def test_default_basic_single_cell_solver(self, cell_model, theta):
"Test basic single cell solver."
time = Constant(0.0)
model = cell_model
Model = cell_model.__class__
if Model == supported_cell_models[3] and theta > 0:
pytest.xfail("failing configuration (but should work)")
model.stimulus = Expression("1000*t", t=time, degree=1)
info_green("\nTesting %s" % model)
vec_solve = self._run_solve(model, time, theta)
if Model == supported_cell_models[3] and theta == 0:
pytest.xfail("failing configuration (but should work)")
if Model in self.references and theta in self.references[Model]:
ind, ref_value = self.references[Model][theta]
print("vec_solve", vec_solve.get_local())
print("ind", ind, "ref", ref_value)
assert_almost_equal(vec_solve[ind], ref_value, 1e-10)
else:
info_red("Missing references for %r, %r" % (Model, theta))
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 setup_model():
"Set-up cardiac model based on a slightly non-standard set of parameters."
# Define cell parameters
k = 0.00004; Vrest = -85.; Vthreshold = -70.; Vpeak = 40.;
v_amp = Vpeak - Vrest
l = 0.63; b = 0.013;
cell_parameters = {"c_1": k*v_amp**2, "c_2": k*v_amp, "c_3": b/l,
"a": (Vthreshold - Vrest)/v_amp, "b": l,
"v_rest":Vrest, "v_peak": Vpeak}
cell = FitzHughNagumoManual(cell_parameters)
# Define conductivities
chi = 2000.0 # cm^{-1}
s_il = 3.0/chi # mS
s_it = 0.3/chi # mS
s_el = 2.0/chi # mS
s_et = 1.3/chi # mS
M_i = as_tensor(((s_il, 0), (0, s_it)))
M_e = as_tensor(((s_el, 0), (0, s_et)))
# Define mesh
domain = UnitSquareMesh(20, 20)
time = Constant(0.0)
heart = CardiacModel(domain, time, M_i, M_e, cell)
return heart
def test_compute_adjoint(self):
"Test that we can compute the adjoint 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)
(vs_, vs) = solver.solution_fields()
# Define functional and compute gradient etc
J = Functional(inner(vs_, vs_) * dx * dt[FINISH_TIME])
# Compute adjoint
info_green("Computing adjoint")
z = compute_adjoint(J)
# Check that no vs_ adjoint is None (== 0.0!)
for (value, var) in z:
if var.name == "vs_":
msg = "Adjoint solution for vs_ is None (#fail)."
assert (value is not None), msg
def setup(self):
self.mesh = UnitCubeMesh(5, 5, 5)
# Create time
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0*t", t=self.time, degree=1)
# Create ac
self.applied_current = Expression("sin(2*pi*x[0])*t",
t=self.time,
degree=3)
# Create conductivity "tensors"
self.M_i = 1.0
self.M_e = 2.0
self.cell_model = FitzHughNagumoManual()
self.cardiac_model = CardiacModel(self.mesh, self.time, self.M_i,
self.M_e, self.cell_model,
self.stimulus, self.applied_current)
dt = 0.1
self.t0 = 0.0
self.dt = [(0.0, dt), (dt * 2, dt / 2), (dt * 4, dt)]
# Test using variable dt interval but using the same dt.
self.T = self.t0 + 5 * dt
self.ics = self.cell_model.initial_conditions()
def __init__(self):
self.mesh = UnitCubeMesh(5, 5, 5)
# Create time
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0*t", t=self.time, degree=1)
# Create ac
self.applied_current = Expression("sin(2*pi*x[0])*t",
t=self.time,
degree=3)
# Create conductivity "tensors"
self.M_i = 1.0
self.M_e = 2.0
self.cell_model = FitzHughNagumoManual()
self.cardiac_model = CardiacModel(self.mesh, self.time, self.M_i,
self.M_e, self.cell_model,
self.stimulus,
self.applied_current)
dt = 0.1
self.t0 = 0.0
if Solver == SplittingSolver:
# FIXME: Dolfin-adjoint fails with adaptive timestep and SplittingSolver
self.dt = dt
else:
self.dt = [(0.0, dt), (dt * 2, dt / 2), (dt * 4, dt)]
