def prepare_evaluate_hessian(self, inputs, hessian_inputs, adj_inputs,
relevant_dependencies):
# First fetch all relevant values
fwd_block_variable = self.get_outputs()[0]
hessian_input = hessian_inputs[0]
tlm_output = fwd_block_variable.tlm_value
if hessian_input is None:
return
if tlm_output is None:
return
F_form = self._create_F_form()
# Using the equation Form we derive dF/du, d^2F/du^2 * du/dm * direction.
dFdu_form = backend.derivative(F_form, fwd_block_variable.saved_output)
d2Fdu2 = ufl.algorithms.expand_derivatives(
backend.derivative(dFdu_form, fwd_block_variable.saved_output,
tlm_output))
adj_sol = self.adj_sol
if adj_sol is None:
raise RuntimeError("Hessian computation was run before adjoint.")
bdy = self._should_compute_boundary_adjoint(relevant_dependencies)
adj_sol2, adj_sol2_bdy = self._assemble_and_solve_soa_eq(
dFdu_form, adj_sol, hessian_input, d2Fdu2, bdy)
r = {}
r["adj_sol2"] = adj_sol2
r["adj_sol2_bdy"] = adj_sol2_bdy
r["form"] = F_form
r["adj_sol"] = adj_sol
return r
def second_derivative_action(self, dependencies, values, inner_variable, inner_contraction_vector, outer_variable, hermitian, action_vector):
if isinstance(self.form, ufl.form.Form):
# Find the dolfin Function corresponding to variable.
dolfin_inner_variable = values[dependencies.index(inner_variable)].data
dolfin_outer_variable = values[dependencies.index(outer_variable)].data
dolfin_dependencies = [dep for dep in _extract_function_coeffs(self.form)]
dolfin_values = [val.data for val in values]
current_form = backend.replace(self.form, dict(zip(dolfin_dependencies, dolfin_values)))
trial = backend.TrialFunction(dolfin_outer_variable.function_space())
d_rhs = backend.derivative(current_form, dolfin_inner_variable, inner_contraction_vector.data)
d_rhs = ufl.algorithms.expand_derivatives(d_rhs)
if len(d_rhs.integrals()) == 0:
return None
d_rhs = backend.derivative(d_rhs, dolfin_outer_variable, trial)
d_rhs = ufl.algorithms.expand_derivatives(d_rhs)
if len(d_rhs.integrals()) == 0:
return None
if hermitian:
action = backend.action(backend.adjoint(d_rhs), action_vector.data)
else:
action = backend.action(d_rhs, action_vector.data)
return adjlinalg.Vector(action)
else:
# RHS is a adjlinalg.Vector. Its derivative is therefore zero.
raise exceptions.LibadjointErrorNotImplemented("No derivative method for constant RHS.")
def second_derivative_action(dependencies, values, inner_variable, inner_contraction_vector, outer_variable, outer_contraction_vector, hermitian, input, coefficient, context):
dolfin_inner_variable = values[dependencies.index(inner_variable)].data
dolfin_outer_variable = values[dependencies.index(outer_variable)].data
dolfin_values = [val.data for val in values]
expressions.update_expressions(frozen_expressions)
constant.update_constants(frozen_constants)
current_form = backend.replace(eq_lhs, dict(zip(diag_coeffs, dolfin_values)))
deriv = backend.derivative(current_form, dolfin_inner_variable)
args = ufl.algorithms.extract_arguments(deriv)
deriv = backend.replace(deriv, {args[1]: inner_contraction_vector.data}) # contract over the middle index
deriv = backend.derivative(deriv, dolfin_outer_variable)
args = ufl.algorithms.extract_arguments(deriv)
deriv = backend.replace(deriv, {args[1]: outer_contraction_vector.data}) # contract over the middle index
# Assemble the G-matrix now, so that we can apply the Dirichlet BCs to it
if len(ufl.algorithms.extract_arguments(ufl.algorithms.expand_derivatives(coefficient*deriv))) == 0:
return adjlinalg.Vector(None)
G = coefficient * deriv
if hermitian:
output = backend.action(backend.adjoint(G), input.data)
else:
output = backend.action(G, input.data)
return adjlinalg.Vector(output)
def _assemble_soa_eq_rhs(self, dFdu_form, adj_sol, hessian_input, d2Fdu2):
# Start piecing together the rhs of the soa equation
b = hessian_input.copy()
b_form = d2Fdu2
for bo in self.get_dependencies():
c = bo.output
c_rep = bo.saved_output
tlm_input = bo.tlm_value
if (c == self.func and not self.linear) or tlm_input is None:
continue
if isinstance(c, compat.MeshType):
X = backend.SpatialCoordinate(c)
dFdu_adj = backend.action(backend.adjoint(dFdu_form), adj_sol)
d2Fdudm = ufl.algorithms.expand_derivatives(
backend.derivative(dFdu_adj, X, tlm_input))
if len(d2Fdudm.integrals()) > 0:
b -= compat.assemble_adjoint_value(d2Fdudm)
elif not isinstance(c, backend.DirichletBC):
b_form += backend.derivative(dFdu_form, c_rep, tlm_input)
b_form = ufl.algorithms.expand_derivatives(b_form)
if len(b_form.integrals()) > 0:
b_form = backend.adjoint(b_form)
