def error_analysis(self, N_generator=None, filename=None, **kwargs):
if "components" in kwargs:
components = kwargs["components"]
else:
components = self.truth_problem.components
def solution_preprocess_setitem(list_over_time):
list_squared_over_time = [v**2 for v in list_over_time]
time_quadrature = TimeQuadrature((0., self.truth_problem.T), list_squared_over_time)
return sqrt(time_quadrature.integrate())
def output_preprocess_setitem(list_over_time):
time_quadrature = TimeQuadrature((0., self.truth_problem.T), list_over_time)
return time_quadrature.integrate()
if len(components) > 1:
all_components_string = ""
for component in components:
all_components_string += component
for column_prefix in ("error_", "relative_error_"):
ErrorAnalysisTable.preprocess_setitem(column_prefix + component, solution_preprocess_setitem)
for column_prefix in ("error_", "error_estimator_", "relative_error_", "relative_error_estimator_"):
ErrorAnalysisTable.preprocess_setitem(column_prefix + all_components_string, solution_preprocess_setitem)
else:
component = components[0]
for column_prefix in ("error_", "error_estimator_", "relative_error_", "relative_error_estimator_"):
ErrorAnalysisTable.preprocess_setitem(column_prefix + component, solution_preprocess_setitem)
for column in ("error_output", "error_estimator_output", "relative_error_output", "relative_error_estimator_output"):
ErrorAnalysisTable.preprocess_setitem(column, solution_preprocess_setitem)
DifferentialProblemReductionMethod_DerivedClass.error_analysis(self, N_generator, filename, **kwargs)
ErrorAnalysisTable.clear_setitem_preprocessing()
def _error_analysis(self, N_generator=None, filename=None, **kwargs):
if N_generator is None:
def N_generator():
N = self.EIM_approximation.N
for n in range(1, N + 1): # n = 1, ... N
yield n
def N_generator_max():
*_, Nmax = N_generator()
return Nmax
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_generator_max())
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 N_generator():
self.EIM_approximation.solve(n)
(_, 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)
# 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)
def error_analysis(self, N_generator=None, filename=None, **kwargs):
# Carry out primal error analysis ...
DifferentialProblemReductionMethod_DerivedClass.error_analysis(self, N_generator, filename, **kwargs)
# ... and then dual error analysis
ErrorAnalysisTable.suppress_group("output_error")
ErrorAnalysisTable.suppress_group("output_relative_error")
self.dual_reduction_method.error_analysis(N_generator, filename, **kwargs)
ErrorAnalysisTable.clear_suppressed_groups()
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)
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)
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())
for component in components:
error_analysis_table.add_column("error_" + component,
group_name="solution_" +
component,
operations=("mean", "max"))
error_analysis_table.add_column("relative_error_" + component,
group_name="solution_" +
component,
operations=("mean", "max"))
error_analysis_table.add_column("error_output",
group_name="output",
operations=("mean", "max"))
error_analysis_table.add_column("relative_error_output",
group_name="output",
operations=("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)
relative_error = self.reduced_problem.compute_relative_error(
**kwargs)
self.reduced_problem.compute_output()
error_output = self.reduced_problem.compute_error_output(
**kwargs)
relative_error_output = self.reduced_problem.compute_relative_error_output(
**kwargs)
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]
else:
component = components[0]
error_analysis_table["error_" + component, n_int,
mu_index] = error
error_analysis_table["relative_error_" + component,
n_int, mu_index] = relative_error
error_analysis_table["error_output", n_int,
mu_index] = error_output
error_analysis_table["relative_error_output", n_int,
mu_index] = relative_error_output
# 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 _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)
for component in components:
error_analysis_table.add_column("error_" + component, group_name="solution_" + component, operations=("mean", "max"))
error_analysis_table.add_column("relative_error_" + component, group_name="solution_" + component, operations=("mean", "max"))
error_analysis_table.add_column("error_output", group_name="output", operations=("mean", "max"))
error_analysis_table.add_column("relative_error_output", group_name="output", operations=("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)
relative_error = self.reduced_problem.compute_relative_error(**kwargs)
self.reduced_problem.compute_output()
error_output = self.reduced_problem.compute_error_output(**kwargs)
relative_error_output = self.reduced_problem.compute_relative_error_output(**kwargs)
else:
if len(components) > 1:
error = {component: NotImplemented for component in components}
relative_error = {component: NotImplemented for component in components}
else:
error = NotImplemented
relative_error = NotImplemented
error_output = NotImplemented
relative_error_output = 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]
else:
component = components[0]
error_analysis_table["error_" + component, n, mu_index] = error
error_analysis_table["relative_error_" + component, n, mu_index] = relative_error
error_analysis_table["error_output", n, mu_index] = error_output
error_analysis_table["relative_error_output", n, mu_index] = relative_error_output
# 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)