def solve(self):
print("solving mock reduced problem at mu =", self.mu)
assert not hasattr(self, "_is_solving")
self._is_solving = True
f = self.truth_problem.solve()
f_N = transpose(
self.basis_functions) * self.truth_problem.inner_product * f
# Return the reduced solution
self._solution = OnlineFunction(f_N)
delattr(self, "_is_solving")
return self._solution
def _compute_output(self, dual_N):
primal_solution = self.primal_reduced_problem._solution
primal_N = primal_solution.N
dual_solution = self._solution
assembled_output_correction_and_estimation_operator = dict()
assembled_output_correction_and_estimation_operator["a"] = sum(
product(
self.primal_reduced_problem.compute_theta("a"),
self.output_correction_and_estimation["a"]
[:dual_N, :primal_N]))
assembled_output_correction_and_estimation_operator["f"] = sum(
product(self.primal_reduced_problem.compute_theta("f"),
self.output_correction_and_estimation["f"][:dual_N]))
self._output = transpose(
dual_solution
) * assembled_output_correction_and_estimation_operator[
"f"] - transpose(
dual_solution
) * assembled_output_correction_and_estimation_operator[
"a"] * primal_solution
def get_residual_norm_squared(self):
residual_norm_squared_over_time = TimeSeries(
self._solution_over_time)
assert len(self._solution_over_time) == len(
self._solution_dot_over_time)
for (k, t) in enumerate(self._solution_over_time.stored_times()):
if not isclose(t, self.t0, self.dt / 2.):
# Set current time
self.set_time(t)
# Set current solution and solution_dot
assign(self._solution, self._solution_over_time[k])
assign(self._solution_dot, self._solution_dot_over_time[k])
# Compute the numerator of the error bound at the current time, first
# by computing residual of elliptic part
elliptic_residual_norm_squared = AbstractParabolicRBReducedProblem_Base.get_residual_norm_squared(
self)
# ... and then adding terms related to time derivative
N = self._solution.N
theta_m = self.compute_theta("m")
theta_a = self.compute_theta("a")
theta_f = self.compute_theta("f")
residual_norm_squared_over_time.append(
elliptic_residual_norm_squared + 2.0 *
(transpose(self._solution_dot) * sum(
product(
theta_m, self.error_estimation_operator[
"m", "f"][:N], theta_f))) + 2.0 *
(transpose(self._solution_dot) * sum(
product(
theta_m, self.error_estimation_operator[
"m", "a"][:N, :N], theta_a)) *
self._solution) +
(transpose(self._solution_dot) * sum(
product(
theta_m, self.error_estimation_operator[
"m", "m"][:N, :N], theta_m)) *
self._solution_dot))
else:
# Error estimator on initial condition does not use the residual
residual_norm_squared_over_time.append(0.)
return residual_norm_squared_over_time
def __add__(self, other):
from rbnics.backends import transpose
self_args = self._arg._args
other_args = other._arg._args
assert len(self_args) in (2, 3)
assert len(self_args) is len(other_args)
assert isinstance(self_args[0], AbstractBasisFunctionsMatrix)
assert isinstance(other_args[0], AbstractBasisFunctionsMatrix)
assert self_args[0] is other_args[0]
assert isinstance(self_args[1], AbstractParametrizedTensorFactory)
assert isinstance(other_args[1], AbstractParametrizedTensorFactory)
if len(self_args) is 2:
output = transpose(
self_args[0]) * (self_args[1] + other_args[1])
elif len(self_args) is 3:
assert isinstance(self_args[2], AbstractBasisFunctionsMatrix)
assert isinstance(other_args[2], AbstractBasisFunctionsMatrix)
assert self_args[2] is other_args[2]
output = transpose(self_args[0]) * (
self_args[1] + other_args[1]) * self_args[2]
else:
raise ValueError("Invalid argument")
assert isinstance(output, DelayedTranspose)
return DelayedTransposeWithArithmetic_Class(output)
def _compute_output(self, N):
assembled_operator = dict()
for term in ("m", "n", "g", "h"):
assert self.terms_order[term] in (0, 1, 2)
if self.terms_order[term] == 2:
assembled_operator[term] = sum(
product(self.compute_theta(term),
self.operator[term][:N, :N]))
elif self.terms_order[term] == 1:
assembled_operator[term] = sum(
product(self.compute_theta(term),
self.operator[term][:N]))
elif self.terms_order[term] == 0:
assembled_operator[term] = sum(
product(self.compute_theta(term), self.operator[term]))
else:
raise ValueError("Invalid value for order of term " + term)
self._output = (
0.5 * (transpose(self._solution) * assembled_operator["m"] *
self._solution) + 0.5 *
(transpose(self._solution) * assembled_operator["n"] *
self._solution) -
transpose(assembled_operator["g"]) * self._solution +
0.5 * assembled_operator["h"])
def get_residual_norm_squared(self):
residual_norm_squared_over_time = list() # of numbers
for (k, (solution, solution_dot)) in enumerate(
zip(self._solution_over_time, self._solution_dot_over_time)):
if k > 0:
# Set current time
self.set_time(k * self.dt)
# Set current solution and solution_dot
self._solution = solution
self._solution_dot = solution_dot
# Compute the numerator of the error bound at the current time, first
# by computing residual of elliptic part
elliptic_residual_norm_squared = ParabolicCoerciveRBReducedProblem_Base.get_residual_norm_squared(
self)
# ... and then adding terms related to time derivative
N = self._solution.N
theta_m = self.compute_theta("m")
theta_a = self.compute_theta("a")
theta_f = self.compute_theta("f")
residual_norm_squared_over_time.append(
elliptic_residual_norm_squared + 2.0 *
(transpose(self._solution_dot) * sum(
product(theta_m, self.error_estimation_operator[
"m", "f"][:N], theta_f))) + 2.0 *
(transpose(self._solution_dot) * sum(
product(
theta_m, self.error_estimation_operator["m", "a"]
[:N, :N], theta_a)) * self._solution) +
transpose(self._solution_dot) * sum(
product(
theta_m, self.error_estimation_operator["m", "m"]
[:N, :N], theta_m)) * self._solution_dot)
else:
# Error estimator on initial condition does not use the residual
residual_norm_squared_over_time.append(0.)
