class Operator(Expr):
"Base class for all operators, i.e. non-terminal expression types."
__slots__ = as_native_strings(("ufl_operands", ))
def __init__(self, operands=None):
Expr.__init__(self)
# If operands is None, the type sets this itself. This is to
# get around some tricky too-fancy __new__/__init__ design in
# algebra.py, for now. It would be nicer to make the classes
# in algebra.py pass operands here.
if operands is not None:
self.ufl_operands = operands
def _ufl_expr_reconstruct_(self, *operands):
"Return a new object of the same type with new operands."
return self._ufl_class_(*operands)
def _ufl_signature_data_(self):
return self._ufl_typecode_
def _ufl_compute_hash_(self):
"Compute a hash code for this expression. Used by sets and dicts."
return hash((self._ufl_typecode_, ) +
tuple(hash(o) for o in self.ufl_operands))
def __repr__(self):
"Default repr string construction for operators."
# This should work for most cases
r = "%s(%s)" % (self._ufl_class_.__name__, ", ".join(
repr(op) for op in self.ufl_operands))
return as_native_str(r)
class BinaryCondition(Condition):
__slots__ = as_native_strings(('_name',))
def __init__(self, name, left, right):
left = as_ufl(left)
right = as_ufl(right)
Condition.__init__(self, (left, right))
self._name = name
if name in ('!=', '=='):
# Since equals and not-equals are used for comparing
# representations, we have to allow any shape here. The
# scalar properties must be checked when used in
# conditional instead!
pass
elif name in ('&&', '||'):
# Binary operators acting on boolean expressions allow
# only conditions
for arg in (left, right):
if not isinstance(arg, Condition):
error("Expecting a Condition, not %s." % ufl_err_str(arg))
else:
# Binary operators acting on non-boolean expressions allow
# only scalars
if left.ufl_shape != () or right.ufl_shape != ():
error("Expecting scalar arguments.")
if left.ufl_free_indices != () or right.ufl_free_indices != ():
error("Expecting scalar arguments.")
def __str__(self):
return "%s %s %s" % (parstr(self.ufl_operands[0], self),
self._name, parstr(self.ufl_operands[1], self))
class Cross(CompoundTensorOperator):
__slots__ = as_native_strings(("ufl_free_indices",
"ufl_index_dimensions"))
def __new__(cls, a, b):
ash = a.ufl_shape
bsh = b.ufl_shape
# Checks
if not (len(ash) == 1 and ash == bsh):
error("Cross product requires arguments of rank 1, got %s and %s." % (
ufl_err_str(a), ufl_err_str(b)))
# Simplification
if isinstance(a, Zero) or isinstance(b, Zero):
fi, fid = merge_nonoverlapping_indices(a, b)
return Zero(ash, fi, fid)
return CompoundTensorOperator.__new__(cls)
def __init__(self, a, b):
CompoundTensorOperator.__init__(self, (a, b))
fi, fid = merge_nonoverlapping_indices(a, b)
self.ufl_free_indices = fi
self.ufl_index_dimensions = fid
ufl_shape = (3,)
def __str__(self):
return "%s x %s" % (parstr(self.ufl_operands[0], self),
parstr(self.ufl_operands[1], self))
class NablaGrad(CompoundDerivative):
__slots__ = as_native_strings(("_dim",))
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 __init__(self, f):
CompoundDerivative.__init__(self, (f,))
self._dim = find_geometric_dimension(f)
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)
@property
def ufl_shape(self):
return (self._dim,) + self.ufl_operands[0].ufl_shape
def __str__(self):
return "nabla_grad(%s)" % self.ufl_operands[0]
class MathFunction(Operator):
"Base class for all unary scalar math functions."
# Freeze member variables for objects in this class
__slots__ = as_native_strings(("_name", ))
def __init__(self, name, argument):
Operator.__init__(self, (argument, ))
if not is_true_ufl_scalar(argument):
error("Expecting scalar argument.")
self._name = name
def evaluate(self, x, mapping, component, index_values):
a = self.ufl_operands[0].evaluate(x, mapping, component, index_values)
try:
if isinstance(a, numbers.Real):
res = getattr(math, self._name)(a)
else:
res = getattr(cmath, self._name)(a)
except ValueError:
warning(
'Value error in evaluation of function %s with argument %s.' %
(self._name, a))
raise
return res
def __str__(self):
return "%s(%s)" % (self._name, self.ufl_operands[0])
class MeasureSum(object):
"""Represents a sum of measures.
This is a notational intermediate object to translate the notation
f*(ds(1)+ds(3))
into
f*ds(1) + f*ds(3)
"""
__slots__ = as_native_strings(("_measures",))
def __init__(self, *measures):
self._measures = measures
def __rmul__(self, other):
integrals = [other*m for m in self._measures]
return sum(integrals)
def __add__(self, other):
if isinstance(other, Measure):
return MeasureSum(*(self._measures + (other,)))
elif isinstance(other, MeasureSum):
return MeasureSum(*(self._measures + other._measures))
return NotImplemented
def __str__(self):
return "{\n " + "\n + ".join(map(str, self._measures)) + "\n}"
class Outer(CompoundTensorOperator):
__slots__ = as_native_strings(("ufl_free_indices",
"ufl_index_dimensions"))
def __new__(cls, a, b):
ash, bsh = a.ufl_shape, b.ufl_shape
if isinstance(a, Zero) or isinstance(b, Zero):
fi, fid = merge_nonoverlapping_indices(a, b)
return Zero(ash + bsh, fi, fid)
if ash == () or bsh == ():
return a * b
return CompoundTensorOperator.__new__(cls)
def __init__(self, a, b):
CompoundTensorOperator.__init__(self, (a, b))
fi, fid = merge_nonoverlapping_indices(a, b)
self.ufl_free_indices = fi
self.ufl_index_dimensions = fid
@property
def ufl_shape(self):
return self.ufl_operands[0].ufl_shape + self.ufl_operands[1].ufl_shape
def __str__(self):
return "%s (X) %s" % (parstr(self.ufl_operands[0], self),
parstr(self.ufl_operands[1], self))
class Index(IndexBase):
"""UFL value: An index with no value assigned.
Used to represent free indices in Einstein indexing notation."""
