def test_coordinates_never_cellwise_constant_vertex():
# The only exception here:
domains = Mesh(Cell("vertex", 3))
assert domains.ufl_cell().cellname() == "vertex"
e = SpatialCoordinate(domains)
assert is_cellwise_constant(e)
e = CellCoordinate(domains)
assert is_cellwise_constant(e)
def test_coordinates_never_cellwise_constant_vertex():
# The only exception here:
domains = Mesh(Cell("vertex", 3))
assert domains.ufl_cell().cellname() == "vertex"
e = SpatialCoordinate(domains)
assert is_cellwise_constant(e)
e = CellCoordinate(domains)
assert is_cellwise_constant(e)
def test_coefficient_sometimes_cellwise_constant(domains_not_linear):
e = Constant(domains_not_linear)
assert is_cellwise_constant(e)
V = FiniteElement("DG", domains_not_linear.ufl_cell(), 0)
e = Coefficient(V)
assert is_cellwise_constant(e)
V = FiniteElement("R", domains_not_linear.ufl_cell(), 0)
e = Coefficient(V)
assert is_cellwise_constant(e)
def test_coefficient_sometimes_cellwise_constant(domains_not_linear):
e = Constant(domains_not_linear)
assert is_cellwise_constant(e)
V = FiniteElement("DG", domains_not_linear.ufl_cell(), 0)
e = Coefficient(V)
assert is_cellwise_constant(e)
V = FiniteElement("R", domains_not_linear.ufl_cell(), 0)
e = Coefficient(V)
assert is_cellwise_constant(e)
def test_always_cellwise_constant_geometric_quantities(domains):
"Test geometric quantities that are always constant over a cell."
e = CellVolume(domains)
assert is_cellwise_constant(e)
e = Circumradius(domains)
assert is_cellwise_constant(e)
e = FacetArea(domains)
assert is_cellwise_constant(e)
e = MinFacetEdgeLength(domains)
assert is_cellwise_constant(e)
e = MaxFacetEdgeLength(domains)
assert is_cellwise_constant(e)
def construct_modified_terminal(mt, terminal):
"""Construct a modified terminal given terminal modifiers from an
analysed modified terminal and a terminal."""
expr = terminal
if mt.reference_value:
expr = ReferenceValue(expr)
dim = expr.ufl_domain().topological_dimension()
for n in range(mt.local_derivatives):
# Return zero if expression is trivially constant. This has to
# happen here because ReferenceGrad has no access to the
# topological dimension of a literal zero.
if is_cellwise_constant(expr):
expr = Zero(expr.ufl_shape + (dim, ), expr.ufl_free_indices,
expr.ufl_index_dimensions)
else:
expr = ReferenceGrad(expr)
# No need to apply restrictions to ConstantValue terminals
if not isinstance(expr, ConstantValue):
if mt.restriction == '+':
expr = PositiveRestricted(expr)
elif mt.restriction == '-':
expr = NegativeRestricted(expr)
return expr
def Dn(f):
"""UFL operator: Take the directional derivative of *f* in the
facet normal direction, Dn(f) := dot(grad(f), n)."""
f = as_ufl(f)
if is_cellwise_constant(f):
return Zero(f.ufl_shape, f.ufl_free_indices, f.ufl_index_dimensions)
return dot(grad(f), FacetNormal(f.ufl_domain()))
def geometric_quantity(self, v):
"Some geometric quantities are cellwise constant. Others are nonpolynomial and thus hard to estimate."
if is_cellwise_constant(v):
return 0
else:
# As a heuristic, just returning domain degree to bump up degree somewhat
return v.ufl_domain().ufl_coordinate_element().degree()
def construct_modified_terminal(mt, terminal):
"""Construct a modified terminal given terminal modifiers from an
analysed modified terminal and a terminal."""
