def speedup_analysis(self, N_generator=None, filename=None, **kwargs):
# Perform first the EIM speedup analysis, ...
if ("with_respect_to" not in
kwargs # otherwise we assume the user was interested in computing the speedup w.r.t.
# an exact parametrized functions,
# so he probably is not interested in the speedup analysis of EIM
and
("EIM" not in
kwargs # otherwise we assume the user was interested in computing the speedup for a fixed number of EIM basis
# functions, thus he has already carried out the speedup analysis of EIM
or ("EIM" in kwargs and kwargs["EIM"] is not None
) # shorthand to disable EIM error analysis
)):
EIM_N_generator = kwargs.pop("EIM_N_generator", None)
assert is_training_finished(self.truth_problem)
set_map_from_problem_to_training_status_off(self.truth_problem)
for (coeff,
EIM_reduction_coeff) in self.EIM_reductions.items():
EIM_reduction_coeff.speedup_analysis(
EIM_N_generator, filename)
set_map_from_problem_to_training_status_on(self.truth_problem)
# ..., and then call the parent method.
if "EIM" in kwargs and kwargs["EIM"] is None:
del kwargs["EIM"]
DifferentialProblemReductionMethod_DerivedClass.speedup_analysis(
self, N_generator, filename, **kwargs)
def _basic_form_on_truth_function_space(form_wrapper, tensor=None):
form = form_wrapper._form
form_name = form_wrapper.name()
mu = get_problem_from_parametrized_operator(form_wrapper).mu
if form_name not in form_on_truth_function_space__reduced_problem_to_truth_solution_cache:
visited = set()
truth_problems = list()
truth_problem_to_components = dict()
truth_problem_to_exact_truth_problem = dict()
truth_problem_to_truth_solution = dict()
reduced_problem_to_components = dict()
reduced_problem_to_truth_solution = dict()
# Look for terminals on truth mesh
for node in wrapping.form_iterator(form):
if node in visited:
continue
# ... problem solutions related to nonlinear terms
elif wrapping.is_problem_solution_or_problem_solution_component_type(
node):
if wrapping.is_problem_solution_or_problem_solution_component(
node):
(preprocessed_node, component, truth_solution
) = wrapping.solution_identify_component(node)
truth_problem = get_problem_from_solution(
truth_solution)
truth_problems.append(truth_problem)
# Store the solution
truth_problem_to_truth_solution[
truth_problem] = truth_solution
# Store the component
if truth_problem not in truth_problem_to_components:
truth_problem_to_components[truth_problem] = list()
truth_problem_to_components[truth_problem].append(
component)
else:
preprocessed_node = node
# Make sure to skip any parent solution related to this one
visited.add(node)
visited.add(preprocessed_node)
for parent_node in wrapping.solution_iterator(
preprocessed_node):
visited.add(parent_node)
# Cache the resulting dicts
form_on_truth_function_space__truth_problems_cache[
form_name] = truth_problems
form_on_truth_function_space__truth_problem_to_components_cache[
form_name] = truth_problem_to_components
form_on_truth_function_space__truth_problem_to_exact_truth_problem_cache[
form_name] = truth_problem_to_exact_truth_problem
form_on_truth_function_space__truth_problem_to_truth_solution_cache[
form_name] = truth_problem_to_truth_solution
form_on_truth_function_space__reduced_problem_to_components_cache[
form_name] = reduced_problem_to_components
form_on_truth_function_space__reduced_problem_to_truth_solution_cache[
form_name] = reduced_problem_to_truth_solution
# Extract from cache
truth_problems = form_on_truth_function_space__truth_problems_cache[
form_name]
truth_problem_to_components = form_on_truth_function_space__truth_problem_to_components_cache[
form_name]
truth_problem_to_exact_truth_problem = form_on_truth_function_space__truth_problem_to_exact_truth_problem_cache[
form_name]
truth_problem_to_truth_solution = form_on_truth_function_space__truth_problem_to_truth_solution_cache[
form_name]
reduced_problem_to_components = form_on_truth_function_space__reduced_problem_to_components_cache[
form_name]
reduced_problem_to_truth_solution = form_on_truth_function_space__reduced_problem_to_truth_solution_cache[
form_name]
# Get list of truth and reduced problems that need to be solved, possibly updating cache
required_truth_problems = list()
required_reduced_problems = list()
for truth_problem in truth_problems:
truth_problem_is_solving = hasattr(truth_problem, "_is_solving")
if is_training_started(truth_problem):
reduced_problem = get_reduced_problem_from_problem(
truth_problem)
reduced_problem_is_solving = hasattr(reduced_problem,
"_is_solving")
else:
reduced_problem = None