__slots__ = as_native_strings(("_count", ))
_globalcount = 0
def __init__(self, count=None):
IndexBase.__init__(self)
counted_init(self, count, Index)
def count(self):
return self._count
def __hash__(self):
return hash(("Index", self._count))
def __eq__(self, other):
return isinstance(other, Index) and (self._count == other._count)
def __str__(self):
c = str(self._count)
if len(c) > 1:
c = "{%s}" % c
return "i_%s" % c
def __repr__(self):
r = "Index(%d)" % self._count
return as_native_str(r)
class Inner(CompoundTensorOperator):
__slots__ = as_native_strings(("ufl_free_indices",
"ufl_index_dimensions"))
def __new__(cls, a, b):
# Checks
ash, bsh = a.ufl_shape, b.ufl_shape
if ash != bsh:
error("Shapes do not match: %s and %s." % (ufl_err_str(a), ufl_err_str(b)))
# Simplification
if isinstance(a, Zero) or isinstance(b, Zero):
fi, fid = merge_nonoverlapping_indices(a, b)
return Zero((), fi, fid)
elif ash == ():
return a*b
return CompoundTensorOperator.__new__(cls)
def __init__(self, a, b):
# sort operands for unique representation, must be independent
# of various counts etc. as explained in cmp_expr
a, b = sorted_expr((a, b))
CompoundTensorOperator.__init__(self, (a, b))
fi, fid = merge_nonoverlapping_indices(a, b)
self.ufl_free_indices = fi
self.ufl_index_dimensions = fid
ufl_shape = ()
def __str__(self):
return "%s : %s" % (parstr(self.ufl_operands[0], self),
parstr(self.ufl_operands[1], self))
class Identity(ConstantValue):
"UFL literal type: Representation of an identity matrix."
__slots__ = as_native_strings(("_dim", "ufl_shape"))
def __init__(self, dim):
ConstantValue.__init__(self)
self._dim = dim
self.ufl_shape = (dim, dim)
def evaluate(self, x, mapping, component, index_values):
"Evaluates the identity matrix on the given components."
a, b = component
return 1 if a == b else 0
def __getitem__(self, key):
if len(key) != 2:
error("Size mismatch for Identity.")
if all(isinstance(k, (int, FixedIndex)) for k in key):
return IntValue(1) if (int(key[0]) == int(key[1])) else Zero()
return Expr.__getitem__(self, key)
def __str__(self):
return "I"
def __repr__(self):
r = "Identity(%d)" % self._dim
return as_native_str(r)
def __eq__(self, other):
return isinstance(other, Identity) and self._dim == other._dim
class ScalarValue(ConstantValue):
"A constant scalar value."
__slots__ = as_native_strings(("_value",))
def __init__(self, value):
ConstantValue.__init__(self)
self._value = value
def value(self):
return self._value
def evaluate(self, x, mapping, component, index_values):
return self._value
def __eq__(self, other):
"""This is implemented to allow comparison with python scalars.
Note that this will make IntValue(1) != FloatValue(1.0),
but ufl-python comparisons like
IntValue(1) == 1.0
FloatValue(1.0) == 1
can still succeed. These will however not have the same
hash value and therefore not collide in a dict.
"""
if isinstance(other, self._ufl_class_):
return self._value == other._value
elif isinstance(other, (int, float)):
# FIXME: Disallow this, require explicit 'expr ==
# IntValue(3)' instead to avoid ambiguities!
return other == self._value
else:
return False
def __str__(self):
return str(self._value)
def __float__(self):
return float(self._value)
def __int__(self):
return int(self._value)
def __complex__(self):
return complex(self._value)
def __neg__(self):
return type(self)(-self._value)
def __abs__(self):
return type(self)(abs(self._value))
def real(self):
return self._value.real
def imag(self):
return self._value.imag
class IntegralData(object):
"""Utility class with the members (domain, integral_type,
subdomain_id, integrals, metadata)
where metadata is an empty dictionary that may be used for
associating metadata with each object.
"""
__slots__ = as_native_strings(
('domain', 'integral_type', 'subdomain_id', 'integrals', 'metadata',
'integral_coefficients', 'enabled_coefficients'))
def __init__(self, domain, integral_type, subdomain_id, integrals,
metadata):
if 1 != len(set(itg.ufl_domain() for itg in integrals)):
error("Multiple domains mismatch in integral data.")
if not all(integral_type == itg.integral_type() for itg in integrals):
error("Integral type mismatch in integral data.")
if not all(subdomain_id == itg.subdomain_id() for itg in integrals):
error("Subdomain id mismatch in integral data.")
self.domain = domain
self.integral_type = integral_type
self.subdomain_id = subdomain_id
self.integrals = integrals
# This is populated in preprocess using data not available at
# this stage:
self.integral_coefficients = None
self.enabled_coefficients = None
# TODO: I think we can get rid of this with some refactoring
# in ffc:
self.metadata = metadata
def __lt__(self, other):
# To preserve behaviour of extract_integral_data:
return ((self.integral_type, self.subdomain_id, self.integrals,
self.metadata) < (other.integral_type, other.subdomain_id,
other.integrals, other.metadata))
def __eq__(self, other):
# Currently only used for tests:
return (self.integral_type == other.integral_type
and self.subdomain_id == other.subdomain_id
and self.integrals == other.integrals
and self.metadata == other.metadata)
def __str__(self):
s = "IntegralData over domain(%s, %s), with integrals:\n%s\nand metadata:\n%s" % (
self.integral_type, self.subdomain_id, '\n\n'.join(
map(str, self.integrals)), self.metadata)
return s
class AbstractCell(object):
"""Representation of an abstract finite element cell with only the
dimensions known.
"""
__slots__ = as_native_strings(
("_topological_dimension", "_geometric_dimension"))
def __init__(self, topological_dimension, geometric_dimension):
# Validate dimensions
if not isinstance(geometric_dimension, numbers.Integral):
error("Expecting integer geometric_dimension.")
if not isinstance(topological_dimension, numbers.Integral):
error("Expecting integer topological_dimension.")
if topological_dimension > geometric_dimension:
error(
"Topological dimension cannot be larger than geometric dimension."
)
# Store validated dimensions
self._topological_dimension = topological_dimension
self._geometric_dimension = geometric_dimension
def topological_dimension(self):
"Return the dimension of the topology of this cell."
return self._topological_dimension
def geometric_dimension(self):
"Return the dimension of the space this cell is embedded in."
return self._geometric_dimension
def is_simplex(self):
"Return True if this is a simplex cell."
raise NotImplementedError(
"Implement this to allow important checks and optimizations.")
def has_simplex_facets(self):
"Return True if all the facets of this cell are simplex cells."
raise NotImplementedError(
"Implement this to allow important checks and optimizations.")
def __lt__(self, other):
"Define an arbitrarily chosen but fixed sort order for all cells."
if not isinstance(other, AbstractCell):
return NotImplemented
# Sort by gdim first, tdim next, then whatever's left
# depending on the subclass
s = (self.geometric_dimension(), self.topological_dimension())
o = (other.geometric_dimension(), other.topological_dimension())
if s != o:
return s < o
return self._ufl_hash_data_() < other._ufl_hash_data_()
class PermutationSymbol(ConstantValue):
"""UFL literal type: Representation of a permutation symbol.
