def project(self, snapshot_over_time, N=None, on_dirichlet_bc=True, **kwargs):
projected_snapshot_N_over_time = TimeSeries(snapshot_over_time)
for snapshot in snapshot_over_time:
projected_snapshot_N = ParametrizedReducedDifferentialProblem_DerivedClass.project(
self, snapshot, N, on_dirichlet_bc, **kwargs)
projected_snapshot_N_over_time.append(projected_snapshot_N)
return projected_snapshot_N_over_time
def postprocess_snapshot(self, snapshot_over_time, snapshot_index):
postprocessed_snapshot = TimeSeries(snapshot_over_time)
for (k, t) in enumerate(snapshot_over_time.stored_times()):
self.reduced_problem.set_time(t)
postprocessed_snapshot_k = DifferentialProblemReductionMethod_DerivedClass.postprocess_snapshot(
self, snapshot_over_time[k], snapshot_index)
postprocessed_snapshot.append(postprocessed_snapshot_k)
return postprocessed_snapshot
def _compute_relative_error_output(self, absolute_error_output_over_time, **kwargs):
relative_error_output_over_time = TimeSeries(self._output_over_time)
assert len(self.truth_problem._output_over_time) == len(absolute_error_output_over_time)
for (k, t) in enumerate(self.truth_problem._output_over_time.stored_times()):
self.set_time(t)
self.truth_problem._output = self.truth_problem._output_over_time[k]
relative_error_output = ParametrizedReducedDifferentialProblem_DerivedClass._compute_relative_error_output(self, absolute_error_output_over_time[k], **kwargs)
relative_error_output_over_time.append(relative_error_output)
return relative_error_output_over_time
def _compute_relative_error(self, absolute_error_over_time, **kwargs):
relative_error_over_time = TimeSeries(self._solution_over_time)
assert len(self._solution_over_time) == len(absolute_error_over_time)
for (k, t) in enumerate(self.truth_problem._solution_over_time.stored_times()):
self.set_time(t)
assign(self.truth_problem._solution, self.truth_problem._solution_over_time[k])
absolute_error = self._convert_error_at_time(k, absolute_error_over_time)
relative_error = ParametrizedReducedDifferentialProblem_DerivedClass._compute_relative_error(self, absolute_error, **kwargs)
relative_error_over_time.append(relative_error)
relative_error_over_time = self._convert_error_over_time(relative_error_over_time)
return relative_error_over_time
def postprocess_snapshot(self, snapshot_over_time, snapshot_index):
# Call parent: this will solve for supremizers at each time step
snapshot_and_supremizer_over_time = AbstractCFDUnsteadyReductionMethod_Base.postprocess_snapshot(self, snapshot_over_time, snapshot_index)
# Convert from a time series of tuple (snapshot, supremizer) to a tuple of two lists (snapshot over time, supremizer over time)
supremizer_over_time = TimeSeries(snapshot_over_time)
for (k, snapshot_and_supremizer) in enumerate(snapshot_and_supremizer_over_time):
assert isinstance(snapshot_and_supremizer, tuple)
assert len(snapshot_and_supremizer) is 2
assert snapshot_and_supremizer[0] is snapshot_over_time[k]
supremizer_over_time.append(snapshot_and_supremizer[1])
# Return a tuple
return (snapshot_over_time, supremizer_over_time)
def _convert_error_over_time(self, error_over_time):
"""
This internal method converts the error over time as follows:
- if the problem has only one component, no conversion is required;
- if the problem has more than one component, then a conversion is preformed such that
the result is a dict from components to error over time for that component, rather than
a list (over time) of dicts (over components)
"""
assert isinstance(error_over_time[0], (dict, Number))
if isinstance(error_over_time[0], dict):
assert all(
[isinstance(error, dict) for error in error_over_time])
components = list(error_over_time[0].keys())
assert all([
list(error.keys()) == components
for error in error_over_time
])
output = dict()
for component in components:
output[component] = TimeSeries(error_over_time)
for error in error_over_time:
output[component].append(error[component])
return output
else:
assert all(
[isinstance(error, Number) for error in error_over_time])
return error_over_time
def get_residual_norm_squared(self):
residual_norm_squared_over_time = TimeSeries(self._solution_over_time)
assert len(self._solution_over_time) == len(self._solution_dot_over_time)
for (k, t) in enumerate(self._solution_over_time.stored_times()):
if not isclose(t, self.t0, self.dt/2.):
# Set current time
self.set_time(t)
# Set current solution and solution_dot
assign(self._solution, self._solution_over_time[k])
assign(self._solution_dot, self._solution_dot_over_time[k])
# Compute the numerator of the error bound at the current time, first
# by computing residual of elliptic part
elliptic_residual_norm_squared = ParabolicCoerciveRBReducedProblem_Base.get_residual_norm_squared(self)
# ... and then adding terms related to time derivative
N = self._solution.N
theta_m = self.compute_theta("m")
theta_a = self.compute_theta("a")
theta_f = self.compute_theta("f")
residual_norm_squared_over_time.append(
elliptic_residual_norm_squared
+ 2.0*(transpose(self._solution_dot)*sum(product(theta_m, self.error_estimation_operator["m", "f"][:N], theta_f)))
+ 2.0*(transpose(self._solution_dot)*sum(product(theta_m, self.error_estimation_operator["m", "a"][:N, :N], theta_a))*self._solution)
+ transpose(self._solution_dot)*sum(product(theta_m, self.error_estimation_operator["m", "m"][:N, :N], theta_m))*self._solution_dot
)
else:
# Error estimator on initial condition does not use the residual
residual_norm_squared_over_time.append(0.)