return residual_norm_squared_over_time
def assemble_operator(self, term, current_stage="online"):
assert current_stage in ("online", "offline")
if term.startswith("initial_condition"):
component = term.replace("initial_condition",
"").replace("_", "")
if current_stage == "online": # load from file
if component != "":
initial_condition = self.initial_condition[component]
else:
initial_condition = self.initial_condition
initial_condition.load(self.folder["reduced_operators"],
term)
elif current_stage == "offline":
if component != "":
truth_initial_condition = self.truth_problem.initial_condition[
component]
initial_condition = self.initial_condition[component]
truth_projection_inner_product = self.truth_problem.projection_inner_product[
component]
else:
truth_initial_condition = self.truth_problem.initial_condition
initial_condition = self.initial_condition
truth_projection_inner_product = self.truth_problem.projection_inner_product
assert len(
truth_projection_inner_product
) == 1 # the affine expansion storage contains only the inner product matrix
for (q, truth_initial_condition_q
) in enumerate(truth_initial_condition):
initial_condition[q] = transpose(
self.basis_functions
) * truth_projection_inner_product[
0] * truth_initial_condition_q
initial_condition.save(self.folder["reduced_operators"],
term)
else:
raise ValueError("Invalid stage in assemble_operator().")
# Assign
if component != "":
assert component in self.components
self.initial_condition[component] = initial_condition
else:
assert len(self.components) == 1
self.initial_condition = initial_condition
# Return
return initial_condition
else:
return ParametrizedReducedDifferentialProblem_DerivedClass.assemble_operator(
self, term, current_stage)
def get_residual_norm_squared(self):
N = self._solution.N
theta_a = self.compute_theta("a")
theta_b = self.compute_theta("b")
theta_bt = self.compute_theta("bt")
theta_f = self.compute_theta("f")
theta_g = self.compute_theta("g")
return (
sum(product(theta_f, self.error_estimation_operator["f", "f"], theta_f))
+ sum(product(theta_g, self.error_estimation_operator["g", "g"], theta_g))
+ 2.0*(transpose(self._solution)*sum(product(theta_a, self.error_estimation_operator["a", "f"][:N], theta_f)))
+ 2.0*(transpose(self._solution)*sum(product(theta_bt, self.error_estimation_operator["bt", "f"][:N], theta_f)))
+ 2.0*(transpose(self._solution)*sum(product(theta_b, self.error_estimation_operator["b", "g"][:N], theta_g)))
+ transpose(self._solution)*sum(product(theta_a, self.error_estimation_operator["a", "a"][:N, :N], theta_a))*self._solution
+ 2.0*(transpose(self._solution)*sum(product(theta_a, self.error_estimation_operator["a", "bt"][:N, :N], theta_bt))*self._solution)
+ transpose(self._solution)*sum(product(theta_bt, self.error_estimation_operator["bt", "bt"][:N, :N], theta_bt))*self._solution
+ transpose(self._solution)*sum(product(theta_b, self.error_estimation_operator["b", "b"][:N, :N], theta_b))*self._solution
)
def _compute_error(self, **kwargs):
"""
It computes the error of the reduced order approximation with respect to the full order one
for the current value of mu.
