def __init__(self, family, cell=None, degree=None, dim=None,
form_degree=None, quad_scheme=None):
"""
Create vector element (repeated mixed element)
*Arguments*
family (string)
The finite element family (or an existing FiniteElement)
cell
The geometric cell, ignored if family is a FiniteElement
degree (int)
The polynomial degree, ignored if family is a FiniteElement
dim (int)
The value dimension of the element (optional)
form_degree (int)
The form degree (FEEC notation, used when field is
viewed as k-form), ignored if family is a FiniteElement
quad_scheme
The quadrature scheme (optional), ignored if family is a FiniteElement
"""
if isinstance(family, FiniteElementBase):
sub_element = family
cell = sub_element.cell()
else:
if cell is not None:
cell = as_cell(cell)
# Create sub element
sub_element = FiniteElement(family, cell, degree,
form_degree=form_degree,
quad_scheme=quad_scheme)
# Set default size if not specified
if dim is None:
if cell is None:
error("Cannot infer vector dimension without a cell.")
dim = cell.geometric_dimension()
# Create list of sub elements for mixed element constructor
sub_elements = [sub_element]*dim
# Compute value shapes
value_shape = (dim,) + sub_element.value_shape()
reference_value_shape = (dim,) + sub_element.reference_value_shape()
# Initialize element data
MixedElement.__init__(self, sub_elements, value_shape=value_shape,
reference_value_shape=reference_value_shape)
# FIXME: Storing this here is strange, isn't that handled by
# subclass?
self._family = sub_element.family()
self._degree = sub_element.degree()
self._sub_element = sub_element
# Cache repr string
self._repr = "VectorElement(%s, dim=%d)" % (
repr(sub_element), len(self._sub_elements))
def __init__(self, family, cell=None, degree=None, dim=None,
form_degree=None, quad_scheme=None):
"""
Create vector element (repeated mixed element)
*Arguments*
family (string)
The finite element family (or an existing FiniteElement)
cell
The geometric cell, ignored if family is a FiniteElement
degree (int)
The polynomial degree, ignored if family is a FiniteElement
dim (int)
The value dimension of the element (optional)
form_degree (int)
The form degree (FEEC notation, used when field is
viewed as k-form), ignored if family is a FiniteElement
quad_scheme
The quadrature scheme (optional), ignored if family is a FiniteElement
"""
if isinstance(family, FiniteElementBase):
sub_element = family
cell = sub_element.cell()
else:
if cell is not None:
cell = as_cell(cell)
# Create sub element
sub_element = FiniteElement(family, cell, degree,
form_degree=form_degree,
quad_scheme=quad_scheme)
# Set default size if not specified
if dim is None:
if cell is None:
error("Cannot infer vector dimension without a cell.")
dim = cell.geometric_dimension()
# Create list of sub elements for mixed element constructor
sub_elements = [sub_element] * dim
# Compute value shapes
value_shape = (dim,) + sub_element.value_shape()
reference_value_shape = (dim,) + sub_element.reference_value_shape()
# Initialize element data
MixedElement.__init__(self, sub_elements, value_shape=value_shape,
reference_value_shape=reference_value_shape)
# FIXME: Storing this here is strange, isn't that handled by
# subclass?
self._family = sub_element.family()
self._degree = sub_element.degree()
self._sub_element = sub_element
# Cache repr string
self._repr = "VectorElement(%s, dim=%d)" % (
repr(sub_element), len(self._sub_elements))
def __init__(self,
family,
cell=None,
degree=None,
shape=None,
symmetry=None,
quad_scheme=None):
"""Create tensor element (repeated mixed element with optional symmetries).
:arg family: The family string, or an existing FiniteElement.
:arg cell: The geometric cell (ignored if family is a FiniteElement).
:arg degree: The polynomial degree (ignored if family is a FiniteElement).
:arg shape: The shape of the element (defaults to a square
tensor given by the geometric dimension of the cell).
:arg symmetry: Optional symmetries.