b -= compat.assemble_adjoint_value(backend.action(b_form, adj_sol))
return b
def equation_partial_second_derivative(self, adjointer, adjoint, i,
variable, m_dot):
form = adjresidual.get_residual(i)
if form is not None:
form = -form
mesh = ufl.algorithms.extract_arguments(
form)[0].function_space().mesh()
fn_space = backend.FunctionSpace(mesh, "R", 0)
dparam = backend.Function(fn_space)
dparam.vector()[:] = 1.0 * float(self.coeff)
d2param = backend.Function(fn_space)
d2param.vector()[:] = 1.0 * float(self.coeff) * m_dot
diff_form = ufl.algorithms.expand_derivatives(
backend.derivative(form, get_constant(self.a), dparam))
if diff_form is None:
return None
diff_form = ufl.algorithms.expand_derivatives(
backend.derivative(diff_form, get_constant(self.a), d2param))
if diff_form is None:
return None
# Let's see if the form actually depends on the parameter m
if len(diff_form.integrals()) != 0:
dFdm = backend.assemble(diff_form) # actually - dF/dm
assert isinstance(dFdm, backend.GenericVector)
out = dFdm.inner(adjoint.vector())
return out
else:
return None # dF/dm is zero, return None
def functional_partial_second_derivative(self, adjointer, J, timestep,
m_dot):
form = J.get_form(adjointer, timestep)
if form is None:
return None
for coeff in ufl.algorithms.extract_coefficients(form):
try:
mesh = coeff.function_space().mesh()
fn_space = backend.FunctionSpace(mesh, "R", 0)
break
except:
pass
dparam = backend.Function(fn_space)
dparam.vector()[:] = 1.0 * float(self.coeff)
d = backend.derivative(form, get_constant(self.a), dparam)
d = ufl.algorithms.expand_derivatives(d)
d2param = backend.Function(fn_space)
d2param.vector()[:] = 1.0 * float(self.coeff) * m_dot
d = backend.derivative(d, get_constant(self.a), d2param)
d = ufl.algorithms.expand_derivatives(d)
if len(d.integrals()) != 0:
return backend.assemble(d)
else:
return None
def __init__(self, form, control):
if not isinstance(control.control, backend.Function):
raise NotImplementedError("Only implemented for Function controls")
args = ufl.algorithms.extract_arguments(form)
if len(args) != 0:
raise ValueError("Must be a rank-zero form, i.e. a functional")
u = control.control
self.V = u.function_space()
# We want to make a copy of the control purely for use
# in the constraint, so that our writing it isn't
# bothering anyone else
self.u = backend_types.Function(self.V)
self.form = ufl.replace(form, {u: self.u})
self.trial = backend.TrialFunction(self.V)
self.dform = backend.derivative(self.form, self.u, self.trial)
if len(
ufl.algorithms.extract_arguments(
ufl.algorithms.expand_derivatives(self.dform))) == 0:
raise ValueError("Form must depend on control")
self.test = backend.TestFunction(self.V)
self.hess = ufl.algorithms.expand_derivatives(
backend.derivative(self.dform, self.u, self.test))
if len(ufl.algorithms.extract_arguments(self.hess)) == 0:
self.zero_hess = True
else:
self.zero_hess = False
def equation_partial_second_derivative(self, adjointer, adjoint, i, variable, m_dot):
form = adjresidual.get_residual(i)
if form is not None:
form = -form
mesh = ufl.algorithms.extract_arguments(form)[0].function_space().mesh()
fn_space = backend.FunctionSpace(mesh, "R", 0)
dparam = backend.Function(fn_space)
dparam.vector()[:] = 1.0 * float(self.coeff)
d2param = backend.Function(fn_space)
d2param.vector()[:] = 1.0 * float(self.coeff) * m_dot
diff_form = ufl.algorithms.expand_derivatives(backend.derivative(form, get_constant(self.a), dparam))
if diff_form is None:
return None
diff_form = ufl.algorithms.expand_derivatives(backend.derivative(diff_form, get_constant(self.a), d2param))
if diff_form is None:
return None
# Let's see if the form actually depends on the parameter m
if len(diff_form.integrals()) != 0:
dFdm = backend.assemble(diff_form) # actually - dF/dm
assert isinstance(dFdm, backend.GenericVector)
out = dFdm.inner(adjoint.vector())
return out
else:
return None # dF/dm is zero, return None
def functional_partial_second_derivative(self, adjointer, J, timestep, m_dot):
form = J.get_form(adjointer, timestep)
if form is None:
return None
for coeff in ufl.algorithms.extract_coefficients(form):
try:
mesh = coeff.function_space().mesh()
fn_space = backend.FunctionSpace(mesh, "R", 0)
break
except:
pass
dparam = backend.Function(fn_space)
dparam.vector()[:] = 1.0 * float(self.coeff)
d = backend.derivative(form, get_constant(self.a), dparam)
d = ufl.algorithms.expand_derivatives(d)
d2param = backend.Function(fn_space)
d2param.vector()[:] = 1.0 * float(self.coeff) * m_dot
d = backend.derivative(d, get_constant(self.a), d2param)