"""
(components, inner_product) = self._preprocess_compute_error_and_relative_error_kwargs(**kwargs)
# Storage
error = dict()
# Compute the error on the solution
if len(components) > 0:
N = self._solution.N
reduced_solution = self.basis_functions[:N] * self._solution
truth_solution = self.truth_problem._solution
error_function = truth_solution - reduced_solution
for component in components:
error_norm_squared_component = transpose(error_function) * inner_product[component] * error_function
assert error_norm_squared_component >= 0. or isclose(error_norm_squared_component, 0.)
error[component] = sqrt(abs(error_norm_squared_component))
# Simplify trivial case
if len(components) == 1:
error = error[components[0]]
#
return error
def _compute_relative_error(self, absolute_error, **kwargs):
"""
It computes the relative error of the reduced order approximation with respect to the full order one
for the current value of mu.
"""
(components, inner_product
) = self._preprocess_compute_error_and_relative_error_kwargs(**kwargs)
# Handle trivial case from compute_error
if len(components) == 1:
absolute_error_ = dict()
absolute_error_[components[0]] = absolute_error
absolute_error = absolute_error_
# Storage
relative_error = dict()
# Compute the relative error on the solution
if len(components) > 0:
truth_solution = self.truth_problem._solution
for component in components:
truth_solution_norm_squared_component = (
transpose(truth_solution) * inner_product[component] *
truth_solution)
assert truth_solution_norm_squared_component >= 0. or isclose(
truth_solution_norm_squared_component, 0.)
if truth_solution_norm_squared_component != 0.:
relative_error[component] = (
absolute_error[component] /
sqrt(abs(truth_solution_norm_squared_component)))
else:
if absolute_error[component] == 0.:
relative_error[component] = 0.
else:
relative_error[component] = float("NaN")
# Simplify trivial case
if len(components) == 1:
relative_error = relative_error[components[0]]
#
return relative_error
def assemble_error_estimation_operators(self, term, current_stage="online"):
if term[0].startswith("initial_condition") and term[1].startswith("initial_condition"):
component0 = term[0].replace("initial_condition", "").replace("_", "")
component1 = term[1].replace("initial_condition", "").replace("_", "")
assert current_stage in ("online", "offline")
if current_stage == "online": # load from file
assert (component0 != "") == (component1 != "")
if component0 != "":
assert component0 in self.components
assert component1 in self.components
self.initial_condition_product[component0, component1].load(self.folder["error_estimation"], "initial_condition_product_" + component0 + "_" + component1)
return self.initial_condition_product[component0, component1]
else:
assert len(self.components) == 1
self.initial_condition_product.load(self.folder["error_estimation"], "initial_condition_product")
return self.initial_condition_product
elif current_stage == "offline":
inner_product = self.truth_problem._combined_projection_inner_product
assert (component0 != "") == (component1 != "")
if component0 != "":
for q0 in range(self.Q_ic[component0]):
for q1 in range(self.Q_ic[component1]):
self.initial_condition_product[component0, component1][q0, q1] = transpose(self.truth_problem.initial_condition[component0][q0])*inner_product*self.truth_problem.initial_condition[component1][q1]
self.initial_condition_product[component0, component1].save(self.folder["error_estimation"], "initial_condition_product_" + component0 + "_" + component1)
return self.initial_condition_product[component0, component1]
else:
assert len(self.components) == 1
for q0 in range(self.Q_ic):
for q1 in range(self.Q_ic):
self.initial_condition_product[q0, q1] = transpose(self.truth_problem.initial_condition[q0])*inner_product*self.truth_problem.initial_condition[q1]
self.initial_condition_product.save(self.folder["error_estimation"], "initial_condition_product")
return self.initial_condition_product
else:
raise ValueError("Invalid stage in assemble_error_estimation_operators().")
else:
return ParametrizedReducedDifferentialProblem_DerivedClass.assemble_error_estimation_operators(self, term, current_stage)
def get_residual_norm_squared(self):
N = self._solution.N
theta_a = self.compute_theta("a")
theta_at = self.compute_theta("a*")
theta_c = self.compute_theta("c")
theta_ct = self.compute_theta("c*")
theta_m = self.compute_theta("m")