:arg quad_scheme: Optional quadrature scheme (ignored if
family is a FiniteElement)."""
if isinstance(family, FiniteElementBase):
sub_element = family
cell = sub_element.cell()
else:
if cell is not None:
cell = as_cell(cell)
# Create scalar sub element
sub_element = FiniteElement(family,
cell,
degree,
quad_scheme=quad_scheme)
# Set default shape if not specified
if shape is None:
if cell is None:
error("Cannot infer tensor shape without a cell.")
dim = cell.geometric_dimension()
shape = (dim, dim)
if symmetry is None:
symmetry = EmptyDict
elif symmetry is True:
# Construct default symmetry dict for matrix elements
if not (len(shape) == 2 and shape[0] == shape[1]):
error("Cannot set automatic symmetry for non-square tensor.")
symmetry = dict(((i, j), (j, i)) for i in range(shape[0])
for j in range(shape[1]) if i > j)
else:
if not isinstance(symmetry, dict):
error("Expecting symmetry to be None (unset), True, or dict.")
# Validate indices in symmetry dict
for i, j in symmetry.items():
if len(i) != len(j):
error("Non-matching length of symmetry index tuples.")
for k in range(len(i)):
if not (i[k] >= 0 and j[k] >= 0 and i[k] < shape[k]
and j[k] < shape[k]):
error("Symmetry dimensions out of bounds.")
# Compute all index combinations for given shape
indices = compute_indices(shape)
# Compute mapping from indices to sub element number,
# accounting for symmetry
sub_elements = []
sub_element_mapping = {}
for index in indices:
if index in symmetry:
continue
sub_element_mapping[index] = len(sub_elements)
sub_elements += [sub_element]
# Update mapping for symmetry
for index in indices:
if index in symmetry:
sub_element_mapping[index] = sub_element_mapping[
symmetry[index]]
flattened_sub_element_mapping = [
sub_element_mapping[index] for i, index in enumerate(indices)
]
# Compute value shape
value_shape = shape
# Compute reference value shape based on symmetries
if symmetry:
# Flatten and subtract symmetries
reference_value_shape = (product(shape) - len(symmetry), )
self._mapping = "symmetries"
else:
# Do not flatten if there are no symmetries
reference_value_shape = shape
self._mapping = "identity"
value_shape = value_shape + sub_element.value_shape()
reference_value_shape = reference_value_shape + sub_element.reference_value_shape(
)
# Initialize element data
MixedElement.__init__(self,
sub_elements,
value_shape=value_shape,
reference_value_shape=reference_value_shape)
self._family = sub_element.family()
self._degree = sub_element.degree()
self._sub_element = sub_element
self._shape = shape
self._symmetry = symmetry
self._sub_element_mapping = sub_element_mapping
self._flattened_sub_element_mapping = flattened_sub_element_mapping
# Cache repr string
self._repr = "TensorElement(%s, shape=%s, symmetry=%s)" % (
repr(sub_element), repr(self._shape), repr(self._symmetry))
def __init__(self, family, cell=None, degree=None, dim=None,
form_degree=None, quad_scheme=None, variant=None):
"""
Create vector element (repeated mixed element)
*Arguments*
family (string)
The finite element family (or an existing FiniteElement)
cell
The geometric cell, ignored if family is a FiniteElement
degree (int)
The polynomial degree, ignored if family is a FiniteElement
dim (int)
The value dimension of the element (optional)
form_degree (int)
The form degree (FEEC notation, used when field is
viewed as k-form), ignored if family is a FiniteElement
quad_scheme
The quadrature scheme (optional), ignored if family is a FiniteElement
variant
Hint for the local basis function variant (optional)
"""
if isinstance(family, FiniteElementBase):
sub_element = family
cell = sub_element.cell()
variant = sub_element.variant()
else:
if cell is not None:
cell = as_cell(cell)
# Create sub element
sub_element = FiniteElement(family, cell, degree,
form_degree=form_degree,
quad_scheme=quad_scheme,
variant=variant)
# Set default size if not specified
if dim is None:
if cell is None:
error("Cannot infer vector dimension without a cell.")
dim = cell.geometric_dimension()
self._mapping = sub_element.mapping()
# Create list of sub elements for mixed element constructor
sub_elements = [sub_element] * dim
# Compute value shapes
value_shape = (dim,) + sub_element.value_shape()
reference_value_shape = (dim,) + sub_element.reference_value_shape()
# Initialize element data
MixedElement.__init__(self, sub_elements, value_shape=value_shape,
reference_value_shape=reference_value_shape)
FiniteElementBase.__init__(self, sub_element.family(), cell, sub_element.degree(), quad_scheme,
value_shape, reference_value_shape)
self._sub_element = sub_element
if variant is None:
var_str = ""
else:
var_str = ", variant='" + variant + "'"
# Cache repr string
self._repr = "VectorElement(%s, dim=%d%s)" % (
repr(sub_element), len(self._sub_elements), var_str)