This is also known as the Levi-Civita symbol, antisymmetric symbol,
or alternating symbol."""
__slots__ = as_native_strings(("ufl_shape", "_dim"))
def __init__(self, dim):
ConstantValue.__init__(self)
self._dim = dim
self.ufl_shape = (dim,)*dim
def evaluate(self, x, mapping, component, index_values):
"Evaluates the permutation symbol."
return self.__eps(component)
def __getitem__(self, key):
if len(key) != self._dim:
error("Size mismatch for PermutationSymbol.")
if all(isinstance(k, (int, FixedIndex)) for k in key):
return self.__eps(key)
return Expr.__getitem__(self, key)
def __str__(self):
return "eps"
def __repr__(self):
r = "PermutationSymbol(%d)" % self._dim
return as_native_str(r)
def __eq__(self, other):
return isinstance(other, PermutationSymbol) and self._dim == other._dim
def __eps(self, x):
"""This function body is taken from
http://www.mathkb.com/Uwe/Forum.aspx/math/29865/N-integer-Levi-Civita
"""
result = IntValue(1)
for i, x1 in enumerate(x):
for j in range(i + 1, len(x)):
x2 = x[j]
if x1 > x2:
result = -result
elif x1 == x2:
return Zero()
return result
class BesselFunction(Operator):
"Base class for all bessel functions"
__slots__ = as_native_strings(("_name", "_classname"))
def __init__(self, name, classname, nu, argument):
if not is_true_ufl_scalar(nu):
error("Expecting scalar nu.")
if not is_true_ufl_scalar(argument):
error("Expecting scalar argument.")
# Use integer representation if suitable
fnu = float(nu)
inu = int(nu)
if fnu == inu:
nu = as_ufl(inu)
else:
nu = as_ufl(fnu)
Operator.__init__(self, (nu, argument))
self._classname = classname
self._name = name
def evaluate(self, x, mapping, component, index_values):
a = self.ufl_operands[1].evaluate(x, mapping, component, index_values)
try:
import scipy.special
except ImportError:
error(
"You must have scipy installed to evaluate bessel functions in python."
)
name = self._name[-1]
if isinstance(self.ufl_operands[0], IntValue):
nu = int(self.ufl_operands[0])
functype = 'n' if name != 'i' else 'v'
else:
nu = self.ufl_operands[0].evaluate(x, mapping, component,
index_values)
functype = 'v'
func = getattr(scipy.special, name + functype)
return func(nu, a)
def __str__(self):
return "%s(%s, %s)" % (self._name, self.ufl_operands[0],
self.ufl_operands[1])
class ExampleCounted(object):
"""An example class for classes of objects identified by a global counter.
Mimic this class to create globally counted objects within a single type.
"""
# Store the count for each object
__slots__ = as_native_strings(("_count", ))
# Store a global counter with the class
_globalcount = 0
# Call counted_init with an optional constructor argument and the class
def __init__(self, count=None):
counted_init(self, count, ExampleCounted)
# Make the count accessible
def count(self):
return self._count
class ExprTupleKey(object):
__slots__ = as_native_strings(('x', ))
def __init__(self, x):
self.x = x
def __lt__(self, other):
# Comparing expression first
c = cmp_expr(self.x[0], other.x[0])
if c < 0:
return True
elif c > 0:
return False
else:
# Comparing form compiler data
mds = canonicalize_metadata(self.x[1])
mdo = canonicalize_metadata(other.x[1])
return mds < mdo
class ReferenceGrad(CompoundDerivative):
__slots__ = as_native_strings(("_dim", ))
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 __init__(self, f):
CompoundDerivative.__init__(self, (f, ))
self._dim = f.ufl_domain().topological_dimension()
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 ReferenceGrad reconstruct.")
if self.ufl_operands[0].ufl_free_indices != op.ufl_free_indices:
error("Free index mismatch in ReferenceGrad reconstruct.")
return Zero(self.ufl_shape, self.ufl_free_indices,
self.ufl_index_dimensions)
return self._ufl_class_(op)
def evaluate(self, x, mapping, component, index_values, derivatives=()):
"Get child from mapping and return the component asked for."
component, i = component[:-1], component[-1]
derivatives = derivatives + (i, )
result = self.ufl_operands[0].evaluate(x,
mapping,
component,
index_values,
derivatives=derivatives)
return result
@property
def ufl_shape(self):
return self.ufl_operands[0].ufl_shape + (self._dim, )
def __str__(self):
return "reference_grad(%s)" % self.ufl_operands[0]
class FixedIndex(IndexBase):
"""UFL value: An index with a specific value assigned."""
__slots__ = as_native_strings(("_value", "_hash"))
_cache = {}
def __getnewargs__(self):
return (self._value, )
def __new__(cls, value):
self = FixedIndex._cache.get(value)
if self is None:
if not isinstance(value, int):
error("Expecting integer value for fixed index.")
self = IndexBase.__new__(cls)
self._init(value)
FixedIndex._cache[value] = self
return self
def _init(self, value):
IndexBase.__init__(self)
self._value = value
self._hash = hash(("FixedIndex", self._value))
def __init__(self, value):
pass
def __hash__(self):
return self._hash
def __eq__(self, other):
return isinstance(other, FixedIndex) and (self._value == other._value)
def __int__(self):
return self._value
def __str__(self):
return "%d" % self._value
def __repr__(self):
r = "FixedIndex(%d)" % self._value
return as_native_str(r)
class Dot(CompoundTensorOperator):
__slots__ = as_native_strings(("ufl_free_indices",
"ufl_index_dimensions"))
def __new__(cls, a, b):
ash = a.ufl_shape
bsh = b.ufl_shape
ar, br = len(ash), len(bsh)
scalar = (ar == 0 and br == 0)
# Checks
if not ((ar >= 1 and br >= 1) or scalar):
error("Dot product requires non-scalar arguments, "
"got arguments with ranks %d and %d." % (ar, br))
if not (scalar or ash[-1] == bsh[0]):
error("Dimension mismatch in dot product.")
# Simplification
if isinstance(a, Zero) or isinstance(b, Zero):
shape = ash[:-1] + bsh[1:]
fi, fid = merge_nonoverlapping_indices(a, b)
return Zero(shape, fi, fid)
elif scalar: # TODO: Move this to def dot()?
return a * b
return CompoundTensorOperator.__new__(cls)
def __init__(self, a, b):
CompoundTensorOperator.__init__(self, (a, b))
fi, fid = merge_nonoverlapping_indices(a, b)
self.ufl_free_indices = fi
self.ufl_index_dimensions = fid
@property
def ufl_shape(self):
return self.ufl_operands[0].ufl_shape[:-1] + self.ufl_operands[1].ufl_shape[1:]
def __str__(self):
return "%s . %s" % (parstr(self.ufl_operands[0], self),
parstr(self.ufl_operands[1], self))
class MeasureProduct(object):
"""Represents a product of measures.
