def __init__(self, truth_problem, **kwargs):
# Call the parent initialization
DifferentialProblemReductionMethod_DerivedClass.__init__(self, truth_problem, **kwargs)
# Declare a GS object
self.GS = None # GramSchmidt (for problems with one component) or dict of GramSchmidt (for problem with several components)
# I/O
self.folder["snapshots"] = os.path.join(self.folder_prefix, "snapshots")
self.folder["post_processing"] = os.path.join(self.folder_prefix, "post_processing")
self.greedy_selected_parameters = GreedySelectedParametersList()
self.greedy_error_estimators = GreedyErrorEstimatorsList()
self.label = "RB"
def __init__(self, SCM_approximation, folder_prefix):
# Call the parent initialization
ReductionMethod.__init__(self, folder_prefix)
# $$ OFFLINE DATA STRUCTURES $$ #
# High fidelity problem
self.SCM_approximation = SCM_approximation
# I/O
self.folder["post_processing"] = os.path.join(self.folder_prefix,
"post_processing")
self.greedy_selected_parameters = SCM_approximation.greedy_selected_parameters
self.greedy_error_estimators = GreedyErrorEstimatorsList()
def __init__(self, SCM_approximation, folder_prefix):
# Call the parent initialization
ReductionMethod.__init__(self, folder_prefix)
# $$ OFFLINE DATA STRUCTURES $$ #
# High fidelity problem
self.SCM_approximation = SCM_approximation
# I/O
self.folder["post_processing"] = os.path.join(self.folder_prefix, "post_processing")
self.greedy_selected_parameters = SCM_approximation.greedy_selected_parameters
self.greedy_error_estimators = GreedyErrorEstimatorsList()
# Get data that were temporarily store in the SCM_approximation
self.bounding_box_minimum_eigensolver_parameters = self.SCM_approximation._input_storage_for_SCM_reduction["bounding_box_minimum_eigensolver_parameters"]
self.bounding_box_maximum_eigensolver_parameters = self.SCM_approximation._input_storage_for_SCM_reduction["bounding_box_maximum_eigensolver_parameters"]
del self.SCM_approximation._input_storage_for_SCM_reduction
def __init__(self, EIM_approximation):
# Call the parent initialization
ReductionMethod.__init__(self, EIM_approximation.folder_prefix)
# $$ OFFLINE DATA STRUCTURES $$ #
# High fidelity problem
self.EIM_approximation = EIM_approximation
# Declare a new container to store the snapshots
self.snapshots_container = self.EIM_approximation.parametrized_expression.create_snapshots_container()
self._training_set_parameters_to_snapshots_container_index = dict()
# I/O
self.folder["snapshots"] = os.path.join(self.folder_prefix, "snapshots")
self.folder["post_processing"] = os.path.join(self.folder_prefix, "post_processing")
self.greedy_selected_parameters = GreedySelectedParametersList()
self.greedy_errors = GreedyErrorEstimatorsList()
#
# By default set a tolerance slightly larger than zero, in order to
# stop greedy iterations in trivial cases by default
self.tol = 1e-15
class EIMApproximationReductionMethod(ReductionMethod):
# Default initialization of members
def __init__(self, EIM_approximation):
# Call the parent initialization
ReductionMethod.__init__(self, EIM_approximation.folder_prefix)
# $$ OFFLINE DATA STRUCTURES $$ #
# High fidelity problem
self.EIM_approximation = EIM_approximation
# Declare a new container to store the snapshots
self.snapshots_container = self.EIM_approximation.parametrized_expression.create_snapshots_container()
self._training_set_parameters_to_snapshots_container_index = dict()
# I/O
self.folder["snapshots"] = os.path.join(self.folder_prefix, "snapshots")
self.folder["post_processing"] = os.path.join(self.folder_prefix, "post_processing")
self.greedy_selected_parameters = GreedySelectedParametersList()
self.greedy_errors = GreedyErrorEstimatorsList()
#
# By default set a tolerance slightly larger than zero, in order to
# stop greedy iterations in trivial cases by default
self.tol = 1e-15
def initialize_training_set(self, ntrain, enable_import=True, sampling=None, **kwargs):
import_successful = ReductionMethod.initialize_training_set(self, self.EIM_approximation.mu_range, ntrain, enable_import, sampling, **kwargs)
# Since exact evaluation is required, we cannot use a distributed training set
self.training_set.distributed_max = False
# Also initialize the map from parameter values to snapshots container index
self._training_set_parameters_to_snapshots_container_index = dict((mu, mu_index) for (mu_index, mu) in enumerate(self.training_set))
return import_successful
def initialize_testing_set(self, ntest, enable_import=False, sampling=None, **kwargs):
return ReductionMethod.initialize_testing_set(self, self.EIM_approximation.mu_range, ntest, enable_import, sampling, **kwargs)
# Perform the offline phase of EIM
def offline(self):
need_to_do_offline_stage = self._init_offline()
if need_to_do_offline_stage:
self._offline()
self._finalize_offline()
return self.EIM_approximation
# Initialize data structures required for the offline phase
def _init_offline(self):
# Prepare folders and init EIM approximation
all_folders = Folders()
all_folders.update(self.folder)
all_folders.update(self.EIM_approximation.folder)
all_folders.pop("testing_set") # this is required only in the error/speedup analysis
all_folders.pop("error_analysis") # this is required only in the error analysis
all_folders.pop("speedup_analysis") # this is required only in the speedup analysis
at_least_one_folder_created = all_folders.create()
if not at_least_one_folder_created:
return False # offline construction should be skipped, since data are already available
else:
self.EIM_approximation.init("offline")
return True # offline construction should be carried out
def _offline(self):
interpolation_method_name = self.EIM_approximation.parametrized_expression.interpolation_method_name()
description = self.EIM_approximation.parametrized_expression.description()
# Evaluate the parametrized expression for all parameters in the training set
print(TextBox(interpolation_method_name + " preprocessing phase begins for" + "\n" + "\n".join(description), fill="="))
print("")
for (mu_index, mu) in enumerate(self.training_set):
print(TextLine(interpolation_method_name + " " + str(mu_index), fill=":"))
self.EIM_approximation.set_mu(mu)
print("evaluate parametrized expression at mu =", mu)
self.EIM_approximation.evaluate_parametrized_expression()
self.EIM_approximation.export_solution(self.folder["snapshots"], "truth_" + str(mu_index))
print("add to snapshots")
self.add_to_snapshots(self.EIM_approximation.snapshot)
print("")
# If basis generation is POD, compute the first POD modes of the snapshots
if self.EIM_approximation.basis_generation == "POD":
print("compute basis")
N_POD = self.compute_basis_POD()
print("")
print(TextBox(interpolation_method_name + " preprocessing phase ends for" + "\n" + "\n".join(description), fill="="))
print("")
print(TextBox(interpolation_method_name + " offline phase begins for" + "\n" + "\n".join(description), fill="="))
print("")
if self.EIM_approximation.basis_generation == "Greedy":
# Arbitrarily start from the first parameter in the training set
self.EIM_approximation.set_mu(self.training_set[0])
# Carry out greedy selection
relative_error_max = 2.*self.tol
while self.EIM_approximation.N < self.Nmax and relative_error_max >= self.tol:
print(TextLine(interpolation_method_name + " N = " + str(self.EIM_approximation.N), fill=":"))
self._print_greedy_interpolation_solve_message()
self.EIM_approximation.solve()
print("compute and locate maximum interpolation error")
self.EIM_approximation.snapshot = self.load_snapshot()
(error, maximum_error, maximum_location) = self.EIM_approximation.compute_maximum_interpolation_error()
print("update locations with", maximum_location)
self.update_interpolation_locations(maximum_location)
print("update basis")
self.update_basis_greedy(error, maximum_error)
print("update interpolation matrix")
self.update_interpolation_matrix()
(error_max, relative_error_max) = self.greedy()
print("maximum interpolation error =", error_max)
print("maximum interpolation relative error =", relative_error_max)
print("")
else:
while self.EIM_approximation.N < N_POD:
print(TextLine(interpolation_method_name + " N = " + str(self.EIM_approximation.N), fill=":"))
print("solve interpolation for basis number", self.EIM_approximation.N)
self.EIM_approximation._solve(self.EIM_approximation.basis_functions[self.EIM_approximation.N])
print("compute and locate maximum interpolation error")
self.EIM_approximation.snapshot = self.EIM_approximation.basis_functions[self.EIM_approximation.N]
(error, maximum_error, maximum_location) = self.EIM_approximation.compute_maximum_interpolation_error()
print("update locations with", maximum_location)
self.update_interpolation_locations(maximum_location)
self.EIM_approximation.N += 1
print("update interpolation matrix")
self.update_interpolation_matrix()
print("")
print(TextBox(interpolation_method_name + " offline phase ends for" + "\n" + "\n".join(description), fill="="))
print("")
# Finalize data structures required after the offline phase
def _finalize_offline(self):
self.EIM_approximation.init("online")
def _print_greedy_interpolation_solve_message(self):
print("solve interpolation for mu =", self.EIM_approximation.mu)
# Update the snapshots container
def add_to_snapshots(self, snapshot):
self.snapshots_container.enrich(snapshot)
# Update basis (greedy version)
def update_basis_greedy(self, error, maximum_error):
if abs(maximum_error) > 0.:
self.EIM_approximation.basis_functions.enrich(error/maximum_error)
else:
# Trivial case, greedy will stop at the first iteration
assert self.EIM_approximation.N == 0
self.EIM_approximation.basis_functions.enrich(error) # error is actually zero
self.EIM_approximation.basis_functions.save(self.EIM_approximation.folder["basis"], "basis")
self.EIM_approximation.N += 1
# Update basis (POD version)
def compute_basis_POD(self):
POD = self.EIM_approximation.parametrized_expression.create_POD_container()
POD.store_snapshot(self.snapshots_container)
(_, _, basis_functions, N) = POD.apply(self.Nmax, self.tol)
self.EIM_approximation.basis_functions.enrich(basis_functions)
self.EIM_approximation.basis_functions.save(self.EIM_approximation.folder["basis"], "basis")
# do not increment self.EIM_approximation.N
POD.print_eigenvalues(N)
POD.save_eigenvalues_file(self.folder["post_processing"], "eigs")
POD.save_retained_energy_file(self.folder["post_processing"], "retained_energy")
return N
def update_interpolation_locations(self, maximum_location):
self.EIM_approximation.interpolation_locations.append(maximum_location)
self.EIM_approximation.interpolation_locations.save(self.EIM_approximation.folder["reduced_operators"], "interpolation_locations")
# Assemble the interpolation matrix
def update_interpolation_matrix(self):
self.EIM_approximation.interpolation_matrix[0] = evaluate(self.EIM_approximation.basis_functions[:self.EIM_approximation.N], self.EIM_approximation.interpolation_locations)
self.EIM_approximation.interpolation_matrix.save(self.EIM_approximation.folder["reduced_operators"], "interpolation_matrix")
# Load the precomputed snapshot
def load_snapshot(self):
assert self.EIM_approximation.basis_generation == "Greedy"
mu = self.EIM_approximation.mu
mu_index = self._training_set_parameters_to_snapshots_container_index[mu]
assert mu == self.training_set[mu_index]
return self.snapshots_container[mu_index]
# Choose the next parameter in the offline stage in a greedy fashion
def greedy(self):
assert self.EIM_approximation.basis_generation == "Greedy"
# Print some additional information on the consistency of the reduced basis
self.EIM_approximation.solve()
self.EIM_approximation.snapshot = self.load_snapshot()
error = self.EIM_approximation.snapshot - self.EIM_approximation.basis_functions*self.EIM_approximation._interpolation_coefficients
error_on_interpolation_locations = evaluate(error, self.EIM_approximation.interpolation_locations)
(maximum_error, _) = max(abs(error))
(maximum_error_on_interpolation_locations, _) = max(abs(error_on_interpolation_locations)) # for consistency check, should be zero
print("interpolation error for current mu =", abs(maximum_error))
print("interpolation error on interpolation locations for current mu =", abs(maximum_error_on_interpolation_locations))
# Carry out the actual greedy search
def solve_and_computer_error(mu):
self.EIM_approximation.set_mu(mu)
self.EIM_approximation.solve()
self.EIM_approximation.snapshot = self.load_snapshot()
(_, maximum_error, _) = self.EIM_approximation.compute_maximum_interpolation_error()
return abs(maximum_error)
print("find next mu")
(error_max, error_argmax) = self.training_set.max(solve_and_computer_error)
self.EIM_approximation.set_mu(self.training_set[error_argmax])
self.greedy_selected_parameters.append(self.training_set[error_argmax])
self.greedy_selected_parameters.save(self.folder["post_processing"], "mu_greedy")
self.greedy_errors.append(error_max)
self.greedy_errors.save(self.folder["post_processing"], "error_max")
if abs(self.greedy_errors[0]) > 0.:
return (abs(error_max), abs(error_max/self.greedy_errors[0]))
else:
# Trivial case, greedy will stop at the first iteration
assert len(self.greedy_errors) == 1
assert self.EIM_approximation.N == 1
return (0., 0.)