reduced_problem_is_solving = False
if not truth_problem_is_solving:
if is_training_finished(truth_problem):
# Store the component
if reduced_problem not in reduced_problem_to_components:
reduced_problem_to_components[
reduced_problem] = truth_problem_to_components[
truth_problem]
# Store the solution
if reduced_problem not in reduced_problem_to_truth_solution:
reduced_problem_to_truth_solution[
reduced_problem] = truth_problem_to_truth_solution[
truth_problem]
# Append to list of required reduced problems
required_reduced_problems.append(
(reduced_problem, reduced_problem_is_solving))
else:
if (hasattr(truth_problem,
"_apply_exact_evaluation_at_stages") and
not hasattr(truth_problem, "_apply_EIM_at_stages")
and not hasattr(truth_problem,
"_apply_DEIM_at_stages")):
# Init truth problem (if required), as it may not have been initialized
truth_problem.init()
# Append to list of required truth problems which are not currently solving
required_truth_problems.append(
(truth_problem, False, reduced_problem_is_solving))
else:
# Store the corresponding exact truth problem
if truth_problem not in truth_problem_to_exact_truth_problem:
exact_truth_problem = exact_problem(truth_problem)
truth_problem_to_exact_truth_problem[
truth_problem] = exact_truth_problem
# Init exact truth problem (if required), as it may not have been initialized
exact_truth_problem.init()
else:
exact_truth_problem = truth_problem_to_exact_truth_problem[
truth_problem]
# Store the component
if exact_truth_problem not in truth_problem_to_components:
truth_problem_to_components[
exact_truth_problem] = truth_problem_to_components[
truth_problem]
# Store the solution
if exact_truth_problem not in truth_problem_to_truth_solution:
truth_problem_to_truth_solution[
exact_truth_problem] = truth_problem_to_truth_solution[
truth_problem]
# Append to list of required truth problems which are not currently solving
required_truth_problems.append(
(exact_truth_problem, False,
reduced_problem_is_solving))
else:
assert not reduced_problem_is_solving
# Append to list of required truth problems which are currently solving
required_truth_problems.append((truth_problem, True, False))
# Solve truth problems (which have not been reduced yet) associated to nonlinear terms
truth_problem_to_truth_solution_copy = dict()
for (truth_problem, truth_problem_is_solving,
reduced_problem_is_solving) in required_truth_problems:
if not reduced_problem_is_solving:
# Solve (if necessary) ...
truth_problem.set_mu(mu)
if not truth_problem_is_solving:
log(
PROGRESS,
"In form_on_truth_function_space, requiring truth problem solve for problem "
+ truth_problem.name())
truth_problem.solve()
else:
log(
PROGRESS,
"In form_on_truth_function_space, loading current truth problem solution for problem "
+ truth_problem.name())
else:
reduced_problem = get_reduced_problem_from_problem(
truth_problem)
log(
PROGRESS,
"In form_on_truth_function_space, replacing current truth problem solution with reduced solution for problem "
+ reduced_problem.truth_problem.name())
# ... and assign to truth_solution
truth_solution = truth_problem_to_truth_solution[truth_problem]
truth_problem_to_truth_solution_copy[truth_problem] = backend.copy(
truth_solution)
for component in truth_problem_to_components[truth_problem]:
solution_to = _sub_from_tuple(truth_solution, component)
if not reduced_problem_is_solving:
solution_from = _sub_from_tuple(truth_problem._solution,
component)
else:
solution_from = _sub_from_tuple(
reduced_problem.basis_functions[:reduced_problem.
_solution.N] *
reduced_problem._solution, component)
backend.assign(solution_to, solution_from)
# Solve reduced problems associated to nonlinear terms
reduced_problem_to_truth_solution_copy = dict()
for (reduced_problem, is_solving) in required_reduced_problems:
# Solve (if necessary) ...
reduced_problem.set_mu(mu)
if not is_solving:
log(
PROGRESS,
"In form_on_truth_function_space, requiring reduced problem solve for problem "
+ reduced_problem.truth_problem.name())
reduced_problem.solve()
else:
log(
PROGRESS,
"In form_on_truth_function_space, loading current reduced problem solution for problem "
+ reduced_problem.truth_problem.name())
# ... and assign to truth_solution
truth_solution = reduced_problem_to_truth_solution[reduced_problem]
reduced_problem_to_truth_solution_copy[
reduced_problem] = backend.copy(truth_solution)
for component in reduced_problem_to_components[reduced_problem]:
solution_to = _sub_from_tuple(truth_solution, component)
solution_from = _sub_from_tuple(
reduced_problem.basis_functions[:reduced_problem._solution.