This is a notational intermediate object to handle the notation
f*(dm1*dm2)
This is work in progress and not functional. It needs support
in other parts of ufl and the rest of the code generation chain.
"""
__slots__ = as_native_strings(("_measures", ))
def __init__(self, *measures):
"Create MeasureProduct from given list of measures."
self._measures = measures
if len(self._measures) < 2:
error("Expecting at least two measures.")
def __mul__(self, other):
"""Flatten multiplication of product measures.
This is to ensure that (dm1*dm2)*dm3 is stored as a simple
list (dm1,dm2,dm3) in a single MeasureProduct.
"""
if isinstance(other, Measure):
measures = self.sub_measures() + [other]
return MeasureProduct(*measures)
else:
return NotImplemented
def __rmul__(self, integrand):
error(
"TODO: Implement MeasureProduct.__rmul__ to construct integral and form somehow."
)
def sub_measures(self):
"Return submeasures."
return self._measures
class HCurlElement(FiniteElementBase):
"""A curl-conforming version of an outer product element, assuming
this makes mathematical sense."""
__slots__ = as_native_strings(("_element", ))
def __init__(self, element):
self._element = element
self._repr = as_native_str("HCurlElement(%s)" % repr(element))
family = "TensorProductElement"
cell = element.cell()
degree = element.degree()
quad_scheme = element.quadrature_scheme()
cell = element.cell()
value_shape = (cell.geometric_dimension(), )
reference_value_shape = (cell.topological_dimension(),
) # TODO: Is this right?
# Skipping TensorProductElement constructor! Bad code smell,
# refactor to avoid this non-inheritance somehow.
FiniteElementBase.__init__(self, family, cell, degree, quad_scheme,
value_shape, reference_value_shape)
def mapping(self):
return "covariant Piola"
def sobolev_space(self):
"Return the underlying Sobolev space."
return HCurl
def reconstruct(self, **kwargs):
return HCurlElement(self._element.reconstruct(**kwargs))
def __str__(self):
return "HCurlElement(%s)" % str(self._element)
def shortstr(self):
"Format as string for pretty printing."
return "HCurlElement(%s)" % str(self._element.shortstr())
class GeometricQuantity(Terminal):
__slots__ = as_native_strings(("_domain", ))
def __init__(self, domain):
Terminal.__init__(self)
self._domain = as_domain(domain)
def ufl_domains(self):
return (self._domain, )
def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell (or over each facet for facet quantities)."
# NB! Geometric quantities are piecewise constant by
# default. Override if needed.
return True
# NB! Geometric quantities are scalar by default. Override if
# needed.
ufl_shape = ()
def _ufl_signature_data_(self, renumbering):
"Signature data of geometric quantities depend on the domain numbering."
return (self._ufl_class_.__name__,
) + self._domain._ufl_signature_data_(renumbering)
def __str__(self):
return self._ufl_class_.name
def __repr__(self):
r = "%s(%s)" % (self._ufl_class_.__name__, repr(self._domain))
return as_native_str(r)
def _ufl_compute_hash_(self):
return hash((type(self).__name__, ) + self._domain._ufl_hash_data_())
def __eq__(self, other):
return isinstance(other,
self._ufl_class_) and other._domain == self._domain
class Label(Terminal):
__slots__ = as_native_strings(("_count", ))
_globalcount = 0
def __init__(self, count=None):
Terminal.__init__(self)
counted_init(self, count, Label)
def count(self):
return self._count
def __str__(self):
return "Label(%d)" % self._count
def __repr__(self):
r = "Label(%d)" % self._count
return as_native_str(r)
@property
def ufl_shape(self):
error("Label has no shape (it is not a tensor expression).")
@property
def ufl_free_indices(self):
error("Label has no free indices (it is not a tensor expression).")
@property
def ufl_index_dimensions(self):
error("Label has no free indices (it is not a tensor expression).")
def is_cellwise_constant(self):
return True
def ufl_domains(self):
"Return tuple of domains related to this terminal object."
return ()
class ReferenceCurl(CompoundDerivative):
__slots__ = as_native_strings(("ufl_shape",))
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 __init__(self, f):
global _curl_shapes
CompoundDerivative.__init__(self, (f,))
self.ufl_shape = _curl_shapes[f.ufl_shape]
def __str__(self):
return "reference_curl(%s)" % self.ufl_operands[0]
class VariableDerivative(Derivative):
__slots__ = as_native_strings((
"ufl_shape",
"ufl_free_indices",
"ufl_index_dimensions",
))
def __new__(cls, f, v):
# Checks
if not isinstance(f, Expr):
error("Expecting an Expr in VariableDerivative.")
if not isinstance(v, (Variable, Coefficient)):
error("Expecting a Variable in VariableDerivative.")
if v.ufl_free_indices:
error("Differentiation variable cannot have free indices.")
# Simplification
# Return zero if expression is trivially independent of variable
if f._ufl_is_terminal_ and f != v:
return Zero(f.ufl_shape + v.ufl_shape, f.ufl_free_indices,
f.ufl_index_dimensions)
# Construction
return Derivative.__new__(cls)
def __init__(self, f, v):
Derivative.__init__(self, (f, v))
self.ufl_free_indices = f.ufl_free_indices
self.ufl_index_dimensions = f.ufl_index_dimensions
self.ufl_shape = f.ufl_shape + v.ufl_shape
def __str__(self):
if isinstance(self.ufl_operands[0], Terminal):
return "d%s/d[%s]" % (self.ufl_operands[0], self.ufl_operands[1])
return "d/d[%s] %s" % (self.ufl_operands[1],
parstr(self.ufl_operands[0], self))
# along with UFL. If not, see <http://www.gnu.org/licenses/>.
#
# Modified by Anders Logg, 2008-2009
# Modified by Massimiliano Leoni, 2016.
import ufl
from ufl.log import error
from ufl.core.expr import Expr
from ufl.checks import is_python_scalar, is_scalar_constant_expression
from ufl.measure import Measure # noqa
from ufl.protocols import id_or_none
from ufl.utils.str import as_native_str
from ufl.utils.str import as_native_strings
# Export list for ufl.classes
__all_classes__ = as_native_strings(["Integral"])
class Integral(object):
"An integral over a single domain."