# Compute the error of the empirical interpolation approximation with respect to the
# exact function over the testing set
def error_analysis(self, N_generator=None, filename=None, **kwargs):
assert len(kwargs) == 0 # not used in this method
self._init_error_analysis(**kwargs)
self._error_analysis(N_generator, filename, **kwargs)
self._finalize_error_analysis(**kwargs)
def _error_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator(n):
return n
N = self.EIM_approximation.N
interpolation_method_name = self.EIM_approximation.parametrized_expression.interpolation_method_name()
description = self.EIM_approximation.parametrized_expression.description()
print(TextBox(interpolation_method_name + " error analysis begins for" + "\n" + "\n".join(description), fill="="))
print("")
error_analysis_table = ErrorAnalysisTable(self.testing_set)
error_analysis_table.set_Nmax(N)
error_analysis_table.add_column("error", group_name="eim", operations=("mean", "max"))
error_analysis_table.add_column("relative_error", group_name="eim", operations=("mean", "max"))
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine(interpolation_method_name + " " + str(mu_index), fill=":"))
self.EIM_approximation.set_mu(mu)
# Evaluate the exact function on the truth grid
self.EIM_approximation.evaluate_parametrized_expression()
for n in range(1, N + 1): # n = 1, ... N
n_arg = N_generator(n)
if n_arg is not None:
self.EIM_approximation.solve(n_arg)
(_, error, _) = self.EIM_approximation.compute_maximum_interpolation_error(n)
(_, relative_error, _) = self.EIM_approximation.compute_maximum_interpolation_relative_error(n)
error_analysis_table["error", n, mu_index] = abs(error)
error_analysis_table["relative_error", n, mu_index] = abs(relative_error)
else:
error_analysis_table["error", n, mu_index] = NotImplemented
error_analysis_table["relative_error", n, mu_index] = NotImplemented
# Print
print("")
print(error_analysis_table)
print("")
print(TextBox(interpolation_method_name + " error analysis ends for" + "\n" + "\n".join(description), fill="="))
print("")
# Export error analysis table
error_analysis_table.save(self.folder["error_analysis"], "error_analysis" if filename is None else filename)
# Compute the speedup of the empirical interpolation approximation with respect to the
# exact function over the testing set
def speedup_analysis(self, N_generator=None, filename=None, **kwargs):
assert len(kwargs) == 0 # not used in this method
self._init_speedup_analysis(**kwargs)
self._speedup_analysis(N_generator, filename, **kwargs)
self._finalize_speedup_analysis(**kwargs)
# Initialize data structures required for the speedup analysis phase
def _init_speedup_analysis(self, **kwargs):
# Make sure to clean up snapshot cache to ensure that parametrized
# expression evaluation is actually carried out
self.EIM_approximation.snapshot_cache.clear()
# ... and also disable the capability of importing/exporting truth solutions
self.disable_import_solution = PatchInstanceMethod(self.EIM_approximation, "import_solution", lambda self_, folder, filename, solution=None: False)
self.disable_export_solution = PatchInstanceMethod(self.EIM_approximation, "export_solution", lambda self_, folder, filename, solution=None: None)
self.disable_import_solution.patch()
self.disable_export_solution.patch()
def _speedup_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator(n):
return n
N = self.EIM_approximation.N
interpolation_method_name = self.EIM_approximation.parametrized_expression.interpolation_method_name()
description = self.EIM_approximation.parametrized_expression.description()
print(TextBox(interpolation_method_name + " speedup analysis begins for" + "\n" + "\n".join(description), fill="="))
print("")
speedup_analysis_table = SpeedupAnalysisTable(self.testing_set)
speedup_analysis_table.set_Nmax(N)
speedup_analysis_table.add_column("speedup", group_name="speedup", operations=("min", "mean", "max"))
evaluate_timer = Timer("parallel")
EIM_timer = Timer("serial")
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine(interpolation_method_name + " " + str(mu_index), fill=":"))
self.EIM_approximation.set_mu(mu)
# Evaluate the exact function on the truth grid
evaluate_timer.start()
self.EIM_approximation.evaluate_parametrized_expression()
elapsed_evaluate = evaluate_timer.stop()
for n in range(1, N + 1): # n = 1, ... N
n_arg = N_generator(n)
if n_arg is not None:
EIM_timer.start()
self.EIM_approximation.solve(n_arg)
elapsed_EIM = EIM_timer.stop()
speedup_analysis_table["speedup", n, mu_index] = elapsed_evaluate/elapsed_EIM
else:
speedup_analysis_table["speedup", n, mu_index] = NotImplemented
# Print
print("")
print(speedup_analysis_table)
print("")
print(TextBox(interpolation_method_name + " speedup analysis ends for" + "\n" + "\n".join(description), fill="="))
print("")
# Export speedup analysis table
speedup_analysis_table.save(self.folder["speedup_analysis"], "speedup_analysis" if filename is None else filename)
# Finalize data structures required after the speedup analysis phase
def _finalize_speedup_analysis(self, **kwargs):
# Restore the capability to import/export truth solutions
self.disable_import_solution.unpatch()
self.disable_export_solution.unpatch()
del self.disable_import_solution
del self.disable_export_solution
class SCMApproximationReductionMethod(ReductionMethod):
# Default initialization of members
def __init__(self, SCM_approximation, folder_prefix):
# Call the parent initialization
ReductionMethod.__init__(self, folder_prefix)
# $$ OFFLINE DATA STRUCTURES $$ #
# High fidelity problem
self.SCM_approximation = SCM_approximation
# I/O
self.folder["post_processing"] = os.path.join(self.folder_prefix,
"post_processing")
self.greedy_selected_parameters = SCM_approximation.greedy_selected_parameters
self.greedy_error_estimators = GreedyErrorEstimatorsList()
# OFFLINE: set the elements in the training set.
def initialize_training_set(self,
ntrain,
enable_import=True,
sampling=None,
**kwargs):
assert enable_import
import_successful = ReductionMethod.initialize_training_set(
self, self.SCM_approximation.mu_range, ntrain, enable_import,
sampling, **kwargs)
self.SCM_approximation.training_set = self.training_set
return import_successful
def initialize_testing_set(self,
ntest,
enable_import=False,
sampling=None,
**kwargs):
return ReductionMethod.initialize_testing_set(
self, self.SCM_approximation.mu_range, ntest, enable_import,
sampling, **kwargs)
# Perform the offline phase of SCM
def offline(self):
need_to_do_offline_stage = self._init_offline()
if need_to_do_offline_stage:
self._offline()
self._finalize_offline()
return self.SCM_approximation
# Initialize data structures required for the offline phase
def _init_offline(self):
# Prepare folders and init SCM approximation
required_folders = Folders()
required_folders.update(self.folder)
required_folders.update(self.SCM_approximation.folder)
optional_folders = Folders()
optional_folders["cache"] = required_folders.pop("cache")
# cache does not affect the availability of offline data
optional_folders["testing_set"] = required_folders.pop("testing_set")
# testing set is required only in the error/speedup analysis
optional_folders["error_analysis"] = required_folders.pop(
"error_analysis")
# error analysis folder is required only in the error analysis
optional_folders["speedup_analysis"] = required_folders.pop(
"speedup_analysis")
# speedup analysis folder is required only in the speedup analysis
at_least_one_required_folder_created = required_folders.create()
at_least_one_optional_folder_created = optional_folders.create(
) # noqa: F841
if not at_least_one_required_folder_created:
return False # offline construction should be skipped, since data are already available
else:
self.SCM_approximation.init("offline")
return True # offline construction should be carried out
def _offline(self):
print(TextBox("SCM offline phase begins", fill="="))
print("")
# Compute the bounding box \mathcal{B}
self.compute_bounding_box()
print("")
# Arbitrarily start from the first parameter in the training set
self.SCM_approximation.set_mu(self.training_set[0])
relative_error_estimator_max = 2. * self.tol
while self.SCM_approximation.N < self.Nmax and relative_error_estimator_max >= self.tol:
print(
TextLine("SCM N = " + str(self.SCM_approximation.N), fill="~"))
# Store the greedy parameter
self.store_greedy_selected_parameters()
# Evaluate the stability factor
print("evaluate the stability factor for mu =",
self.SCM_approximation.mu)
(stability_factor,
eigenvector) = self.SCM_approximation.evaluate_stability_factor()
print("stability factor =", stability_factor)
# Update data structures related to upper bound vectors
upper_bound_vector = self.compute_upper_bound_vector(eigenvector)
self.update_upper_bound_vectors(upper_bound_vector)
# Prepare for next iteration
print("find next mu")
(error_estimator_max, relative_error_estimator_max) = self.greedy()
print("maximum SCM error estimator =", error_estimator_max)
print("maximum SCM relative error estimator =",
relative_error_estimator_max)
print("")
print(TextBox("SCM offline phase ends", fill="="))
print("")
# Finalize data structures required after the offline phase
def _finalize_offline(self):
self.SCM_approximation.init("online")
# Compute the bounding box \mathcal{B}
def compute_bounding_box(self):
# Resize the bounding box storage
Q = self.SCM_approximation.truth_problem.Q[
"stability_factor_left_hand_matrix"]
for q in range(Q):
# Compute the minimum eigenvalue
minimum_eigenvalue_calculator = ParametrizedStabilityFactorEigenProblem(
self.SCM_approximation.truth_problem,
"smallest",
self.SCM_approximation.truth_problem.