theta_n = self.compute_theta("n")
theta_f = self.compute_theta("f")
theta_g = self.compute_theta("g")
return (sum(product(theta_g, self.error_estimation_operator["g", "g"], theta_g))
+ sum(product(theta_f, self.error_estimation_operator["f", "f"], theta_f))
+ 2.0 * (transpose(self._solution)
* sum(product(theta_m, self.error_estimation_operator["m", "g"][:N], theta_g)))
+ 2.0 * (transpose(self._solution)
* sum(product(theta_at, self.error_estimation_operator["a*", "g"][:N], theta_g)))
+ 2.0 * (transpose(self._solution)
* sum(product(theta_a, self.error_estimation_operator["a", "f"][:N], theta_f)))
- 2.0 * (transpose(self._solution)
* sum(product(theta_c, self.error_estimation_operator["c", "f"][:N], theta_f)))
+ (transpose(self._solution)
* sum(product(theta_m, self.error_estimation_operator["m", "m"][:N, :N], theta_m))
* self._solution)
+ (transpose(self._solution)
* sum(product(theta_at, self.error_estimation_operator["a*", "a*"][:N, :N], theta_at))
* self._solution)
+ 2.0 * (transpose(self._solution)
* sum(product(theta_m, self.error_estimation_operator["m", "a*"][:N, :N], theta_at))
* self._solution)
+ (transpose(self._solution)
* sum(product(theta_n, self.error_estimation_operator["n", "n"][:N, :N], theta_n))
* self._solution)
+ (transpose(self._solution)
* sum(product(theta_ct, self.error_estimation_operator["c*", "c*"][:N, :N], theta_ct))
* self._solution)
- 2.0 * (transpose(self._solution)
* sum(product(theta_n, self.error_estimation_operator["n", "c*"][:N, :N], theta_ct))
* self._solution)
+ (transpose(self._solution)
* sum(product(theta_a, self.error_estimation_operator["a", "a"][:N, :N], theta_a))
* self._solution)
+ (transpose(self._solution)
* sum(product(theta_c, self.error_estimation_operator["c", "c"][:N, :N], theta_c))
* self._solution)
- 2.0 * (transpose(self._solution)
* sum(product(theta_a, self.error_estimation_operator["a", "c"][:N, :N], theta_c))
* self._solution)
)
def _offline(self):
# Change default online solve arguments during offline stage to use online stabilization
# instead of vanishing viscosity one (which will be prepared in a postprocessing stage)
self.reduced_problem._online_solve_default_kwargs[
"online_stabilization"] = True
self.reduced_problem._online_solve_default_kwargs[
"online_vanishing_viscosity"] = False
self.reduced_problem.OnlineSolveKwargs = OnlineSolveKwargsGenerator(
**self.reduced_problem._online_solve_default_kwargs)
# Call standard offline phase
EllipticCoerciveReductionMethod_DerivedClass._offline(self)
# Start vanishing viscosity postprocessing
print(
TextBox(
self.truth_problem.name() + " " + self.label +
" offline vanishing viscosity postprocessing phase begins",
fill="="))
print("")
# Prepare storage for copy of lifting basis functions matrix
lifting_basis_functions = BasisFunctionsMatrix(
self.truth_problem.V)
lifting_basis_functions.init(self.truth_problem.components)
# Copy current lifting basis functions to lifting_basis_functions
N_bc = self.reduced_problem.N_bc
for i in range(N_bc):
lifting_basis_functions.enrich(
self.reduced_problem.basis_functions[i])
# Prepare storage for unrotated basis functions matrix, without lifting
unrotated_basis_functions = BasisFunctionsMatrix(
self.truth_problem.V)
unrotated_basis_functions.init(self.truth_problem.components)
# Copy current basis functions (except lifting) to unrotated_basis_functions
N = self.reduced_problem.N
for i in range(N_bc, N):
unrotated_basis_functions.enrich(
self.reduced_problem.basis_functions[i])
# Prepare new storage for non-hierarchical basis functions matrix and
# corresponding affine expansions
self.reduced_problem.init(
"offline_vanishing_viscosity_postprocessing")
# Rotated basis functions matrix are not hierarchical, i.e. a different
# rotation will be applied for each basis size n.
for n in range(1, N + 1):
# Prepare storage for rotated basis functions matrix
rotated_basis_functions = BasisFunctionsMatrix(
self.truth_problem.V)
rotated_basis_functions.init(self.truth_problem.components)
# Rotate basis
print("rotate basis functions matrix for n =", n)
truth_operator_k = self.truth_problem.operator["k"]
truth_operator_m = self.truth_problem.operator["m"]
assert len(truth_operator_k) == 1
assert len(truth_operator_m) == 1
reduced_operator_k = (
transpose(unrotated_basis_functions[:n]) *
truth_operator_k[0] * unrotated_basis_functions[:n])
reduced_operator_m = (
transpose(unrotated_basis_functions[:n]) *
