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_solver(self, Model, Scheme, time=0.0, stim=None, params=None):
''' Generate a new solver object with the given start time, stimulus and parameters. '''
# Create model instance
if isinstance(Model, str):
Model = eval(Model)
model = Model(params=params)
# Initialize time and stimulus (note t=time construction!)
if stim is None:
stim = Expression("1000*t", t=time, degree=1)
# Initialize solver
mesh = UnitIntervalMesh(5)
params = CardiacODESolver.default_parameters()
params["scheme"] = Scheme
solver = CardiacODESolver(mesh, time, model, I_s=stim, params=params)
# Create scheme
info_green("\nTesting %s with %s scheme" % (model, Scheme))
# Start with native initial conditions
(vs_, vs) = solver.solution_fields()
vs_.assign(model.initial_conditions())
vs.assign(vs_)
return solver
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 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 applied current
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
self.T = 5*self.dt
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 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 _setup_solver(self, Model, Scheme, mesh, time, stim=None, params=None):
# Create model instance
model = Model(params=params)
# Initialize time and stimulus (note t=time construction!)
if stim is None:
stim = Expression("1000*t", t=time, degree=1)
# Initialize solver
params = CardiacODESolver.default_parameters()
params["scheme"] = Scheme
solver = CardiacODESolver(mesh, time, model, I_s=stim, params=params)
# Create scheme
info_green("\nTesting %s with %s scheme" % (model, Scheme))
# Start with native initial conditions
(vs_, vs) = solver.solution_fields()
vs_.assign(model.initial_conditions())
vs.assign(vs_)
return solver
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)