_eigen_solver_parameters["bounding_box_minimum"],
self.folder_prefix,
expansion_index=q)
minimum_eigenvalue_calculator.init()
(self.SCM_approximation.bounding_box_min[q],
_) = minimum_eigenvalue_calculator.solve()
print("bounding_box_min[" + str(q) + "] = " +
str(self.SCM_approximation.bounding_box_min[q]))
# Compute the maximum eigenvalue
maximum_eigenvalue_calculator = ParametrizedStabilityFactorEigenProblem(
self.SCM_approximation.truth_problem,
"largest",
self.SCM_approximation.truth_problem.
_eigen_solver_parameters["bounding_box_maximum"],
self.folder_prefix,
expansion_index=q)
maximum_eigenvalue_calculator.init()
(self.SCM_approximation.bounding_box_max[q],
_) = maximum_eigenvalue_calculator.solve()
print("bounding_box_max[" + str(q) + "] = " +
str(self.SCM_approximation.bounding_box_max[q]))
# Save to file
self.SCM_approximation.bounding_box_min.save(
self.SCM_approximation.folder["reduced_operators"],
"bounding_box_min")
self.SCM_approximation.bounding_box_max.save(
self.SCM_approximation.folder["reduced_operators"],
"bounding_box_max")
# Store the greedy parameter
def store_greedy_selected_parameters(self):
mu = self.SCM_approximation.mu
self.SCM_approximation.greedy_selected_parameters.append(mu)
self.SCM_approximation.N = len(
self.SCM_approximation.greedy_selected_parameters)
# Save to file
self.SCM_approximation.greedy_selected_parameters.save(
self.SCM_approximation.folder["reduced_operators"],
"greedy_selected_parameters")
def compute_upper_bound_vector(self, u):
Q = self.SCM_approximation.truth_problem.Q[
"stability_factor_left_hand_matrix"]
A = self.SCM_approximation.truth_problem.operator[
"stability_factor_left_hand_matrix"]
B = self.SCM_approximation.truth_problem.operator[
"stability_factor_right_hand_matrix"]
assert len(B) == 1
normalization = transpose(u) * B[0] * u
upper_bound_vector = OnlineVector(Q)
for q in range(Q):
upper_bound_vector[q] = (transpose(u) * A[q] * u) / normalization
return upper_bound_vector
def update_upper_bound_vectors(self, upper_bound_vector):
self.SCM_approximation.upper_bound_vectors.append(upper_bound_vector)
self.SCM_approximation.upper_bound_vectors.save(
self.SCM_approximation.folder["reduced_operators"],
"upper_bound_vectors")
# Choose the next parameter in the offline stage in a greedy fashion
def greedy(self):
def solve_and_estimate_error(mu):
self.SCM_approximation.set_mu(mu)
stability_factor_lower_bound = self.SCM_approximation.get_stability_factor_lower_bound(
)
stability_factor_upper_bound = self.SCM_approximation.get_stability_factor_upper_bound(
)
ratio = stability_factor_lower_bound / stability_factor_upper_bound
if ratio < 0. and not isclose(ratio, 0.): # if ratio << 0
print("SCM warning at mu = " + str(mu) +
": stability factor lower bound = " +
str(stability_factor_lower_bound) + " < 0")
if ratio > 1. and not isclose(ratio, 1.): # if ratio >> 1
print("SCM warning at mu = " + str(mu) +
": stability factor lower bound = " +
str(stability_factor_lower_bound) +
" > stability factor upper bound = " +
str(stability_factor_upper_bound))
error_estimator = 1. - ratio
return error_estimator
(error_estimator_max, error_estimator_argmax
) = self.training_set.max(solve_and_estimate_error)
self.SCM_approximation.set_mu(
self.training_set[error_estimator_argmax])
self.greedy_error_estimators.append(error_estimator_max)
self.greedy_error_estimators.save(self.folder["post_processing"],
"error_estimator_max")
return (error_estimator_max,
error_estimator_max / self.greedy_error_estimators[0])
# Initialize data structures required for the error analysis phase
def _init_error_analysis(self, **kwargs):
# Initialize reduced order data structures in the SCM online problem
self.SCM_approximation.init("online")
# Compute the error of the scm approximation with respect to the
# exact stability factor over the testing set
def error_analysis(self, N_generator=None, filename=None, **kwargs):
assert len(kwargs) == 0 # not used in this method
self._init_error_analysis(**kwargs)
self._error_analysis(N_generator, filename, **kwargs)
self._finalize_error_analysis(**kwargs)
def _error_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator():
N = self.SCM_approximation.N
for n in range(1, N + 1): # n = 1, ... N
yield n
def N_generator_max():
*_, Nmax = N_generator()
return Nmax
print(TextBox("SCM error analysis begins", fill="="))
print("")
error_analysis_table = ErrorAnalysisTable(self.testing_set)
error_analysis_table.set_Nmax(N_generator_max())
error_analysis_table.add_column("normalized_error",
group_name="scm",
operations=("min", "mean", "max"))
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine("SCM " + str(mu_index), fill="~"))
self.SCM_approximation.set_mu(mu)
(exact_stability_factor,
_) = self.SCM_approximation.evaluate_stability_factor()
for n in N_generator():
stability_factor_lower_bound = self.SCM_approximation.get_stability_factor_lower_bound(
n)
stability_factor_upper_bound = self.SCM_approximation.get_stability_factor_upper_bound(
n)
ratio_lower_bound_to_upper_bound = stability_factor_lower_bound / stability_factor_upper_bound
ratio_lower_bound_to_exact = stability_factor_lower_bound / exact_stability_factor
if ratio_lower_bound_to_upper_bound < 0. and not isclose(
ratio_lower_bound_to_upper_bound, 0.):
# if ratio_lower_bound_to_upper_bound << 0
print("SCM warning at mu = " + str(mu) +
": stability factor lower bound = " +
str(stability_factor_lower_bound) + " < 0")
if ratio_lower_bound_to_upper_bound > 1. and not isclose(
ratio_lower_bound_to_upper_bound, 1.):
# if ratio_lower_bound_to_upper_bound >> 1
print("SCM warning at mu = " + str(mu) +
": stability factor lower bound = " +
str(stability_factor_lower_bound) +
" > stability factor upper bound = " +
str(stability_factor_upper_bound))
if ratio_lower_bound_to_exact > 1. and not isclose(
ratio_lower_bound_to_exact, 1.):
# if ratio_lower_bound_to_exact >> 1
print("SCM warning at mu = " + str(mu) +
": stability factor lower bound = " +
str(stability_factor_lower_bound) +
" > exact stability factor =" +
str(exact_stability_factor))
error_analysis_table["normalized_error", n, mu_index] = (
exact_stability_factor - stability_factor_lower_bound
) / stability_factor_upper_bound
# Print
print("")
print(error_analysis_table)
print("")
print(TextBox("SCM error analysis ends", fill="="))
print("")
# Export error analysis table
error_analysis_table.save(
self.folder["error_analysis"],
"error_analysis" if filename is None else filename)
# Compute the speedup of the scm approximation with respect to the
# exact stability factor over the testing set
def speedup_analysis(self, N_generator=None, filename=None, **kwargs):
assert len(kwargs) == 0 # not used in this method
self._init_speedup_analysis(**kwargs)
self._speedup_analysis(N_generator, filename, **kwargs)
self._finalize_speedup_analysis(**kwargs)
# Initialize data structures required for the speedup analysis phase
def _init_speedup_analysis(self, **kwargs):
# Make sure to clean up snapshot cache to ensure that parametrized
# expression evaluation is actually carried out
self.SCM_approximation._stability_factor_lower_bound_cache.clear()
self.SCM_approximation._stability_factor_upper_bound_cache.clear()
self.SCM_approximation.stability_factor_calculator._eigenvalue_cache.clear(
)
self.SCM_approximation.stability_factor_calculator._eigenvector_cache.clear(
)
def _speedup_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator():
N = self.SCM_approximation.N
for n in range(1, N + 1): # n = 1, ... N
yield n
def N_generator_max():
*_, Nmax = N_generator()
return Nmax
print(TextBox("SCM speedup analysis begins", fill="="))
print("")
speedup_analysis_table = SpeedupAnalysisTable(self.testing_set)
speedup_analysis_table.set_Nmax(N_generator_max())
speedup_analysis_table.add_column("speedup",
group_name="speedup",
operations=("min", "mean", "max"))
exact_timer = Timer("parallel")
SCM_timer = Timer("serial")
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine("SCM " + str(mu_index), fill="~"))
self.SCM_approximation.set_mu(mu)
exact_timer.start()
self.SCM_approximation.evaluate_stability_factor()
elapsed_exact = exact_timer.stop()
for n in N_generator():
SCM_timer.start()
self.SCM_approximation.get_stability_factor_lower_bound(n)
self.SCM_approximation.get_stability_factor_upper_bound(n)
elapsed_SCM = SCM_timer.stop()
speedup_analysis_table["speedup", n,
mu_index] = elapsed_exact / elapsed_SCM
# Print
print("")
print(speedup_analysis_table)
print("")
print(TextBox("SCM speedup analysis ends", fill="="))
print("")
# Export speedup analysis table
speedup_analysis_table.save(
self.folder["speedup_analysis"],
"speedup_analysis" if filename is None else filename)
class RBReduction_Class(DifferentialProblemReductionMethod_DerivedClass):
"""
The folders used to store the snapshots and for the post processing data, the parameters for the greedy algorithm and the error estimator evaluations are initialized.