d = ufl.algorithms.expand_derivatives(d)
if len(d.integrals()) != 0:
return backend.assemble(d)
else:
return None
def evaluate_hessian_component(self,
inputs,
hessian_inputs,
adj_inputs,
block_variable,
idx,
relevant_dependencies,
prepared=None):
form = prepared
hessian_input = hessian_inputs[0]
adj_input = adj_inputs[0]
c1 = block_variable.output
c1_rep = block_variable.saved_output
if isinstance(c1, backend.Function):
dc = backend.TestFunction(c1.function_space())
elif isinstance(c1, compat.ExpressionType):
mesh = form.ufl_domain().ufl_cargo()
W = c1._ad_function_space(mesh)
dc = backend.TestFunction(W)
elif isinstance(c1, backend.Constant):
mesh = compat.extract_mesh_from_form(form)
dc = backend.TestFunction(c1._ad_function_space(mesh))
elif isinstance(c1, compat.MeshType):
pass
else:
return None
if isinstance(c1, compat.MeshType):
X = backend.SpatialCoordinate(c1)
dform = backend.derivative(form, X)
else:
dform = backend.derivative(form, c1_rep, dc)
hessian_outputs = hessian_input * compat.assemble_adjoint_value(dform)
for other_idx, bv in relevant_dependencies:
c2_rep = bv.saved_output
tlm_input = bv.tlm_value
if tlm_input is None:
continue
if isinstance(c2_rep, compat.MeshType):
X = backend.SpatialCoordinate(c2_rep)
ddform = backend.derivative(dform, X, tlm_input)
else:
ddform = backend.derivative(dform, c2_rep, tlm_input)
hessian_outputs += adj_input * compat.assemble_adjoint_value(
ddform)
if isinstance(c1, compat.ExpressionType):
return [(hessian_outputs, W)]
else:
return hessian_outputs
def evaluate_tlm_component(self,
inputs,
tlm_inputs,
block_variable,
idx,
prepared=None):
F_form = prepared["form"]
dFdu = prepared["dFdu"]
V = self.get_outputs()[idx].output.function_space()
bcs = []
dFdm = 0.
dFdm_shape = 0.
for block_variable in self.get_dependencies():
tlm_value = block_variable.tlm_value
c = block_variable.output
c_rep = block_variable.saved_output
if isinstance(c, backend.DirichletBC):
if tlm_value is None:
bcs.append(compat.create_bc(c, homogenize=True))
else:
bcs.append(tlm_value)
continue
elif isinstance(c, compat.MeshType):
X = backend.SpatialCoordinate(c)
c_rep = X
if tlm_value is None:
continue
if c == self.func and not self.linear:
continue
if isinstance(c, compat.MeshType):
dFdm_shape += compat.assemble_adjoint_value(
backend.derivative(-F_form, c_rep, tlm_value))
else:
dFdm += backend.derivative(-F_form, c_rep, tlm_value)
if isinstance(dFdm, float):
v = dFdu.arguments()[0]
dFdm = backend.inner(backend.Constant(numpy.zeros(v.ufl_shape)),
v) * backend.dx
dFdm = compat.assemble_adjoint_value(dFdm) + dFdm_shape
dudm = backend.Function(V)
return self._assemble_and_solve_tlm_eq(
compat.assemble_adjoint_value(dFdu, bcs=bcs), dFdm, dudm, bcs)
def derivative_action(self, dependencies, values, variable, contraction_vector, hermitian):
if contraction_vector.data is None:
return adjlinalg.Vector(None)
if isinstance(self.form, ufl.form.Form):
# Find the dolfin Function corresponding to variable.
dolfin_variable = values[dependencies.index(variable)].data
dolfin_dependencies = [dep for dep in _extract_function_coeffs(self.form)]
dolfin_values = [val.data for val in values]
current_form = backend.replace(self.form, dict(zip(dolfin_dependencies, dolfin_values)))
trial = backend.TrialFunction(dolfin_variable.function_space())
d_rhs = backend.derivative(current_form, dolfin_variable, trial)
if hermitian:
action = backend.action(backend.adjoint(d_rhs), contraction_vector.data)
else:
action = backend.action(d_rhs, contraction_vector.data)
return adjlinalg.Vector(action)
else:
# RHS is a adjlinalg.Vector. Its derivative is therefore zero.
return adjlinalg.Vector(None)
def prepare_evaluate_adj(self, inputs, adj_inputs, relevant_dependencies):
fwd_block_variable = self.get_outputs()[0]
u = fwd_block_variable.output
dJdu = adj_inputs[0]
F_form = self._create_F_form()
dFdu = backend.derivative(F_form, fwd_block_variable.saved_output,
backend.TrialFunction(u.function_space()))
dFdu_form = backend.adjoint(dFdu)
dJdu = dJdu.copy()
compute_bdy = self._should_compute_boundary_adjoint(
relevant_dependencies)
adj_sol, adj_sol_bdy = self._assemble_and_solve_adj_eq(
dFdu_form, dJdu, compute_bdy)
self.adj_sol = adj_sol
if self.adj_cb is not None:
self.adj_cb(adj_sol)
if self.adj_bdy_cb is not None and compute_bdy:
self.adj_bdy_cb(adj_sol_bdy)
r = {}
r["form"] = F_form
r["adj_sol"] = adj_sol
r["adj_sol_bdy"] = adj_sol_bdy
return r
def __init__(self, form, F, u, bcs, mass, solver_parameters, J):
'''form is M.u - F(u). F is the nonlinear equation, F(u) := 0.'''