truth_operator_m[0] * unrotated_basis_functions[:n])
rotation_eigensolver = OnlineEigenSolver(
unrotated_basis_functions[:n], reduced_operator_k,
reduced_operator_m)
parameters = {
"problem_type": "hermitian",
"spectrum": "smallest real"
}
rotation_eigensolver.set_parameters(parameters)
rotation_eigensolver.solve()
# Store and save rotated basis
rotation_eigenvalues = ExportableList("text")
rotation_eigenvalues.extend([
rotation_eigensolver.get_eigenvalue(i)[0] for i in range(n)
])
for i in range(0, n):
print("lambda_" + str(i) + " = " +
str(rotation_eigenvalues[i]))
rotation_eigenvalues.save(self.folder["post_processing"],
"rotation_eigs_n=" + str(n))
for i in range(N_bc):
rotated_basis_functions.enrich(lifting_basis_functions[i])
for i in range(0, n):
(eigenvector_i,
_) = rotation_eigensolver.get_eigenvector(i)
rotated_basis_functions.enrich(
unrotated_basis_functions[:n] * eigenvector_i)
self.reduced_problem.basis_functions[:
n] = rotated_basis_functions
# Attach eigenvalues to the vanishing viscosity reduced operator
self.reduced_problem.vanishing_viscosity_eigenvalues.append(
rotation_eigenvalues)
# Save basis functions
self.reduced_problem.basis_functions.save(
self.reduced_problem.folder["basis"], "basis")
# Re-compute all reduced operators, since the basis functions have changed
print("build reduced operators")
self.reduced_problem.build_reduced_operators(
"offline_vanishing_viscosity_postprocessing")
# Clean up reduced solution and output cache, since the basis has changed
self.reduced_problem._solution_cache.clear()
self.reduced_problem._output_cache.clear()
print(
TextBox(
self.truth_problem.name() + " " + self.label +
" offline vanishing viscosity postprocessing phase ends",
fill="="))
print("")
# Restore default online solve arguments for online stage
self.reduced_problem._online_solve_default_kwargs[
"online_stabilization"] = False
self.reduced_problem._online_solve_default_kwargs[
"online_vanishing_viscosity"] = True
self.reduced_problem.OnlineSolveKwargs = OnlineSolveKwargsGenerator(
**self.reduced_problem._online_solve_default_kwargs)
def _compute_output(self):
self._output = transpose(self._solution) * sum(
product(self.compute_theta("s"), self.operator["s"]))
def _compute_output(self, N):
self._output = transpose(self._solution) * sum(product(self.compute_theta("f"), self.operator["f"][:N]))
def __init__(self, inner_product, basis_functions, N):
self.N = N
self.basis_functions = basis_functions
self.inner_product = inner_product
self.inner_product_N = transpose(
self.basis_functions) * self.inner_product * self.basis_functions
def assemble_operator(self, term, current_stage="online"):
if term == "vanishing_viscosity":
assert current_stage in ("online", "offline_vanishing_viscosity_postprocessing")
if current_stage == "online": # load from file
self.operator["vanishing_viscosity"].load(self.folder["reduced_operators"], "operator_vanishing_viscosity")
return self.operator["vanishing_viscosity"]
elif current_stage == "offline_vanishing_viscosity_postprocessing":
assert len(self.vanishing_viscosity_eigenvalues) is self.N
assert all([len(vanishing_viscosity_eigenvalues_n) is n + 1 for (n, vanishing_viscosity_eigenvalues_n) in enumerate(self.vanishing_viscosity_eigenvalues)])
print("build reduced vanishing viscosity operator")
for n in range(1, self.N + 1):
vanishing_viscosity_expansion = OnlineAffineExpansionStorage(1)
vanishing_viscosity_eigenvalues = self.vanishing_viscosity_eigenvalues[n - 1]
vanishing_viscosity_operator = OnlineMatrix(n, n)
n_min = int(n*self._N_threshold_min)
n_max = int(n*self._N_threshold_max)
lambda_n_min = vanishing_viscosity_eigenvalues[n_min]
lambda_n_max = vanishing_viscosity_eigenvalues[n_max]
for i in range(n):
lambda_i = vanishing_viscosity_eigenvalues[i]
if i < n_min:
viscosity_i = 0.
elif i < n_max:
viscosity_i = (
self._viscosity *
(lambda_i - lambda_n_min)**2/(lambda_n_max - lambda_n_min)**3 *
(2*lambda_n_max**2 - (lambda_n_min + lambda_n_max)*lambda_i)
)
else:
viscosity_i = self._viscosity*lambda_i
vanishing_viscosity_operator[i, i] = viscosity_i*lambda_i
vanishing_viscosity_expansion[0] = vanishing_viscosity_operator
self.operator["vanishing_viscosity"][:n, :n] = vanishing_viscosity_expansion
# Save to file
self.operator["vanishing_viscosity"].save(self.folder["reduced_operators"], "operator_vanishing_viscosity")
return self.operator["vanishing_viscosity"]
else:
raise ValueError("Invalid stage in assemble_operator().")