:param truth_problem: class of the truth problem to be solved.
:return: reduced RB class.
"""
def __init__(self, truth_problem, **kwargs):
# Call the parent initialization
DifferentialProblemReductionMethod_DerivedClass.__init__(
self, truth_problem, **kwargs)
# Declare a GS object
self.GS = None # GramSchmidt (for problems with one component) or dict of GramSchmidt (for problem with several components)
# I/O
self.folder["snapshots"] = os.path.join(self.folder_prefix,
"snapshots")
self.folder["post_processing"] = os.path.join(
self.folder_prefix, "post_processing")
self.greedy_selected_parameters = GreedySelectedParametersList()
self.greedy_error_estimators = GreedyErrorEstimatorsList()
self.label = "RB"
def _init_offline(self):
# Call parent to initialize inner product and reduced problem
output = DifferentialProblemReductionMethod_DerivedClass._init_offline(
self)
# Declare a new GS for each basis component
if len(self.truth_problem.components) > 1:
self.GS = dict()
for component in self.truth_problem.components:
assert len(
self.truth_problem.inner_product[component]) == 1
inner_product = self.truth_problem.inner_product[
component][0]
self.GS[component] = GramSchmidt(self.truth_problem.V,
inner_product)
else:
assert len(self.truth_problem.inner_product) == 1
inner_product = self.truth_problem.inner_product[0]
self.GS = GramSchmidt(self.truth_problem.V, inner_product)
# Return
return output
def offline(self):
"""
It performs the offline phase of the reduced order model.
:return: reduced_problem where all offline data are stored.
"""
need_to_do_offline_stage = self._init_offline()
if need_to_do_offline_stage:
self._offline()
self._finalize_offline()
return self.reduced_problem
@snapshot_links_to_cache
def _offline(self):
print(
TextBox(self.truth_problem.name() + " " + self.label +
" offline phase begins",
fill="="))
print("")
# Initialize first parameter to be used
self.reduced_problem.build_reduced_operators()
self.reduced_problem.build_error_estimation_operators()
(absolute_error_estimator_max,
relative_error_estimator_max) = self.greedy()
print(
"initial maximum absolute error estimator over training set =",
absolute_error_estimator_max)
print(
"initial maximum relative error estimator over training set =",
relative_error_estimator_max)
print("")
iteration = 0
while self.reduced_problem.N < self.Nmax and relative_error_estimator_max >= self.tol:
print(TextLine("N = " + str(self.reduced_problem.N), fill="#"))
print("truth solve for mu =", self.truth_problem.mu)
snapshot = self.truth_problem.solve()
self.truth_problem.export_solution(self.folder["snapshots"],
"truth_" + str(iteration),
snapshot)
snapshot = self.postprocess_snapshot(snapshot, iteration)
print("update basis matrix")
self.update_basis_matrix(snapshot)
iteration += 1
print("build reduced operators")
self.reduced_problem.build_reduced_operators()
print("reduced order solve")
self.reduced_problem.solve()
print("build operators for error estimation")
self.reduced_problem.build_error_estimation_operators()
(absolute_error_estimator_max,
relative_error_estimator_max) = self.greedy()
print("maximum absolute error estimator over training set =",
absolute_error_estimator_max)
print("maximum relative error estimator over training set =",
relative_error_estimator_max)
print("")
print(
TextBox(self.truth_problem.name() + " " + self.label +
" offline phase ends",
fill="="))
print("")
def update_basis_matrix(self, snapshot):
"""
It updates basis matrix.
:param snapshot: last offline solution calculated.
"""
if len(self.truth_problem.components) > 1:
for component in self.truth_problem.components:
new_basis_function = self.GS[component].apply(
snapshot,
self.reduced_problem.basis_functions[component]
[self.reduced_problem.N_bc[component]:],
component=component)
self.reduced_problem.basis_functions.enrich(
new_basis_function, component=component)
self.reduced_problem.N[component] += 1
self.reduced_problem.basis_functions.save(
self.reduced_problem.folder["basis"], "basis")
else:
new_basis_function = self.GS.apply(
snapshot, self.reduced_problem.
basis_functions[self.reduced_problem.N_bc:])
self.reduced_problem.basis_functions.enrich(new_basis_function)
self.reduced_problem.N += 1
self.reduced_problem.basis_functions.save(
self.reduced_problem.folder["basis"], "basis")
def greedy(self):
"""
It chooses the next parameter in the offline stage in a greedy fashion: wrapper with post processing of the result (in particular, set greedily selected parameter and save to file)
:return: max error estimator and the comparison with the first one calculated.
"""
(error_estimator_max, error_estimator_argmax) = self._greedy()
self.truth_problem.set_mu(
self.training_set[error_estimator_argmax])
self.greedy_selected_parameters.append(
self.training_set[error_estimator_argmax])
self.greedy_selected_parameters.save(
self.folder["post_processing"], "mu_greedy")
self.greedy_error_estimators.append(error_estimator_max)
self.greedy_error_estimators.save(self.folder["post_processing"],
"error_estimator_max")
return (error_estimator_max,
error_estimator_max / self.greedy_error_estimators[0])
def _greedy(self):
"""
It chooses the next parameter in the offline stage in a greedy fashion. Internal method.
:return: max error estimator and the respective parameter.
"""
if self.reduced_problem.N > 0: # skip during initialization
# Print some additional information on the consistency of the reduced basis
print("absolute error for current mu =",
self.reduced_problem.compute_error())
print("absolute error estimator for current mu =",
self.reduced_problem.estimate_error())
# Carry out the actual greedy search
def solve_and_estimate_error(mu):
self.reduced_problem.set_mu(mu)
self.reduced_problem.solve()
error_estimator = self.reduced_problem.estimate_error()
logger.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 error_analysis(self, N_generator=None, filename=None, **kwargs):
"""
It computes the error of the reduced order approximation with respect to the full order one over the testing set.
:param N_generator: generator of dimension of reduced problem.
"""
self._init_error_analysis(**kwargs)
self._error_analysis(N_generator, filename, **kwargs)
self._finalize_error_analysis(**kwargs)
def _error_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator():
N = self.reduced_problem.N
if isinstance(N, dict):
N = min(N.values())
for n in range(1, N + 1): # n = 1, ... N
yield n
if "components" in kwargs:
components = kwargs["components"]
else:
components = self.truth_problem.components
def N_generator_items():
for n in N_generator():
assert isinstance(n, (dict, int))
if isinstance(n, int):
yield (n, n)
elif isinstance(n, dict):
assert len(n) == 1
(n_int, n_online_size_dict) = n.popitem()
assert isinstance(n_int, int)
assert isinstance(n_online_size_dict, OnlineSizeDict)
yield (n_int, n_online_size_dict)
else:
raise TypeError(
"Invalid item generated by N_generator")
def N_generator_max():
*_, Nmax = N_generator_items()
assert isinstance(Nmax, tuple)
assert len(Nmax) == 2
assert isinstance(Nmax[0], int)
return Nmax[0]
print(
TextBox(self.truth_problem.name() + " " + self.label +
" error analysis begins",
fill="="))
print("")
error_analysis_table = ErrorAnalysisTable(self.testing_set)
error_analysis_table.set_Nmax(N_generator_max())
if len(components) > 1:
all_components_string = "".join(components)
for component in components:
error_analysis_table.add_column("error_" + component,
group_name="solution_" +
component + "_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_error_" + component,
group_name="solution_" + component + "_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"error_" + all_components_string,
group_name="solution_" + all_components_string + "_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"error_estimator_" + all_components_string,
group_name="solution_" + all_components_string + "_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"effectivity_" + all_components_string,
group_name="solution_" + all_components_string + "_error",
operations=("min", "mean", "max"))
error_analysis_table.add_column(
"relative_error_" + all_components_string,
group_name="solution_" + all_components_string +
"_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_error_estimator_" + all_components_string,
group_name="solution_" + all_components_string +
"_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_effectivity_" + all_components_string,
group_name="solution_" + all_components_string +
"_relative_error",
operations=("min", "mean", "max"))
else:
component = components[0]
error_analysis_table.add_column("error_" + component,
group_name="solution_" +
component + "_error",
operations=("mean", "max"))
error_analysis_table.add_column("error_estimator_" + component,
group_name="solution_" +
component + "_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"effectivity_" + component,
group_name="solution_" + component + "_error",
operations=("min", "mean", "max"))
error_analysis_table.add_column("relative_error_" + component,
group_name="solution_" +
component + "_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_error_estimator_" + component,
group_name="solution_" + component + "_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_effectivity_" + component,
group_name="solution_" + component + "_relative_error",
operations=("min", "mean", "max"))
error_analysis_table.add_column("error_output",
group_name="output_error",
operations=("mean", "max"))
error_analysis_table.add_column("error_estimator_output",
group_name="output_error",
operations=("mean", "max"))
error_analysis_table.add_column("effectivity_output",
group_name="output_error",
operations=("min", "mean", "max"))
error_analysis_table.add_column("relative_error_output",
group_name="output_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column("relative_error_estimator_output",
group_name="output_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column("relative_effectivity_output",
group_name="output_relative_error",
operations=("min", "mean", "max"))
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine(str(mu_index), fill="#"))
self.reduced_problem.set_mu(mu)
for (n_int, n_arg) in N_generator_items():
self.reduced_problem.solve(n_arg, **kwargs)
error = self.reduced_problem.compute_error(**kwargs)
if len(components) > 1:
error[all_components_string] = sqrt(
sum([
error[component]**2 for component in components
]))
error_estimator = self.reduced_problem.estimate_error()
relative_error = self.reduced_problem.compute_relative_error(
**kwargs)
if len(components) > 1:
relative_error[all_components_string] = sqrt(
sum([
relative_error[component]**2
for component in components
]))
relative_error_estimator = self.reduced_problem.estimate_relative_error(
)
self.reduced_problem.compute_output()
error_output = self.reduced_problem.compute_error_output(
**kwargs)
error_output_estimator = self.reduced_problem.estimate_error_output(
)
relative_error_output = self.reduced_problem.compute_relative_error_output(
**kwargs)
relative_error_output_estimator = self.reduced_problem.estimate_relative_error_output(
)
if len(components) > 1:
for component in components:
error_analysis_table["error_" + component, n_int,
mu_index] = error[component]
error_analysis_table[
"relative_error_" + component, n_int,
mu_index] = relative_error[component]
error_analysis_table[
"error_" + all_components_string, n_int,
mu_index] = error[all_components_string]
error_analysis_table["error_estimator_" +
all_components_string, n_int,
mu_index] = error_estimator
error_analysis_table[
"effectivity_" + all_components_string, n_int,
mu_index] = error_analysis_table[
"error_estimator_" + all_components_string,
n_int, mu_index] / error_analysis_table[
"error_" + all_components_string, n_int,
mu_index]
error_analysis_table[
"relative_error_" + all_components_string, n_int,
mu_index] = relative_error[all_components_string]
error_analysis_table[
"relative_error_estimator_" +
all_components_string, n_int,
mu_index] = relative_error_estimator
error_analysis_table[
"relative_effectivity_" + all_components_string,
n_int, mu_index] = error_analysis_table[
"relative_error_estimator_" +
all_components_string, n_int,
mu_index] / error_analysis_table[
"relative_error_" + all_components_string,
n_int, mu_index]
else:
component = components[0]
error_analysis_table["error_" + component, n_int,
mu_index] = error
error_analysis_table["error_estimator_" + component,
n_int, mu_index] = error_estimator
error_analysis_table[
"effectivity_" + component, n_int,
mu_index] = error_analysis_table[
"error_estimator_" + component, n_int,
mu_index] / error_analysis_table[
"error_" + component, n_int, mu_index]
error_analysis_table["relative_error_" + component,
n_int, mu_index] = relative_error
error_analysis_table[
"relative_error_estimator_" + component, n_int,
mu_index] = relative_error_estimator
error_analysis_table[
"relative_effectivity_" + component, n_int,
mu_index] = error_analysis_table[
"relative_error_estimator_" + component, n_int,
mu_index] / error_analysis_table[
"relative_error_" + component, n_int,
mu_index]
error_analysis_table["error_output", n_int,
mu_index] = error_output
error_analysis_table["error_estimator_output", n_int,
mu_index] = error_output_estimator
error_analysis_table[
"effectivity_output", n_int,
mu_index] = error_analysis_table[
"error_estimator_output", n_int,
mu_index] / error_analysis_table["error_output",
n_int, mu_index]
error_analysis_table["relative_error_output", n_int,
mu_index] = relative_error_output
error_analysis_table[
"relative_error_estimator_output", n_int,
mu_index] = relative_error_output_estimator
error_analysis_table[
"relative_effectivity_output", n_int,
mu_index] = error_analysis_table[
"relative_error_estimator_output", n_int,
mu_index] / error_analysis_table[
"relative_error_output", n_int, mu_index]
# Print
print("")
print(error_analysis_table)
print("")
print(
TextBox(self.truth_problem.name() + " " + self.label +
" error analysis ends",
fill="="))
print("")
# Export error analysis table
error_analysis_table.save(
self.folder["error_analysis"],
"error_analysis" if filename is None else filename)
def speedup_analysis(self, N_generator=None, filename=None, **kwargs):
"""
It computes the speedup of the reduced order approximation with respect to the full order one over the testing set.