# Test using variable dt interval but using the same dt.
self.T = self.t0 + 5 * dt
# Create solver object
params = Solver.default_parameters()
if Solver == SplittingSolver:
params.enable_adjoint = enable_adjoint
params.BidomainSolver.linear_solver_type = solver_type
params.BidomainSolver.petsc_krylov_solver.relative_tolerance = 1e-12
else:
params.BasicBidomainSolver.linear_variational_solver.linear_solver = \
"gmres" if solver_type == "iterative" else "lu"
params.BasicBidomainSolver.linear_variational_solver.krylov_solver.relative_tolerance = 1e-12
params.BasicBidomainSolver.linear_variational_solver.preconditioner = 'ilu'
self.solver = Solver(self.cardiac_model, params=params)
(vs_, vs, vur) = self.solver.solution_fields()
if ics is None:
self.ics = self.cell_model.initial_conditions()
vs_.assign(self.ics)
else:
vs_.vector()[:] = ics.vector()
def setUp(self):
self.mesh = UnitCubeMesh(5, 5, 5)
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0", degree=1)
# Create conductivity "tensors"
self.M_i = 1.0
self.t0 = 0.0
self.dt = 0.1
def test_compare_against_reference(self, Model, Scheme):
''' Runs the given cell model with the numerical scheme
and compares the result with the reference value. '''
solver = self._setup_solver(Model, Scheme, time=Constant(0))
(vs_, vs) = solver.solution_fields()
next_dt = 0.01
solver.step((0.0, next_dt))
vs_.assign(vs)
solver.step((next_dt, 2 * next_dt))
self.compare_against_reference(vs.vector(), Model, Scheme)
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 _setup_solver(self, model, Scheme, mesh):
# Initialize time and stimulus (note t=time construction!)
time = Constant(0.0)
stim = Expression("(time >= stim_start) && (time < stim_start + stim_duration)"
" ? stim_amplitude : 0.0 ", time=time, stim_amplitude=52.0,
stim_start=0.0, stim_duration=1.0, name="stim", degree=1)
# Initialize solver
params = CardiacODESolver.default_parameters()
params["scheme"] = Scheme
solver = CardiacODESolver(mesh, time, model, I_s=stim, params=params)
return solver
def main(N, dt, T, theta):
if dolfin_adjoint:
adj_reset()
# Create cardiac model
mesh = UnitSquareMesh(N, N)
time = Constant(0.0)
cell_model = NoCellModel()
ac_str = "cos(t)*cos(2*pi*x[0])*cos(2*pi*x[1]) + 4*pow(pi, 2)*cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)"
stimulus = Expression(ac_str, t=time, degree=3)
heart = CardiacModel(mesh, time, 1.0, 1.0, cell_model, stimulus=stimulus)
# Set-up solver
ps = BasicSplittingSolver.default_parameters()
ps["theta"] = theta
ps["BasicBidomainSolver"]["linear_variational_solver"][
"linear_solver"] = "direct"
solver = BasicSplittingSolver(heart, params=ps)
# Define exact solution (Note: v is returned at end of time
# interval(s), u is computed at somewhere in the time interval
# depending on theta)
v_exact = Expression("cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)", t=T, degree=3)
u_exact = Expression("-cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)/2.0",
t=T - (1 - theta) * dt,
degree=3)
# Define initial condition(s)
vs0 = Function(solver.VS)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(vs0)
# Solve
solutions = solver.solve((0, T), dt)
for (timestep, (vs_, vs, vur)) in solutions:
continue
# Compute errors
(v, s) = vs.split(deepcopy=True)
v_error = errornorm(v_exact, v, "L2", degree_rise=2)
(v, u, r) = vur.split(deepcopy=True)
u_error = errornorm(u_exact, u, "L2", degree_rise=2)
return (v_error, u_error, mesh.hmin(), dt, T)
def setUp(self):
self.mesh = UnitCubeMesh(5, 5, 5)
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0", degree=1)
# Create ac
self.applied_current = Expression("sin(2*pi*x[0])*t",
t=self.time,
degree=3)
# Create conductivity "tensors"
self.M_i = 1.0
self.M_e = 2.0
self.t0 = 0.0
self.dt = 0.1
def test_replay(self):