return residual_norm_squared_over_time
def _init_time_series(self, current_stage="online"):
try:
monitor_t0 = self._time_stepping_parameters["monitor"]["initial_time"]
except KeyError:
monitor_t0 = self.t0
try:
monitor_dt = self._time_stepping_parameters["monitor"]["time_step_size"]
except KeyError:
assert self.dt is not None
monitor_dt = self.dt
assert self.T is not None
monitor_T = self.T
self._solution_over_time = TimeSeries((monitor_t0, monitor_T), monitor_dt)
self._solution_dot_over_time = TimeSeries((monitor_t0, monitor_T), monitor_dt)
self._output_over_time = TimeSeries((monitor_t0, monitor_T), monitor_dt)
def estimate_error(self):
eps2_over_time = self.get_residual_norm_squared()
alpha = self.get_stability_factor()
# Compute error bound
error_bound_over_time = TimeSeries(eps2_over_time)
for (k, t) in enumerate(eps2_over_time.stored_times()):
if not isclose(t, self.t0, self.dt/2.):
eps2 = eps2_over_time[k]
assert eps2 >= 0. or isclose(eps2, 0.)
assert alpha >= 0.
error_bound_over_time.append(sqrt(abs(eps2)/alpha))
else:
initial_error_estimate_squared = self.get_initial_error_estimate_squared()
assert initial_error_estimate_squared >= 0. or isclose(initial_error_estimate_squared, 0.)
error_bound_over_time.append(sqrt(abs(initial_error_estimate_squared)))
#
return error_bound_over_time
def _solution_dot_cache_import(filename):
solution_dot_over_time = TimeSeries(
self._solution_dot_over_time)
self.import_solution(self.folder["cache"], filename + "_dot",
solution_dot_over_time)
return solution_dot_over_time
class TimeDependentProblem_Class(
ParametrizedDifferentialProblem_DerivedClass):
# Default initialization of members
def __init__(self, V, **kwargs):
# Call the parent initialization
ParametrizedDifferentialProblem_DerivedClass.__init__(
self, V, **kwargs)
# Store quantities related to the time discretization
self.t = 0.
self.t0 = 0.
self.dt = None
self.T = None
# Additional options for time stepping may be stored in the following dict
self._time_stepping_parameters = dict()
self._time_stepping_parameters["initial_time"] = self.t0
# Matrices/vectors resulting from the truth discretization
# initial_condition: AffineExpansionStorage (for problems with one component) or dict of
# AffineExpansionStorage (for problem with several components)
self.initial_condition = None
# initial_condition_is_homogeneous: bool (for problems with one component) or dict of
# bools (for problem with several components)
self.initial_condition_is_homogeneous = None
# Time derivative of the solution, at the current time
self._solution_dot = Function(self.V)
# Solution and output over time
self._solution_over_time = None # TimeSeries of Functions
self._solution_dot_over_time = None # TimeSeries of Functions
self._output_over_time = None # TimeSeries of numbers
# I/O
def _solution_cache_key_generator(*args, **kwargs):
assert len(args) == 1
assert args[0] == self.mu
return self._cache_key_from_kwargs(**kwargs)
def _solution_cache_import(filename):
solution_over_time = TimeSeries(self._solution_over_time)
self.import_solution(self.folder["cache"], filename,
solution_over_time)
return solution_over_time
def _solution_cache_export(filename, solution, suffix):
self.export_solution(self.folder["cache"],
filename,
solution,
suffix=suffix)
def _solution_cache_filename_generator(*args, **kwargs):
assert len(args) == 1
assert args[0] == self.mu
return self._cache_file_from_kwargs(**kwargs)
self._solution_over_time_cache = TimeSeriesCache(
"problems",
key_generator=_solution_cache_key_generator,
import_=_solution_cache_import,
export=_solution_cache_export,
filename_generator=_solution_cache_filename_generator)
def _solution_dot_cache_key_generator(*args, **kwargs):
assert len(args) == 1
assert args[0] == self.mu
return self._cache_key_from_kwargs(**kwargs)
def _solution_dot_cache_import(filename):
solution_dot_over_time = TimeSeries(
self._solution_dot_over_time)
self.import_solution(self.folder["cache"], filename + "_dot",
solution_dot_over_time)
return solution_dot_over_time
def _solution_dot_cache_export(filename, solution_dot, suffix):
self.export_solution(self.folder["cache"],
filename + "_dot",
solution_dot,
suffix=suffix)
def _solution_dot_cache_filename_generator(*args, **kwargs):
assert len(args) == 1
assert args[0] == self.mu
return self._cache_file_from_kwargs(**kwargs)
self._solution_dot_over_time_cache = TimeSeriesCache(
"problems",
key_generator=_solution_dot_cache_key_generator,
import_=_solution_dot_cache_import,
export=_solution_dot_cache_export,
filename_generator=_solution_dot_cache_filename_generator)
del self._solution_cache
def _output_cache_key_generator(*args, **kwargs):
assert len(args) == 1
assert args[0] == self.mu
return self._cache_key_from_kwargs(**kwargs)
def _output_cache_import(filename):
output_over_time = list()
self.import_output(self.folder["cache"], filename,
output_over_time)
return output_over_time
def _output_cache_export(filename):
self.export_output(self.folder["cache"], filename)