:param N_generator: generator of dimension of the reduced problem.
"""
self._init_speedup_analysis(**kwargs)
self._speedup_analysis(N_generator, filename, **kwargs)
self._finalize_speedup_analysis(**kwargs)
def _speedup_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator():
N = self.reduced_problem.N
if isinstance(N, dict):
N = min(N.values())
for n in range(1, N + 1): # n = 1, ... N
yield n
def N_generator_items():
for n in N_generator():
assert isinstance(n, (dict, int))
if isinstance(n, int):
yield (n, n)
elif isinstance(n, dict):
assert len(n) == 1
(n_int, n_online_size_dict) = n.popitem()
assert isinstance(n_int, int)
assert isinstance(n_online_size_dict, OnlineSizeDict)
yield (n_int, n_online_size_dict)
else:
raise TypeError(
"Invalid item generated by N_generator")
def N_generator_max():
*_, Nmax = N_generator_items()
assert isinstance(Nmax, tuple)
assert len(Nmax) == 2
assert isinstance(Nmax[0], int)
return Nmax[0]
print(
TextBox(self.truth_problem.name() + " " + self.label +
" speedup analysis begins",
fill="="))
print("")
speedup_analysis_table = SpeedupAnalysisTable(self.testing_set)
speedup_analysis_table.set_Nmax(N_generator_max())
speedup_analysis_table.add_column("speedup_solve",
group_name="speedup_solve",
operations=("min", "mean",
"max"))
speedup_analysis_table.add_column(
"speedup_solve_and_estimate_error",
group_name="speedup_solve_and_estimate_error",
operations=("min", "mean", "max"))
speedup_analysis_table.add_column(
"speedup_solve_and_estimate_relative_error",
group_name="speedup_solve_and_estimate_relative_error",
operations=("min", "mean", "max"))
speedup_analysis_table.add_column("speedup_output",
group_name="speedup_output",
operations=("min", "mean",
"max"))
speedup_analysis_table.add_column(
"speedup_output_and_estimate_error_output",
group_name="speedup_output_and_estimate_error_output",
operations=("min", "mean", "max"))
speedup_analysis_table.add_column(
"speedup_output_and_estimate_relative_error_output",
group_name="speedup_output_and_estimate_relative_error_output",
operations=("min", "mean", "max"))
truth_timer = Timer("parallel")
reduced_timer = Timer("serial")
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine(str(mu_index), fill="#"))
self.reduced_problem.set_mu(mu)
truth_timer.start()
self.truth_problem.solve(**kwargs)
elapsed_truth_solve = truth_timer.stop()
truth_timer.start()
self.truth_problem.compute_output()
elapsed_truth_output = truth_timer.stop()
for (n_int, n_arg) in N_generator_items():
reduced_timer.start()
solution = self.reduced_problem.solve(n_arg, **kwargs)
elapsed_reduced_solve = reduced_timer.stop()
truth_timer.start()
self.reduced_problem.compute_error(**kwargs)
elapsed_error = truth_timer.stop()
reduced_timer.start()
error_estimator = self.reduced_problem.estimate_error()
elapsed_error_estimator = reduced_timer.stop()
truth_timer.start()
self.reduced_problem.compute_relative_error(**kwargs)
elapsed_relative_error = truth_timer.stop()
reduced_timer.start()
relative_error_estimator = self.reduced_problem.estimate_relative_error(
)
elapsed_relative_error_estimator = reduced_timer.stop()
reduced_timer.start()
output = self.reduced_problem.compute_output()
elapsed_reduced_output = reduced_timer.stop()
truth_timer.start()
self.reduced_problem.compute_error_output(**kwargs)
elapsed_error_output = truth_timer.stop()
reduced_timer.start()
error_estimator_output = self.reduced_problem.estimate_error_output(
)
elapsed_error_estimator_output = reduced_timer.stop()
truth_timer.start()
self.reduced_problem.compute_relative_error_output(
**kwargs)
elapsed_relative_error_output = truth_timer.stop()
reduced_timer.start()
relative_error_estimator_output = self.reduced_problem.estimate_relative_error_output(
)
elapsed_relative_error_estimator_output = reduced_timer.stop(
)
if solution is not NotImplemented:
speedup_analysis_table[
"speedup_solve", n_int,
mu_index] = elapsed_truth_solve / elapsed_reduced_solve
else:
speedup_analysis_table["speedup_solve", n_int,
mu_index] = NotImplemented
if error_estimator is not NotImplemented:
speedup_analysis_table[
"speedup_solve_and_estimate_error", n_int,
mu_index] = (elapsed_truth_solve + elapsed_error
) / (elapsed_reduced_solve +
elapsed_error_estimator)
else:
speedup_analysis_table[
"speedup_solve_and_estimate_error", n_int,
mu_index] = NotImplemented
if relative_error_estimator is not NotImplemented:
speedup_analysis_table[
"speedup_solve_and_estimate_relative_error", n_int,
mu_index] = (elapsed_truth_solve +
elapsed_relative_error) / (
elapsed_reduced_solve +
elapsed_relative_error_estimator)
else:
speedup_analysis_table[
"speedup_solve_and_estimate_relative_error", n_int,
mu_index] = NotImplemented
if output is not NotImplemented:
speedup_analysis_table[
"speedup_output", n_int,
mu_index] = (elapsed_truth_solve +
elapsed_truth_output) / (
elapsed_reduced_solve +
elapsed_reduced_output)
else:
speedup_analysis_table["speedup_output", n_int,
mu_index] = NotImplemented
if error_estimator_output is not NotImplemented:
assert output is not NotImplemented
speedup_analysis_table[
"speedup_output_and_estimate_error_output", n_int,
mu_index] = (elapsed_truth_solve +
elapsed_truth_output +
elapsed_error_output) / (
elapsed_reduced_solve +
elapsed_reduced_output +
elapsed_error_estimator_output)
else:
speedup_analysis_table[
"speedup_output_and_estimate_error_output", n_int,
mu_index] = NotImplemented
if relative_error_estimator_output is not NotImplemented:
assert output is not NotImplemented
speedup_analysis_table[
"speedup_output_and_estimate_relative_error_output",
n_int, mu_index] = (
elapsed_truth_solve + elapsed_truth_output +
elapsed_relative_error_output) / (
elapsed_reduced_solve +
elapsed_reduced_output +
elapsed_relative_error_estimator_output)
else:
speedup_analysis_table[
"speedup_output_and_estimate_relative_error_output",
n_int, mu_index] = NotImplemented
# Print
print("")
print(speedup_analysis_table)
print("")
print(
TextBox(self.truth_problem.name() + " " + self.label +
" speedup analysis ends",
fill="="))
print("")
# Export speedup analysis table
speedup_analysis_table.save(
self.folder["speedup_analysis"],
"speedup_analysis" if filename is None else filename)
class SCMApproximationReductionMethod(ReductionMethod):
# Default initialization of members
def __init__(self, SCM_approximation, folder_prefix):
# Call the parent initialization
ReductionMethod.__init__(self, folder_prefix)
# $$ OFFLINE DATA STRUCTURES $$ #
# High fidelity problem
self.SCM_approximation = SCM_approximation
# I/O
self.folder["post_processing"] = os.path.join(self.folder_prefix, "post_processing")
self.greedy_selected_parameters = SCM_approximation.greedy_selected_parameters
self.greedy_error_estimators = GreedyErrorEstimatorsList()
# Get data that were temporarily store in the SCM_approximation
self.bounding_box_minimum_eigensolver_parameters = self.SCM_approximation._input_storage_for_SCM_reduction["bounding_box_minimum_eigensolver_parameters"]
self.bounding_box_maximum_eigensolver_parameters = self.SCM_approximation._input_storage_for_SCM_reduction["bounding_box_maximum_eigensolver_parameters"]