__slots__ = as_native_strings((
"_integrand",
"_integral_type",
"_ufl_domain",
"_subdomain_id",
"_metadata",
"_subdomain_data",
))
def __init__(self, integrand, integral_type, domain, subdomain_id,
metadata, subdomain_data):
# (at your option) any later version.
#
# UFL is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with UFL. If not, see <http://www.gnu.org/licenses/>.
from ufl.utils.str import as_native_strings
from ufl.log import error
from ufl.finiteelement import FiniteElement, VectorElement, TensorElement, \
MixedElement, EnrichedElement, NodalEnrichedElement
__all__ = as_native_strings(['increase_order', 'tear'])
def increase_order(element):
"Return element of same family, but a polynomial degree higher."
return _increase_degree(element, +1)
def change_regularity(element, family):
"""
For a given finite element, return the corresponding space
specified by 'family'.
"""
return element.reconstruct(family=family)
# Modified by Kristian B. Oelgaard, 2009
# Modified by Marie E. Rognes 2012
# Modified by Andrew T. T. McRae, 2014
# Modified by Massimiliano Leoni, 2016
import numbers
import functools
from ufl.utils.str import as_native_str
from ufl.utils.str import as_native_strings
from ufl.log import error
from ufl.core.ufl_type import attach_operators_from_hash_data
# Export list for ufl.classes
__all_classes__ = as_native_strings(["AbstractCell", "Cell", "TensorProductCell"])
# --- The most abstract cell class, base class for other cell types
class AbstractCell(object):
"""Representation of an abstract finite element cell with only the
dimensions known.
"""
__slots__ = as_native_strings(("_topological_dimension",
"_geometric_dimension"))
def __init__(self, topological_dimension, geometric_dimension):
# Validate dimensions
if not isinstance(geometric_dimension, numbers.Integral):
# (at your option) any later version.
#
# UFL is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with UFL. If not, see <http://www.gnu.org/licenses/>.
from ufl.log import error
from ufl.utils.str import as_native_str
from ufl.utils.str import as_native_strings
# Export list for ufl.classes
__all_classes__ = as_native_strings(["Equation"])
class Equation(object):
"""This class is used to represent equations expressed by the "=="
operator. Examples include a == L and F == 0 where a, L and F are
Form objects."""
def __init__(self, lhs, rhs):
"Create equation lhs == rhs"
self.lhs = lhs
self.rhs = rhs
def __bool__(self):
"""Evaluate bool(lhs_form == rhs_form).
import logging
from logging import DEBUG, INFO, WARNING, ERROR, CRITICAL # noqa: F401
from ufl.utils.str import as_native_strings
log_functions = ["log", "debug", "info", "deprecate", "warning", "error",
"begin", "end",
"set_level", "push_level", "pop_level", "set_indent",
"add_indent",
"set_handler", "get_handler", "get_logger", "add_logfile",
"set_prefix",
"info_red", "info_green", "info_blue",
"warning_red", "warning_green", "warning_blue"]
__all__ = as_native_strings(
log_functions +
["Logger", "log_functions"] +
["DEBUG", "INFO", "DEPRECATE", "WARNING", "ERROR", "CRITICAL"]
)
DEPRECATE = (INFO + WARNING) // 2
# This is used to override emit() in StreamHandler for printing
# without newline
def emit(self, record):
message = self.format(record)
format_string = "%s" if getattr(record, "continued", False) else "%s\n"
self.stream.write(format_string % message)
self.flush()
class IndexSum(Operator):
__slots__ = as_native_strings((
"_dimension",
"ufl_free_indices",
"ufl_index_dimensions",
))
def __new__(cls, summand, index):
# Error checks
if not isinstance(summand, Expr):
error("Expecting Expr instance, got %s" % ufl_err_str(summand))
if not isinstance(index, MultiIndex):
error("Expecting MultiIndex instance, got %s" % ufl_err_str(index))
if len(index) != 1:
error("Expecting a single Index but got %d." % len(index))
# Simplification to zero
if isinstance(summand, Zero):
sh = summand.ufl_shape
j, = index
fi = summand.ufl_free_indices
fid = summand.ufl_index_dimensions
pos = fi.index(j.count())
fi = fi[:pos] + fi[pos + 1:]
fid = fid[:pos] + fid[pos + 1:]
return Zero(sh, fi, fid)
return Operator.__new__(cls)
def __init__(self, summand, index):
j, = index
fi = summand.ufl_free_indices
fid = summand.ufl_index_dimensions
pos = fi.index(j.count())
self._dimension = fid[pos]
self.ufl_free_indices = fi[:pos] + fi[pos + 1:]
self.ufl_index_dimensions = fid[:pos] + fid[pos + 1:]
Operator.__init__(self, (summand, index))
def index(self):
return self.ufl_operands[1][0]
def dimension(self):
return self._dimension
@property
def ufl_shape(self):
return self.ufl_operands[0].ufl_shape
def evaluate(self, x, mapping, component, index_values):
i, = self.ufl_operands[1]
tmp = 0
for k in range(self._dimension):
index_values.push(i, k)
tmp += self.ufl_operands[0].evaluate(x, mapping, component,
index_values)
index_values.pop()
return tmp
def __str__(self):
return "sum_{%s} %s " % (str(
self.ufl_operands[1]), parstr(self.ufl_operands[0], self))
#
# You should have received a copy of the GNU Lesser General Public License
# along with UFL. If not, see <http://www.gnu.org/licenses/>.
#
# Modified by Massimiliano Leoni, 2016.
from ufl.utils.str import as_native_str
from ufl.utils.str import as_native_strings
from ufl.log import error
from ufl.utils.counted import counted_init
from ufl.core.ufl_type import ufl_type
from ufl.core.terminal import Terminal
# Export list for ufl.classes
__all_classes__ = as_native_strings(["IndexBase", "FixedIndex", "Index"])
class IndexBase(object):
"""Base class for all indices."""
__slots__ = ()
def __init__(self):
pass
class FixedIndex(IndexBase):
"""UFL value: An index with a specific value assigned."""
