def test_compute_gradient(self):
"Test that we can compute the gradient for some given functional"
set_dolfin_parameters()
model = Model()
params = BasicSingleCellSolver.default_parameters()
params["theta"] = theta
time = Constant(0.0)
solver = BasicSingleCellSolver(model, time, params=params)
# Get initial conditions (Projection of expressions
# don't get annotated, which is fine, because there is
# no need.)
ics = project(model.initial_conditions(), solver.VS)
# Run forward model
info_green("Running forward %s with theta %g" % (model, theta))
self._run(solver, model, ics)
# Define functional
(vs_, vs) = solver.solution_fields()
J = Functional(inner(vs, vs) * dx * dt[FINISH_TIME])
# Compute gradient with respect to vs_. Highly unclear
# why with respect to ics and vs fail.
info_green("Computing gradient")
dJdics = compute_gradient(J, Control(vs_))
assert (dJdics is not None), "Gradient is None (#fail)."
print(dJdics.vector().array())
def test_adjoint_cell_model_parameter(self, cell_model, Scheme):
""" Test that the gradient computed with the adjoint model is correct. """
if isinstance(cell_model, fails_with_RK4) and Scheme == "RK4":
pytest.xfail(
"RK4 is unstable for some models with this timestep (0.01)")
if isinstance(cell_model,
fails_with_forward_euler) and Scheme == "ForwardEuler":
pytest.xfail(
"ForwardEuler is unstable for some models with this timestep (0.01)"
)
J, Jhat, m, Jics = self.tlm_adj_setup_cellmodel_parameters(
cell_model, Scheme)
# Seed for taylor test
seed = seed_collection_adm.get(cell_model.__class__)
# Compute gradient with respect to vs.
info_green("Computing gradient")
dJdics = compute_gradient(J, m, forget=False)
assert (dJdics is not None), "Gradient is None (#fail)."
conv_rate = taylor_test(Jhat, m, Jics, dJdics, seed=seed)
# Check that minimal rate is greater than some given number
assert_greater(conv_rate, 1.9)
def test_adjoint(self, Solver, solver_type):
"""Test that adjoint model of basic bidomain solver converges at 2nd order."""
info_green("Running adjoint basic (%s)" % solver_type)
J, Jhat, m, Jics = self.tlm_adj_setup(Solver, solver_type)
# Check adjoint correctness
dJdics = compute_gradient(J, m, forget=False)
assert (dJdics is not None), "Gradient is None (#fail)."
conv_rate = taylor_test(Jhat, m, Jics, dJdics, seed=1e-3)
# Check that minimal convergence rate is greater than some given number
assert_greater(conv_rate, 1.9)
def test_taylor_remainder(self):
"Run Taylor remainder tests for selection of models and solvers."
set_dolfin_parameters()
model = Model()
params = BasicSingleCellSolver.default_parameters()
params["theta"] = theta
time = Constant(0.0)
solver = BasicSingleCellSolver(model, time, params=params)
# Get initial conditions (Projection of expressions
# don't get annotated, which is fine, because there is
# no need.)
ics = project(model.initial_conditions(), solver.VS)
# Run forward model
info_green("Running forward %s with theta %g" % (model, theta))
self._run(solver, model, ics)
# Define functional
(vs_, vs) = solver.solution_fields()
form = lambda w: inner(w, w)*dx
J = Functional(form(vs)*dt[FINISH_TIME])
# Compute value of functional with current ics
Jics = assemble(form(vs))
# Compute gradient with respect to vs_ (ics?)
dJdics = compute_gradient(J, Control(vs_),
forget=False)
# Stop annotating
parameters["adjoint"]["stop_annotating"] = True
# Set-up runner
def Jhat(ics):
self._run(solver, model, ics)
(vs_, vs) = solver.solution_fields()
return assemble(form(vs))
# Run taylor test
if isinstance(model, Tentusscher_2004_mcell):
seed=1.e-5
else:
seed=None
conv_rate = taylor_test(Jhat, Control(vs_),
Jics, dJdics, seed=seed)
# Check that minimal rate is greater than some given number
assert_greater(conv_rate, 1.8)
def test_AdjointModelOfSplittingSolver_PassesTaylorTest(
self, Solver, solver_type):
"""Test that basic and optimised splitting solvers yield
very comparative results when configured identically."""
J, Jhat, m, Jics = self.tlm_adj_setup(Solver, solver_type)
# Check adjoint model correctness
info_green("Compute gradient with adjoint linear model")
dJdics = compute_gradient(J, m, forget=False)
assert (dJdics is not None), "Gradient is None (#fail)."
conv_rate = taylor_test(Jhat, m, Jics, dJdics, seed=1.)
# Check that minimal convergence rate is greater than some given number
assert_greater(conv_rate, 1.9)