del self.SCM_approximation._input_storage_for_SCM_reduction
# OFFLINE: set the elements in the training set.
def initialize_training_set(self, ntrain, enable_import=True, sampling=None, **kwargs):
assert enable_import
import_successful = ReductionMethod.initialize_training_set(self, self.SCM_approximation.mu_range, ntrain, enable_import, sampling, **kwargs)
self.SCM_approximation.training_set = self.training_set
return import_successful
def initialize_testing_set(self, ntest, enable_import=False, sampling=None, **kwargs):
return ReductionMethod.initialize_testing_set(self, self.SCM_approximation.mu_range, ntest, enable_import, sampling, **kwargs)
# Perform the offline phase of SCM
def offline(self):
need_to_do_offline_stage = self._init_offline()
if need_to_do_offline_stage:
self._offline()
self._finalize_offline()
return self.SCM_approximation
# Initialize data structures required for the offline phase
def _init_offline(self):
# Prepare folders and init SCM approximation
all_folders = Folders()
all_folders.update(self.folder)
all_folders.update(self.SCM_approximation.folder)
all_folders.pop("testing_set") # this is required only in the error/speedup analysis
all_folders.pop("error_analysis") # this is required only in the error analysis
all_folders.pop("speedup_analysis") # this is required only in the speedup analysis
at_least_one_folder_created = all_folders.create()
if not at_least_one_folder_created:
return False # offline construction should be skipped, since data are already available
else:
self.SCM_approximation.init("offline")
return True # offline construction should be carried out
def _offline(self):
print(TextBox("SCM offline phase begins", fill="="))
print("")
# Compute the bounding box \mathcal{B}
self.compute_bounding_box()
print("")
# Arbitrarily start from the first parameter in the training set
self.SCM_approximation.set_mu(self.training_set[0])
relative_error_estimator_max = 2.*self.tol
while self.SCM_approximation.N < self.Nmax and relative_error_estimator_max >= self.tol:
print(TextLine("SCM N = " + str(self.SCM_approximation.N), fill="~"))
# Store the greedy parameter
self.store_greedy_selected_parameters()
# Evaluate the coercivity constant
print("evaluate the stability factor for mu =", self.SCM_approximation.mu)
(alpha, eigenvector) = self.SCM_approximation.evaluate_stability_factor()
print("stability factor =", alpha)
# Update data structures related to upper bound vectors
UB_vector = self.compute_UB_vector(eigenvector)
self.update_UB_vectors(UB_vector)
# Prepare for next iteration
print("find next mu")
(error_estimator_max, relative_error_estimator_max) = self.greedy()
print("maximum SCM error estimator =", error_estimator_max)
print("maximum SCM relative error estimator =", relative_error_estimator_max)
print("")
print(TextBox("SCM offline phase ends", fill="="))
print("")
# Finalize data structures required after the offline phase
def _finalize_offline(self):
self.SCM_approximation.init("online")
# Compute the bounding box \mathcal{B}
def compute_bounding_box(self):
# Resize the bounding box storage
Q = self.SCM_approximation.truth_problem.Q["a"]
for q in range(Q):
# Compute the minimum eigenvalue
minimum_eigenvalue_calculator = ParametrizedCoercivityConstantEigenProblem(self.SCM_approximation.truth_problem, ("a", q), False, "smallest", self.bounding_box_minimum_eigensolver_parameters, self.folder_prefix)
minimum_eigenvalue_calculator.init()
(self.SCM_approximation.B_min[q], _) = minimum_eigenvalue_calculator.solve()
print("B_min[" + str(q) + "] = " + str(self.SCM_approximation.B_min[q]))
# Compute the maximum eigenvalue
maximum_eigenvalue_calculator = ParametrizedCoercivityConstantEigenProblem(self.SCM_approximation.truth_problem, ("a", q), False, "largest", self.bounding_box_maximum_eigensolver_parameters, self.folder_prefix)
maximum_eigenvalue_calculator.init()
(self.SCM_approximation.B_max[q], _) = maximum_eigenvalue_calculator.solve()
print("B_max[" + str(q) + "] = " + str(self.SCM_approximation.B_max[q]))
# Save to file
self.SCM_approximation.B_min.save(self.SCM_approximation.folder["reduced_operators"], "B_min")
self.SCM_approximation.B_max.save(self.SCM_approximation.folder["reduced_operators"], "B_max")
# Store the greedy parameter
def store_greedy_selected_parameters(self):
mu = self.SCM_approximation.mu
self.SCM_approximation.greedy_selected_parameters.append(mu)
self.SCM_approximation.N = len(self.SCM_approximation.greedy_selected_parameters)
# Save to file
self.SCM_approximation.greedy_selected_parameters.save(self.SCM_approximation.folder["reduced_operators"], "greedy_selected_parameters")
# Compute the ratio between a_q(u,u) and s(u,u), for all q in vec
def compute_UB_vector(self, u):
Q = self.SCM_approximation.truth_problem.Q["a"]
inner_product = self.SCM_approximation.truth_problem.inner_product[0]
UB_vector = OnlineVector(Q)
norm_S_squared = transpose(u)*inner_product*u
for q in range(Q):
A_q = self.SCM_approximation.truth_problem.operator["a"][q]
UB_vector[q] = (transpose(u)*A_q*u)/norm_S_squared
return UB_vector
def update_UB_vectors(self, UB_vector):
self.SCM_approximation.UB_vectors.append(UB_vector)
self.SCM_approximation.UB_vectors.save(self.SCM_approximation.folder["reduced_operators"], "UB_vectors")
# Choose the next parameter in the offline stage in a greedy fashion
def greedy(self):
def solve_and_estimate_error(mu):
self.SCM_approximation.set_mu(mu)
LB = self.SCM_approximation.get_stability_factor_lower_bound()
UB = self.SCM_approximation.get_stability_factor_upper_bound()
error_estimator = (UB - LB)/UB
if LB/UB < 0 and not isclose(LB/UB, 0.): # if LB/UB << 0
print("SCM warning at mu = " + str(mu) + ": LB = " + str(LB) + " < 0")
if LB/UB > 1 and not isclose(LB/UB, 1.): # if LB/UB >> 1
print("SCM warning at mu = " + str(mu) + ": LB = " + str(LB) + " > UB = " + str(UB))
return error_estimator
(error_estimator_max, error_estimator_argmax) = self.training_set.max(solve_and_estimate_error)
self.SCM_approximation.set_mu(self.training_set[error_estimator_argmax])
self.greedy_error_estimators.append(error_estimator_max)
self.greedy_error_estimators.save(self.folder["post_processing"], "error_estimator_max")
return (error_estimator_max, error_estimator_max/self.greedy_error_estimators[0])
# Initialize data structures required for the error analysis phase
def _init_error_analysis(self, **kwargs):
# Initialize the exact coercivity constant object
self.SCM_approximation.exact_coercivity_constant_calculator.init()
# Initialize reduced order data structures in the SCM online problem
self.SCM_approximation.init("online")
# Compute the error of the scm approximation with respect to the
# exact coercivity over the testing set
def error_analysis(self, N_generator=None, filename=None, **kwargs):
assert len(kwargs) == 0 # not used in this method
self._init_error_analysis(**kwargs)
self._error_analysis(N_generator, filename, **kwargs)
self._finalize_error_analysis(**kwargs)
def _error_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator(n):
return n
N = self.SCM_approximation.N
print(TextBox("SCM error analysis begins", fill="="))
print("")
error_analysis_table = ErrorAnalysisTable(self.testing_set)
error_analysis_table.set_Nmax(N)
error_analysis_table.add_column("normalized_error", group_name="scm", operations=("min", "mean", "max"))
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine("SCM " + str(mu_index), fill="~"))
self.SCM_approximation.set_mu(mu)
(exact, _) = self.SCM_approximation.evaluate_stability_factor()
for n in range(1, N + 1): # n = 1, ... N
n_arg = N_generator(n)
if n_arg is not None:
LB = self.SCM_approximation.get_stability_factor_lower_bound(n_arg)
UB = self.SCM_approximation.get_stability_factor_upper_bound(n_arg)
if LB/UB < 0 and not isclose(LB/UB, 0.): # if LB/UB << 0
print("SCM warning at mu = " + str(mu) + ": LB = " + str(LB) + " < 0")
if LB/UB > 1 and not isclose(LB/UB, 1.): # if LB/UB >> 1
print("SCM warning at mu = " + str(mu) + ": LB = " + str(LB) + " > UB = " + str(UB))
if LB/exact > 1 and not isclose(LB/exact, 1.): # if LB/exact >> 1
print("SCM warning at mu = " + str(mu) + ": LB = " + str(LB) + " > exact =" + str(exact))
error_analysis_table["normalized_error", n, mu_index] = (exact - LB)/UB
else:
error_analysis_table["normalized_error", n, mu_index] = NotImplemented
# Print
print("")
print(error_analysis_table)
print("")
print(TextBox("SCM error analysis ends", fill="="))
print("")
# Export error analysis table
error_analysis_table.save(self.folder["error_analysis"], "error_analysis" if filename is None else filename)
# Compute the speedup of the scm approximation with respect to the
# exact coercivity over the testing set
def speedup_analysis(self, N_generator=None, filename=None, **kwargs):
assert len(kwargs) == 0 # not used in this method
self._init_speedup_analysis(**kwargs)
self._speedup_analysis(N_generator, filename, **kwargs)
self._finalize_speedup_analysis(**kwargs)
# Initialize data structures required for the speedup analysis phase
def _init_speedup_analysis(self, **kwargs):
# Make sure to clean up snapshot cache to ensure that parametrized
# expression evaluation is actually carried out
self.SCM_approximation._alpha_LB_cache.clear()
self.SCM_approximation._alpha_UB_cache.clear()
self.SCM_approximation.exact_coercivity_constant_calculator._eigenvalue_cache.clear()
self.SCM_approximation.exact_coercivity_constant_calculator._eigenvector_cache.clear()
def _speedup_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator(n):
return n
N = self.SCM_approximation.N
print(TextBox("SCM speedup analysis begins", fill="="))
print("")
speedup_analysis_table = SpeedupAnalysisTable(self.testing_set)
speedup_analysis_table.set_Nmax(N)
speedup_analysis_table.add_column("speedup", group_name="speedup", operations=("min", "mean", "max"))
exact_timer = Timer("parallel")
SCM_timer = Timer("serial")
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine("SCM " + str(mu_index), fill="~"))
self.SCM_approximation.set_mu(mu)
exact_timer.start()
self.SCM_approximation.evaluate_stability_factor()
elapsed_exact = exact_timer.stop()
for n in range(1, N + 1): # n = 1, ... N
n_arg = N_generator(n)
if n_arg is not None:
SCM_timer.start()
self.SCM_approximation.get_stability_factor_lower_bound(n_arg)
self.SCM_approximation.get_stability_factor_upper_bound(n_arg)
elapsed_SCM = SCM_timer.stop()
speedup_analysis_table["speedup", n, mu_index] = elapsed_exact/elapsed_SCM
else:
speedup_analysis_table["speedup", n, mu_index] = NotImplemented
# Print
print("")
print(speedup_analysis_table)
print("")
print(TextBox("SCM speedup analysis ends", fill="="))
print("")
# Export speedup analysis table
speedup_analysis_table.save(self.folder["speedup_analysis"], "speedup_analysis" if filename is None else filename)
class RBReduction_Class(DifferentialProblemReductionMethod_DerivedClass):
"""
The folders used to store the snapshots and for the post processing data, the parameters for the greedy algorithm and the error estimator evaluations are initialized.