def _output_cache_filename_generator(*args, **kwargs):
assert len(args) == 1
assert args[0] == self.mu
return self._cache_file_from_kwargs(**kwargs)
self._output_over_time_cache = Cache(
"problems",
key_generator=_output_cache_key_generator,
import_=_output_cache_import,
export=_output_cache_export,
filename_generator=_output_cache_filename_generator)
del self._output_cache
# Set current time
def set_time(self, t):
assert isinstance(t, Number)
self.t = t
# Set initial time
def set_initial_time(self, t0):
assert isinstance(t0, Number)
self.t0 = t0
self._time_stepping_parameters["initial_time"] = t0
# Set time step size
def set_time_step_size(self, dt):
assert isinstance(dt, Number)
self.dt = dt
self._time_stepping_parameters["time_step_size"] = dt
# Set final time
def set_final_time(self, T):
assert isinstance(T, Number)
self.T = T
self._time_stepping_parameters["final_time"] = T
# Export solution to file
def export_solution(self,
folder=None,
filename=None,
solution_over_time=None,
component=None,
suffix=None):
if folder is None:
folder = self.folder_prefix
if filename is None:
filename = "solution"
if solution_over_time is None:
solution_over_time = self._solution_over_time
if isinstance(solution_over_time, AbstractTimeSeries):
assert suffix is None
for (k, solution) in enumerate(solution_over_time):
ParametrizedDifferentialProblem_DerivedClass.export_solution(
self,
folder,
filename,
solution,
component=component,
suffix=k)
else:
# Used only for cache export
solution = solution_over_time
assert suffix is not None
ParametrizedDifferentialProblem_DerivedClass.export_solution(
self,
folder,
filename,
solution,
component=component,
suffix=suffix)
# Import solution from file
def import_solution(self,
folder=None,
filename=None,
solution_over_time=None,
component=None,
suffix=None):
if folder is None:
folder = self.folder_prefix
if filename is None:
filename = "solution"
if solution_over_time is None:
solution_over_time = self._solution_over_time
if isinstance(solution_over_time, AbstractTimeSeries):
solution = Function(self.V)
assert suffix is None
solution_over_time.clear()
for (k, _) in enumerate(
self._solution_over_time.expected_times()):
ParametrizedDifferentialProblem_DerivedClass.import_solution(
self, folder, filename, solution, component, suffix=k)
solution_over_time.append(copy(solution))
else:
# Used only for cache import
solution = solution_over_time
assert suffix is not None
ParametrizedDifferentialProblem_DerivedClass.import_solution(
self,
folder,
filename,
solution,
component=component,
suffix=suffix)
def export_output(self,
folder=None,
filename=None,
output_over_time=None,
suffix=None):
if folder is None:
folder = self.folder_prefix
if filename is None:
filename = "solution"
if output_over_time is None:
output_over_time = self._output_over_time
assert suffix is None
for (k, output) in enumerate(output_over_time):
ParametrizedDifferentialProblem_DerivedClass.export_output(
self, folder, filename, [output], suffix=k)
def import_output(self,
folder=None,
filename=None,
output_over_time=None,
suffix=None):
if folder is None:
folder = self.folder_prefix
if filename is None:
filename = "solution"
output = [0.]
if output_over_time is None:
output_over_time = self._output_over_time
assert suffix is None
output_over_time.clear()
for (k, _) in enumerate(self._output_over_time.expected_times()):
ParametrizedDifferentialProblem_DerivedClass.import_output(
self, folder, filename, output, suffix=k)
assert len(output) == 1
output_over_time.append(output[0])
# Initialize data structures required for the offline phase
def init(self):
ParametrizedDifferentialProblem_DerivedClass.init(self)
self._init_initial_condition()
self._init_time_series()
def _init_initial_condition(self):
# Get helper strings depending on the number of basis components
n_components = len(self.components)
assert n_components > 0
if n_components > 1:
initial_condition_string = "initial_condition_{c}"
else:
initial_condition_string = "initial_condition"
# Assemble initial condition
# we do not assert for
# (self.initial_condition is None) == (self.initial_condition_is_homogeneous is None)
# because self.initial_condition may still be None after initialization, if there
# were no initial condition at all and the problem had only one component
if self.initial_condition_is_homogeneous is None: # init was not called already
initial_condition = dict()
initial_condition_is_homogeneous = dict()
for component in self.components:
try:
operator_ic = AffineExpansionStorage(
self.assemble_operator(
initial_condition_string.format(c=component)))
except ValueError: # there were no initial condition: assume homogeneous one
initial_condition[component] = None
initial_condition_is_homogeneous[component] = True
else:
initial_condition[component] = operator_ic
initial_condition_is_homogeneous[component] = False
if n_components == 1:
self.initial_condition = initial_condition[
self.components[0]]
self.initial_condition_is_homogeneous = initial_condition_is_homogeneous[
self.components[0]]
else:
self.initial_condition = initial_condition
self.initial_condition_is_homogeneous = initial_condition_is_homogeneous
# We enforce consistency between Dirichlet BCs and IC, as in the following cases:
# a) (homogeneous Dirichlet BCs, homogeneous IC): nothing to be enforced
# b) (non homogeneous Dirichlet BCs, homogeneous IC): we enforce that the theta
# term of each Dirichlet BC is zero at t = 0, resulting in homogeneous Dirichlet BCs
# at t = 0. This is needed e.g. in order to make sure that while post processing a snapshot
# subtracting the lifting at t = 0 doesn't change the solution (which must remain zero)
# c) (homogeneous Dirichlet BCs, non homogeneous IC): we trust that the non homogeneous IC
# provided by the user is actually zero on the Dirichlet boundaries, otherwise there will
# be no way to accurately recover it by projecting on a space which only has bases equal
# to zero on the Dirichlet boundary.
# d) (non homogeneous Dirichlet BCs, non homogeneous IC): we trust that the restriction of IC
# on the Dirichlet boundary is equal to the evaluation of the Dirichlet BCs at t = 0.
# If that were not true, than post processing a snapshot subtracting the lifting at t = 0
# would result in a postprocessed snapshot which is not zero on the Dirichlet boundary, thus
# adding an element with non zero value on the Dirichlet boundary to the basis
for component in self.components:
if len(self.components) > 1:
has_homogeneous_dirichlet_bc = self.dirichlet_bc_are_homogeneous[
component]
has_homogeneous_initial_condition = self.initial_condition_is_homogeneous[
component]
dirichlet_bc_string = "dirichlet_bc_{c}"
else:
has_homogeneous_dirichlet_bc = self.dirichlet_bc_are_homogeneous
has_homogeneous_initial_condition = self.initial_condition_is_homogeneous
dirichlet_bc_string = "dirichlet_bc"
if has_homogeneous_dirichlet_bc and has_homogeneous_initial_condition: # case a)
pass
elif not has_homogeneous_dirichlet_bc and has_homogeneous_initial_condition: # case b)
def generate_modified_compute_theta(component):
standard_compute_theta = self.compute_theta
def modified_compute_theta(self_, term):
if term == dirichlet_bc_string.format(
c=component):
theta_bc = standard_compute_theta(term)
if self_.t == 0.:
return (0., ) * len(theta_bc)
else:
return theta_bc
else:
return standard_compute_theta(term)
return modified_compute_theta
PatchInstanceMethod(
self, "compute_theta",
generate_modified_compute_theta(
component)).patch()
elif has_homogeneous_dirichlet_bc and not has_homogeneous_initial_condition: # case c)
pass
elif not has_homogeneous_dirichlet_bc and not has_homogeneous_initial_condition: # case d)
pass
else:
raise RuntimeError("Impossible to arrive here.")
def _init_time_series(self):
try:
monitor_t0 = self._time_stepping_parameters["monitor"][
"initial_time"]
except KeyError:
monitor_t0 = self.t0
try:
monitor_dt = self._time_stepping_parameters["monitor"][
"time_step_size"]
except KeyError:
assert self.dt is not None
monitor_dt = self.dt
assert self.T is not None
monitor_T = self.T
self._solution_over_time = TimeSeries((monitor_t0, monitor_T),
monitor_dt)
self._solution_dot_over_time = TimeSeries((monitor_t0, monitor_T),
monitor_dt)
self._output_over_time = TimeSeries((monitor_t0, monitor_T),
monitor_dt)
def solve(self, **kwargs):
self._latest_solve_kwargs = kwargs
key_error_raised = False
self._solution_over_time.clear()
try:
assign(self._solution_over_time,
self._solution_over_time_cache[self.mu, kwargs])
# **kwargs is not supported by __getitem__
except KeyError:
key_error_raised = True
self._solution_dot_over_time.clear()
try:
assign(self._solution_dot_over_time,
self._solution_dot_over_time_cache[self.mu, kwargs])
except KeyError:
key_error_raised = True
if key_error_raised:
# Solutions might still have been loaded from file, only not up to the final time
assert (
len(self._solution_over_time) == len(
self._solution_dot_over_time)
# simulation was stopped after the solution_dot was written out
or len(self._solution_over_time)
== len(self._solution_dot_over_time) + 1
# simulation was stopped after the solution was written out, but before corresponding
# solution_dot was.
)
if len(self._solution_over_time) == len(
self._solution_dot_over_time) + 1:
del self._solution_over_time[-1]
assert len(self._solution_over_time) == len(
self._solution_dot_over_time)
bak_t0 = self.t0
if len(self._solution_over_time) == 0:
assign(self._solution, Function(self.V))
assign(self._solution_dot, Function(self.V))
else:
t0 = self._solution_over_time.stored_times()[-1]
self.set_initial_time(t0)
assign(self._solution, self._solution_over_time[-1])
del self._solution_over_time[-1]
assign(self._solution_dot,
self._solution_dot_over_time[-1])
del self._solution_dot_over_time[-1]
# Solve
assert not hasattr(self, "_is_solving")
self._is_solving = True
self._solve(**kwargs)
delattr(self, "_is_solving")
# Restore initial time, if it was changed
self.set_initial_time(bak_t0)
assign(self._solution, self._solution_over_time[-1])
assign(self._solution_dot, self._solution_dot_over_time[-1])
return self._solution_over_time
class ProblemSolver(
ParametrizedDifferentialProblem_DerivedClass.ProblemSolver,
TimeDependentProblemWrapper):
def set_time(self, t):
problem = self.problem
problem.set_time(t)
def bc_eval(self, t):
assert self.problem.t == t
return ParametrizedDifferentialProblem_DerivedClass.ProblemSolver.bc_eval(
self)
def ic_eval(self):
problem = self.problem
if len(problem.components) > 1:
all_initial_conditions = list()
all_initial_conditions_thetas = list()
for component in problem.components:
if problem.initial_condition[component] is not None:
all_initial_conditions.extend(
problem.initial_condition[component])
all_initial_conditions_thetas.extend(
problem.compute_theta("initial_condition_" +
component))
if len(all_initial_conditions) > 0:
all_initial_conditions = tuple(all_initial_conditions)
all_initial_conditions = AffineExpansionStorage(
all_initial_conditions)
all_initial_conditions_thetas = tuple(
all_initial_conditions_thetas)
else:
all_initial_conditions = None
all_initial_conditions_thetas = None
else:
if problem.initial_condition is not None:
all_initial_conditions = problem.initial_condition
all_initial_conditions_thetas = problem.compute_theta(
"initial_condition")
else:
all_initial_conditions = None
all_initial_conditions_thetas = None
assert (all_initial_conditions is
None) == (all_initial_conditions_thetas is None)
if all_initial_conditions is not None:
return sum(
product(all_initial_conditions_thetas,
all_initial_conditions))
else:
return None
def monitor(self, t, solution, solution_dot):
problem = self.problem
solution_copy = copy(solution)
problem._solution_over_time.append(solution_copy)
problem._solution_over_time_cache[
problem.mu, self.kwargs].append(solution_copy)
solution_dot_copy = copy(solution_dot)
problem._solution_dot_over_time.append(solution_dot_copy)
problem._solution_dot_over_time_cache[
problem.mu, self.kwargs].append(solution_dot_copy)
def solve(self):
problem = self.problem
problem._solution_over_time_cache[
problem.mu,
self.kwargs] = copy(problem._solution_over_time)
problem._solution_dot_over_time_cache[
problem.mu,
self.kwargs] = copy(problem._solution_dot_over_time)
solver = TimeStepping(self, problem._solution,
problem._solution_dot)
solver.set_parameters(problem._time_stepping_parameters)
solver.solve()
# Perform a truth evaluation of the output
def compute_output(self):
"""
:return: output evaluation.