RHS.__init__(self, form)
self.F = F
self.u = u
self.bcs = bcs
self.mass = mass
self.solver_parameters = solver_parameters
self.J = J or backend.derivative(F, u)
# We want to mark that the RHS term /also/ depends on
# the previous value of u, as that's what we need to initialise
# the nonlinear solver.
var = adjglobals.adj_variables[self.u]
self.ic_var = None
if backend.parameters["adjoint"]["fussy_replay"]:
can_depend = True
try:
prev_var = find_previous_variable(var)
except:
can_depend = False
if can_depend:
self.ic_var = prev_var
self.deps += [self.ic_var]
self.coeffs += [u]
else:
self.ic_copy = backend.Function(u)
self.ic_var = None
def derivative_action(self, dependencies, values, variable,
contraction_vector, hermitian):
if contraction_vector.data is None:
return adjlinalg.Vector(None)
if isinstance(self.form, ufl.form.Form):
# Find the dolfin Function corresponding to variable.
dolfin_variable = values[dependencies.index(variable)].data
dolfin_dependencies = [
dep for dep in _extract_function_coeffs(self.form)
]
dolfin_values = [val.data for val in values]
current_form = backend.replace(
self.form, dict(zip(dolfin_dependencies, dolfin_values)))
trial = backend.TrialFunction(dolfin_variable.function_space())
d_rhs = backend.derivative(current_form, dolfin_variable, trial)
if hermitian:
action = backend.action(backend.adjoint(d_rhs),
contraction_vector.data)
else:
action = backend.action(d_rhs, contraction_vector.data)
return adjlinalg.Vector(action)
else:
# RHS is a adjlinalg.Vector. Its derivative is therefore zero.
return adjlinalg.Vector(None)
def derivative_assembly(self, dependencies, values, variable, hermitian):
replace_map = {}
for i in range(len(self.deps)):
if self.deps[i] == self.ic_var: continue
j = dependencies.index(self.deps[i])
replace_map[self.coeffs[i]] = values[j].data
diff_var = values[dependencies.index(variable)].data
current_form = backend.replace(self.form, replace_map)
deriv = backend.derivative(current_form, diff_var)
if hermitian:
deriv = backend.adjoint(deriv)
bcs = [
utils.homogenize(bc)
for bc in self.bcs if isinstance(bc, backend.DirichletBC)
] + [
bc
for bc in self.bcs if not isinstance(bc, backend.DirichletBC)
]
else:
bcs = self.bcs
return adjlinalg.Matrix(deriv, bcs=bcs)
def __init__(self, form, F, u, bcs, mass, solver_parameters, J):
'''form is M.u - F(u). F is the nonlinear equation, F(u) := 0.'''
RHS.__init__(self, form)
self.F = F
self.u = u
self.bcs = bcs
self.mass = mass
self.solver_parameters = solver_parameters
self.J = J or backend.derivative(F, u)
# We want to mark that the RHS term /also/ depends on
# the previous value of u, as that's what we need to initialise
# the nonlinear solver.
var = adjglobals.adj_variables[self.u]
self.ic_var = None
if backend.parameters["adjoint"]["fussy_replay"]:
can_depend = True
try:
prev_var = find_previous_variable(var)
except:
can_depend = False
if can_depend:
self.ic_var = prev_var
self.deps += [self.ic_var]
self.coeffs += [u]
else:
self.ic_copy = backend.Function(u)
self.ic_var = None
def equation_partial_derivative(self, adjointer, adjoint, i, variable):
form = adjresidual.get_residual(i)
if form is None:
return None
else:
form = -form
fn_space = ufl.algorithms.extract_arguments(form)[0].function_space()
dparam = backend.Function(
backend.FunctionSpace(fn_space.mesh(), "R", 0))
dparam.vector()[:] = 1.0
dJdv = numpy.zeros(len(self.v))
for (i, a) in enumerate(self.v):
diff_form = ufl.algorithms.expand_derivatives(
backend.derivative(form, a, dparam))
dFdm = backend.assemble(diff_form) # actually - dF/dm
assert isinstance(dFdm, backend.GenericVector)
out = dFdm.inner(adjoint.vector())
dJdv[i] = out
return dJdv
def second_derivative(self, adjointer, variable, dependencies, values, contraction):
if contraction.data is None:
return adjlinalg.Vector(None)
functional_value = None
for timestep in self._derivative_timesteps(adjointer, variable):
functional_value = _add(functional_value,
self._substitute_form(adjointer, timestep, dependencies, values))
d = backend.derivative(functional_value, values[dependencies.index(variable)].data)
d = ufl.algorithms.expand_derivatives(d)
d = backend.derivative(d, values[dependencies.index(variable)].data, contraction.data)
if len(d.integrals()) == 0:
raise SystemExit, "This isn't supposed to happen -- your functional is supposed to depend on %s" % variable
return adjlinalg.Vector(d)
def functional_partial_derivative(self, adjointer, J, timestep):
form = J.get_form(adjointer, timestep)
if form is None:
return None
# OK. Now that we have the form for the functional at this timestep, let's differentiate it with respect to
# my dear Constant, and be done.
for coeff in ufl.algorithms.extract_coefficients(form):
try:
mesh = coeff.function_space().mesh()
fn_space = backend.FunctionSpace(mesh, "R", 0)
break
except:
pass
dparam = backend.Function(fn_space)
dparam.vector()[:] = 1.0 * float(self.coeff)
d = backend.derivative(form, get_constant(self.a), dparam)
d = ufl.algorithms.expand_derivatives(d)
# Add the derivatives of Expressions wrt to the Constant
d = self.expression_derivative(form, d)
if len(d.integrals()) != 0:
return backend.assemble(d)
else:
return None
def equation_partial_derivative(self, adjointer, adjoint, i, variable):
form = adjresidual.get_residual(i)
if form is not None:
form = -form
mesh = ufl.algorithms.extract_arguments(
form)[0].function_space().mesh()
fn_space = backend.FunctionSpace(mesh, "R", 0)
dparam = backend.Function(fn_space)
dparam.vector()[:] = 1.0 * float(self.coeff)
diff_form = ufl.algorithms.expand_derivatives(
backend.derivative(form, get_constant(self.a), dparam))
# Add the derivatives of Expressions wrt to the Constant
diff_form = self.expression_derivative(form, diff_form)
# Let's see if the form actually depends on the parameter m
if len(diff_form.integrals()) != 0:
dFdm = backend.assemble(diff_form) # actually - dF/dm
out = adjoint.vector().inner(dFdm)
else:
out = None # dF/dm is zero, return None
return out
def functional_partial_derivative(self, adjointer, J, timestep):
form = J.get_form(adjointer, timestep)
if form is None:
return None
# OK. Now that we have the form for the functional at this timestep, let's differentiate it with respect to
# my dear Constant, and be done.
for coeff in ufl.algorithms.extract_coefficients(form):
try:
mesh = coeff.function_space().mesh()
fn_space = backend.FunctionSpace(mesh, "R", 0)
break
except:
pass
dparam = backend.Function(fn_space)
dparam.vector()[:] = 1.0 * float(self.coeff)
d = backend.derivative(form, get_constant(self.a), dparam)
d = ufl.algorithms.expand_derivatives(d)
# Add the derivatives of Expressions wrt to the Constant
d = self.expression_derivative(form, d)
if len(d.integrals()) != 0:
return backend.assemble(d)
else:
return None
def evaluate_adj_component(self,
inputs,
adj_inputs,
block_variable,
idx,
prepared=None):
if not self.linear and self.func == block_variable.output:
# We are not able to calculate derivatives wrt initial guess.
return None
F_form = prepared["form"]
adj_sol = prepared["adj_sol"]
adj_sol_bdy = prepared["adj_sol_bdy"]
c = block_variable.output
c_rep = block_variable.saved_output
if isinstance(c, backend.Function):
trial_function = backend.TrialFunction(c.function_space())
elif isinstance(c, backend.Constant):
mesh = compat.extract_mesh_from_form(F_form)
trial_function = backend.TrialFunction(c._ad_function_space(mesh))
elif isinstance(c, compat.ExpressionType):
mesh = F_form.ufl_domain().ufl_cargo()
c_fs = c._ad_function_space(mesh)
trial_function = backend.TrialFunction(c_fs)
elif isinstance(c, backend.DirichletBC):
tmp_bc = compat.create_bc(c,
value=extract_subfunction(
adj_sol_bdy, c.function_space()))
return [tmp_bc]
elif isinstance(c, compat.MeshType):
# Using CoordianteDerivative requires us to do action before
# differentiating, might change in the future.
F_form_tmp = backend.action(F_form, adj_sol)
X = backend.SpatialCoordinate(c_rep)
dFdm = backend.derivative(-F_form_tmp, X)
dFdm = compat.assemble_adjoint_value(dFdm, **self.assemble_kwargs)
return dFdm
dFdm = -backend.derivative(F_form, c_rep, trial_function)
dFdm = backend.adjoint(dFdm)
dFdm = dFdm * adj_sol
dFdm = compat.assemble_adjoint_value(dFdm, **self.assemble_kwargs)
if isinstance(c, compat.ExpressionType):
return [[dFdm, c_fs]]
else:
return dFdm
def second_derivative_action(self, dependencies, values, inner_variable,
inner_contraction_vector, outer_variable,
hermitian, action_vector):
if isinstance(self.form, ufl.form.Form):
# Find the dolfin Function corresponding to variable.
dolfin_inner_variable = values[dependencies.index(
inner_variable)].data
dolfin_outer_variable = values[dependencies.index(
outer_variable)].data
dolfin_dependencies = [
dep for dep in _extract_function_coeffs(self.form)
]
dolfin_values = [val.data for val in values]
current_form = backend.replace(
self.form, dict(zip(dolfin_dependencies, dolfin_values)))
trial = backend.TrialFunction(
dolfin_outer_variable.function_space())
d_rhs = backend.derivative(current_form, dolfin_inner_variable,
inner_contraction_vector.data)
d_rhs = ufl.algorithms.expand_derivatives(d_rhs)
if len(d_rhs.integrals()) == 0:
return None
d_rhs = backend.derivative(d_rhs, dolfin_outer_variable, trial)
d_rhs = ufl.algorithms.expand_derivatives(d_rhs)
if len(d_rhs.integrals()) == 0:
return None
if hermitian:
action = backend.action(backend.adjoint(d_rhs),
action_vector.data)
else:
action = backend.action(d_rhs, action_vector.data)
return adjlinalg.Vector(action)
else:
# RHS is a adjlinalg.Vector. Its derivative is therefore zero.
raise libadjoint.exceptions.LibadjointErrorNotImplemented(
"No derivative method for constant RHS.")