:param truth_problem: class of the truth problem to be solved.
:return: reduced RB class.
"""
def __init__(self, truth_problem, **kwargs):
# Call the parent initialization
DifferentialProblemReductionMethod_DerivedClass.__init__(
self, truth_problem, **kwargs)
# Declare a GS object
self.GS = None # GramSchmidt (for problems with one component) or dict of GramSchmidt (for problem with several components)
# I/O
self.folder["snapshots"] = os.path.join(self.folder_prefix,
"snapshots")
self.folder["post_processing"] = os.path.join(
self.folder_prefix, "post_processing")
self.greedy_selected_parameters = GreedySelectedParametersList()
self.greedy_error_estimators = GreedyErrorEstimatorsList()
self.label = "RB"
def _init_offline(self):
# Call parent to initialize inner product and reduced problem
output = DifferentialProblemReductionMethod_DerivedClass._init_offline(
self)
# Declare a new GS for each basis component
if len(self.truth_problem.components) > 1:
self.GS = dict()
for component in self.truth_problem.components:
assert len(
self.truth_problem.inner_product[component]) == 1
inner_product = self.truth_problem.inner_product[
component][0]
self.GS[component] = GramSchmidt(inner_product)
else:
assert len(self.truth_problem.inner_product) == 1
inner_product = self.truth_problem.inner_product[0]
self.GS = GramSchmidt(inner_product)
# The current value of mu may have been already used when computing lifting functions.
# If so, we do not want to use that value again at the first greedy iteration, because
# for steady linear problems with only one paremtrized BC the resulting first snapshot
# would have been already stored in the basis, being exactly equal to the lifting.
# To this end, we arbitrarily change the current value of mu to the first parameter
# in the training set.
if output: # do not bother changing current mu if offline stage has been already completed
need_to_change_mu = False
if len(self.truth_problem.components) > 1:
for component in self.truth_problem.components:
if self.reduced_problem.dirichlet_bc[
component] and not self.reduced_problem.dirichlet_bc_are_homogeneous[
component]:
need_to_change_mu = True
break
else:
if self.reduced_problem.dirichlet_bc and not self.reduced_problem.dirichlet_bc_are_homogeneous:
need_to_change_mu = True
if (need_to_change_mu and len(
self.truth_problem.mu
) > 0 # there is not much we can change in the trivial case without any parameter!
):
new_mu = self.training_set[0]
assert self.truth_problem.mu != new_mu
self.truth_problem.set_mu(new_mu)
# Return
return output
def offline(self):
"""
It performs the offline phase of the reduced order model.
:return: reduced_problem where all offline data are stored.
"""
need_to_do_offline_stage = self._init_offline()
if need_to_do_offline_stage:
self._offline()
self._finalize_offline()
return self.reduced_problem
def _offline(self):
print(
TextBox(self.truth_problem.name() + " " + self.label +
" offline phase begins",
fill="="))
print("")
iteration = 0
relative_error_estimator_max = 2. * self.tol
while self.reduced_problem.N < self.Nmax and relative_error_estimator_max >= self.tol:
print(TextLine("N = " + str(self.reduced_problem.N), fill="#"))
print("truth solve for mu =", self.truth_problem.mu)
snapshot = self.truth_problem.solve()
self.truth_problem.export_solution(self.folder["snapshots"],
"truth_" + str(iteration),
snapshot)
snapshot = self.postprocess_snapshot(snapshot, iteration)
print("update basis matrix")
self.update_basis_matrix(snapshot)
iteration += 1
print("build reduced operators")
self.reduced_problem.build_reduced_operators()
print("reduced order solve")
self.reduced_problem.solve()
print("build operators for error estimation")
self.reduced_problem.build_error_estimation_operators()
(absolute_error_estimator_max,
relative_error_estimator_max) = self.greedy()
print("maximum absolute error estimator over training set =",
absolute_error_estimator_max)
print("maximum relative error estimator over training set =",
relative_error_estimator_max)
print("")
print(
TextBox(self.truth_problem.name() + " " + self.label +
" offline phase ends",
fill="="))
print("")
def update_basis_matrix(self, snapshot):
"""
It updates basis matrix.
:param snapshot: last offline solution calculated.
"""
if len(self.truth_problem.components) > 1:
for component in self.truth_problem.components:
self.reduced_problem.basis_functions.enrich(
snapshot, component=component)
self.GS[component].apply(
self.reduced_problem.basis_functions[component],
self.reduced_problem.N_bc[component])
self.reduced_problem.N[component] += 1
self.reduced_problem.basis_functions.save(
self.reduced_problem.folder["basis"], "basis")
else:
self.reduced_problem.basis_functions.enrich(snapshot)
self.GS.apply(self.reduced_problem.basis_functions,
self.reduced_problem.N_bc)
self.reduced_problem.N += 1
self.reduced_problem.basis_functions.save(
self.reduced_problem.folder["basis"], "basis")
def greedy(self):
"""
It chooses the next parameter in the offline stage in a greedy fashion: wrapper with post processing of the result (in particular, set greedily selected parameter and save to file)
:return: max error estimator and the comparison with the first one calculated.
"""
(error_estimator_max, error_estimator_argmax) = self._greedy()
self.truth_problem.set_mu(
self.training_set[error_estimator_argmax])
self.greedy_selected_parameters.append(
self.training_set[error_estimator_argmax])
self.greedy_selected_parameters.save(
self.folder["post_processing"], "mu_greedy")
self.greedy_error_estimators.append(error_estimator_max)
self.greedy_error_estimators.save(self.folder["post_processing"],
"error_estimator_max")
return (error_estimator_max,
error_estimator_max / self.greedy_error_estimators[0])
def _greedy(self):
"""
It chooses the next parameter in the offline stage in a greedy fashion. Internal method.
:return: max error estimator and the respective parameter.
"""
# Print some additional information on the consistency of the reduced basis
print("absolute error for current mu =",
self.reduced_problem.compute_error())
print("absolute error estimator for current mu =",
self.reduced_problem.estimate_error())
# Carry out the actual greedy search
def solve_and_estimate_error(mu):
self.reduced_problem.set_mu(mu)
self.reduced_problem.solve()
error_estimator = self.reduced_problem.estimate_error()
log(
DEBUG, "Error estimator for mu = " + str(mu) + " is " +
str(error_estimator))
return error_estimator
print("find next mu")
return self.training_set.max(solve_and_estimate_error)
def error_analysis(self, N_generator=None, filename=None, **kwargs):
"""
It computes the error of the reduced order approximation with respect to the full order one over the testing set.
:param N: dimension of reduced problem.