"""
kwargs = self._latest_solve_kwargs
try:
assign(self._output_over_time,
self._output_over_time_cache[self.mu, kwargs])
# **kwargs is not supported by __getitem__
except KeyError:
try:
self._compute_output()
except ValueError: # raised by compute_theta if output computation is optional
self._output_over_time.clear()
self._output_over_time.extend(
[NotImplemented] * len(self._solution_over_time))
self._output = NotImplemented
self._output_over_time_cache[self.mu,
kwargs] = self._output_over_time
else:
self._output = self._output_over_time[-1]
return self._output_over_time
# Perform a truth evaluation of the output
def _compute_output(self):
self._output_over_time.clear()
self._output_over_time.extend([NotImplemented] *
len(self._solution_over_time))
self._output = NotImplemented
class TimeDependentReducedProblem_Class(
ParametrizedReducedDifferentialProblem_DerivedClass):
# Default initialization of members
@sync_setters("truth_problem", "set_time", "t")
@sync_setters("truth_problem", "set_initial_time", "t0")
@sync_setters("truth_problem", "set_time_step_size", "dt")
@sync_setters("truth_problem", "set_final_time", "T")
def __init__(self, truth_problem, **kwargs):
# Call the parent initialization
ParametrizedReducedDifferentialProblem_DerivedClass.__init__(
self, truth_problem, **kwargs)
# Store quantities related to the time discretization
assert truth_problem.t == 0.
self.t = 0.
self.t0 = truth_problem.t0
assert truth_problem.dt is not None
self.dt = truth_problem.dt
assert truth_problem.T is not None
self.T = truth_problem.T
# Additional options for time stepping may be stored in the following dict
self._time_stepping_parameters = dict()
self._time_stepping_parameters["initial_time"] = self.t0
self._time_stepping_parameters["time_step_size"] = self.dt
self._time_stepping_parameters["final_time"] = self.T
if "monitor" in truth_problem._time_stepping_parameters:
self._time_stepping_parameters[
"monitor"] = truth_problem._time_stepping_parameters[
"monitor"]
# Online reduced space dimension
# initial_condition: bool (for problems with one component) or dict of bools (for problem with
# several components)
self.initial_condition = None
# initial_condition_is_homogeneous: bool (for problems with one component) or dict of bools
# (for problem with several components)
self.initial_condition_is_homogeneous = None
# Number of terms in the affine expansion
# Q_ic: integer (for problems with one component) or dict of integers (for problem with several components)
self.Q_ic = None
# Time derivative of the solution, at the current time
self._solution_dot = None # OnlineFunction
# Solution and output over time
self._solution_over_time = None # TimeSeries of Functions
self._solution_dot_over_time = None # TimeSeries of Functions
self._output_over_time = None # TimeSeries of numbers
# I/O
def _solution_cache_key_generator(*args, **kwargs):
assert len(args) == 2
assert args[0] == self.mu
return self._cache_key_from_N_and_kwargs(args[1], **kwargs)
self._solution_over_time_cache = TimeSeriesCache(
"reduced problems",
key_generator=_solution_cache_key_generator)
self._solution_dot_over_time_cache = TimeSeriesCache(
"reduced problems",
key_generator=_solution_cache_key_generator)
del self._solution_cache
def _output_cache_key_generator(*args, **kwargs):
assert len(args) == 2
assert args[0] == self.mu
return self._cache_key_from_N_and_kwargs(args[1], **kwargs)
self._output_over_time_cache = Cache(
"reduced problems", key_generator=_output_cache_key_generator)
del self._output_cache
# Set current time
def set_time(self, t):
self.t = t
# Set initial time
def set_initial_time(self, t0):
assert isinstance(t0, Number)
self.t0 = t0
self._time_stepping_parameters["initial_time"] = t0
# Set time step size
def set_time_step_size(self, dt):
assert isinstance(dt, Number)
self.dt = dt
self._time_stepping_parameters["time_step_size"] = dt
# Set final time
def set_final_time(self, T):
assert isinstance(T, Number)
self.T = T
self._time_stepping_parameters["final_time"] = T
# Initialize data structures required for the online phase
def init(self, current_stage="online"):
# Initialize first data structures related to initial conditions
self._init_initial_condition(current_stage)
self._init_time_series(current_stage)
