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) if sub_element.value_shape() != (): error("Expecting only scalar valued subelement for TensorElement.") # 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" # 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, 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)