def inner(a, b):
"UFL operator: Take the inner product of a and b."
a = as_ufl(a)
b = as_ufl(b)
if a.shape() == () and b.shape() == ():
return a*b
return Inner(a, b)
def inner(a, b):
"UFL operator: Take the inner product of *a* and *b*. The complex conjugate of the second argument is taken."
a = as_ufl(a)
b = as_ufl(b)
if a.ufl_shape == () and b.ufl_shape == ():
return a * Conj(b)
return Inner(a, b)
def dot(a, b):
"UFL operator: Take the dot product of *a* and *b*. The complex conjugate of the second argument is taken."
a = as_ufl(a)
b = as_ufl(b)
if a.ufl_shape == () and b.ufl_shape == ():
return a * b
return Dot(a, b)
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 dot(a, b):
"UFL operator: Take the dot product of a and b."
a = as_ufl(a)
b = as_ufl(b)
if a.shape() == () and b.shape() == ():
return a*b
return Dot(a, b)
def __new__(cls, a, b):
a = as_ufl(a)
b = as_ufl(b)
# Assertions
# TODO: Enabled workaround for nonscalar division in __div__,
# so maybe we can keep this assertion. Some algorithms may need updating.
if not is_ufl_scalar(a):
error("Expecting scalar nominator in Division.")
if not is_true_ufl_scalar(b):
error("Division by non-scalar is undefined.")
if isinstance(b, Zero):
error("Division by zero!")
# Simplification a/b -> a
if isinstance(a, Zero) or b == 1:
return a
# Simplification "literal a / literal b" -> "literal value of a/b"
# Avoiding integer division by casting to float
if isinstance(a, ScalarValue) and isinstance(b, ScalarValue):
return as_ufl(float(a._value) / float(b._value))
# Simplification "a / a" -> "1"
if not a.free_indices() and not a.shape() and a == b:
return as_ufl(1)
# construct and initialize a new Division object
self = AlgebraOperator.__new__(cls)
self._init(a, b)
return self
def cross(a, b):
"UFL operator: Take the cross product of a and b."
a = as_ufl(a)
b = as_ufl(b)
#ufl_assert(a.shape() == (3,) and b.shape() == (3,),
# "Expecting 3D vectors in cross product.")
return Cross(a, b)
def atan_2(f1,f2):
"UFL operator: Take the inverse tangent of f."
f1 = as_ufl(f1)
f2 = as_ufl(f2)
r = Atan2(f1, f2)
if isinstance(r, (ScalarValue, Zero, int, float)):
return float(r)
return r
def derivative(form, coefficient, argument=None, coefficient_derivatives=None):
"""UFL form operator:
Compute the Gateaux derivative of *form* w.r.t. *coefficient* in direction
of *argument*.
If the argument is omitted, a new ``Argument`` is created
in the same space as the coefficient, with argument number
one higher than the highest one in the form.
The resulting form has one additional ``Argument``
in the same finite element space as the coefficient.
A tuple of ``Coefficient`` s may be provided in place of
a single ``Coefficient``, in which case the new ``Argument``
argument is based on a ``MixedElement`` created from this tuple.
An indexed ``Coefficient`` from a mixed space may be provided,
in which case the argument should be in the corresponding
subspace of the coefficient space.
If provided, *coefficient_derivatives* should be a mapping from
``Coefficient`` instances to their derivatives w.r.t. *coefficient*.