N] *
reduced_problem._solution, component)
backend.assign(solution_to, solution_from)
# Assemble
assembled_form = wrapping.assemble(form, tensor)
assembled_form.generator = form_wrapper # for I/O
form_rank = assembled_form.rank()
# Undo any side effect of truth problem solves
for (truth_problem, _, _) in required_truth_problems:
truth_solution = truth_problem_to_truth_solution[truth_problem]
truth_solution_copy = truth_problem_to_truth_solution_copy[
truth_problem]
for component in truth_problem_to_components[truth_problem]:
solution_to = _sub_from_tuple(truth_solution, component)
solution_from = _sub_from_tuple(truth_solution_copy, component)
backend.assign(solution_to, solution_from)
# Undo any side effect of reduced problem solves
for (reduced_problem, _) in required_reduced_problems:
truth_solution = reduced_problem_to_truth_solution[reduced_problem]
truth_solution_copy = reduced_problem_to_truth_solution_copy[
reduced_problem]
for component in reduced_problem_to_components[reduced_problem]:
solution_to = _sub_from_tuple(truth_solution, component)
solution_from = _sub_from_tuple(truth_solution_copy, component)
backend.assign(solution_to, solution_from)
# Return
return (assembled_form, form_rank)
def _basic_expression_on_reduced_mesh(expression_wrapper, at):
expression = expression_wrapper._expression
expression_name = expression_wrapper.name()
reduced_space = at.get_reduced_function_space()
mu = get_problem_from_parametrized_expression(expression_wrapper).mu
reduced_mesh = at.get_reduced_mesh()
if (expression_name, reduced_mesh
) not in expression_on_reduced_mesh__expression_cache:
visited = set()
replacements = dict()
truth_problems = list()
truth_problem_to_components = dict()
truth_problem_to_exact_truth_problem = dict()
truth_problem_to_reduced_mesh_solution = dict()
truth_problem_to_reduced_mesh_interpolator = dict()
reduced_problem_to_components = dict()
reduced_problem_to_reduced_mesh_solution = dict()
reduced_problem_to_reduced_basis_functions = dict()
# Look for terminals on truth mesh
for node in wrapping.expression_iterator(expression):
if node in visited:
continue
# ... problem solutions related to nonlinear terms
elif wrapping.is_problem_solution_or_problem_solution_component_type(
node):
if wrapping.is_problem_solution_or_problem_solution_component(
node):
(preprocessed_node, component, truth_solution
) = wrapping.solution_identify_component(node)
truth_problem = get_problem_from_solution(
truth_solution)
truth_problems.append(truth_problem)
# Store the component
if truth_problem not in truth_problem_to_components:
truth_problem_to_components[truth_problem] = list()
truth_problem_to_components[truth_problem].append(
component)
# Get the function space corresponding to preprocessed_node on the reduced mesh
auxiliary_reduced_V = at.get_auxiliary_reduced_function_space(
truth_problem, component)
# Define and store the replacement
if truth_problem not in truth_problem_to_reduced_mesh_solution:
truth_problem_to_reduced_mesh_solution[
truth_problem] = list()
replacements[preprocessed_node] = backend.Function(
auxiliary_reduced_V)
truth_problem_to_reduced_mesh_solution[
truth_problem].append(
replacements[preprocessed_node])
# Get interpolator on reduced mesh
if truth_problem not in truth_problem_to_reduced_mesh_interpolator:
truth_problem_to_reduced_mesh_interpolator[
truth_problem] = list()
truth_problem_to_reduced_mesh_interpolator[
truth_problem].append(
at.get_auxiliary_function_interpolator(
truth_problem, component))
else:
(
auxiliary_problem, component
) = wrapping.get_auxiliary_problem_for_non_parametrized_function(
node)
preprocessed_node = node
# Get the function space corresponding to preprocessed_node on the reduced mesh
auxiliary_reduced_V = at.get_auxiliary_reduced_function_space(
auxiliary_problem, component)
# Get interpolator on reduced mesh
auxiliary_truth_problem_to_reduced_mesh_interpolator = at.get_auxiliary_function_interpolator(
auxiliary_problem, component)
# Define and store the replacement
replacements[