"Test that replay reports success for basic single cell solver"
set_dolfin_parameters()
model = Model()
# Initialize solver
params = BasicSingleCellSolver.default_parameters()
params["theta"] = theta
time = Constant(0.0)
solver = BasicSingleCellSolver(model, time, params=params)
info_green("Running %s with theta %g" % (model, theta))
ics = project(model.initial_conditions(), solver.VS).copy(deepcopy=True, name="ics")
self._run(solver, model, ics)
info_green("Replaying")
success = replay_dolfin(tol=0.0, stop=True)
assert_true(success)
def test_compare_against_reference_constant(self, Model, Scheme):
''' Runs the given cell model with the numerical scheme
and compares the result with the reference value. '''
Model = eval(Model)
params = Model.default_parameters()
self.replace_with_constants(params)
solver = self._setup_solver(Model,
Scheme,
time=Constant(0),
params=params)
(vs_, vs) = solver.solution_fields()
next_dt = 0.01
solver.step((0.0, next_dt))
vs_.assign(vs)
solver.step((next_dt, 2 * next_dt))
self.compare_against_reference(vs.vector(), Model, Scheme)
def tlm_adj_setup_cellmodel_parameters(self, cell_model, Scheme):
mesh = UnitIntervalMesh(3)
Model = cell_model.__class__
# Initiate solver, with model and Scheme
cell_params = Model.default_parameters()
param_name = cellmodel_parameters_seeds[Model][0]
cell_params[param_name] = Constant(cell_params[param_name],
name=param_name)
model = Model(params=cell_params)
solver = self._setup_solver(model, Scheme, mesh)
info_green("Running forward %s with %s (setup)" % (model, Scheme))
ics = Function(project(model.initial_conditions(), solver.VS),
name="ics")
self._run(solver, 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))
# Set-up runner
def Jhat(val):
cell_params[param_name].assign(val)
ics = Function(project(model.initial_conditions(), solver.VS),
name="ics")
self._run(solver, ics)
(vs_, vs) = solver.solution_fields()
return assemble(form(vs))
# Stop annotating
solver.parameters["enable_adjoint"] = False
m = ConstantControl(cell_params[param_name])
return J, Jhat, m, Jics
def _run(cell):
if dolfin_adjoint:
from dolfin_adjoint import adj_reset
adj_reset()
solver = BasicSingleCellSolver(cell, Constant(0.0))
# Setup initial condition
(vs_, vs) = solver.solution_fields()
vs_.vector()[0] = 30. # Non-resting state
vs_.vector()[1] = 0.
T = 2
solutions = solver.solve((0, T), 0.25)
times = []
v_values = []
s_values = []
for ((t0, t1), vs) in solutions:
times += [0.5 * (t0 + t1)]
v_values.append(vs.vector()[0])
s_values.append(vs.vector()[1])
return (v_values, s_values, times)
def test_solver_with_domains():
mesh = UnitCubeMesh(5, 5, 5)
time = Constant(0.0)
stimulus = Expression("2.0*t", t=time, degree=1)
# Create ac
applied_current = Expression("sin(2*pi*x[0])*t", t=time, degree=3)
# Create conductivity "tensors"
M_i = 1.0
M_e = 2.0
cell_model = FitzHughNagumoManual()
cardiac_model = CardiacModel(mesh, time, M_i, M_e, cell_model,
stimulus, applied_current)
dt = 0.1
t0 = 0.0
dt = dt
T = t0 + 5*dt
ics = cell_model.initial_conditions()
# Create basic solver
params = SplittingSolver.default_parameters()
params["ode_solver_choice"] = "BasicCardiacODESolver"
solver = SplittingSolver(cardiac_model, params=params)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(ics)
# Solve
solutions = solver.solve((t0, T), dt)
for (interval, fields) in solutions:
(vs_, vs, vur) = fields
def replace_with_constants(self, params):
''' Replace all float values in params by Constants. '''
for param_name in params.keys():
value = params[param_name]
params[param_name] = Constant(value)
def test_fitzhugh_nagumo_manual(self):
"""Test that the manually written FitzHugh-Nagumo model gives
comparable results to a given reference from Sundnes et al,
2006."""