expr = terminal
if mt.reference_value:
expr = ReferenceValue(expr)
dim = expr.ufl_domain().topological_dimension()
for n in range(mt.local_derivatives):
# Return zero if expression is trivially constant. This has to
# happen here because ReferenceGrad has no access to the
# topological dimension of a literal zero.
if is_cellwise_constant(expr):
expr = Zero(expr.ufl_shape + (dim,), expr.ufl_free_indices,
expr.ufl_index_dimensions)
else:
expr = ReferenceGrad(expr)
if mt.averaged == "cell":
expr = CellAvg(expr)
elif mt.averaged == "facet":
expr = FacetAvg(expr)
# No need to apply restrictions to ConstantValue terminals
if not isinstance(expr, ConstantValue):
if mt.restriction == '+':
expr = PositiveRestricted(expr)
elif mt.restriction == '-':
expr = NegativeRestricted(expr)
return expr
def geometric_quantity(self, v):
"Some geometric quantities are cellwise constant. Others are nonpolynomial and thus hard to estimate."
if is_cellwise_constant(v):
return 0
else:
# As a heuristic, just returning domain degree to bump up degree somewhat
return v.ufl_domain().ufl_coordinate_element().degree()
def Dn(f):
"""UFL operator: Take the directional derivative of *f* in the
facet normal direction, Dn(f) := dot(grad(f), n)."""
f = as_ufl(f)
if is_cellwise_constant(f):
return Zero(f.ufl_shape, f.ufl_free_indices, f.ufl_index_dimensions)
return dot(grad(f), FacetNormal(f.ufl_domain()))
def __new__(cls, f):
# Return zero if expression is trivially constant
if is_cellwise_constant(f):
dim = f.ufl_domain().topological_dimension()
return Zero(f.ufl_shape + (dim,), f.ufl_free_indices,
f.ufl_index_dimensions)
return CompoundDerivative.__new__(cls)
def __new__(cls, f):
# Return zero if expression is trivially constant
if is_cellwise_constant(f):
dim = find_geometric_dimension(f)
return Zero((dim,) + f.ufl_shape, f.ufl_free_indices,
f.ufl_index_dimensions)
return CompoundDerivative.__new__(cls)
def geometric_quantity(self, o):
"dg/dX = 0 if piecewise constant, otherwise ReferenceGrad(g)"
if is_cellwise_constant(o):
return self.independent_terminal(o)
else:
# TODO: Which types does this involve? I don't think the
# form compilers will handle this.
return ReferenceGrad(o)
def geometric_quantity(self, o):
"dg/dX = 0 if piecewise constant, otherwise ReferenceGrad(g)"
if is_cellwise_constant(o):
return self.independent_terminal(o)
else:
# TODO: Which types does this involve? I don't think the
# form compilers will handle this.
return ReferenceGrad(o)
def jacobian_inverse(self, o):
# grad(K) == K_ji rgrad(K)_rj
if is_cellwise_constant(o):
return self.independent_terminal(o)
if not o._ufl_is_terminal_:
error("ReferenceValue can only wrap a terminal")
Do = grad_to_reference_grad(o, o)
return Do
def geometric_quantity(self, o):
"""Default for geometric quantities is dg/dx = 0 if piecewise constant, otherwise keep Grad(g).
Override for specific types if other behaviour is needed."""
if is_cellwise_constant(o):
return self.independent_terminal(o)
else:
# TODO: Which types does this involve? I don't think the
# form compilers will handle this.
return Grad(o)
def geometric_quantity(self, o):
"""Default for geometric quantities is dg/dx = 0 if piecewise constant, otherwise keep Grad(g).
Override for specific types if other behaviour is needed."""
if is_cellwise_constant(o):
return self.independent_terminal(o)
else:
# TODO: Which types does this involve? I don't think the
# form compilers will handle this.
return Grad(o)
def __new__(cls, f):
if f.ufl_free_indices:
error("Free indices in the divergence argument is not allowed.")