def derivative_action(self, variable, contraction_vector, hermitian, input, coefficient):
deriv = backend.derivative(self.current_form, variable)
args = ufl.algorithms.extract_arguments(deriv)
deriv = backend.replace(deriv, {args[1]: contraction_vector})
if hermitian:
deriv = backend.adjoint(deriv)
action = coefficient * backend.action(deriv, input)
return action
def prepare_evaluate_tlm(self, inputs, tlm_inputs, relevant_outputs):
fwd_block_variable = self.get_outputs()[0]
u = fwd_block_variable.output
F_form = self._create_F_form()
# Obtain dFdu.
dFdu = backend.derivative(F_form, fwd_block_variable.saved_output,
backend.TrialFunction(u.function_space()))
return {"form": F_form, "dFdu": dFdu}
def derivative_action(self, variable, contraction_vector, hermitian, input,
coefficient):
deriv = backend.derivative(self.current_form, variable)
args = ufl.algorithms.extract_arguments(deriv)
deriv = backend.replace(deriv, {args[1]: contraction_vector})
if hermitian:
deriv = backend.adjoint(deriv)
action = coefficient * backend.action(deriv, input)
return action
def second_derivative(self, adjointer, variable, dependencies, values,
contraction):
if contraction.data is None:
return adjlinalg.Vector(None)
functional_value = None
for timestep in self._derivative_timesteps(adjointer, variable):
functional_value = _add(
functional_value,
self._substitute_form(adjointer, timestep, dependencies,
values))
d = backend.derivative(functional_value,
values[dependencies.index(variable)].data)
d = ufl.algorithms.expand_derivatives(d)
d = backend.derivative(d, values[dependencies.index(variable)].data,
contraction.data)
if len(d.integrals()) == 0:
raise SystemExit(
"This isn't supposed to happen -- your functional is supposed to depend on %s"
% variable)
return adjlinalg.Vector(d)
def __call__(self, adjointer, i, dependencies, values, variable):
form = adjresidual.get_residual(i)
if form is not None:
form = -form
fn_space = ufl.algorithms.extract_arguments(form)[0].function_space()
dparam = backend.Function(backend.FunctionSpace(fn_space.mesh(), "R", 0))
dparam.vector()[:] = 1.0 * float(self.coeff)
diff_form = ufl.algorithms.expand_derivatives(backend.derivative(form, get_constant(self.a), dparam))
return adjlinalg.Vector(diff_form)
else:
return None
def evaluate_tlm_component(self,
inputs,
tlm_inputs,
block_variable,
idx,
prepared=None):
form = prepared
dform = 0.
dform_shape = 0.
for bv in self.get_dependencies():
c_rep = bv.saved_output
tlm_value = bv.tlm_value
if tlm_value is None:
continue
if isinstance(c_rep, compat.MeshType):
X = backend.SpatialCoordinate(c_rep)
dform_shape += compat.assemble_adjoint_value(
backend.derivative(form, X, tlm_value))
else:
dform += backend.derivative(form, c_rep, tlm_value)
if not isinstance(dform, float):
dform = compat.assemble_adjoint_value(dform)
return dform + dform_shape
def evaluate_adj_component(self,
inputs,
adj_inputs,
block_variable,
idx,
prepared=None):
form = prepared
adj_input = adj_inputs[0]
c = block_variable.output
c_rep = block_variable.saved_output
if isinstance(c, compat.ExpressionType):
# Create a FunctionSpace from self.form and Expression.
# And then make a TestFunction from this space.
mesh = self.form.ufl_domain().ufl_cargo()
V = c._ad_function_space(mesh)
dc = backend.TestFunction(V)
dform = backend.derivative(form, c_rep, dc)
output = compat.assemble_adjoint_value(dform)
return [[adj_input * output, V]]
elif isinstance(c, compat.MeshType):
X = backend.SpatialCoordinate(c_rep)
dform = backend.derivative(form, X)
output = compat.assemble_adjoint_value(dform)
return adj_input * output
if isinstance(c, backend.Function):
dc = backend.TestFunction(c.function_space())
elif isinstance(c, backend.Constant):
mesh = compat.extract_mesh_from_form(self.form)
dc = backend.TestFunction(c._ad_function_space(mesh))
dform = backend.derivative(form, c_rep, dc)
output = compat.assemble_adjoint_value(dform)
return adj_input * output
def expression_derivative(self, form, diff_form):
""" Applies the chain rule on diff_form to add derivatives of Expressions
with respect to the control. """
coeffs = ufl.algorithms.extract_coefficients(form)
# Take the derivative of Expressions with respect to Constants only
# if the derivative is provided explicitly by the user
expr_deriv_coeffs = []
for coeff in coeffs:
# Check if the coefficient is an expression with user-defined
# derivatives
if not hasattr(coeff, "deval"):
continue
if not hasattr(coeff, "dependencies"):
raise ValueError, "An expression with deval() must also \
implement the dependencies() function."
if not hasattr(coeff, "copy"):
raise ValueError, "An expression with deval() must also \
implement the copy() function."