preprocessed_node] = auxiliary_truth_problem_to_reduced_mesh_interpolator(
preprocessed_node)
# Make sure to skip any parent solution related to this one
visited.add(node)
visited.add(preprocessed_node)
for parent_node in wrapping.solution_iterator(
preprocessed_node):
visited.add(parent_node)
# ... geometric quantities
elif isinstance(node, GeometricQuantity):
replacements[node] = type(node)(reduced_mesh)
visited.add(node)
# ... and replace them
replaced_expression = wrapping.expression_replace(
expression, replacements)
# Cache the resulting dicts
expression_on_reduced_mesh__expression_cache[(
expression_name, reduced_mesh)] = replaced_expression
expression_on_reduced_mesh__truth_problems_cache[(
expression_name, reduced_mesh)] = truth_problems
expression_on_reduced_mesh__truth_problem_to_components_cache[(
expression_name, reduced_mesh)] = truth_problem_to_components
expression_on_reduced_mesh__truth_problem_to_exact_truth_problem_cache[
(expression_name,
reduced_mesh)] = truth_problem_to_exact_truth_problem
expression_on_reduced_mesh__truth_problem_to_reduced_mesh_solution_cache[
(expression_name,
reduced_mesh)] = truth_problem_to_reduced_mesh_solution
expression_on_reduced_mesh__truth_problem_to_reduced_mesh_interpolator_cache[
(expression_name,
reduced_mesh)] = truth_problem_to_reduced_mesh_interpolator
expression_on_reduced_mesh__reduced_problem_to_components_cache[(
expression_name, reduced_mesh)] = reduced_problem_to_components
expression_on_reduced_mesh__reduced_problem_to_reduced_mesh_solution_cache[
(expression_name,
reduced_mesh)] = reduced_problem_to_reduced_mesh_solution
expression_on_reduced_mesh__reduced_problem_to_reduced_basis_functions_cache[
(expression_name,
reduced_mesh)] = reduced_problem_to_reduced_basis_functions
# Extract from cache
replaced_expression = expression_on_reduced_mesh__expression_cache[(
expression_name, reduced_mesh)]
truth_problems = expression_on_reduced_mesh__truth_problems_cache[(
expression_name, reduced_mesh)]
truth_problem_to_components = expression_on_reduced_mesh__truth_problem_to_components_cache[
(expression_name, reduced_mesh)]
truth_problem_to_exact_truth_problem = expression_on_reduced_mesh__truth_problem_to_exact_truth_problem_cache[
(expression_name, reduced_mesh)]
truth_problem_to_reduced_mesh_solution = expression_on_reduced_mesh__truth_problem_to_reduced_mesh_solution_cache[
(expression_name, reduced_mesh)]
truth_problem_to_reduced_mesh_interpolator = expression_on_reduced_mesh__truth_problem_to_reduced_mesh_interpolator_cache[
(expression_name, reduced_mesh)]
reduced_problem_to_components = expression_on_reduced_mesh__reduced_problem_to_components_cache[
(expression_name, reduced_mesh)]
reduced_problem_to_reduced_mesh_solution = expression_on_reduced_mesh__reduced_problem_to_reduced_mesh_solution_cache[
(expression_name, reduced_mesh)]
reduced_problem_to_reduced_basis_functions = expression_on_reduced_mesh__reduced_problem_to_reduced_basis_functions_cache[
(expression_name, reduced_mesh)]
# Get list of truth and reduced problems that need to be solved, possibly updating cache
required_truth_problems = list()
required_reduced_problems = list()
for truth_problem in truth_problems:
truth_problem_is_solving = hasattr(truth_problem, "_is_solving")
if is_training_started(truth_problem):
reduced_problem = get_reduced_problem_from_problem(
truth_problem)
reduced_problem_is_solving = hasattr(reduced_problem,
"_is_solving")
else:
reduced_problem = None
reduced_problem_is_solving = False
if not truth_problem_is_solving:
if is_training_finished(truth_problem):
# Store the component
if reduced_problem not in reduced_problem_to_components:
reduced_problem_to_components[
reduced_problem] = truth_problem_to_components[
truth_problem]
# Store the replacement
if reduced_problem not in reduced_problem_to_reduced_mesh_solution:
reduced_problem_to_reduced_mesh_solution[
reduced_problem] = truth_problem_to_reduced_mesh_solution[
truth_problem]