else:
if current_stage == "offline_vanishing_viscosity_postprocessing":
if term in self.terms:
for n in range(1, self.N + 1):
assert self.Q[term] == self.truth_problem.Q[term]
term_expansion = OnlineAffineExpansionStorage(self.Q[term])
assert self.terms_order[term] in (1, 2)
if self.terms_order[term] == 2:
for q in range(self.Q[term]):
term_expansion[q] = transpose(self.basis_functions[:n])*self.truth_problem.operator[term][q]*self.basis_functions[:n]
self.operator[term][:n, :n] = term_expansion
elif self.terms_order[term] == 1:
for q in range(self.Q[term]):
term_expansion[q] = transpose(self.basis_functions[:n])*self.truth_problem.operator[term][q]
self.operator[term][:n] = term_expansion
else:
raise ValueError("Invalid value for order of term " + term)
self.operator[term].save(self.folder["reduced_operators"], "operator_" + term)
return self.operator[term]
elif term.startswith("inner_product"):
assert len(self.inner_product) == 1 # the affine expansion storage contains only the inner product matrix
assert len(self.truth_problem.inner_product) == 1 # the affine expansion storage contains only the inner product matrix
for n in range(1, self.N + 1):
inner_product_expansion = OnlineAffineExpansionStorage(1)
inner_product_expansion[0] = transpose(self.basis_functions[:n])*self.truth_problem.inner_product[0]*self.basis_functions[:n]
self.inner_product[:n, :n] = inner_product_expansion
self.inner_product.save(self.folder["reduced_operators"], term)
return self.inner_product
elif term.startswith("projection_inner_product"):
assert len(self.projection_inner_product) == 1 # the affine expansion storage contains only the inner product matrix
assert len(self.truth_problem.projection_inner_product) == 1 # the affine expansion storage contains only the inner product matrix
for n in range(1, self.N + 1):
projection_inner_product_expansion = OnlineAffineExpansionStorage(1)
projection_inner_product_expansion[0] = transpose(self.basis_functions[:n])*self.truth_problem.projection_inner_product[0]*self.basis_functions[:n]
self.projection_inner_product[:n, :n] = projection_inner_product_expansion
self.projection_inner_product.save(self.folder["reduced_operators"], term)
return self.projection_inner_product
elif term.startswith("dirichlet_bc"):
raise ValueError("There should be no need to assemble Dirichlet BCs when querying the offline vanishing viscosity postprocessing stage.")
else:
raise ValueError("Invalid term for assemble_operator().")
else:
return EllipticCoerciveReducedProblem_DerivedClass.assemble_operator(self, term, current_stage)
def assemble_operator(self, term, current_stage="online"):
if term == "projection_truth_snapshots":
assert current_stage in (
"online", "offline_rectification_postprocessing")
if current_stage == "online": # load from file
self.operator["projection_truth_snapshots"].load(
self.folder["reduced_operators"],
"projection_truth_snapshots")
return self.operator["projection_truth_snapshots"]
elif current_stage == "offline_rectification_postprocessing":
assert len(
self.truth_problem.inner_product
) == 1 # the affine expansion storage contains only the inner product matrix
inner_product = self.truth_problem.inner_product[0]
for n in range(1, self.N + 1):
assert len(
self.inner_product
) == 1 # the affine expansion storage contains only the inner product matrix
inner_product_n = self.inner_product[:n, :n][0]
basis_functions_n = self.basis_functions[:n]
projection_truth_snapshots_expansion = OnlineAffineExpansionStorage(
1)
projection_truth_snapshots = OnlineMatrix(n, n)
for (i, snapshot_i) in enumerate(self.snapshots[:n]):
projected_truth_snapshot_i = OnlineFunction(n)
solver = LinearSolver(
inner_product_n, projected_truth_snapshot_i,
transpose(basis_functions_n) * inner_product *
snapshot_i)
solver.set_parameters(
self._linear_solver_parameters)
solver.solve()
for j in range(n):
projection_truth_snapshots[
j,
i] = projected_truth_snapshot_i.vector()[j]
projection_truth_snapshots_expansion[
0] = projection_truth_snapshots
print("\tcondition number for n = " + str(n) + ": " +
str(cond(projection_truth_snapshots)))
self.operator[
"projection_truth_snapshots"][:n, :
n] = projection_truth_snapshots_expansion
# Save
self.operator["projection_truth_snapshots"].save(
self.folder["reduced_operators"],
"projection_truth_snapshots")
return self.operator["projection_truth_snapshots"]
else:
raise ValueError("Invalid stage in assemble_operator().")
elif term == "projection_reduced_snapshots":
assert current_stage in (
"online", "offline_rectification_postprocessing")
if current_stage == "online": # load from file
self.operator["projection_reduced_snapshots"].load(
self.folder["reduced_operators"],
"projection_reduced_snapshots")
return self.operator["projection_reduced_snapshots"]
elif current_stage == "offline_rectification_postprocessing":
# Backup mu
bak_mu = self.mu
# Prepare rectification for all possible online solve arguments
for n in range(1, self.N + 1):
print("\tcondition number for n = " + str(n))
projection_reduced_snapshots_expansion = OnlineAffineExpansionStorage(
len(self.online_solve_kwargs_without_rectification)
)
for (q, online_solve_kwargs) in enumerate(
self.online_solve_kwargs_without_rectification
):
projection_reduced_snapshots = OnlineMatrix(n, n)
for (i, mu_i) in enumerate(self.snapshots_mu[:n]):
self.set_mu(mu_i)
projected_reduced_snapshot_i = self.solve(
n, **online_solve_kwargs)
for j in range(n):
projection_reduced_snapshots[
j,
i] = projected_reduced_snapshot_i.vector(
)[j]
projection_reduced_snapshots_expansion[
q] = projection_reduced_snapshots
print("\t\tonline solve options " + str(
dict(self.
online_solve_kwargs_with_rectification[q])
) + ": " + str(cond(projection_reduced_snapshots)))
self.operator[
"projection_reduced_snapshots"][:n, :
n] = projection_reduced_snapshots_expansion
# Save and restore previous mu
self.set_mu(bak_mu)
self.operator["projection_reduced_snapshots"].save(
self.folder["reduced_operators"],
"projection_reduced_snapshots")
return self.operator["projection_reduced_snapshots"]
else:
raise ValueError("Invalid stage in assemble_operator().")
else:
return EllipticCoerciveReducedProblem_DerivedClass.assemble_operator(
self, term, current_stage)
def assemble_error_estimation_operators(self,
term,
current_stage="online"):
"""
It assembles operators for error estimation.
