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 coordinate_derivative(self, o, f, dummy_w, dummy_v, dummy_cd):
o_ = o.ufl_operands
key = (CoordinateDerivative, o_[0])
return CoordinateDerivative(map_expr_dag(self, o_[0],
vcache=self.vcaches[key],
rcache=self.rcaches[key]),
o_[1], o_[2], o_[3])
def scale_coordinate_derivative(o, scale):
o_ = o.ufl_operands
if isinstance(o, CoordinateDerivative):
return CoordinateDerivative(
scale_coordinate_derivative(o_[0], scale), o_[1], o_[2],
o_[3])
else:
return scale * o
def attach_coordinate_derivatives(integral, coordinate_derivatives):
if coordinate_derivatives is None:
return integral
if isinstance(integral, Integral):
integrand = integral.integrand()
# apply the stored coordinate derivatives back onto the integrand
for tup in reversed(coordinate_derivatives):
integrand = CoordinateDerivative(integrand, tup[0], tup[1], tup[2])
return integral.reconstruct(integrand=integrand)
else:
error("Invalid type %s" % (integral.__class__.__name__,))
def attach_coordinate_derivatives(form, coordinate_derivatives):
if coordinate_derivatives is None:
return form
if isinstance(form, Form):
cds = coordinate_derivatives
new_integrals = [attach_coordinate_derivatives(integ, cds) for integ in form.integrals()]
return Form(new_integrals)
elif isinstance(form, Integral):
integral = form
integrand = integral.integrand()
# apply the stored coordinate derivatives back onto the integrand
for tup in reversed(coordinate_derivatives):
integrand = CoordinateDerivative(integrand, tup[0], tup[1], tup[2])
return integral.reconstruct(integrand=integrand)
else:
error("Invalid type %s" % (form.__class__.__name__,))
def coordinate_derivative(self, o, f, dummy_w, dummy_v, dummy_cd):
o_ = o.ufl_operands
return CoordinateDerivative(map_expr_dag(self, o_[0]), o_[1], o_[2],
o_[3])
def coordinate_derivative(self, o):
o = o.ufl_operands
return CoordinateDerivative(map_expr_dag(self, o[0]), o[1], o[2], o[3])