# ... since the Parent call may be overridden to need them!
ParametrizedReducedDifferentialProblem_DerivedClass.init(
self, current_stage)
def _init_initial_condition(self, current_stage="online"):
assert current_stage in ("online", "offline")
n_components = len(self.components)
# Get helper strings depending on the number of components
if n_components > 1:
initial_condition_string = "initial_condition_{c}"
else:
initial_condition_string = "initial_condition"
# Detect how many theta terms are related to boundary conditions
# we do not assert for
# (self.initial_condition is None) == (self.initial_condition_is_homogeneous is None)
# because self.initial_condition may still be None after initialization, if there
# were no initial condition at all and the problem had only one component
if self.initial_condition_is_homogeneous is None: # init was not called already
initial_condition = dict()
initial_condition_is_homogeneous = dict()
Q_ic = dict()
for component in self.components:
try:
theta_ic = self.compute_theta(
initial_condition_string.format(c=component))
except ValueError: # there were no initial condition to be imposed by lifting
initial_condition[component] = None
initial_condition_is_homogeneous[component] = True
Q_ic[component] = 0
else:
initial_condition_is_homogeneous[component] = False
Q_ic[component] = len(theta_ic)
initial_condition[
component] = OnlineAffineExpansionStorage(
Q_ic[component])
if n_components == 1:
self.initial_condition = initial_condition[
self.components[0]]
self.initial_condition_is_homogeneous = initial_condition_is_homogeneous[
self.components[0]]
self.Q_ic = Q_ic[self.components[0]]
else:
self.initial_condition = initial_condition
self.initial_condition_is_homogeneous = initial_condition_is_homogeneous
self.Q_ic = Q_ic
assert self.initial_condition_is_homogeneous == self.truth_problem.initial_condition_is_homogeneous
# Load initial conditions from file if we are online
if current_stage == "online":
for component in self.components:
if not initial_condition_is_homogeneous[component]:
self.assemble_operator(
initial_condition_string.format(c=component),
"online")
elif current_stage == "offline":
pass # Nothing else to be done
else:
raise ValueError(
"Invalid stage in _init_initial_condition().")
def _init_time_series(self, current_stage="online"):
try:
monitor_t0 = self._time_stepping_parameters["monitor"][
"initial_time"]
except KeyError:
monitor_t0 = self.t0
try:
monitor_dt = self._time_stepping_parameters["monitor"][
"time_step_size"]
except KeyError:
assert self.dt is not None
monitor_dt = self.dt
assert self.T is not None
monitor_T = self.T
self._solution_over_time = TimeSeries((monitor_t0, monitor_T),
monitor_dt)
self._solution_dot_over_time = TimeSeries((monitor_t0, monitor_T),
monitor_dt)
self._output_over_time = TimeSeries((monitor_t0, monitor_T),
monitor_dt)
# Assemble the reduced order affine expansion.
def build_reduced_operators(self, current_stage="offline"):
ParametrizedReducedDifferentialProblem_DerivedClass.build_reduced_operators(
self, current_stage)
# Initial condition
self._build_reduced_initial_condition(current_stage)
def _build_reduced_initial_condition(self, current_stage="offline"):
if len(self.components) > 1:
initial_condition_string = "initial_condition_{c}"
for component in self.components:
if not self.initial_condition_is_homogeneous[component]:
self.initial_condition[
component] = self.assemble_operator(
initial_condition_string.format(c=component),
current_stage)
else:
if not self.initial_condition_is_homogeneous:
self.initial_condition = self.assemble_operator(
"initial_condition", "offline")
# Assemble the reduced order affine expansion
def assemble_operator(self, term, current_stage="online"):
assert current_stage in ("online", "offline")
if term.startswith("initial_condition"):
component = term.replace("initial_condition",
"").replace("_", "")
if current_stage == "online": # load from file
if component != "":
initial_condition = self.initial_condition[component]
else:
initial_condition = self.initial_condition
initial_condition.load(self.folder["reduced_operators"],
term)
elif current_stage == "offline":
if component != "":
truth_initial_condition = self.truth_problem.initial_condition[
component]
initial_condition = self.initial_condition[component]
truth_projection_inner_product = self.truth_problem.projection_inner_product[
component]
else:
truth_initial_condition = self.truth_problem.initial_condition
initial_condition = self.initial_condition
truth_projection_inner_product = self.truth_problem.projection_inner_product
assert len(truth_projection_inner_product) == 1
# the affine expansion storage contains only the inner product matrix
for (q, truth_initial_condition_q
) in enumerate(truth_initial_condition):
initial_condition[q] = (
transpose(self.basis_functions) *
truth_projection_inner_product[0] *
truth_initial_condition_q)
initial_condition.save(self.folder["reduced_operators"],
term)
else:
raise ValueError("Invalid stage in assemble_operator().")