__slots__ = as_native_strings(("_value", "_hash"))
_cache = {}
import sys
import types
import logging
from logging import DEBUG, INFO, WARNING, ERROR, CRITICAL # noqa: F401
from ufl.utils.str import as_native_strings
log_functions = [
"log", "debug", "info", "deprecate", "warning", "error", "begin", "end",
"set_level", "push_level", "pop_level", "set_indent", "add_indent",
"set_handler", "get_handler", "get_logger", "add_logfile", "set_prefix",
"info_red", "info_green", "info_blue", "warning_red", "warning_green",
"warning_blue"
]
__all__ = as_native_strings(
log_functions + ["Logger", "log_functions"] +
["DEBUG", "INFO", "DEPRECATE", "WARNING", "ERROR", "CRITICAL"])
DEPRECATE = (INFO + WARNING) // 2
# This is used to override emit() in StreamHandler for printing
# without newline
def emit(self, record):
message = self.format(record)
format_string = "%s" if getattr(record, "continued", False) else "%s\n"
self.stream.write(format_string % message)
self.flush()
# Colors if the terminal supports it (disabled e.g. when piped to
# Modified by Marie E. Rognes 2012
import numbers
from ufl.utils.str import as_native_str
from ufl.utils.str import as_native_strings
from ufl.core.ufl_type import attach_operators_from_hash_data
from ufl.core.ufl_id import attach_ufl_id
from ufl.corealg.traversal import traverse_unique_terminals
from ufl.log import error
from ufl.cell import as_cell, AbstractCell, TensorProductCell
from ufl.finiteelement.tensorproductelement import TensorProductElement
# Export list for ufl.classes
__all_classes__ = as_native_strings(["AbstractDomain", "Mesh", "MeshView", "TensorProductMesh"])
class AbstractDomain(object):
"""Symbolic representation of a geometric domain with only a geometric
and topological dimension.
"""
def __init__(self, topological_dimension, geometric_dimension):
# Validate dimensions
if not isinstance(geometric_dimension, numbers.Integral):
error("Expecting integer geometric dimension, not %s" % (geometric_dimension.__class__,))
if not isinstance(topological_dimension, numbers.Integral):
error("Expecting integer topological dimension, not %s" % (topological_dimension.__class__,))
if topological_dimension > geometric_dimension:
__all__ = as_native_strings([
'product',
'get_handler', 'get_logger', 'set_handler', 'set_level', 'add_logfile',
'UFLException', 'DEBUG', 'INFO', 'WARNING', 'ERROR', 'CRITICAL',
'as_cell', 'AbstractCell', 'Cell', 'TensorProductCell',
'as_domain', 'AbstractDomain', 'Mesh', 'MeshView', 'TensorProductMesh',
'L2', 'H1', 'H2', 'HCurl', 'HDiv',
'SpatialCoordinate',
'CellVolume', 'CellDiameter', 'Circumradius',
'MinCellEdgeLength', 'MaxCellEdgeLength',
'FacetArea', 'MinFacetEdgeLength', 'MaxFacetEdgeLength',
'FacetNormal', 'CellNormal',
'Jacobian', 'JacobianDeterminant', 'JacobianInverse',
'FiniteElementBase', 'FiniteElement',
'MixedElement', 'VectorElement', 'TensorElement', 'EnrichedElement',
'NodalEnrichedElement', 'RestrictedElement', 'TensorProductElement',
'HDivElement', 'HCurlElement',
'BrokenElement', 'FacetElement', 'InteriorElement',
'register_element', 'show_elements',
'FunctionSpace',
'Argument', 'TestFunction', 'TrialFunction',
'Arguments', 'TestFunctions', 'TrialFunctions',
'Coefficient', 'Coefficients',
'Constant', 'VectorConstant', 'TensorConstant',
'split',
'PermutationSymbol', 'Identity', 'zero', 'as_ufl',
'Index', 'indices',
'as_tensor', 'as_vector', 'as_matrix', 'relabel',
'unit_vector', 'unit_vectors', 'unit_matrix', 'unit_matrices',
'rank', 'shape', 'conj', 'real', 'imag',
'outer', 'inner', 'dot', 'cross', 'perp',
'det', 'inv', 'cofac',
'transpose', 'tr', 'diag', 'diag_vector', 'dev', 'skew', 'sym',
'sqrt', 'exp', 'ln', 'erf',
'cos', 'sin', 'tan',
'acos', 'asin', 'atan', 'atan_2',
'cosh', 'sinh', 'tanh',
'bessel_J', 'bessel_Y', 'bessel_I', 'bessel_K',
'eq', 'ne', 'le', 'ge', 'lt', 'gt', 'And', 'Or', 'Not',
'conditional', 'sign', 'max_value', 'min_value', 'Max', 'Min',
'variable', 'diff',
'Dx', 'grad', 'div', 'curl', 'rot', 'nabla_grad', 'nabla_div', 'Dn', 'exterior_derivative',
'jump', 'avg', 'cell_avg', 'facet_avg',
'elem_mult', 'elem_div', 'elem_pow', 'elem_op',
'Form',
'Integral', 'Measure', 'register_integral_type', 'integral_types', 'custom_integral_types',
'replace', 'replace_integral_domains', 'derivative', 'action', 'energy_norm', 'rhs', 'lhs', 'block_split',
'system', 'functional', 'adjoint', 'sensitivity_rhs',
'dx', 'ds', 'dS', 'dP',
'dc', 'dC', 'dO', 'dI', 'dX',
'ds_b', 'ds_t', 'ds_tb', 'ds_v', 'dS_h', 'dS_v',
'vertex', 'interval', 'triangle', 'tetrahedron',
'quadrilateral', 'hexahedron', 'facet',
'i', 'j', 'k', 'l', 'p', 'q', 'r', 's',
'e', 'pi',
])
class Measure(object):
__slots__ = as_native_strings(("_integral_type",
"_domain",
"_subdomain_id",
"_metadata",
"_subdomain_data"))
"""Representation of an integration measure.
The Measure object holds information about integration properties
to be transferred to a Form on multiplication with a scalar
expression.
"""
def __init__(self,
integral_type, # "dx" etc
domain=None,
subdomain_id="everywhere",
metadata=None,
subdomain_data=None):
"""
integral_type:
str, one of "cell", etc.,
or short form "dx", etc.
domain:
an AbstractDomain object (most often a Mesh)
subdomain_id:
either string "everywhere",
a single subdomain id int,
or tuple of ints
metadata:
dict, with additional compiler-specific parameters
affecting how code is generated, including parameters
for optimization or debugging of generated code.
subdomain_data:
object representing data to interpret subdomain_id with.
"""
# Map short name to long name and require a valid one
self._integral_type = as_integral_type(integral_type)
# Check that we either have a proper AbstractDomain or none
self._domain = None if domain is None else as_domain(domain)
if not (self._domain is None or isinstance(self._domain, AbstractDomain)):
error("Invalid domain.")
# Store subdomain data
self._subdomain_data = subdomain_data
# FIXME: Cannot require this (yet) because we currently have
# no way to implement ufl_id for dolfin SubDomain
# if not (self._subdomain_data is None or hasattr(self._subdomain_data, "ufl_id")):
# error("Invalid domain data, missing ufl_id() implementation.")
# Accept "everywhere", single subdomain, or multiple
# subdomains
if isinstance(subdomain_id, tuple):
for did in subdomain_id:
if not isinstance(did, numbers.Integral):
error("Invalid subdomain_id %s." % (did,))
else:
if not (subdomain_id in ("everywhere",) or isinstance(subdomain_id, numbers.Integral)):
error("Invalid subdomain_id %s." % (subdomain_id,))
self._subdomain_id = subdomain_id
# Validate compiler options are None or dict
if metadata is not None and not isinstance(metadata, dict):
error("Invalid metadata.")
self._metadata = metadata or EmptyDict
def integral_type(self):
"""Return the domain type.
