lowering(expression)
expression = apply_derivatives(expression)
# Replace coordinates (if any)
if expression.ufl_domain():
assert fs.mesh() == expression.ufl_domain()
expression = ufl_utils.replace_coordinates(expression, fs.mesh().coordinates)
if extract_arguments(expression):
return ValueError("Cannot interpolate UFL expression with Arguments!")
builder = KernelBuilderBase()
args = []
coefficients = extract_coefficients(expression)
for i, coefficient in enumerate(coefficients):
args.append(builder.coefficient(coefficient, "w_%d" % i))
point_index = gem.Index(name='p')
ir = fem.compile_ufl(expression,
cell=fs.mesh().ufl_cell(),
points=to_pts,
point_index=point_index,
coefficient_mapper=builder.coefficient_mapper)
assert len(ir) == 1
# Deal with non-scalar expressions
tensor_indices = ()
if fs.shape:
tensor_indices = tuple(gem.Index() for s in fs.shape)
ir = [gem.Indexed(ir[0], tensor_indices)]
# Build kernel body
return_var = gem.Variable('A', (len(to_pts),) + fs.shape)
return_expr = gem.Indexed(return_var, (point_index,) + tensor_indices)
impero_c = impero_utils.compile_gem([return_expr], ir, [point_index])
body = generate_coffee(impero_c, index_names={point_index: 'p'})
oriented = needs_cell_orientations(ir)
if oriented:
args.insert(0, cell_orientations_coffee_arg)
# Build kernel
args.insert(0, ast.Decl("double", ast.Symbol('A', rank=(len(to_pts),) + fs.shape)))
kernel_code = builder.construct_kernel("expression_kernel", args, body)
return op2.Kernel(kernel_code, kernel_code.name), oriented, coefficients
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