def tabulate(self, ufl_element, max_deriv):
"""Prepare the tabulations of a finite element up to a given
derivative order.
:arg ufl_element: UFL element to tabulate
:arg max_deriv: tabulate derivatives up this order
"""
store = collections.defaultdict(list)
for tabulator in self.tabulators:
for c, D, table in tabulator(ufl_element, max_deriv):
store[(ufl_element, c, D)].append(table)
for key, tables in iteritems(store):
table = gem.ListTensor(tables)
if len(table.shape) == 2:
# Cellwise constant; must not depend on the facet
assert compat.allclose(table.array, table.array.mean(axis=0, keepdims=True), equal_nan=True)
table = gem.Literal(table.array[0])
self.tables[key] = table
def tabulate(ufl_element, order, points, entity, epsilon):
"""Ask FIAT to tabulate ``points`` up to order ``order``, then
rearranges the result into a series of ``(c, D, table)`` tuples,
where:
c: component index (for vector-valued and tensor-valued elements)
D: derivative tuple (e.g. (1, 2) means d/dx d^2/dy^2)
table: tabulation matrix for the given component and derivative.
shape: len(points) x space_dimension
:arg ufl_element: element to tabulate
:arg order: FIAT gives all derivatives up to this order
:arg points: points to tabulate the element on
:arg entity: particular entity to tabulate on
"""
element = create_element(ufl_element)
phi = element.space_dimension()
C = ufl_element.reference_value_size()
q = len(points)
for D, fiat_table in iteritems(element.tabulate(order, points, entity)):
if isinstance(fiat_table, Exception):
# In the case an exception is found in the fiat table, do not
# perform any rounding
gem_fail = gem.Failure((q, phi), fiat_table)
for c in range(C):
yield c, D, gem_fail
else:
reordered_table = fiat_table.reshape(phi, C, q).transpose(1, 2, 0) # (C, q, phi)
for c, table in enumerate(reordered_table):
# Copied from FFC (ffc/quadrature/quadratureutils.py)
table[abs(table) < epsilon] = 0
table[abs(table - 1.0) < epsilon] = 1.0
table[abs(table + 1.0) < epsilon] = -1.0
table[abs(table - 0.5) < epsilon] = 0.5
table[abs(table + 0.5) < epsilon] = -0.5
if spanning_degree(ufl_element) <= sum(D) and ufl_element.family() != "HDiv Trace":
assert compat.allclose(table, table.mean(axis=0, keepdims=True), equal_nan=True)
table = table[0]
yield c, D, gem.Literal(table)