# Return zero if expression is trivially constant
if is_cellwise_constant(f):
return Zero(f.ufl_shape[1:]) # No free indices asserted above
return CompoundDerivative.__new__(cls)
def jacobian_inverse(self, o):
# grad(K) == K_ji rgrad(K)_rj
if is_cellwise_constant(o):
return self.independent_terminal(o)
if not o._ufl_is_terminal_:
error("ReferenceValue can only wrap a terminal")
r = indices(len(o.ufl_shape))
i, j = indices(2)
Do = as_tensor(o[j, i] * ReferenceGrad(o)[r + (j, )], r + (i, ))
return Do
def jacobian_inverse(self, o):
# grad(K) == K_ji rgrad(K)_rj
if is_cellwise_constant(o):
return self.independent_terminal(o)
if not o._ufl_is_terminal_:
error("ReferenceValue can only wrap a terminal")
r = indices(len(o.ufl_shape))
i, j = indices(2)
Do = as_tensor(o[j, i]*ReferenceGrad(o)[r + (j,)], r + (i,))
return Do
def _ufl_expr_reconstruct_(self, op):
"Return a new object of the same type with new operands."
if is_cellwise_constant(op):
if op.ufl_shape != self.ufl_operands[0].ufl_shape:
error("Operand shape mismatch in NablaGrad reconstruct.")
if self.ufl_operands[0].ufl_free_indices != op.ufl_free_indices:
error("Free index mismatch in NablaGrad reconstruct.")
return Zero(self.ufl_shape, self.ufl_free_indices,
self.ufl_index_dimensions)
return self._ufl_class_(op)
def analyse_dependencies(F, mt_unique_table_reference):
# Sets 'status' of all nodes to either: 'inactive', 'piecewise' or 'varying'
# Children of 'target' nodes are either 'piecewise' or 'varying'.
# All other nodes are 'inactive'.
# Varying nodes are identified by their tables ('tr'). All their parent
# nodes are also set to 'varying' - any remaining active nodes are 'piecewise'.
# Set targets, and dependencies to 'active'
targets = [i for i, v in F.nodes.items() if v.get('target')]
for i, v in F.nodes.items():
v['status'] = 'inactive'
while targets:
s = targets.pop()
F.nodes[s]['status'] = 'active'
for j in F.out_edges[s]:
if F.nodes[j]['status'] == 'inactive':
targets.append(j)
# Build piecewise/varying markers for factorized_vertices
varying_ttypes = ("varying", "uniform", "quadrature")
varying_indices = []
for i, v in F.nodes.items():
if v.get('mt') is None:
continue
tr = v.get('tr')
if tr is not None:
ttype = tr.ttype
# Check if table computations have revealed values varying over points
# Note: uniform means entity-wise uniform, varying over points
if ttype in varying_ttypes:
varying_indices.append(i)
else:
if ttype not in ("fixed", "piecewise", "ones", "zeros"):
raise RuntimeError("Invalid ttype %s" % (ttype, ))
elif not is_cellwise_constant(v['expression']):
raise RuntimeError("Error")
# Keeping this check to be on the safe side,
# not sure which cases this will cover (if any)
# varying_indices.append(i)
# Set all parents of active varying nodes to 'varying'
while varying_indices:
s = varying_indices.pop()
if F.nodes[s]['status'] == 'active':
F.nodes[s]['status'] = 'varying'
for j in F.in_edges[s]:
varying_indices.append(j)
# Any remaining active nodes must be 'piecewise'
for i, v in F.nodes.items():
if v['status'] == 'active':
v['status'] = 'piecewise'
def geometric_quantity(self, o):
"""Default for geometric quantities is do/dx = 0 if piecewise constant,
otherwise transform derivatives to reference derivatives.