# Get reduced problem basis functions on reduced mesh
if reduced_problem not in reduced_problem_to_reduced_basis_functions:
reduced_problem_to_reduced_basis_functions[
reduced_problem] = list()
for component in reduced_problem_to_components[
reduced_problem]:
reduced_problem_to_reduced_basis_functions[
reduced_problem].append(
at.get_auxiliary_basis_functions_matrix(
truth_problem, reduced_problem,
component))
# Append to list of required reduced problems
required_reduced_problems.append(
(reduced_problem, reduced_problem_is_solving))
else:
if (hasattr(truth_problem,
"_apply_exact_evaluation_at_stages") and
not hasattr(truth_problem, "_apply_EIM_at_stages")
and not hasattr(truth_problem,
"_apply_DEIM_at_stages")):
# Init truth problem (if required), as it may not have been initialized
truth_problem.init()
# Append to list of required truth problems which are not currently solving
required_truth_problems.append(
(truth_problem, False, reduced_problem_is_solving))
else:
# Store the corresponding exact truth problem
if truth_problem not in truth_problem_to_exact_truth_problem:
exact_truth_problem = exact_problem(truth_problem)
truth_problem_to_exact_truth_problem[
truth_problem] = exact_truth_problem
# Init exact truth problem (if required), as it may not have been initialized
exact_truth_problem.init()
else:
exact_truth_problem = truth_problem_to_exact_truth_problem[
truth_problem]
# Store the component
if exact_truth_problem not in truth_problem_to_components:
truth_problem_to_components[
exact_truth_problem] = truth_problem_to_components[
truth_problem]
# Store the replacement
if exact_truth_problem not in truth_problem_to_reduced_mesh_solution:
truth_problem_to_reduced_mesh_solution[
exact_truth_problem] = truth_problem_to_reduced_mesh_solution[
truth_problem]
# Get interpolator on reduced mesh
if exact_truth_problem not in truth_problem_to_reduced_mesh_interpolator:
truth_problem_to_reduced_mesh_interpolator[
exact_truth_problem] = list()
for component in truth_problem_to_components[
exact_truth_problem]:
truth_problem_to_reduced_mesh_interpolator[
exact_truth_problem].append(
at.get_auxiliary_function_interpolator(
exact_truth_problem, component))
# Append to list of required truth problems which are not currently solving
required_truth_problems.append(
(exact_truth_problem, False,
reduced_problem_is_solving))
else:
assert not reduced_problem_is_solving
# Append to list of required truth problems which are currently solving
required_truth_problems.append((truth_problem, True, False))
# Solve truth problems (which have not been reduced yet) associated to nonlinear terms
for (truth_problem, truth_problem_is_solving,
reduced_problem_is_solving) in required_truth_problems:
if not reduced_problem_is_solving:
# Solve (if necessary) ...
truth_problem.set_mu(mu)
if not truth_problem_is_solving:
log(
PROGRESS,
"In expression_on_reduced_mesh, requiring truth problem solve for problem "
+ truth_problem.name())
truth_problem.solve()
else:
log(
PROGRESS,
"In expression_on_reduced_mesh, loading current truth problem solution for problem "
+ truth_problem.name())
else:
reduced_problem = get_reduced_problem_from_problem(
truth_problem)
log(
PROGRESS,
"In expression_on_reduced_mesh, replacing current truth problem solution with reduced solution for problem "
+ reduced_problem.truth_problem.name())
# ... and assign to reduced_mesh_solution
for (reduced_mesh_solution, reduced_mesh_interpolator) in zip(
truth_problem_to_reduced_mesh_solution[truth_problem],
truth_problem_to_reduced_mesh_interpolator[truth_problem]):
solution_to = reduced_mesh_solution
if not reduced_problem_is_solving:
solution_from = reduced_mesh_interpolator(
truth_problem._solution)
else:
solution_from = reduced_mesh_interpolator(
reduced_problem.basis_functions[:reduced_problem.
_solution.N] *
reduced_problem._solution)
backend.assign(solution_to, solution_from)
# Solve reduced problems associated to nonlinear terms
for (reduced_problem, is_solving) in required_reduced_problems:
# Solve (if necessary) ...
reduced_problem.set_mu(mu)
if not is_solving:
log(
PROGRESS,
"In expression_on_reduced_mesh, requiring reduced problem solve for problem "
+ reduced_problem.truth_problem.name())
reduced_problem.solve()
else:
log(
PROGRESS,
"In expression_on_reduced_mesh, loading current reduced problem solution for problem "
+ reduced_problem.truth_problem.name())
# ... and assign to reduced_mesh_solution
for (reduced_mesh_solution, reduced_basis_functions) in zip(
reduced_problem_to_reduced_mesh_solution[reduced_problem],
reduced_problem_to_reduced_basis_functions[reduced_problem]
):
solution_to = reduced_mesh_solution
solution_from_N = OnlineSizeDict()
for c, v in reduced_problem._solution.N.items():
if c in reduced_basis_functions._components_name:
solution_from_N[c] = v
solution_from = online_backend.OnlineFunction(solution_from_N)
online_backend.online_assign(solution_from,
reduced_problem._solution)
solution_from = reduced_basis_functions[:solution_from_N] * solution_from
backend.assign(solution_to, solution_from)
# Evaluate and return
reduced_function = backend.Function(reduced_space)
wrapping.evaluate_expression(expression, reduced_function,
replaced_expression)
return reduced_function
def _basic_form_on_reduced_function_space(form_wrapper, at):
form = form_wrapper._form
form_name = form_wrapper.name()
mu = get_problem_from_parametrized_operator(form_wrapper).mu
reduced_V = at.get_reduced_function_spaces()
reduced_subdomain_data = at.get_reduced_subdomain_data()
if (form_name,
reduced_V) not in form_on_reduced_function_space__form_cache:
visited = set()
replacements = dict()
truth_problems = list()
truth_problem_to_components = dict()
truth_problem_to_exact_truth_problem = dict()
truth_problem_to_reduced_mesh_solution = dict()
truth_problem_to_reduced_mesh_interpolator = dict()
reduced_problem_to_components = dict()
reduced_problem_to_reduced_mesh_solution = dict()
reduced_problem_to_reduced_basis_functions = dict()
# Look for terminals on truth mesh
for node in wrapping.form_iterator(form, "nodes"):
if node in visited:
continue
# ... test and trial functions
elif isinstance(node, Argument):
replacements[node] = wrapping.form_argument_replace(
node, reduced_V)
visited.add(node)
# ... problem solutions related to nonlinear terms
elif wrapping.is_problem_solution_or_problem_solution_component_type(
node):
if wrapping.is_problem_solution_or_problem_solution_component(
node):
(preprocessed_node, component, truth_solution
) = wrapping.solution_identify_component(node)
truth_problem = get_problem_from_solution(
truth_solution)
truth_problems.append(truth_problem)
# Store the component
if truth_problem not in truth_problem_to_components:
truth_problem_to_components[truth_problem] = list()
truth_problem_to_components[truth_problem].append(
component)
# Get the function space corresponding to preprocessed_node on the reduced mesh
auxiliary_reduced_V = at.get_auxiliary_reduced_function_space(
truth_problem, component)
# Define and store the replacement
if truth_problem not in truth_problem_to_reduced_mesh_solution:
truth_problem_to_reduced_mesh_solution[
truth_problem] = list()
replacements[preprocessed_node] = backend.Function(
auxiliary_reduced_V)
truth_problem_to_reduced_mesh_solution[
truth_problem].append(
replacements[preprocessed_node])
# Get interpolator on reduced mesh
if truth_problem not in truth_problem_to_reduced_mesh_interpolator:
truth_problem_to_reduced_mesh_interpolator[
truth_problem] = list()
truth_problem_to_reduced_mesh_interpolator[
truth_problem].append(
at.get_auxiliary_function_interpolator(
truth_problem, component))
else:
(
auxiliary_problem, component
) = wrapping.get_auxiliary_problem_for_non_parametrized_function(
node)
preprocessed_node = node
# Get the function space corresponding to preprocessed_node on the reduced mesh
auxiliary_reduced_V = at.get_auxiliary_reduced_function_space(
auxiliary_problem, component)
# Get interpolator on reduced mesh
auxiliary_truth_problem_to_reduced_mesh_interpolator = at.get_auxiliary_function_interpolator(
auxiliary_problem, component)
# Define and store the replacement
replacements[
preprocessed_node] = auxiliary_truth_problem_to_reduced_mesh_interpolator(
preprocessed_node)
# Make sure to skip any parent solution related to this one
visited.add(node)
visited.add(preprocessed_node)
for parent_node in wrapping.solution_iterator(
preprocessed_node):
visited.add(parent_node)
# ... geometric quantities
elif isinstance(node, GeometricQuantity):
if len(reduced_V) == 2:
assert reduced_V[0].mesh().ufl_domain(
) == reduced_V[1].mesh().ufl_domain()
replacements[node] = type(node)(reduced_V[0].mesh())
visited.add(node)
# ... and replace them
replaced_form = wrapping.form_replace(form, replacements, "nodes")