"""
self._init_error_analysis(**kwargs)
self._error_analysis(N_generator, filename, **kwargs)
self._finalize_error_analysis(**kwargs)
def _error_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator(n):
return n
if "components" in kwargs:
components = kwargs["components"]
else:
components = self.truth_problem.components
N = self.reduced_problem.N
if isinstance(N, dict):
N = min(N.values())
print(
TextBox(self.truth_problem.name() + " " + self.label +
" error analysis begins",
fill="="))
print("")
error_analysis_table = ErrorAnalysisTable(self.testing_set)
error_analysis_table.set_Nmax(N)
if len(components) > 1:
all_components_string = "".join(components)
for component in components:
error_analysis_table.add_column("error_" + component,
group_name="solution_" +
component + "_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_error_" + component,
group_name="solution_" + component + "_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"error_" + all_components_string,
group_name="solution_" + all_components_string + "_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"error_estimator_" + all_components_string,
group_name="solution_" + all_components_string + "_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"effectivity_" + all_components_string,
group_name="solution_" + all_components_string + "_error",
operations=("min", "mean", "max"))
error_analysis_table.add_column(
"relative_error_" + all_components_string,
group_name="solution_" + all_components_string +
"_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_error_estimator_" + all_components_string,
group_name="solution_" + all_components_string +
"_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_effectivity_" + all_components_string,
group_name="solution_" + all_components_string +
"_relative_error",
operations=("min", "mean", "max"))
else:
component = components[0]
error_analysis_table.add_column("error_" + component,
group_name="solution_" +
component + "_error",
operations=("mean", "max"))
error_analysis_table.add_column("error_estimator_" + component,
group_name="solution_" +
component + "_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"effectivity_" + component,
group_name="solution_" + component + "_error",
operations=("min", "mean", "max"))
error_analysis_table.add_column("relative_error_" + component,
group_name="solution_" +
component + "_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_error_estimator_" + component,
group_name="solution_" + component + "_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column(
"relative_effectivity_" + component,
group_name="solution_" + component + "_relative_error",
operations=("min", "mean", "max"))
error_analysis_table.add_column("error_output",
group_name="output_error",
operations=("mean", "max"))
error_analysis_table.add_column("error_estimator_output",
group_name="output_error",
operations=("mean", "max"))
error_analysis_table.add_column("effectivity_output",
group_name="output_error",
operations=("min", "mean", "max"))
error_analysis_table.add_column("relative_error_output",
group_name="output_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column("relative_error_estimator_output",
group_name="output_relative_error",
operations=("mean", "max"))
error_analysis_table.add_column("relative_effectivity_output",
group_name="output_relative_error",
operations=("min", "mean", "max"))
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine(str(mu_index), fill="#"))
self.reduced_problem.set_mu(mu)
for n in range(1, N + 1): # n = 1, ... N
n_arg = N_generator(n)
if n_arg is not None:
self.reduced_problem.solve(n_arg, **kwargs)
error = self.reduced_problem.compute_error(**kwargs)
if len(components) > 1:
error[all_components_string] = sqrt(
sum([
error[component]**2
for component in components
]))
error_estimator = self.reduced_problem.estimate_error()
relative_error = self.reduced_problem.compute_relative_error(
**kwargs)
if len(components) > 1:
relative_error[all_components_string] = sqrt(
sum([
relative_error[component]**2
for component in components
]))
relative_error_estimator = self.reduced_problem.estimate_relative_error(
)
self.reduced_problem.compute_output()
error_output = self.reduced_problem.compute_error_output(
**kwargs)
error_output_estimator = self.reduced_problem.estimate_error_output(
)
relative_error_output = self.reduced_problem.compute_relative_error_output(
**kwargs)
relative_error_output_estimator = self.reduced_problem.estimate_relative_error_output(
)
else:
if len(components) > 1:
error = {
component: NotImplemented
for component in components
}
error[all_components_string] = NotImplemented
else:
error = NotImplemented
error_estimator = NotImplemented
if len(components) > 1:
relative_error = {
component: NotImplemented
for component in components
}
relative_error[
all_components_string] = NotImplemented
else:
relative_error = NotImplemented
relative_error_estimator = NotImplemented
error_output = NotImplemented
error_output_estimator = NotImplemented
relative_error_output = NotImplemented
relative_error_output_estimator = NotImplemented
if len(components) > 1:
for component in components:
error_analysis_table["error_" + component, n,
mu_index] = error[component]
error_analysis_table[
"relative_error_" + component, n,
mu_index] = relative_error[component]
error_analysis_table[
"error_" + all_components_string, n,
mu_index] = error[all_components_string]
error_analysis_table["error_estimator_" +
all_components_string, n,
mu_index] = error_estimator
error_analysis_table[
"effectivity_" + all_components_string, n,
mu_index] = error_analysis_table[
"error_estimator_" + all_components_string, n,
mu_index] / error_analysis_table[
"error_" + all_components_string, n,
mu_index]
error_analysis_table[
"relative_error_" + all_components_string, n,
mu_index] = relative_error[all_components_string]
error_analysis_table[
"relative_error_estimator_" +
all_components_string, n,
mu_index] = relative_error_estimator
error_analysis_table[
"relative_effectivity_" + all_components_string, n,
mu_index] = error_analysis_table[
"relative_error_estimator_" +
all_components_string, n,
mu_index] / error_analysis_table[
"relative_error_" + all_components_string,
n, mu_index]
else:
component = components[0]
error_analysis_table["error_" + component, n,
mu_index] = error
error_analysis_table["error_estimator_" + component, n,
mu_index] = error_estimator
error_analysis_table[
"effectivity_" + component, n,
mu_index] = error_analysis_table[
"error_estimator_" + component, n,
mu_index] / error_analysis_table["error_" +
component, n,
mu_index]
error_analysis_table["relative_error_" + component, n,
mu_index] = relative_error
error_analysis_table[
"relative_error_estimator_" + component, n,
mu_index] = relative_error_estimator
error_analysis_table[
"relative_effectivity_" + component, n,
mu_index] = error_analysis_table[
"relative_error_estimator_" + component, n,
mu_index] / error_analysis_table[
"relative_error_" + component, n, mu_index]
error_analysis_table["error_output", n,
mu_index] = error_output
error_analysis_table["error_estimator_output", n,
mu_index] = error_output_estimator
error_analysis_table["effectivity_output", n,
mu_index] = error_analysis_table[
"error_estimator_output", n,
mu_index] / error_analysis_table[
"error_output", n, mu_index]
error_analysis_table["relative_error_output", n,
mu_index] = relative_error_output
error_analysis_table[
"relative_error_estimator_output", n,
mu_index] = relative_error_output_estimator
error_analysis_table[
"relative_effectivity_output", n,
mu_index] = error_analysis_table[
"relative_error_estimator_output", n,
mu_index] / error_analysis_table[
"relative_error_output", n, mu_index]
# Print
print("")
print(error_analysis_table)
print("")
print(
TextBox(self.truth_problem.name() + " " + self.label +
" error analysis ends",
fill="="))
print("")
# Export error analysis table
error_analysis_table.save(
self.folder["error_analysis"],
"error_analysis" if filename is None else filename)
def speedup_analysis(self, N_generator=None, filename=None, **kwargs):
"""
It computes the speedup of the reduced order approximation with respect to the full order one over the testing set.
:param N: dimension of the reduced problem.
"""
self._init_speedup_analysis(**kwargs)
self._speedup_analysis(N_generator, filename, **kwargs)
self._finalize_speedup_analysis(**kwargs)
def _speedup_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator(n):
return n
N = self.reduced_problem.N
if isinstance(N, dict):
N = min(N.values())
print(
TextBox(self.truth_problem.name() + " " + self.label +
" speedup analysis begins",
fill="="))
print("")
speedup_analysis_table = SpeedupAnalysisTable(self.testing_set)
speedup_analysis_table.set_Nmax(N)
speedup_analysis_table.add_column("speedup_solve",
group_name="speedup_solve",
operations=("min", "mean",
"max"))
speedup_analysis_table.add_column(
"speedup_solve_and_estimate_error",
group_name="speedup_solve_and_estimate_error",
operations=("min", "mean", "max"))
speedup_analysis_table.add_column(
"speedup_solve_and_estimate_relative_error",
group_name="speedup_solve_and_estimate_relative_error",
operations=("min", "mean", "max"))
speedup_analysis_table.add_column("speedup_output",
group_name="speedup_output",
operations=("min", "mean",
"max"))
speedup_analysis_table.add_column(
"speedup_output_and_estimate_error_output",
group_name="speedup_output_and_estimate_error_output",
operations=("min", "mean", "max"))
speedup_analysis_table.add_column(
"speedup_output_and_estimate_relative_error_output",
group_name="speedup_output_and_estimate_relative_error_output",
operations=("min", "mean", "max"))
truth_timer = Timer("parallel")
reduced_timer = Timer("serial")
for (mu_index, mu) in enumerate(self.testing_set):
print(TextLine(str(mu_index), fill="#"))
self.reduced_problem.set_mu(mu)
truth_timer.start()
self.truth_problem.solve(**kwargs)
elapsed_truth_solve = truth_timer.stop()
truth_timer.start()
self.truth_problem.compute_output()
elapsed_truth_output = truth_timer.stop()
for n in range(1, N + 1): # n = 1, ... N
n_arg = N_generator(n)
if n_arg is not None:
reduced_timer.start()
solution = self.reduced_problem.solve(n_arg, **kwargs)
elapsed_reduced_solve = reduced_timer.stop()
truth_timer.start()
self.reduced_problem.compute_error(**kwargs)
elapsed_error = truth_timer.stop()
reduced_timer.start()
error_estimator = self.reduced_problem.estimate_error()
elapsed_error_estimator = reduced_timer.stop()
truth_timer.start()
self.reduced_problem.compute_relative_error(**kwargs)
elapsed_relative_error = truth_timer.stop()
reduced_timer.start()
relative_error_estimator = self.reduced_problem.estimate_relative_error(
)
elapsed_relative_error_estimator = reduced_timer.stop()
reduced_timer.start()
output = self.reduced_problem.compute_output()
elapsed_reduced_output = reduced_timer.stop()
truth_timer.start()
self.reduced_problem.compute_error_output(**kwargs)
elapsed_error_output = truth_timer.stop()
reduced_timer.start()
error_estimator_output = self.reduced_problem.estimate_error_output(
)
elapsed_error_estimator_output = reduced_timer.stop()
truth_timer.start()
self.reduced_problem.compute_relative_error_output(
**kwargs)
elapsed_relative_error_output = truth_timer.stop()
reduced_timer.start()
relative_error_estimator_output = self.reduced_problem.estimate_relative_error_output(
)
elapsed_relative_error_estimator_output = reduced_timer.stop(
)
else:
solution = NotImplemented
error_estimator = NotImplemented
relative_error_estimator = NotImplemented
output = NotImplemented
error_estimator_output = NotImplemented
relative_error_estimator_output = NotImplemented
if solution is not NotImplemented:
speedup_analysis_table[
"speedup_solve", n,
mu_index] = elapsed_truth_solve / elapsed_reduced_solve
else:
speedup_analysis_table["speedup_solve", n,
mu_index] = NotImplemented
if error_estimator is not NotImplemented:
speedup_analysis_table[
"speedup_solve_and_estimate_error", n,
mu_index] = (elapsed_truth_solve + elapsed_error
) / (elapsed_reduced_solve +
elapsed_error_estimator)
else:
speedup_analysis_table[
"speedup_solve_and_estimate_error", n,
mu_index] = NotImplemented
if relative_error_estimator is not NotImplemented:
speedup_analysis_table[
"speedup_solve_and_estimate_relative_error", n,
mu_index] = (elapsed_truth_solve +
elapsed_relative_error) / (
elapsed_reduced_solve +
elapsed_relative_error_estimator)
else:
speedup_analysis_table[
"speedup_solve_and_estimate_relative_error", n,
mu_index] = NotImplemented
if output is not NotImplemented:
speedup_analysis_table[
"speedup_output", n,
mu_index] = (elapsed_truth_solve +
elapsed_truth_output) / (
elapsed_reduced_solve +
elapsed_reduced_output)
else:
speedup_analysis_table["speedup_output", n,
mu_index] = NotImplemented
if error_estimator_output is not NotImplemented:
assert output is not NotImplemented
speedup_analysis_table[
"speedup_output_and_estimate_error_output", n,
mu_index] = (elapsed_truth_solve +
elapsed_truth_output +
elapsed_error_output) / (
elapsed_reduced_solve +
elapsed_reduced_output +
elapsed_error_estimator_output)
else:
speedup_analysis_table[
"speedup_output_and_estimate_error_output", n,
mu_index] = NotImplemented
if relative_error_estimator_output is not NotImplemented:
assert output is not NotImplemented
speedup_analysis_table[
"speedup_output_and_estimate_relative_error_output",
n, mu_index] = (
elapsed_truth_solve + elapsed_truth_output +
elapsed_relative_error_output) / (
elapsed_reduced_solve +
elapsed_reduced_output +
elapsed_relative_error_estimator_output)
else:
speedup_analysis_table[
"speedup_output_and_estimate_relative_error_output",
n, mu_index] = NotImplemented
# Print
print("")
print(speedup_analysis_table)
print("")
print(
TextBox(self.truth_problem.name() + " " + self.label +
" speedup analysis ends",
fill="="))
print("")
# Export speedup analysis table
speedup_analysis_table.save(
self.folder["speedup_analysis"],
"speedup_analysis" if filename is None else filename)