class Stimulus(Expression):
def __init__(self, **kwargs):
self.t = kwargs["t"]
def eval(self, value, x):
if float(self.t) >= 50 and float(self.t) < 60:
v_amp = 125
value[0] = 0.05 * v_amp
else:
value[0] = 0.0
if dolfin_adjoint:
from dolfin_adjoint import adj_reset
adj_reset()
cell = FitzHughNagumoManual()
time = Constant(0.0)
cell.stimulus = Stimulus(t=time, degree=0)
solver = BasicSingleCellSolver(cell, time)
# Setup initial condition
(vs_, vs) = solver.solution_fields()
ic = cell.initial_conditions()
vs_.assign(ic)
# Initial set-up
interval = (0, 400)
dt = 1.0
times = []
v_values = []
s_values = []
# Solve
solutions = solver.solve(interval, dt=dt)
for (timestep, vs) in solutions:
(t0, t1) = timestep
times += [(t0 + t1) / 2]
v_values += [vs.vector()[0]]
s_values += [vs.vector()[1]]
# Regression test
v_max_reference = 2.6883308148064152e+01
s_max_reference = 6.8660144687023219e+01
tolerance = 1.e-14
print "max(v_values) %.16e" % max(v_values)
print "max(s_values) %.16e" % max(s_values)
msg = "Maximal %s value does not match reference: diff is %.16e"
v_diff = abs(max(v_values) - v_max_reference)
s_diff = abs(max(s_values) - s_max_reference)
assert (v_diff < tolerance), msg % ("v", v_diff)
assert (s_diff < tolerance), msg % ("s", s_diff)
# Correctness test
import os
if int(os.environ.get("DOLFIN_NOPLOT", 0)) != 1:
import pylab
pylab.plot(times, v_values, 'b*')
pylab.plot(times, s_values, 'r-')
def long_run_compare(self):
mesh = UnitIntervalMesh(5)
# FIXME: We need to make this run in paralell.
if MPI.size(mesh.mpi_comm()) > 1:
return
Model = Tentusscher_2004_mcell
tstop = 10
ind_V = 0
dt_ref = 0.1
time_ref = np.linspace(0, tstop, int(tstop/dt_ref)+1)
dir_path = os.path.dirname(__file__)
Vm_reference = np.fromfile(os.path.join(dir_path, "Vm_reference.npy"))
params = Model.default_parameters()
time = Constant(0.0)
stim = Expression("(time >= stim_start) && (time < stim_start + stim_duration)"\
" ? stim_amplitude : 0.0 ", time=time, stim_amplitude=52.0, \
stim_start=1.0, stim_duration=1.0, degree=1)
# Initiate solver, with model and Scheme
if dolfin_adjoint:
adj_reset()
solver = self._setup_solver(Model, Scheme, mesh, time, stim, params)
solver._pi_solver.parameters["newton_solver"]["relative_tolerance"] = 1e-8
solver._pi_solver.parameters["newton_solver"]["maximum_iterations"] = 30
solver._pi_solver.parameters["newton_solver"]["report"] = False
scheme = solver._scheme
(vs_, vs) = solver.solution_fields()
vs.assign(vs_)
dof_to_vertex_map_values = dof_to_vertex_map(vs.function_space())
scheme.t().assign(0.0)
vs_array = np.zeros(mesh.num_vertices()*\
vs.function_space().dofmap().num_entity_dofs(0))
vs_array[dof_to_vertex_map_values] = vs.vector().array()
output = [vs_array[ind_V]]
time_output = [0.0]
dt = dt_org
# Time step
next_dt = max(min(tstop-float(scheme.t()), dt), 0.0)
t0 = 0.0
while next_dt > 0.0:
# Step solver
solver.step((t0, t0 + next_dt))
vs_.assign(vs)
# Collect plt output data
vs_array[dof_to_vertex_map_values] = vs.vector().array()
output.append(vs_array[ind_V])
time_output.append(float(scheme.t()))
# Next time step
t0 += next_dt
next_dt = max(min(tstop-float(scheme.t()), dt), 0.0)
# Compare solution from CellML run using opencell
assert_almost_equal(output[-1], Vm_reference[-1], abs_tol)
output = np.array(output)
time_output = np.array(time_output)
output = np.interp(time_ref, time_output, output)
value = np.sqrt(np.sum(((Vm_reference-output)/Vm_reference)**2))/len(Vm_reference)
assert_almost_equal(value, 0.0, rel_tol)