# Look for measures ...
if len(reduced_V) == 2:
assert reduced_V[0].mesh().ufl_domain() == reduced_V[1].mesh(
).ufl_domain()
measure_reduced_domain = reduced_V[0].mesh().ufl_domain()
replacements_measures = dict()
for integral in wrapping.form_iterator(replaced_form, "integrals"):
# Prepare measure for the new form (from firedrake/mg/ufl_utils.py)
integral_subdomain_data = integral.subdomain_data()
if integral_subdomain_data is not None:
integral_reduced_subdomain_data = reduced_subdomain_data[
integral_subdomain_data]
else:
integral_reduced_subdomain_data = None
measure = Measure(
integral.integral_type(),
domain=measure_reduced_domain,
subdomain_id=integral.subdomain_id(),
subdomain_data=integral_reduced_subdomain_data,
metadata=integral.metadata())
replacements_measures[integral.integrand(),
integral.integral_type(),
integral.subdomain_id()] = measure
# ... and replace them
replaced_form_with_replaced_measures = wrapping.form_replace(
replaced_form, replacements_measures, "measures")
# Cache the resulting dicts
form_on_reduced_function_space__form_cache[(
form_name, reduced_V)] = replaced_form_with_replaced_measures
form_on_reduced_function_space__truth_problems_cache[(
form_name, reduced_V)] = truth_problems
form_on_reduced_function_space__truth_problem_to_components_cache[(
form_name, reduced_V)] = truth_problem_to_components
form_on_reduced_function_space__truth_problem_to_exact_truth_problem_cache[
(form_name, reduced_V)] = truth_problem_to_exact_truth_problem
form_on_reduced_function_space__truth_problem_to_reduced_mesh_solution_cache[
(form_name,
reduced_V)] = truth_problem_to_reduced_mesh_solution
form_on_reduced_function_space__truth_problem_to_reduced_mesh_interpolator_cache[
(form_name,
reduced_V)] = truth_problem_to_reduced_mesh_interpolator
form_on_reduced_function_space__reduced_problem_to_components_cache[
(form_name, reduced_V)] = reduced_problem_to_components
form_on_reduced_function_space__reduced_problem_to_reduced_mesh_solution_cache[
(form_name,
reduced_V)] = reduced_problem_to_reduced_mesh_solution
form_on_reduced_function_space__reduced_problem_to_reduced_basis_functions_cache[
(form_name,
reduced_V)] = reduced_problem_to_reduced_basis_functions
# Extract from cache
replaced_form_with_replaced_measures = form_on_reduced_function_space__form_cache[
(form_name, reduced_V)]
truth_problems = form_on_reduced_function_space__truth_problems_cache[(
form_name, reduced_V)]
truth_problem_to_components = form_on_reduced_function_space__truth_problem_to_components_cache[
(form_name, reduced_V)]
truth_problem_to_exact_truth_problem = form_on_reduced_function_space__truth_problem_to_exact_truth_problem_cache[
(form_name, reduced_V)]
truth_problem_to_reduced_mesh_solution = form_on_reduced_function_space__truth_problem_to_reduced_mesh_solution_cache[
(form_name, reduced_V)]
truth_problem_to_reduced_mesh_interpolator = form_on_reduced_function_space__truth_problem_to_reduced_mesh_interpolator_cache[
(form_name, reduced_V)]
reduced_problem_to_components = form_on_reduced_function_space__reduced_problem_to_components_cache[
(form_name, reduced_V)]
reduced_problem_to_reduced_mesh_solution = form_on_reduced_function_space__reduced_problem_to_reduced_mesh_solution_cache[
(form_name, reduced_V)]
reduced_problem_to_reduced_basis_functions = form_on_reduced_function_space__reduced_problem_to_reduced_basis_functions_cache[
(form_name, reduced_V)]
# Get list of truth and reduced problems that need to be solved, possibly updating cache
required_truth_problems = list()
required_reduced_problems = list()
for truth_problem in truth_problems:
truth_problem_is_solving = hasattr(truth_problem, "_is_solving")
if is_training_started(truth_problem):
reduced_problem = get_reduced_problem_from_problem(
truth_problem)
reduced_problem_is_solving = hasattr(reduced_problem,
"_is_solving")
else:
reduced_problem = None
reduced_problem_is_solving = False
if not truth_problem_is_solving:
if is_training_finished(truth_problem):
# Store the component
if reduced_problem not in reduced_problem_to_components:
reduced_problem_to_components[
reduced_problem] = truth_problem_to_components[
truth_problem]
# Store the replacement
if reduced_problem not in reduced_problem_to_reduced_mesh_solution:
reduced_problem_to_reduced_mesh_solution[
reduced_problem] = truth_problem_to_reduced_mesh_solution[
truth_problem]
# Get reduced problem basis functions on reduced mesh
if reduced_problem not in reduced_problem_to_reduced_basis_functions:
reduced_problem_to_reduced_basis_functions[
reduced_problem] = list()
for component in reduced_problem_to_components[
reduced_problem]:
reduced_problem_to_reduced_basis_functions[
reduced_problem].append(
at.get_auxiliary_basis_functions_matrix(
truth_problem, reduced_problem,
component))
