def point_evaluation(self, order, point, entity=None):
entities = self._factor_entity(entity)
entity_dim, _ = zip(*entities)
# Split point expression
assert len(self.cell.cells) == len(entity_dim)
point_dims = [
cell.construct_subelement(dim).get_spatial_dimension()
for cell, dim in zip(self.cell.cells, entity_dim)
]
assert isinstance(point,
gem.Node) and point.shape == (sum(point_dims), )
slices = TensorProductCell._split_slices(point_dims)
point_factors = []
for s in slices:
point_factors.append(
gem.ListTensor([
gem.Indexed(point, (i, )) for i in range(s.start, s.stop)
]))
# Subelement results
factor_results = [
fe.point_evaluation(order, p_, e)
for fe, p_, e in zip(self.factors, point_factors, entities)
]
return self._merge_evaluations(factor_results)
def basis_evaluation(self, order, ps, entity=None):
# Default entity
if entity is None:
entity = (self.cell.get_dimension(), 0)
entity_dim, entity_id = entity
# Factor entity
assert isinstance(entity_dim, tuple)
assert len(entity_dim) == len(self.factors)
shape = tuple(
len(c.get_topology()[d])
for c, d in zip(self.cell.cells, entity_dim))
entities = list(zip(entity_dim, numpy.unravel_index(entity_id, shape)))
# Factor point set
ps_factors = factor_point_set(self.cell, entity_dim, ps)
# Subelement results
factor_results = [
fe.basis_evaluation(order, ps_, e)
for fe, ps_, e in zip(self.factors, ps_factors, entities)
]
# Spatial dimension
dimension = self.cell.get_spatial_dimension()
# A list of slices that are used to select dimensions
# corresponding to each subelement.
dim_slices = TensorProductCell._split_slices(
[c.get_spatial_dimension() for c in self.cell.cells])
# A list of multiindices, one multiindex per subelement, each
# multiindex describing the shape of basis functions of the
# subelement.
alphas = [fe.get_indices() for fe in self.factors]
result = {}
for derivative in range(order + 1):
for Delta in mis(dimension, derivative):
# Split the multiindex for the subelements
deltas = [Delta[s] for s in dim_slices]
# GEM scalars (can have free indices) for collecting
# the contributions from the subelements.
scalars = []
for fr, delta, alpha in zip(factor_results, deltas, alphas):
# Turn basis shape to free indices, select the
# right derivative entry, and collect the result.
scalars.append(gem.Indexed(fr[delta], alpha))
# Multiply the values from the subelements and wrap up
# non-point indices into shape.
result[Delta] = gem.ComponentTensor(
reduce(gem.Product, scalars), tuple(chain(*alphas)))
return result
def _merge_evaluations(self, factor_results):
# Spatial dimension
dimension = self.cell.get_spatial_dimension()
# Derivative order
order = max(map(sum, chain(*factor_results)))
# A list of slices that are used to select dimensions
# corresponding to each subelement.
dim_slices = TensorProductCell._split_slices([c.get_spatial_dimension()
for c in self.cell.cells])
# A list of multiindices, one multiindex per subelement, each
# multiindex describing the shape of basis functions of the
# subelement.
alphas = [fe.get_indices() for fe in self.factors]
# A list of multiindices, one multiindex per subelement, each
# multiindex describing the value shape of the subelement.
zetas = [fe.get_value_indices() for fe in self.factors]
result = {}
for derivative in range(order + 1):
for Delta in mis(dimension, derivative):
# Split the multiindex for the subelements
deltas = [Delta[s] for s in dim_slices]
# GEM scalars (can have free indices) for collecting
# the contributions from the subelements.
scalars = []
for fr, delta, alpha, zeta in zip(factor_results, deltas, alphas, zetas):
# Turn basis shape to free indices, select the
# right derivative entry, and collect the result.
scalars.append(gem.Indexed(fr[delta], alpha + zeta))
# Multiply the values from the subelements and wrap up
# non-point indices into shape.
result[Delta] = gem.ComponentTensor(
reduce(gem.Product, scalars),
tuple(chain(*(alphas + zetas)))
)
return result
def _merge_evaluations(self, factor_results):
# Spatial dimension
dimension = self.cell.get_spatial_dimension()
# Derivative order
order = max(map(sum, chain(*factor_results)))
# A list of slices that are used to select dimensions
# corresponding to each subelement.
dim_slices = TensorProductCell._split_slices([c.get_spatial_dimension()
for c in self.cell.cells])