Override for specific types if other behaviour is needed."""
if is_cellwise_constant(o):
return self.independent_terminal(o)
else:
domain = o.ufl_domain()
K = JacobianInverse(domain)
Do = grad_to_reference_grad(o, K)
return Do
def default_partition_seed(expr, rank):
"""
Partition 0: Piecewise constant on each cell (including Real and DG0 coefficients)
Partition 1: Depends on x
Partition 2: Depends on x and coefficients
Partitions [3,3+rank): depend on argument with count partition-3
"""
# TODO: Use named constants for the partition numbers here
modifiers = (Grad, Restricted, Indexed
) # FIXME: Add CellAvg, FacetAvg types here, others?
if isinstance(expr, modifiers):
return default_partition_seed(expr.ufl_operands[0], rank)
elif isinstance(expr, Argument):
ac = expr.number()
assert 0 <= ac < rank
poffset = 3
p = poffset + ac
return p
elif isinstance(expr, Coefficient):
if is_cellwise_constant(
expr): # This is crap, doesn't include grad modifier
return 0
else:
return 2
elif isinstance(expr, GeometricQuantity):
if is_cellwise_constant(
expr): # This is crap, doesn't include grad modifier
return 0
else:
return 1
elif isinstance(expr, ConstantValue):
return 0
else:
error("Don't know how to handle %s" % expr)
def __new__(cls, f):
# Validate input
sh = f.ufl_shape
if f.ufl_shape not in ((), (2,), (3,)):
error("Expecting a scalar, 2D vector or 3D vector.")
if f.ufl_free_indices:
error("Free indices in the curl argument is not allowed.")
# Return zero if expression is trivially constant
if is_cellwise_constant(f):
sh = {(): (2,), (2,): (), (3,): (3,)}[sh]
return Zero(sh) # No free indices asserted above
return CompoundDerivative.__new__(cls)
def analyse_dependencies(V, V_deps, V_targets,
modified_terminal_indices,
modified_terminals,
mt_unique_table_reference):
# Count the number of dependencies every subexpr has
V_depcount = compute_dependency_count(V_deps)
# Build the 'inverse' of the sparse dependency matrix
inv_deps = invert_dependencies(V_deps, V_depcount)
# Mark subexpressions of V that are actually needed for final result
active, num_active = mark_active(V_deps, V_targets)
# Build piecewise/varying markers for factorized_vertices
varying_ttypes = ("varying", "uniform", "quadrature")
varying_indices = []
for i, mt in zip(modified_terminal_indices, modified_terminals):
tr = mt_unique_table_reference.get(mt)
if tr is not None:
ttype = tr.ttype
# Check if table computations have revealed values varying over points
# Note: uniform means entity-wise uniform, varying over points
if ttype in varying_ttypes:
varying_indices.append(i)
else:
if ttype not in ("fixed", "piecewise", "ones", "zeros"):
error("Invalid ttype %s" % (ttype,))
elif not is_cellwise_constant(V[i]):
# Keeping this check to be on the safe side,
# not sure which cases this will cover (if any)
varying_indices.append(i)
# Mark every subexpression that is computed
# from the spatially dependent terminals
varying, num_varying = mark_image(inv_deps, varying_indices)
# The rest of the subexpressions are piecewise constant (1-1=0, 1-0=1)
piecewise = 1 - varying
# Unmark non-active subexpressions
varying *= active
piecewise *= active
# TODO: Skip literals in both varying and piecewise
# nonliteral = ...
# varying *= nonliteral
# piecewise *= nonliteral
return inv_deps, active, piecewise, varying
def default_partition_seed(expr, rank):
"""
Partition 0: Piecewise constant on each cell (including Real and DG0 coefficients)
Partition 1: Depends on x
Partition 2: Depends on x and coefficients
Partitions [3,3+rank): depend on argument with count partition-3
"""
# TODO: Use named constants for the partition numbers here
modifiers = (Grad, Restricted, Indexed) # FIXME: Add CellAvg, FacetAvg types here, others?