"""
coefficients, arguments = _handle_derivative_arguments(form, coefficient,
argument)
if coefficient_derivatives is None:
coefficient_derivatives = ExprMapping()
else:
cd = []
for k in sorted_expr(coefficient_derivatives.keys()):
cd += [as_ufl(k), as_ufl(coefficient_derivatives[k])]
coefficient_derivatives = ExprMapping(*cd)
# Got a form? Apply derivatives to the integrands in turn.
if isinstance(form, Form):
integrals = []
for itg in form.integrals():
if not isinstance(coefficient, SpatialCoordinate):
fd = CoefficientDerivative(itg.integrand(), coefficients,
arguments, coefficient_derivatives)
else:
fd = CoordinateDerivative(itg.integrand(), coefficients,
arguments, coefficient_derivatives)
integrals.append(itg.reconstruct(fd))
return Form(integrals)
elif isinstance(form, Expr):
# What we got was in fact an integrand
if not isinstance(coefficient, SpatialCoordinate):
return CoefficientDerivative(form, coefficients,
arguments, coefficient_derivatives)
else:
return CoordinateDerivative(form, coefficients,
arguments, coefficient_derivatives)
error("Invalid argument type %s." % str(type(form)))
def atan_2(f1, f2):
"UFL operator: Take the inverse tangent with two the arguments *f1* and *f2*."
f1 = as_ufl(f1)
f2 = as_ufl(f2)
if isinstance(f1, (ComplexValue, complex)) or isinstance(f2, (ComplexValue, complex)):
raise TypeError('atan_2 is incompatible with complex numbers.')
r = Atan2(f1, f2)
if isinstance(r, (RealValue, Zero, int, float)):
return float(r)
if isinstance(r, (ComplexValue, complex)):
return complex(r)
return r
def __init__(self, name, classname, nu, argument):
Operator.__init__(self)
ufl_assert(is_true_ufl_scalar(nu), "Expecting scalar nu.")
ufl_assert(is_true_ufl_scalar(argument), "Expecting scalar argument.")
fnu = float(nu)
inu = int(nu)
if fnu == inu:
nu = as_ufl(inu)
else:
nu = as_ufl(fnu)
self._classname = classname
self._name = name
self._nu = nu
self._argument = argument
def test_float(self):
f1 = as_ufl(1)
f2 = as_ufl(1.0)
f3 = FloatValue(1)
f4 = FloatValue(1.0)
f5 = 3 - FloatValue(1) - 1
f6 = 3 * FloatValue(2) / 6
assert f1 == f1
self.assertNotEqual(f1, f2) # IntValue vs FloatValue, == compares representations!
assert f2 == f3
assert f2 == f4
assert f2 == f5
assert f2 == f6
def test_int(self):
f1 = as_ufl(1)
f2 = as_ufl(1.0)
f3 = IntValue(1)
f4 = IntValue(1.0)
f5 = 3 - IntValue(1) - 1
f6 = 3 * IntValue(2) / 6
assert f1 == f1
self.assertNotEqual(f1, f2) # IntValue vs FloatValue, == compares representations!
assert f1 == f3
assert f1 == f4
assert f1 == f5
assert f2 == f6 # Division produces a FloatValue
def outer(*operands):
"UFL operator: Take the outer product of two or more operands. The complex conjugate of the first argument is taken."
n = len(operands)
if n == 1:
return operands[0]
elif n == 2:
a, b = operands
else:
a = outer(*operands[:-1])
b = operands[-1]
a = as_ufl(a)
b = as_ufl(b)
if a.ufl_shape == () and b.ufl_shape == ():
return Conj(a) * b
return Outer(a, b)
def outer(*operands):
"UFL operator: Take the outer product of two or more operands."
n = len(operands)
if n == 1:
return operands[0]
elif n == 2:
a, b = operands
else:
a = outer(*operands[:-1])
b = operands[-1]
a = as_ufl(a)
b = as_ufl(b)
if a.shape() == () and b.shape() == ():
return a*b
return Outer(a, b)
def Dn(f):
"""UFL operator: Take the directional derivative of *f* in the
facet normal direction, Dn(f) := dot(grad(f), n)."""