# Assign
if component != "":
assert component in self.components
self.initial_condition[component] = initial_condition
else:
assert len(self.components) == 1
self.initial_condition = initial_condition
# Return
return initial_condition
else:
return ParametrizedReducedDifferentialProblem_DerivedClass.assemble_operator(
self, term, current_stage)
def solve(self, N=None, **kwargs):
N, kwargs = self._online_size_from_kwargs(N, **kwargs)
N += self.N_bc
self._latest_solve_kwargs = kwargs
self._solution = OnlineFunction(N)
self._solution_over_time.clear()
self._solution_dot = OnlineFunction(N)
self._solution_dot_over_time.clear()
if N == 0: # trivial case
self._solution_over_time.extend([
self._solution
for _ in self._solution_over_time.expected_times()
])
self._solution_dot_over_time.extend([
self._solution_dot
for _ in self._solution_dot_over_time.expected_times()
])
return self._solution_over_time
try:
assign(self._solution_over_time,
self._solution_over_time_cache[self.mu, N, kwargs])
# **kwargs is not supported by __getitem__
assign(self._solution_dot_over_time,
self._solution_dot_over_time_cache[self.mu, N, kwargs])
except KeyError:
assert not hasattr(self, "_is_solving")
self._is_solving = True
self._solve(N, **kwargs)
delattr(self, "_is_solving")
assign(self._solution, self._solution_over_time[-1])
assign(self._solution_dot, self._solution_dot_over_time[-1])
return self._solution_over_time
class ProblemSolver(
ParametrizedReducedDifferentialProblem_DerivedClass.
ProblemSolver, TimeDependentProblemWrapper):
def set_time(self, t):
problem = self.problem
problem.set_time(t)
def bc_eval(self, t):
assert self.problem.t == t
return ParametrizedReducedDifferentialProblem_DerivedClass.ProblemSolver.bc_eval(
self)
def ic_eval(self):
problem = self.problem
N = self.N
if len(problem.components) > 1:
all_initial_conditions = list()
all_initial_conditions_thetas = list()
for component in problem.components:
if (problem.initial_condition[component]
and not problem.
initial_condition_is_homogeneous[component]):
all_initial_conditions.extend(
problem.initial_condition[component][:N])
all_initial_conditions_thetas.extend(
problem.compute_theta("initial_condition_" +
component))
if len(all_initial_conditions) > 0:
all_initial_conditions = tuple(all_initial_conditions)
all_initial_conditions = OnlineAffineExpansionStorage(
all_initial_conditions)
all_initial_conditions_thetas = tuple(
all_initial_conditions_thetas)
else:
all_initial_conditions = None
all_initial_conditions_thetas = None
else:
if problem.initial_condition and not problem.initial_condition_is_homogeneous:
all_initial_conditions = problem.initial_condition[:N]
all_initial_conditions_thetas = problem.compute_theta(
"initial_condition")
else:
all_initial_conditions = None
all_initial_conditions_thetas = None
assert (all_initial_conditions is
None) == (all_initial_conditions_thetas is None)
if all_initial_conditions is not None:
inner_product_N = problem._combined_projection_inner_product[:
N, :
N]
projected_initial_condition = OnlineFunction(N)
solver = OnlineLinearSolver(
inner_product_N, projected_initial_condition,
sum(
product(all_initial_conditions_thetas,
all_initial_conditions)))
solver.set_parameters(problem._linear_solver_parameters)
solver.solve()
return projected_initial_condition
else:
return None
def monitor(self, t, solution, solution_dot):
problem = self.problem
solution_copy = copy(solution)
problem._solution_over_time.append(solution_copy)
problem._solution_over_time_cache[
problem.mu, self.N, self.kwargs].append(solution_copy)
solution_dot_copy = copy(solution_dot)
problem._solution_dot_over_time.append(solution_dot_copy)
problem._solution_dot_over_time_cache[
problem.mu, self.N, self.kwargs].append(solution_dot_copy)
def solve(self):
problem = self.problem
assert len(problem._solution_over_time) == 0
problem._solution_over_time_cache[
problem.mu, self.N,
self.kwargs] = copy(problem._solution_over_time)
assert len(problem._solution_dot_over_time) == 0
problem._solution_dot_over_time_cache[
problem.mu, self.N,
self.kwargs] = copy(problem._solution_dot_over_time)
solver = OnlineTimeStepping(self, problem._solution,
problem._solution_dot)
solver.set_parameters(problem._time_stepping_parameters)
solver.solve()
# Perform an online evaluation of the output
def compute_output(self):
N = self._solution.N
kwargs = self._latest_solve_kwargs
try:
assign(self._output_over_time,
self._output_over_time_cache[self.mu, N, kwargs])
# **kwargs is not supported by __getitem__
except KeyError:
try:
self._compute_output(N)
except ValueError: # raised by compute_theta if output computation is optional
self._output_over_time.clear()
self._output_over_time.extend(
[NotImplemented] * len(self._solution_over_time))
self._output = NotImplemented
self._output_over_time_cache[self.mu, N,
kwargs] = self._output_over_time
else:
self._output = self._output_over_time[-1]
return self._output_over_time
# Perform an online evaluation of the output. Internal method
def _compute_output(self, N):
self._output_over_time.clear()
self._output_over_time.extend([NotImplemented] *
len(self._solution_over_time))
self._output = NotImplemented
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 project(self,
snapshot_over_time,
N=None,
on_dirichlet_bc=True,
**kwargs):
projected_snapshot_N_over_time = TimeSeries(snapshot_over_time)
for snapshot in snapshot_over_time:
projected_snapshot_N = ParametrizedReducedDifferentialProblem_DerivedClass.project(
self, snapshot, N, on_dirichlet_bc, **kwargs)
projected_snapshot_N_over_time.append(projected_snapshot_N)
return projected_snapshot_N_over_time
# Internal method for error computation
def _compute_error(self, **kwargs):
error_over_time = TimeSeries(self._solution_over_time)
assert len(self.truth_problem._solution_over_time) == len(
self._solution_over_time)
for (k, t) in enumerate(
self.truth_problem._solution_over_time.stored_times()):
self.set_time(t)