"""
assert current_stage in ("online", "offline")
assert isinstance(term, tuple)
assert len(term) == 2
if current_stage == "online": # load from file
self.error_estimation_operator[term].load(
self.folder["error_estimation"],
"error_estimation_operator_" + term[0] + "_" + term[1])
return self.error_estimation_operator[term]
elif current_stage == "offline":
assert self.terms_order[term[0]] in (1, 2)
assert self.terms_order[term[1]] in (1, 2)
assert self.terms_order[term[0]] >= self.terms_order[
term[1]], "Please swap the order of " + str(
term
) + " in self.error_estimation_terms" # otherwise for (term1, term2) of orders (1, 2) we would have a row vector, rather than a column one
if self.terms_order[term[0]] == 2 and self.terms_order[
term[1]] == 2:
for q0 in range(self.Q[term[0]]):
for q1 in range(self.Q[term[1]]):
self.error_estimation_operator[term][
q0, q1] = transpose(
self.riesz[term[0]][q0]
) * self._error_estimation_inner_product * self.riesz[
term[1]][q1]
elif self.terms_order[term[0]] == 2 and self.terms_order[
term[1]] == 1:
for q0 in range(self.Q[term[0]]):
for q1 in range(self.Q[term[1]]):
assert len(self.riesz[term[1]][q1]) == 1
self.error_estimation_operator[term][
q0, q1] = transpose(
self.riesz[term[0]][q0]
) * self._error_estimation_inner_product * self.riesz[
term[1]][q1][0]
elif self.terms_order[term[0]] == 1 and self.terms_order[
term[1]] == 1:
for q0 in range(self.Q[term[0]]):
assert len(self.riesz[term[0]][q0]) == 1
for q1 in range(self.Q[term[1]]):
assert len(self.riesz[term[1]][q1]) == 1
self.error_estimation_operator[term][
q0, q1] = transpose(
self.riesz[term[0]][q0][0]
) * self._error_estimation_inner_product * self.riesz[
term[1]][q1][0]
else:
raise ValueError(
"Invalid term order for assemble_error_estimation_operators()."
)
self.error_estimation_operator[term].save(
self.folder["error_estimation"],
"error_estimation_operator_" + term[0] + "_" + term[1])
return self.error_estimation_operator[term]
else:
raise ValueError(
"Invalid stage in assemble_error_estimation_operators().")
def assemble_operator(self, term, current_stage="online"):
"""
Terms and respective thetas are assembled.
:param term: the forms of the class of the problem.
:param current_stage: online or offline stage.
"""
assert current_stage in ("online", "offline")
if current_stage == "online": # load from file
# Note that it would not be needed to return the loaded operator in
# init(), since it has been already modified in-place. We do this, however,
# because we want this interface to be compatible with the one in
# EllipticCoerciveProblem, i.e. we would like to be able to use a reduced
# problem also as a truth problem for a nested reduction
if term in self.terms:
self.operator[term].load(self.folder["reduced_operators"],
"operator_" + term)
return self.operator[term]
elif term.startswith("inner_product"):
component = term.replace("inner_product", "").replace("_", "")
if component != "":
assert component in self.components
self.inner_product[component].load(
self.folder["reduced_operators"], term)
return self.inner_product[component]
else:
assert len(self.components) == 1
self.inner_product.load(self.folder["reduced_operators"],
term)
return self.inner_product
elif term.startswith("projection_inner_product"):
component = term.replace("projection_inner_product",
"").replace("_", "")
if component != "":
assert component in self.components
self.projection_inner_product[component].load(
self.folder["reduced_operators"], term)
return self.projection_inner_product[component]
else:
assert len(self.components) == 1
self.projection_inner_product.load(
self.folder["reduced_operators"], term)
return self.projection_inner_product
elif term.startswith("dirichlet_bc"):
raise ValueError(
"There should be no need to assemble Dirichlet BCs when querying online reduced problems."