Valid domain types are "cell", "exterior_facet", "interior_facet", etc.
"""
return self._integral_type
def ufl_domain(self):
"""Return the domain associated with this measure.
This may be None or a Domain object.
"""
return self._domain
def subdomain_id(self):
"Return the domain id of this measure (integer)."
return self._subdomain_id
def metadata(self):
"""Return the integral metadata. This data is not interpreted by UFL.
It is passed to the form compiler which can ignore it or use
it to compile each integral of a form in a different way.
"""
return self._metadata
def reconstruct(self,
integral_type=None,
subdomain_id=None,
domain=None,
metadata=None,
subdomain_data=None):
"""Construct a new Measure object with some properties replaced with
new values.
Example:
<dm = Measure instance>
b = dm.reconstruct(subdomain_id=2)
c = dm.reconstruct(metadata={ "quadrature_degree": 3 })
Used by the call operator, so this is equivalent:
b = dm(2)
c = dm(0, { "quadrature_degree": 3 })
"""
if subdomain_id is None:
subdomain_id = self.subdomain_id()
if domain is None:
domain = self.ufl_domain()
if metadata is None:
metadata = self.metadata()
if subdomain_data is None:
subdomain_data = self.subdomain_data()
return Measure(self.integral_type(),
domain=domain, subdomain_id=subdomain_id,
metadata=metadata, subdomain_data=subdomain_data)
def subdomain_data(self):
"""Return the integral subdomain_data. This data is not interpreted by
UFL. Its intension is to give a context in which the domain
id is interpreted.
"""
return self._subdomain_data
# Note: Must keep the order of the first two arguments here
# (subdomain_id, metadata) for backwards compatibility, because
# some tutorials write e.g. dx(0, {...}) to set metadata.
def __call__(self, subdomain_id=None, metadata=None, domain=None,
subdomain_data=None, degree=None, scheme=None, rule=None):
"""Reconfigure measure with new domain specification or metadata."""
# Deprecation of 'rule' in favour of 'scheme'
if rule is not None:
deprecate("Measure argument 'rule' has been renamed to 'scheme'.")
assert scheme is None or scheme == rule
scheme = rule
# Let syntax dx() mean integral over everywhere
all_args = (subdomain_id, metadata, domain, subdomain_data,
degree, scheme)
if all(arg is None for arg in all_args):
return self.reconstruct(subdomain_id="everywhere")
# Let syntax dx(domain) or dx(domain, metadata) mean integral
# over entire domain. To do this we need to hijack the first
# argument:
if subdomain_id is not None and (isinstance(subdomain_id,
AbstractDomain) or
hasattr(subdomain_id, 'ufl_domain')):
if domain is not None:
error("Ambiguous: setting domain both as keyword argument and first argument.")
subdomain_id, domain = "everywhere", as_domain(subdomain_id)
# If degree or scheme is set, inject into metadata. This is a
# quick fix to enable the dx(..., degree=3) notation.
# TODO: Make degree and scheme properties of integrals instead of adding to metadata.
if (degree, scheme) != (None, None):
metadata = {} if metadata is None else metadata.copy()
if degree is not None:
metadata["quadrature_degree"] = degree
if scheme is not None:
metadata["quadrature_rule"] = scheme
# If we get any keywords, use them to reconstruct Measure.
# Note that if only one argument is given, it is the
# subdomain_id, e.g. dx(3) == dx(subdomain_id=3)
return self.reconstruct(subdomain_id=subdomain_id, domain=domain,
metadata=metadata,
subdomain_data=subdomain_data)
def __getitem__(self, data):
"""This operator supports legacy syntax in python dolfin programs.
The old documentation reads: Return a new Measure for same
integration type with an attached context for interpreting
domain ids. By default this new Measure integrates over
everywhere, but it can be restricted with a domain id as
usual. Example: dx = dx[boundaries]; L = f*v*dx + g*v+dx(1).
"""
deprecate("Notation dx[meshfunction] is deprecated. Please use dx(subdomain_data=meshfunction) instead.")
return self(subdomain_data=data)
def __str__(self):
global integral_type_to_measure_name
name = integral_type_to_measure_name[self._integral_type]
args = []
if self._subdomain_id is not None:
args.append("subdomain_id=%s" % (self._subdomain_id,))
if self._domain is not None:
args.append("domain=%s" % (self._domain,))
if self._metadata: # Stored as EmptyDict if None
args.append("metadata=%s" % (self._metadata,))
if self._subdomain_data is not None:
args.append("subdomain_data=%s" % (self._subdomain_data,))
return "%s(%s)" % (name, ', '.join(args))
def __repr__(self):
"Return a repr string for this Measure."
global integral_type_to_measure_name
args = []
args.append(repr(self._integral_type))
if self._subdomain_id is not None:
args.append("subdomain_id=%s" % repr(self._subdomain_id))
if self._domain is not None:
args.append("domain=%s" % repr(self._domain))
if self._metadata: # Stored as EmptyDict if None
args.append("metadata=%s" % repr(self._metadata))
if self._subdomain_data is not None:
args.append("subdomain_data=%s" % repr(self._subdomain_data))
r = "%s(%s)" % (type(self).__name__, ', '.join(args))
return as_native_str(r)
def __hash__(self):
"Return a hash value for this Measure."
hashdata = (self._integral_type,
self._subdomain_id,
hash(self._domain),
metadata_hashdata(self._metadata),
id_or_none(self._subdomain_data))
return hash(hashdata)
def __eq__(self, other):
"Checks if two Measures are equal."
return (isinstance(other, Measure) and
self._integral_type == other._integral_type and
self._subdomain_id == other._subdomain_id and
self._domain == other._domain and
id_or_none(self._subdomain_data) == id_or_none(other._subdomain_data) and
metadata_equal(self._metadata, other._metadata))
def __add__(self, other):
"""Add two measures (self+other).
Creates an intermediate object used for the notation
expr * (dx(1) + dx(2)) := expr * dx(1) + expr * dx(2)
"""
if isinstance(other, Measure):
# Let dx(1) + dx(2) equal dx((1,2))
return MeasureSum(self, other)
else:
# Can only add Measures
return NotImplemented
def __mul__(self, other):
"""Multiply two measures (self*other).