assign(self._solution, self._solution_over_time[k])
assign(self.truth_problem._solution,
self.truth_problem._solution_over_time[k])
error = ParametrizedReducedDifferentialProblem_DerivedClass._compute_error(
self, **kwargs)
error_over_time.append(error)
error_over_time = self._convert_error_over_time(error_over_time)
return error_over_time
# Internal method for relative error computation
def _compute_relative_error(self, absolute_error_over_time, **kwargs):
relative_error_over_time = TimeSeries(self._solution_over_time)
if isinstance(absolute_error_over_time, dict):
for (_, absolute_error_over_time_for_component
) in absolute_error_over_time.items():
assert len(self._solution_over_time) == len(
absolute_error_over_time_for_component)
else:
assert len(
self._solution_over_time) == len(absolute_error_over_time)
for (k, t) in enumerate(
self.truth_problem._solution_over_time.stored_times()):
self.set_time(t)
assign(self.truth_problem._solution,
self.truth_problem._solution_over_time[k])
absolute_error = self._convert_error_at_time(
k, absolute_error_over_time)
relative_error = ParametrizedReducedDifferentialProblem_DerivedClass._compute_relative_error(
self, absolute_error, **kwargs)
relative_error_over_time.append(relative_error)
relative_error_over_time = self._convert_error_over_time(
relative_error_over_time)
return relative_error_over_time
# Internal method for output error computation
def _compute_error_output(self, **kwargs):
error_output_over_time = TimeSeries(self._output_over_time)
assert len(self.truth_problem._output_over_time) == len(
self._output_over_time)
for (k, t) in enumerate(
self.truth_problem._output_over_time.stored_times()):
self.set_time(t)
self._output = self._output_over_time[k]
self.truth_problem._output = self.truth_problem._output_over_time[
k]
error_output = ParametrizedReducedDifferentialProblem_DerivedClass._compute_error_output(
self, **kwargs)
error_output_over_time.append(error_output)
return error_output_over_time
# Internal method for output relative error computation
def _compute_relative_error_output(self,
absolute_error_output_over_time,
**kwargs):
relative_error_output_over_time = TimeSeries(
self._output_over_time)
assert len(self.truth_problem._output_over_time) == len(
absolute_error_output_over_time)
for (k, t) in enumerate(
self.truth_problem._output_over_time.stored_times()):
self.set_time(t)
self.truth_problem._output = self.truth_problem._output_over_time[
k]
relative_error_output = (
ParametrizedReducedDifferentialProblem_DerivedClass.
_compute_relative_error_output(
self, absolute_error_output_over_time[k], **kwargs))
relative_error_output_over_time.append(relative_error_output)
return relative_error_output_over_time
def _convert_error_over_time(self, error_over_time):
"""
This internal method converts the error over time as follows:
- if the problem has only one component, no conversion is required;
- if the problem has more than one component, then a conversion is preformed such that
the result is a dict from components to error over time for that component, rather than
a list (over time) of dicts (over components)
"""
assert isinstance(error_over_time[0], (dict, Number))
if isinstance(error_over_time[0], dict):
assert all(
[isinstance(error, dict) for error in error_over_time])
components = list(error_over_time[0].keys())
assert all([
list(error.keys()) == components
for error in error_over_time
])
output = dict()
for component in components:
output[component] = TimeSeries(error_over_time)
for error in error_over_time:
output[component].append(error[component])
return output
else:
assert all(
[isinstance(error, Number) for error in error_over_time])
return error_over_time
def _convert_error_at_time(self, k, converted_error_over_time):
"""
This internal method converts back the error at time step k as follows:
- if the problem has only one component, no conversion is required, and the error at time
k is returned by extracting the k-th index of the input;
- if the problem has more than one component, then a conversion is performed such that
the result is a dict from components to error at time step k
"""
assert (
isinstance(converted_error_over_time, dict)
or hasattr(converted_error_over_time, "__iter__")
# replaces isinstance(converted_error_over_time, TimeSeries)
)
if isinstance(converted_error_over_time, dict):
output = dict()
for (component, error_over_time_for_component
) in converted_error_over_time.items():
assert all([
isinstance(error, Number)
for error in error_over_time_for_component
])
output[component] = error_over_time_for_component[k]
return output
else:
assert all([
isinstance(error, Number)
for error in converted_error_over_time
])
return converted_error_over_time[k]
# Export solution to file
def export_solution(self,
folder=None,
filename=None,
solution_over_time=None,
component=None,
suffix=None):
if solution_over_time is None:
solution_over_time = self._solution_over_time
for (k, solution) in enumerate(solution_over_time):
N = solution.N
assert suffix is None
self.truth_problem.export_solution(folder,
filename,
self.basis_functions[:N] *
solution,
component=component,
suffix=k)
def export_error(self,
folder=None,
filename=None,
component=None,
suffix=None,
**kwargs):
self.truth_problem.solve(**kwargs)
assert len(self.truth_problem._solution_over_time) == len(
self._solution_over_time)
for (k, t) in enumerate(
self.truth_problem._solution_over_time.stored_times()):
self.set_time(t)
assign(self._solution, self._solution_over_time[k])
assign(self.truth_problem._solution,
self.truth_problem._solution_over_time[k])
assert suffix is None
self.truth_problem.export_solution(
folder,
filename,
self.truth_problem._solution -
self.basis_functions[:self._solution.N] * self._solution,
component=component,
suffix=k)
def export_output(self,
folder=None,
filename=None,
output_over_time=None,
suffix=None):
self.truth_problem.export_output(folder, filename,
output_over_time, suffix)