f = as_ufl(f)
if is_cellwise_constant(f):
return Zero(f.ufl_shape, f.ufl_free_indices, f.ufl_index_dimensions)
return dot(grad(f), FacetNormal(f.ufl_domain()))
def test_scalar_sums(self):
n = 10
s = [as_ufl(i) for i in range(n)]
for i in range(n):
self.assertNotEqual(s[i], i+1)
for i in range(n):
assert s[i] == i
for i in range(n):
assert 0 + s[i] == i
for i in range(n):
assert s[i] + 0 == i
for i in range(n):
assert 0 + s[i] + 0 == i
for i in range(n):
assert 1 + s[i] - 1 == i
assert s[1] + s[1] == 2
assert s[1] + s[2] == 3
assert s[1] + s[2] + s[3] == s[6]
assert s[5] - s[2] == 3
assert 1*s[5] == 5
assert 2*s[5] == 10
assert s[6]/3 == 2
def test_complex(self):
f1 = as_ufl(1 + 1j)
f2 = as_ufl(1)
f3 = as_ufl(1j)
f4 = ComplexValue(1 + 1j)
f5 = ComplexValue(1.0 + 1.0j)
f6 = as_ufl(1.0)
f7 = as_ufl(1.0j)
assert f1 == f1
assert f1 == f4
assert f1 == f5 # ComplexValue uses floats
assert f1 == f2 + f3 # Type promotion of IntValue to ComplexValue with arithmetic
assert f4 == f2 + f3
assert f5 == f2 + f3
assert f4 == f5
assert f6 + f7 == f2 + f3
def Dn(f):
"""UFL operator: Take the directional derivative of f in the
facet normal direction, Dn(f) := dot(grad(f), n)."""
f = as_ufl(f)
cell = f.cell()
if cell is None: # FIXME: Rather if f.is_cellwise_constant()?
return Zero(f.shape(), f.free_indices(), f.index_dimensions())
return dot(grad(f), cell.n)
def _mathfunction(f, cls):
f = as_ufl(f)
r = cls(f)
if isinstance(r, (RealValue, Zero, int, float)):
return float(r)
if isinstance(r, (ComplexValue, complex)):
return complex(r)
return r
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 __init__(self, condition, true_value, false_value):
Operator.__init__(self)
ufl_assert(isinstance(condition, Condition), "Expectiong condition as first argument.")
true_value = as_ufl(true_value)
false_value = as_ufl(false_value)
tsh = true_value.shape()
fsh = false_value.shape()
ufl_assert(tsh == fsh, "Shape mismatch between conditional branches.")
tfi = true_value.free_indices()
ffi = false_value.free_indices()
ufl_assert(tfi == ffi, "Free index mismatch between conditional branches.")
if isinstance(condition, (EQ,NE)):
ufl_assert(condition._left.shape() == ()
and condition._left.free_indices() == ()
and condition._right.shape() == ()
and condition._right.free_indices() == (),
"Non-scalar == or != is not allowed.")
self._condition = condition
self._true_value = true_value
self._false_value = false_value
def __init__(self, condition, true_value, false_value):
if not isinstance(condition, Condition):
error("Expectiong condition as first argument.")
true_value = as_ufl(true_value)
false_value = as_ufl(false_value)
tsh = true_value.ufl_shape
fsh = false_value.ufl_shape
if tsh != fsh:
error("Shape mismatch between conditional branches.")
tfi = true_value.ufl_free_indices
ffi = false_value.ufl_free_indices
if tfi != ffi:
error("Free index mismatch between conditional branches.")
if isinstance(condition, (EQ, NE)):
if not all((condition.ufl_operands[0].ufl_shape == (),
condition.ufl_operands[0].ufl_free_indices == (),
condition.ufl_operands[1].ufl_shape == (),
condition.ufl_operands[1].ufl_free_indices == ())):
error("Non-scalar == or != is not allowed.")
Operator.__init__(self, (condition, true_value, false_value))
def elem_op(op, *args):
"UFL operator: Take the elementwise application of operator *op* on scalar values from one or more tensor arguments."
args = [as_ufl(arg) for arg in args]
sh = args[0].ufl_shape
if not all(sh == x.ufl_shape for x in args):
error("Cannot take elementwise operation with different shapes.")
if sh == ():
return op(*args)
def op_ind(ind, *args):
return op(*[x[ind] for x in args])
return as_tensor(elem_op_items(op_ind, (), *args))
def nabla_div(f):
"""UFL operator: Take the divergence of f.
