def _greedy(self):
if self.reduced_problem.N > 0: # skip during initialization
# Print some additional information related to the current value of the parameter
error_over_time = self.reduced_problem.compute_error()
error_squared_over_time = [v**2 for v in error_over_time]
error_time_quadrature = TimeQuadrature((0., self.truth_problem.T), error_squared_over_time)
error = sqrt(error_time_quadrature.integrate())
print("absolute error for current mu =", error)
error_estimator_over_time = self.reduced_problem.estimate_error()
error_estimator_squared_over_time = [v**2 for v in error_estimator_over_time]
error_estimator_time_quadrature = TimeQuadrature((0., self.truth_problem.T), error_estimator_squared_over_time)
error_estimator = sqrt(error_estimator_time_quadrature.integrate())
print("absolute error estimator for current mu =", error_estimator)
# Carry out the actual greedy search
def solve_and_estimate_error(mu):
self.reduced_problem.set_mu(mu)
self.reduced_problem.solve()
error_estimator_over_time = self.reduced_problem.estimate_error()
error_estimator_squared_over_time = [v**2 for v in error_estimator_over_time]
time_quadrature = TimeQuadrature((0., self.truth_problem.T), error_estimator_squared_over_time)
error_estimator = sqrt(time_quadrature.integrate())
log(DEBUG, "Error estimator for mu = " + str(mu) + " is " + str(error_estimator))
return error_estimator
if self.reduced_problem.N == 0:
print("find initial mu")
else:
print("find next mu")
return self.training_set.max(solve_and_estimate_error)
def _lifting_truth_solve(self, term, i):
assert term.startswith("dirichlet_bc")
component = term.replace("dirichlet_bc", "").replace("_", "")
# Since lifting solves for different values of i are associated to the same parameter
# but with a patched call to compute_theta(), which returns the i-th component, we set
# a custom cache_key so that they are properly differentiated when reading from cache.
lifting_over_time = self.truth_problem.solve(
cache_key="lifting_" + component + "_" + str(i))
times = lifting_over_time.stored_times()
theta_over_time = list()
for t in times:
self.truth_problem.set_time(t)
theta_over_time.append(
self.truth_problem.compute_theta(term)[i])
# We average the time dependent solution to be used as time independent lifting.
# Do not even bother adding the initial condition if it is zero
if not isclose(times[0], self.truth_problem.t0,
self.truth_problem.dt / 2):
has_non_homogeneous_initial_condition = True
else:
if component != "":
assert component in self.truth_problem.components
has_non_homogeneous_initial_condition = self.truth_problem.initial_condition[
component] and not self.truth_problem.initial_condition_is_homogeneous[
component]
else:
assert len(self.truth_problem.components) == 1
component = None
has_non_homogeneous_initial_condition = (
self.truth_problem.initial_condition and
not self.truth_problem.initial_condition_is_homogeneous
)
if has_non_homogeneous_initial_condition:
time_interval = (times[0], times[-1])
else:
time_interval = (times[1], times[-1])
lifting_over_time = lifting_over_time[1:]
theta_over_time = theta_over_time[1:]
# Compute the average and return
lifting_quadrature = TimeQuadrature(time_interval,
lifting_over_time)
theta_quadrature = TimeQuadrature(time_interval, theta_over_time)
lifting = lifting_quadrature.integrate()
lifting /= theta_quadrature.integrate()
return lifting
def solve_and_estimate_error(mu):
self.reduced_problem.set_mu(mu)
self.reduced_problem.solve()
error_estimator_over_time = self.reduced_problem.estimate_error()
error_estimator_squared_over_time = [v**2 for v in error_estimator_over_time]
time_quadrature = TimeQuadrature((0., self.truth_problem.T), error_estimator_squared_over_time)
error_estimator = sqrt(time_quadrature.integrate())
log(DEBUG, "Error estimator for mu = " + str(mu) + " is " + str(error_estimator))
return error_estimator
def output_preprocess_setitem(list_over_time):
time_quadrature = TimeQuadrature((0., self.truth_problem.T),
list_over_time)
return time_quadrature.integrate()
def solution_preprocess_setitem(list_over_time):
list_squared_over_time = [v**2 for v in list_over_time]
time_quadrature = TimeQuadrature((0., self.truth_problem.T),
list_squared_over_time)
return sqrt(time_quadrature.integrate())