)
else:
raise ValueError("Invalid term for assemble_operator().")
elif current_stage == "offline":
# As in the previous case, there is no need to return anything because
# we are still training the reduced order model, so the previous remark
# (on the usage of a reduced problem as a truth one) cannot hold here.
# However, in order to have a consistent interface we return the assembled
# operator
if term in self.terms:
assert self.Q[term] == self.truth_problem.Q[term]
for q in range(self.Q[term]):
assert self.terms_order[term] in (0, 1, 2)
if self.terms_order[term] == 2:
self.operator[term][q] = transpose(
self.basis_functions
) * self.truth_problem.operator[term][
q] * self.basis_functions
elif self.terms_order[term] == 1:
self.operator[term][q] = transpose(
self.basis_functions
) * self.truth_problem.operator[term][q]
elif self.terms_order[term] == 0:
self.operator[term][q] = self.truth_problem.operator[
term][q]
else:
raise ValueError("Invalid value for order of term " +
term)
self.operator[term].save(self.folder["reduced_operators"],
"operator_" + term)
return self.operator[term]
elif term.startswith("inner_product"):
component = term.replace("inner_product", "").replace("_", "")
if component != "":
assert component in self.components
assert len(
self.inner_product[component]
) == 1 # the affine expansion storage contains only the inner product matrix
assert len(
self.truth_problem.inner_product[component]
) == 1 # the affine expansion storage contains only the inner product matrix
self.inner_product[component][0] = transpose(
self.basis_functions
) * self.truth_problem.inner_product[component][
0] * self.basis_functions
self.inner_product[component].save(
self.folder["reduced_operators"], term)
return self.inner_product[component]
else:
assert len(self.components) == 1 # single component case
assert len(
self.inner_product
) == 1 # the affine expansion storage contains only the inner product matrix
assert len(
self.truth_problem.inner_product
) == 1 # the affine expansion storage contains only the inner product matrix
self.inner_product[0] = transpose(
self.basis_functions
) * self.truth_problem.inner_product[
0] * self.basis_functions
self.inner_product.save(self.folder["reduced_operators"],
term)
return self.inner_product
elif term.startswith("projection_inner_product"):
component = term.replace("projection_inner_product",
"").replace("_", "")
if component != "":
assert component in self.components
assert len(
self.projection_inner_product[component]
) == 1 # the affine expansion storage contains only the inner product matrix
assert len(
self.truth_problem.projection_inner_product[component]
) == 1 # the affine expansion storage contains only the inner product matrix
self.projection_inner_product[component][0] = transpose(
self.basis_functions
) * self.truth_problem.projection_inner_product[component][
0] * self.basis_functions
self.projection_inner_product[component].save(
self.folder["reduced_operators"], term)
return self.projection_inner_product[component]
else:
assert len(self.components) == 1 # single component case
assert len(
self.projection_inner_product
) == 1 # the affine expansion storage contains only the inner product matrix
assert len(
self.truth_problem.projection_inner_product
) == 1 # the affine expansion storage contains only the inner product matrix
self.projection_inner_product[0] = transpose(
self.basis_functions
) * self.truth_problem.projection_inner_product[
0] * self.basis_functions
self.projection_inner_product.save(
self.folder["reduced_operators"], term)
return self.projection_inner_product
elif term.startswith("dirichlet_bc"):
component = term.replace("dirichlet_bc", "").replace("_", "")
if component != "":
assert component in self.components
has_non_homogeneous_dirichlet_bc = self.dirichlet_bc[
component] and not self.dirichlet_bc_are_homogeneous[
component]
else:
assert len(self.components) == 1
component = None
has_non_homogeneous_dirichlet_bc = self.dirichlet_bc and not self.dirichlet_bc_are_homogeneous
if has_non_homogeneous_dirichlet_bc:
# Compute lifting functions for the value of mu possibly provided by the user
Q_dirichlet_bcs = len(self.compute_theta(term))
# Temporarily override compute_theta method to return only one nonzero
# theta term related to boundary conditions
standard_compute_theta = self.truth_problem.compute_theta
for i in range(Q_dirichlet_bcs):
def modified_compute_theta(self, term_):
if term_ == term:
theta_bc = standard_compute_theta(term_)
modified_theta_bc = list()
for j in range(Q_dirichlet_bcs):
if j != i:
modified_theta_bc.append(0.)
else:
modified_theta_bc.append(theta_bc[i])
return tuple(modified_theta_bc)
else:
return standard_compute_theta(term_)
PatchInstanceMethod(self.truth_problem,
"compute_theta",
modified_compute_theta).patch()
# ... and store the solution of the truth problem corresponding to that boundary condition
# as lifting function
solve_message = "Computing and storing lifting function n. " + str(
i)
if component is not None:
solve_message += " for component " + component
solve_message += " (obtained for mu = " + str(
self.mu) + ") in the basis matrix"
print(solve_message)
lifting = self._lifting_truth_solve(term, i)
self.basis_functions.enrich(lifting,
component=component)
# Restore the standard compute_theta method
self.truth_problem.compute_theta = standard_compute_theta
else:
raise ValueError("Invalid term for assemble_operator().")
else:
raise ValueError("Invalid stage in assemble_operator().")