if isinstance(expr, modifiers):
return default_partition_seed(expr.ufl_operands[0], rank)
elif isinstance(expr, Argument):
ac = expr.number()
assert 0 <= ac < rank
poffset = 3
p = poffset + ac
return p
elif isinstance(expr, Coefficient):
if is_cellwise_constant(expr): # This is crap, doesn't include grad modifier
return 0
else:
return 2
elif isinstance(expr, GeometricQuantity):
if is_cellwise_constant(expr): # This is crap, doesn't include grad modifier
return 0
else:
return 1
elif isinstance(expr, ConstantValue):
return 0
else:
error("Don't know how to handle %s" % expr)
def analyse_dependencies(V, V_deps, V_targets, modified_terminal_indices,
modified_terminals, mt_unique_table_reference):
# Count the number of dependencies every subexpr has
V_depcount = compute_dependency_count(V_deps)
# Build the 'inverse' of the sparse dependency matrix
inv_deps = invert_dependencies(V_deps, V_depcount)
# Mark subexpressions of V that are actually needed for final result
active, num_active = mark_active(V_deps, V_targets)
# Build piecewise/varying markers for factorized_vertices
varying_ttypes = ("varying", "uniform", "quadrature")
varying_indices = []
for i, mt in zip(modified_terminal_indices, modified_terminals):
tr = mt_unique_table_reference.get(mt)
if tr is not None:
ttype = tr.ttype
# Check if table computations have revealed values varying over points
# Note: uniform means entity-wise uniform, varying over points
if ttype in varying_ttypes:
varying_indices.append(i)
else:
if ttype not in ("fixed", "piecewise", "ones", "zeros"):
error("Invalid ttype %s" % (ttype, ))
elif not is_cellwise_constant(V[i]):
# Keeping this check to be on the safe side,
# not sure which cases this will cover (if any)
varying_indices.append(i)
# Mark every subexpression that is computed
# from the spatially dependent terminals
varying, num_varying = mark_image(inv_deps, varying_indices)
# The rest of the subexpressions are piecewise constant (1-1=0, 1-0=1)
piecewise = 1 - varying
# Unmark non-active subexpressions
varying *= active
piecewise *= active
# TODO: Skip literals in both varying and piecewise
# nonliteral = ...
# varying *= nonliteral
# piecewise *= nonliteral
return inv_deps, active, piecewise, varying
def test_always_cellwise_constant_geometric_quantities(domains):
"Test geometric quantities that are always constant over a cell."
e = CellVolume(domains)
assert is_cellwise_constant(e)
e = CellDiameter(domains)
assert is_cellwise_constant(e)
e = Circumradius(domains)
assert is_cellwise_constant(e)
e = FacetArea(domains)
assert is_cellwise_constant(e)
e = MinFacetEdgeLength(domains)
assert is_cellwise_constant(e)
e = MaxFacetEdgeLength(domains)
assert is_cellwise_constant(e)
def mappings_are_cellwise_constant(domain, test):
e = Jacobian(domain)
assert is_cellwise_constant(e) == test
e = JacobianDeterminant(domain)
assert is_cellwise_constant(e) == test
e = JacobianInverse(domain)
assert is_cellwise_constant(e) == test
if domain.topological_dimension() != 1:
e = FacetJacobian(domain)
assert is_cellwise_constant(e) == test
e = FacetJacobianDeterminant(domain)
assert is_cellwise_constant(e) == test
e = FacetJacobianInverse(domain)
assert is_cellwise_constant(e) == test
def mappings_are_cellwise_constant(domain, test):
e = Jacobian(domain)
assert is_cellwise_constant(e) == test
e = JacobianDeterminant(domain)
assert is_cellwise_constant(e) == test
e = JacobianInverse(domain)
assert is_cellwise_constant(e) == test
if domain.topological_dimension() != 1:
e = FacetJacobian(domain)
assert is_cellwise_constant(e) == test
e = FacetJacobianDeterminant(domain)
assert is_cellwise_constant(e) == test
e = FacetJacobianInverse(domain)
assert is_cellwise_constant(e) == test
def test_coordinates_never_cellwise_constant(domains):
e = SpatialCoordinate(domains)
assert not is_cellwise_constant(e)
e = CellCoordinate(domains)
assert not is_cellwise_constant(e)
def facetnormal_cellwise_constant(domain, test):
e = FacetNormal(domain)
assert is_cellwise_constant(e) == test
def test_coefficient_mostly_not_cellwise_constant(domains_not_linear):
V = FiniteElement("DG", domains_not_linear.ufl_cell(), 1)
e = Coefficient(V)
assert not is_cellwise_constant(e)
e = TestFunction(V)
assert not is_cellwise_constant(e)
def grad(self, o):
# Peel off the Grads and count them, and get restriction if
# it's between the grad and the terminal
ngrads = 0
restricted = ''
rv = False
while not o._ufl_is_terminal_:
if isinstance(o, Grad):
o, = o.ufl_operands
ngrads += 1
elif isinstance(o, Restricted):
restricted = o.side()
o, = o.ufl_operands
elif isinstance(o, ReferenceValue):
rv = True
o, = o.ufl_operands
else:
error("Invalid type %s" % o._ufl_class_.__name__)
f = o
if rv:
f = ReferenceValue(f)
# Get domain and create Jacobian inverse object
domain = o.ufl_domain()
Jinv = JacobianInverse(domain)
if is_cellwise_constant(Jinv):
# Optimise slightly by turning Grad(Grad(...)) into
# J^(-T)J^(-T)RefGrad(RefGrad(...))
# rather than J^(-T)RefGrad(J^(-T)RefGrad(...))
# Create some new indices
ii = indices(len(f.ufl_shape)) # Indices to get to the scalar component of f
jj = indices(ngrads) # Indices to sum over the local gradient axes with the inverse Jacobian
kk = indices(ngrads) # Indices for the leftover inverse Jacobian axes
# Preserve restricted property
if restricted:
Jinv = Jinv(restricted)
f = f(restricted)
# Apply the same number of ReferenceGrad without mappings
lgrad = f
for i in range(ngrads):
lgrad = ReferenceGrad(lgrad)
# Apply mappings with scalar indexing operations (assumes
# ReferenceGrad(Jinv) is zero)
jinv_lgrad_f = lgrad[ii + jj]
for j, k in zip(jj, kk):
jinv_lgrad_f = Jinv[j, k] * jinv_lgrad_f
# Wrap back in tensor shape, derivative axes at the end
jinv_lgrad_f = as_tensor(jinv_lgrad_f, ii + kk)
else:
# J^(-T)RefGrad(J^(-T)RefGrad(...))
# Preserve restricted property
if restricted:
Jinv = Jinv(restricted)
f = f(restricted)
jinv_lgrad_f = f
for foo in range(ngrads):
ii = indices(len(jinv_lgrad_f.ufl_shape)) # Indices to get to the scalar component of f
j, k = indices(2)
lgrad = ReferenceGrad(jinv_lgrad_f)
jinv_lgrad_f = Jinv[j, k] * lgrad[ii + (j,)]
# Wrap back in tensor shape, derivative axes at the end
jinv_lgrad_f = as_tensor(jinv_lgrad_f, ii + (k,))
return jinv_lgrad_f
def coefficient(self, o):
if is_cellwise_constant(o):
return self.independent_terminal(o)
return Grad(o)
def coefficient(self, o):
if is_cellwise_constant(o):
return self.independent_terminal(o)
return Grad(o)
def test_coefficient_mostly_not_cellwise_constant(domains_not_linear):
V = FiniteElement("DG", domains_not_linear.ufl_cell(), 1)
e = Coefficient(V)
assert not is_cellwise_constant(e)
e = TestFunction(V)
assert not is_cellwise_constant(e)
def test_coordinates_never_cellwise_constant(domains):
e = SpatialCoordinate(domains)
assert not is_cellwise_constant(e)
e = CellCoordinate(domains)
assert not is_cellwise_constant(e)
def facetnormal_cellwise_constant(domain, test):
e = FacetNormal(domain)
assert is_cellwise_constant(e) == test