# A list of multiindices, one multiindex per subelement, each
# multiindex describing the shape of basis functions of the
# subelement.
alphas = [fe.get_indices() for fe in self.factors]
# A list of multiindices, one multiindex per subelement, each
# multiindex describing the value shape of the subelement.
zetas = [fe.get_value_indices() for fe in self.factors]
result = {}
for derivative in range(order + 1):
for Delta in mis(dimension, derivative):
# Split the multiindex for the subelements
deltas = [Delta[s] for s in dim_slices]
# GEM scalars (can have free indices) for collecting
# the contributions from the subelements.
scalars = []
for fr, delta, alpha, zeta in zip(factor_results, deltas, alphas, zetas):
# Turn basis shape to free indices, select the
# right derivative entry, and collect the result.
scalars.append(gem.Indexed(fr[delta], alpha + zeta))
# Multiply the values from the subelements and wrap up
# non-point indices into shape.
result[Delta] = gem.ComponentTensor(
reduce(gem.Product, scalars),
tuple(chain(*(alphas + zetas)))
)
return result
def point_evaluation(self, order, point, entity=None):
entities = self._factor_entity(entity)
entity_dim, _ = zip(*entities)
# Split point expression
assert len(self.cell.cells) == len(entity_dim)
point_dims = [cell.construct_subelement(dim).get_spatial_dimension()
for cell, dim in zip(self.cell.cells, entity_dim)]
assert isinstance(point, gem.Node) and point.shape == (sum(point_dims),)
slices = TensorProductCell._split_slices(point_dims)
point_factors = []
for s in slices:
point_factors.append(gem.ListTensor(
[gem.Indexed(point, (i,))
for i in range(s.start, s.stop)]
))
# Subelement results
factor_results = [fe.point_evaluation(order, p_, e)
for fe, p_, e in zip(self.factors, point_factors, entities)]
return self._merge_evaluations(factor_results)
def factor_point_set(product_cell, product_dim, point_set):
"""Factors a point set for the product element into a point sets for
each subelement.
:arg product_cell: a TensorProductCell
:arg product_dim: entity dimension for the product cell
:arg point_set: point set for the product element
"""
assert len(product_cell.cells) == len(product_dim)
point_dims = [
cell.construct_subelement(dim).get_spatial_dimension()
for cell, dim in zip(product_cell.cells, product_dim)
]
if isinstance(point_set, TensorPointSet):
# Just give the factors asserting matching dimensions.
assert len(point_set.factors) == len(point_dims)
assert all(ps.dimension == dim
for ps, dim in zip(point_set.factors, point_dims))
return point_set.factors
# Split the point coordinates along the point dimensions
# required by the subelements.
assert point_set.dimension == sum(point_dims)
slices = TensorProductCell._split_slices(point_dims)
if isinstance(point_set, PointSingleton):
return [PointSingleton(point_set.point[s]) for s in slices]
elif isinstance(point_set, PointSet):
# Use the same point index for the new point sets.
result = []
for s in slices:
ps = PointSet(point_set.points[:, s])
ps.indices = point_set.indices
result.append(ps)
return result
raise NotImplementedError("How to tabulate TensorProductElement on %s?" %
(type(point_set).__name__, ))
def factor_point_set(product_cell, product_dim, point_set):
"""Factors a point set for the product element into a point sets for
each subelement.
:arg product_cell: a TensorProductCell
:arg product_dim: entity dimension for the product cell
:arg point_set: point set for the product element
"""
assert len(product_cell.cells) == len(product_dim)
point_dims = [cell.construct_subelement(dim).get_spatial_dimension()
for cell, dim in zip(product_cell.cells, product_dim)]
if isinstance(point_set, TensorPointSet):
# Just give the factors asserting matching dimensions.
assert len(point_set.factors) == len(point_dims)
assert all(ps.dimension == dim
for ps, dim in zip(point_set.factors, point_dims))
return point_set.factors
# Split the point coordinates along the point dimensions
# required by the subelements.
assert point_set.dimension == sum(point_dims)
slices = TensorProductCell._split_slices(point_dims)
if isinstance(point_set, PointSingleton):
return [PointSingleton(point_set.point[s]) for s in slices]
elif isinstance(point_set, PointSet):
# Use the same point index for the new point sets.
result = []
for s in slices:
ps = PointSet(point_set.points[:, s])
ps.indices = point_set.indices
result.append(ps)
return result
raise NotImplementedError("How to tabulate TensorProductElement on %s?" % (type(point_set).__name__,))