This operator follows the div convention where
nabla_div(v) = v[i].dx(i)
nabla_div(T)[:] = T[i,:].dx(i)
for vector expressions v, and
arbitrary rank tensor expressions T.
"""
f = as_ufl(f)
return NablaDiv(f)
def __new__(cls, a, b):
a = as_ufl(a)
b = as_ufl(b)
if not is_true_ufl_scalar(a): error("Cannot take the power of a non-scalar expression.")
if not is_true_ufl_scalar(b): error("Cannot raise an expression to a non-scalar power.")
if isinstance(a, ScalarValue) and isinstance(b, ScalarValue):
return as_ufl(a._value ** b._value)
if a == 0 and isinstance(b, ScalarValue):
bf = float(b)
if bf < 0:
error("Division by zero, annot raise 0 to a negative power.")
else:
return zero()
if b == 1:
return a
if b == 0:
return IntValue(1)
# construct and initialize a new Power object
self = AlgebraOperator.__new__(cls)
self._init(a, b)
return self
def test_zero(self):
z1 = Zero(())
z2 = Zero(())
z3 = as_ufl(0)
z4 = as_ufl(0.0)
z5 = FloatValue(0)
z6 = FloatValue(0.0)
# self.assertTrue(z1 is z2)
# self.assertTrue(z1 is z3)
# self.assertTrue(z1 is z4)
# self.assertTrue(z1 is z5)
# self.assertTrue(z1 is z6)
assert z1 == z1
assert int(z1) == 0
assert float(z1) == 0.0
assert complex(z1) == 0.0 + 0.0j
self.assertNotEqual(z1, 1.0)
self.assertFalse(z1)
# If zero() == 0 is to be allowed, it must not have the same hash or it will collide with 0 as key in dicts...
self.assertNotEqual(hash(z1), hash(0.0))
self.assertNotEqual(hash(z1), hash(0))
def __init__(self, name, left, right):
Operator.__init__(self)
self._name = name
self._left = as_ufl(left)
self._right = as_ufl(right)
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
ufl_assert(isinstance(self._left, Condition),
"Expecting a Condition, not a %s." % self._left._uflclass)
ufl_assert(isinstance(self._right, Condition),
"Expecting a Condition, not a %s." % self._right._uflclass)
else:
# Binary operators acting on non-boolean expressions allow only scalars
ufl_assert(self._left.shape() == () \
and self._right.shape() == (),
"Expecting scalar arguments.")
ufl_assert(self._left.free_indices() == () \
and self._right.free_indices() == (),
"Expecting scalar arguments.")
def __init__(self, expression, label=None):
# Conversion
expression = as_ufl(expression)
if label is None:
label = Label()
# Checks
if not isinstance(expression, Expr):
error("Expecting Expr.")
if not isinstance(label, Label):
error("Expecting a Label.")
if expression.ufl_free_indices:
error("Variable cannot wrap an expression with free indices.")
Operator.__init__(self, (expression, label))
def test_dolfin_expression_compilation_of_scalar_literal():
# Define some literal ufl expression
uexpr = as_ufl(3.14)
# Define expected output from compilation
expected_lines = ['double s[1];',
's[0] = 3.14;',
'values[0] = s[0];']
# Define expected evaluation values: [(x,value), (x,value), ...]
expected_values = [((0.0, 0.0), (3.14,)),
((0.6, 0.7), (3.14,)),
]
# Execute all tests
check_dolfin_expression_compilation(uexpr, expected_lines, expected_values)
def Dx(f, *i):
"""UFL operator: Take the partial derivative of f with respect
to spatial variable number i. Equivalent to f.dx(\*i)."""
f = as_ufl(f)
return f.dx(*i)