Creates an intermediate object used for the notation
expr * (dm1 * dm2) := expr * dm1 * dm2
This is work in progress and not functional.
"""
if isinstance(other, Measure):
# Tensor product measure support
return MeasureProduct(self, other)
else:
# Can't multiply Measure from the right with non-Measure type
return NotImplemented
def __rmul__(self, integrand):
"""Multiply a scalar expression with measure to construct a form with
a single integral.
This is to implement the notation
form = integrand * self
Integration properties are taken from this Measure object.
"""
# Avoid circular imports
from ufl.integral import Integral
from ufl.form import Form
# Allow python literals: 1*dx and 1.0*dx
if isinstance(integrand, (int, float)):
integrand = as_ufl(integrand)
# Let other types implement multiplication with Measure if
# they want to (to support the dolfin-adjoint TimeMeasure)
if not isinstance(integrand, Expr):
return NotImplemented
# Allow only scalar integrands
if not is_true_ufl_scalar(integrand):
error("Can only integrate scalar expressions. The integrand is a "
"tensor expression with value shape %s and free indices with labels %s." %
(integrand.ufl_shape, integrand.ufl_free_indices))
# If we have a tuple of domain ids, delegate composition to
# Integral.__add__:
subdomain_id = self.subdomain_id()
if isinstance(subdomain_id, tuple):
return sum(integrand*self.reconstruct(subdomain_id=d) for d in subdomain_id)
# Check that we have an integer subdomain or a string
# ("everywhere" or "otherwise", any more?)
if not isinstance(subdomain_id, (str, numbers.Integral,)):
error("Expecting integer or string domain id.")
# If we don't have an integration domain, try to find one in
# integrand
domain = self.ufl_domain()
if domain is None:
domains = extract_domains(integrand)
if len(domains) == 1:
domain, = domains
elif len(domains) == 0:
error("This integral is missing an integration domain.")
else:
error("Multiple domains found, making the choice of integration domain ambiguous.")
# Otherwise create and return a one-integral form
integral = Integral(integrand=integrand,
integral_type=self.integral_type(),
domain=domain,
subdomain_id=subdomain_id,
metadata=self.metadata(),
subdomain_data=self.subdomain_data())
return Form([integral])
import numbers
from ufl.utils.str import as_native_strings
from ufl.utils.str import as_native_str
from ufl.log import error, deprecate
from ufl.core.expr import Expr
from ufl.checks import is_true_ufl_scalar
from ufl.constantvalue import as_ufl
from ufl.utils.dicts import EmptyDict
from ufl.domain import as_domain, AbstractDomain, extract_domains
from ufl.protocols import id_or_none, metadata_equal, metadata_hashdata
# Export list for ufl.classes
__all_classes__ = as_native_strings(["Measure", "MeasureSum", "MeasureProduct"])
# TODO: Design a class IntegralType(name, shortname, codim, num_cells, ...)?
# TODO: Improve descriptions below:
# Enumeration of valid domain types
_integral_types = [
# === Integration over full topological dimension:
("cell", "dx"), # Over cells of a mesh
# ("macro_cell", "dE"), # Over a group of adjacent cells (TODO: Arbitrary cell group? Not currently used.)
# === Integration over topological dimension - 1:
("exterior_facet", "ds"), # Over one-sided exterior facets of a mesh
("interior_facet", "dS"), # Over two-sided facets between pairs of adjacent cells of a mesh
import ufl.finiteelement # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.finiteelement, locals()) import ufl.domain # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.domain, locals()) import ufl.functionspace # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.functionspace, locals()) import ufl.core.multiindex # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.core.multiindex, locals()) import ufl.argument # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.argument, locals()) import ufl.measure # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.measure, locals()) import ufl.integral # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.integral, locals()) import ufl.form # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.form, locals()) import ufl.equation # noqa E401 __all__ += populate_namespace_with_module_classes(ufl.equation, locals()) __all__ = as_native_strings(__all__)
from itertools import chain
from collections import defaultdict
from ufl.log import error, warning
from ufl.domain import sort_domains
from ufl.integral import Integral
from ufl.checks import is_scalar_constant_expression
from ufl.equation import Equation
from ufl.core.expr import Expr
from ufl.core.expr import ufl_err_str
from ufl.constantvalue import Zero
from ufl.utils.str import as_native_strings, as_native_str
# Export list for ufl.classes
__all_classes__ = as_native_strings(["Form"])
# --- The Form class, representing a complete variational form or functional ---
def _sorted_integrals(integrals):
"""Sort integrals by domain id, integral type, subdomain id
for a more stable signature computation."""
# Group integrals in multilevel dict by keys
# [domain][integral_type][subdomain_id]
integrals_dict = defaultdict(lambda: defaultdict(lambda: defaultdict(list)))
for integral in integrals:
d = integral.ufl_domain()
if d is None:
error("Each integral in a form must have a uniquely defined integration domain.")
__all__ = as_native_strings([
"estimate_total_polynomial_degree",
"sort_elements",
"compute_form_data",
"purge_list_tensors",
"apply_transformer",
"ReuseTransformer",
"load_ufl_file",
"Transformer",
"MultiFunction",
"extract_unique_elements",
"extract_type",
"extract_elements",
"extract_sub_elements",
"preprocess_expression",
"expand_indices",
"replace",
"expand_derivatives",
"extract_coefficients",
"strip_variables",
"post_traversal",
"change_to_reference_grad",
"expand_compounds",
"validate_form",
"ufl2latex",
"FormSplitter",
"extract_arguments",
"compute_form_adjoint",
"compute_form_action",
"compute_energy_norm",
"compute_form_lhs",
"compute_form_rhs",
"compute_form_functional",
"compute_form_signature",
"tree_format",
])
# Modified by Anders Logg, 2008-2009.
# Modified by Massimiliano Leoni, 2016.
import numbers
from ufl.utils.str import as_native_str
from ufl.utils.str import as_native_strings
from ufl.log import error
from ufl.core.ufl_type import ufl_type
from ufl.core.terminal import FormArgument
from ufl.split_functions import split
from ufl.finiteelement import FiniteElementBase
from ufl.domain import default_domain
from ufl.functionspace import AbstractFunctionSpace, FunctionSpace
# Export list for ufl.classes (TODO: not actually classes: drop? these are in ufl.*)
__all_classes__ = as_native_strings(["TestFunction", "TrialFunction", "TestFunctions", "TrialFunctions"])
# --- Class representing an argument (basis function) in a form ---
@ufl_type()
class Argument(FormArgument):
"""UFL value: Representation of an argument to a form."""
__slots__ = as_native_strings((
"_ufl_function_space",
"_ufl_shape",
"_number",
"_part",
"_repr",
))