# Check that that expression depends on self.a
elif self.a not in coeff.dependencies():
continue
else:
expr_deriv_coeffs.append(coeff)
# Ok, so diff_form has the expression "coeff" which depends on self.a
# For the following computation we temporarly change this expression
# such that it returns the derivative wrt to self.a instead of
# plain evaluation.
# Now apply the chain rule to expand the diff_form through these
# expressions
for c in expr_deriv_coeffs:
dc = c.copy()
eval_deriv_a = lambda expr, value, x: expr.deval(value, x, self.a)
dc.eval = types.MethodType(eval_deriv_a, dc)
diff_form += ufl.algorithms.expand_derivatives(
backend.derivative(form, c, dc))
return diff_form
def derivative(self, adjointer, variable, dependencies, values):
functional_value = None
for timestep in self._derivative_timesteps(adjointer, variable):
functional_value = _add(functional_value,
self._substitute_form(adjointer, timestep, dependencies, values))
if functional_value is None:
backend.info_red("Your functional is supposed to depend on %s, but does not?" % variable)
raise libadjoint.exceptions.LibadjointErrorInvalidInputs
d = backend.derivative(functional_value, values[dependencies.index(variable)].data)
d = ufl.algorithms.expand_derivatives(d)
if len(d.integrals()) == 0:
raise SystemExit, "This isn't supposed to happen -- your functional is supposed to depend on %s" % variable
return adjlinalg.Vector(d)
def __call__(self, adjointer, i, dependencies, values, variable):
form = adjresidual.get_residual(i)
if form is not None:
form = -form
fn_space = ufl.algorithms.extract_arguments(
form)[0].function_space()
dparam = backend.Function(
backend.FunctionSpace(fn_space.mesh(), "R", 0))
dparam.vector()[:] = 1.0 * float(self.coeff)
diff_form = ufl.algorithms.expand_derivatives(
backend.derivative(form, get_constant(self.a), dparam))
return adjlinalg.Vector(diff_form)
else:
return None
def derivative_assembly(self, dependencies, values, variable, hermitian):
replace_map = {}
for i in range(len(self.deps)):
if self.deps[i] == self.ic_var: continue
j = dependencies.index(self.deps[i])
replace_map[self.coeffs[i]] = values[j].data
diff_var = values[dependencies.index(variable)].data
current_form = backend.replace(self.form, replace_map)
deriv = backend.derivative(current_form, diff_var)
if hermitian:
deriv = backend.adjoint(deriv)
bcs = [utils.homogenize(bc) for bc in self.bcs if isinstance(bc, backend.DirichletBC)] + [bc for bc in self.bcs if not isinstance(bc, backend.DirichletBC)]
else:
bcs = self.bcs
return adjlinalg.Matrix(deriv, bcs=bcs)
def expression_derivative(self, form, diff_form):
""" Applies the chain rule on diff_form to add derivatives of Expressions
with respect to the control. """
coeffs = ufl.algorithms.extract_coefficients(form)
# Take the derivative of Expressions with respect to Constants only
# if the derivative is provided explicitly by the user
expr_deriv_coeffs = []
for coeff in coeffs:
# Check if the coefficient is an expression with user-defined
# derivatives
if not hasattr(coeff, "dependencies"):
continue
if not hasattr(coeff, "user_defined_derivatives"):
raise ValueError, "An expression with dependencies must also \
provide the user_defined_derivatives \
dictionary."
# Check that that expression depends on self.a
elif self.a not in coeff.dependencies:
continue
else:
expr_deriv_coeffs.append(coeff)
# Ok, so diff_form has the expression "coeff" which depends on self.a
# For the following computation we temporarly change this expression
# such that it returns the derivative wrt to self.a instead of
# plain evaluation.
# Now apply the chain rule to expand the diff_form through these
# expressions
for c in expr_deriv_coeffs:
diff_form += ufl.algorithms.expand_derivatives(
backend.derivative(form, c, c.user_defined_derivatives[self.a]))
return diff_form
def expression_derivative(self, form, diff_form):
""" Applies the chain rule on diff_form to add derivatives of Expressions
with respect to the control. """
coeffs = ufl.algorithms.extract_coefficients(form)
# Take the derivative of Expressions with respect to Constants only
# if the derivative is provided explicitly by the user
expr_deriv_coeffs = []
for coeff in coeffs:
# Check if the coefficient is an expression with user-defined
# derivatives
if not hasattr(coeff, "dependencies"):
continue
if not hasattr(coeff, "user_defined_derivatives"):
raise ValueError("An expression with dependencies must also \
provide the user_defined_derivatives \
dictionary.")
# Check that that expression depends on self.a
elif self.a not in coeff.dependencies:
continue
else:
expr_deriv_coeffs.append(coeff)
# Ok, so diff_form has the expression "coeff" which depends on self.a
# For the following computation we temporarly change this expression
# such that it returns the derivative wrt to self.a instead of
# plain evaluation.
# Now apply the chain rule to expand the diff_form through these
# expressions
for c in expr_deriv_coeffs:
diff_form += ufl.algorithms.expand_derivatives(
backend.derivative(form, c,
c.user_defined_derivatives[self.a]))
return diff_form
def equation_partial_derivative(self, adjointer, adjoint, i, variable):
form = adjresidual.get_residual(i)
if form is None:
return None
else:
form = -form
fn_space = ufl.algorithms.extract_arguments(form)[0].function_space()
dparam = backend.Function(backend.FunctionSpace(fn_space.mesh(), "R", 0))
dparam.vector()[:] = 1.0
dJdv = numpy.zeros(len(self.v))
for (i, a) in enumerate(self.v):
diff_form = ufl.algorithms.expand_derivatives(backend.derivative(form, a, dparam))
dFdm = backend.assemble(diff_form) # actually - dF/dm
assert isinstance(dFdm, backend.GenericVector)
out = dFdm.inner(adjoint.vector())
dJdv[i] = out
return dJdv
def __call__(self, adjointer, i, dependencies, values, variable):
diff_form = None
assert self.dv is not None, "Need a perturbation direction to use in the TLM."