# Append to list of required reduced problems
required_reduced_problems.append(
(reduced_problem, reduced_problem_is_solving))
else:
if (hasattr(truth_problem,
"_apply_exact_evaluation_at_stages") and
not hasattr(truth_problem, "_apply_EIM_at_stages")
and not hasattr(truth_problem,
"_apply_DEIM_at_stages")):
# Init truth problem (if required), as it may not have been initialized
truth_problem.init()
# Append to list of required truth problems which are not currently solving
required_truth_problems.append(
(truth_problem, False, reduced_problem_is_solving))
else:
# Store the corresponding exact truth problem
if truth_problem not in truth_problem_to_exact_truth_problem:
exact_truth_problem = exact_problem(truth_problem)
truth_problem_to_exact_truth_problem[
truth_problem] = exact_truth_problem
# Init exact truth problem (if required), as it may not have been initialized
exact_truth_problem.init()
else:
exact_truth_problem = truth_problem_to_exact_truth_problem[
truth_problem]
# Store the component
if exact_truth_problem not in truth_problem_to_components:
truth_problem_to_components[
exact_truth_problem] = truth_problem_to_components[
truth_problem]
# Store the replacement
if exact_truth_problem not in truth_problem_to_reduced_mesh_solution:
truth_problem_to_reduced_mesh_solution[
exact_truth_problem] = truth_problem_to_reduced_mesh_solution[
truth_problem]
# Get interpolator on reduced mesh
if exact_truth_problem not in truth_problem_to_reduced_mesh_interpolator:
truth_problem_to_reduced_mesh_interpolator[
exact_truth_problem] = list()
for component in truth_problem_to_components[
exact_truth_problem]:
truth_problem_to_reduced_mesh_interpolator[
exact_truth_problem].append(
at.get_auxiliary_function_interpolator(
exact_truth_problem, component))
# Append to list of required truth problems which are not currently solving
required_truth_problems.append(
(exact_truth_problem, False,
reduced_problem_is_solving))
else:
assert not reduced_problem_is_solving
# Append to list of required truth problems which are currently solving
required_truth_problems.append((truth_problem, True, False))
# Solve truth problems (which have not been reduced yet) associated to nonlinear terms
for (truth_problem, truth_problem_is_solving,
reduced_problem_is_solving) in required_truth_problems:
if not reduced_problem_is_solving:
# Solve (if necessary) ...
truth_problem.set_mu(mu)
if not truth_problem_is_solving:
log(
PROGRESS,
"In form_on_reduced_function_space, requiring truth problem solve for problem "
+ truth_problem.name())
truth_problem.solve()
else:
log(
PROGRESS,
"In form_on_reduced_function_space, loading current truth problem solution for problem "
+ truth_problem.name())
else:
reduced_problem = get_reduced_problem_from_problem(
truth_problem)
log(
PROGRESS,
"In form_on_reduced_function_space, replacing current truth problem solution with reduced solution for problem "
+ reduced_problem.truth_problem.name())
# ... and assign to reduced_mesh_solution
for (reduced_mesh_solution, reduced_mesh_interpolator) in zip(
truth_problem_to_reduced_mesh_solution[truth_problem],
truth_problem_to_reduced_mesh_interpolator[truth_problem]):
solution_to = reduced_mesh_solution
if not reduced_problem_is_solving:
solution_from = reduced_mesh_interpolator(
truth_problem._solution)
else:
solution_from = reduced_mesh_interpolator(
reduced_problem.basis_functions[:reduced_problem.
_solution.N] *
reduced_problem._solution)
backend.assign(solution_to, solution_from)
# Solve reduced problems associated to nonlinear terms
for (reduced_problem, is_solving) in required_reduced_problems:
# Solve (if necessary) ...
reduced_problem.set_mu(mu)
if not is_solving:
log(
PROGRESS,
"In form_on_reduced_function_space, requiring reduced problem solve for problem "
+ reduced_problem.truth_problem.name())
reduced_problem.solve()
else:
log(
PROGRESS,
"In form_on_reduced_function_space, loading current reduced problem solution for problem "
+ reduced_problem.truth_problem.name())
# ... and assign to reduced_mesh_solution
for (reduced_mesh_solution, reduced_basis_functions) in zip(
reduced_problem_to_reduced_mesh_solution[reduced_problem],
reduced_problem_to_reduced_basis_functions[reduced_problem]
):
solution_to = reduced_mesh_solution
solution_from_N = OnlineSizeDict()
for c, v in reduced_problem._solution.N.items():
if c in reduced_basis_functions._components_name:
solution_from_N[c] = v
solution_from = online_backend.OnlineFunction(solution_from_N)
online_backend.online_assign(solution_from,
reduced_problem._solution)
solution_from = reduced_basis_functions[:solution_from_N] * solution_from
backend.assign(solution_to, solution_from)
# Assemble and return
assembled_replaced_form = wrapping.assemble(
replaced_form_with_replaced_measures)
form_rank = assembled_replaced_form.rank()
return (assembled_replaced_form, form_rank)