form = adjresidual.get_residual(i)
if form is None:
return None
else:
form = -form
fn_space = ufl.algorithms.extract_arguments(form)[0].function_space()
dparam = backend.Function(backend.FunctionSpace(fn_space.mesh(), "R", 0))
dparam.vector()[:] = 1.0
for (a, da) in zip(self.v, self.dv):
out_form = da * backend.derivative(form, a, dparam)
if diff_form is None:
diff_form = out_form
else:
diff_form += out_form
return adjlinalg.Vector(diff_form)
def derivative(self, adjointer, variable, dependencies, values):
functional_value = None
for timestep in self._derivative_timesteps(adjointer, variable):
functional_value = _add(
functional_value,
self._substitute_form(adjointer, timestep, dependencies,
values))
if functional_value is None:
backend.info_red(
"Your functional is supposed to depend on %s, but does not?" %
variable)
raise libadjoint.exceptions.LibadjointErrorInvalidInputs
d = backend.derivative(functional_value,
values[dependencies.index(variable)].data)
d = ufl.algorithms.expand_derivatives(d)
if len(d.integrals()) == 0:
raise SystemExit(
"This isn't supposed to happen -- your functional is supposed to depend on %s"
% variable)
return adjlinalg.Vector(d)
def __call__(self, adjointer, i, dependencies, values, variable):
diff_form = None
assert self.dv is not None, "Need a perturbation direction to use in the TLM."
form = adjresidual.get_residual(i)
if form is None:
return None
else:
form = -form
fn_space = ufl.algorithms.extract_arguments(form)[0].function_space()
dparam = backend.Function(
backend.FunctionSpace(fn_space.mesh(), "R", 0))
dparam.vector()[:] = 1.0
for (a, da) in zip(self.v, self.dv):
out_form = da * backend.derivative(form, a, dparam)
if diff_form is None:
diff_form = out_form
else:
diff_form += out_form
return adjlinalg.Vector(diff_form)
def evaluate_hessian_component(self,
inputs,
hessian_inputs,
adj_inputs,
block_variable,
idx,
relevant_dependencies,
prepared=None):
c = block_variable.output
if c == self.func and not self.linear:
return None
adj_sol2 = prepared["adj_sol2"]
adj_sol2_bdy = prepared["adj_sol2_bdy"]
F_form = prepared["form"]
adj_sol = prepared["adj_sol"]
fwd_block_variable = self.get_outputs()[0]
tlm_output = fwd_block_variable.tlm_value
c_rep = block_variable.saved_output
# If m = DirichletBC then d^2F(u,m)/dm^2 = 0 and d^2F(u,m)/dudm = 0,
# so we only have the term dF(u,m)/dm * adj_sol2
if isinstance(c, backend.DirichletBC):
tmp_bc = compat.create_bc(c,
value=extract_subfunction(
adj_sol2_bdy, c.function_space()))
return [tmp_bc]
if isinstance(c_rep, backend.Constant):
mesh = compat.extract_mesh_from_form(F_form)
W = c._ad_function_space(mesh)
elif isinstance(c, compat.ExpressionType):
mesh = F_form.ufl_domain().ufl_cargo()
W = c._ad_function_space(mesh)
elif isinstance(c, compat.MeshType):
X = backend.SpatialCoordinate(c)
element = X.ufl_domain().ufl_coordinate_element()
W = backend.FunctionSpace(c, element)
else:
W = c.function_space()
dc = backend.TestFunction(W)
form_adj = backend.action(F_form, adj_sol)
form_adj2 = backend.action(F_form, adj_sol2)
if isinstance(c, compat.MeshType):
dFdm_adj = backend.derivative(form_adj, X, dc)
dFdm_adj2 = backend.derivative(form_adj2, X, dc)
else:
dFdm_adj = backend.derivative(form_adj, c_rep, dc)
dFdm_adj2 = backend.derivative(form_adj2, c_rep, dc)
# TODO: Old comment claims this might break on split. Confirm if true or not.
d2Fdudm = ufl.algorithms.expand_derivatives(
backend.derivative(dFdm_adj, fwd_block_variable.saved_output,
tlm_output))
hessian_output = 0
# We need to add terms from every other dependency
# i.e. the terms d^2F/dm_1dm_2
for _, bv in relevant_dependencies:
c2 = bv.output
c2_rep = bv.saved_output
if isinstance(c2, backend.DirichletBC):
continue
tlm_input = bv.tlm_value
if tlm_input is None:
continue
if c2 == self.func and not self.linear:
continue
# TODO: If tlm_input is a Sum, this crashes in some instances?
if isinstance(c2_rep, compat.MeshType):
X = backend.SpatialCoordinate(c2_rep)
d2Fdm2 = ufl.algorithms.expand_derivatives(
backend.derivative(dFdm_adj, X, tlm_input))
else:
d2Fdm2 = ufl.algorithms.expand_derivatives(
backend.derivative(dFdm_adj, c2_rep, tlm_input))
if d2Fdm2.empty():
continue
hessian_output -= compat.assemble_adjoint_value(d2Fdm2)
if not d2Fdudm.empty():
# FIXME: This can be empty in the multimesh case, ask sebastian
hessian_output -= compat.assemble_adjoint_value(d2Fdudm)
hessian_output -= compat.assemble_adjoint_value(dFdm_adj2)
if isinstance(c, compat.ExpressionType):
return [(hessian_output, W)]
else:
return hessian_output
