sampling module¶
Sampling for multidisciplinary design problems under uncertainty.
Sampling
is an
UMDOFormulation
estimating the statistics with (quasi) Monte Carlo techniques.
E.g. \(\mathbb{E}[f(x,U)] \approx \frac{1}{N}\sum_{i=1}^N f\left(x,U^{(i)}\right)\) or \(\mathbb{V}[f(x,U)] \approx \frac{1}{N}\sum_{i=1}^N \left(f\left(x,U^{(i)}\right)- \frac{1}{N}\sum_{j=1}^N f\left(x,U^{(j)}\right)\right)^2\) where \(U\) is normally distributed with mean \(\mu\) and unit variance \(\sigma\) and \(U^{(1)},\ldots,U^{(1)}\) are \(N\) realizations of \(U\) obtained with an optimized Latin hypercube sampling technique.
- class gemseo_umdo.formulations.sampling.Sampling(disciplines, objective_name, design_space, mdo_formulation, uncertain_space, objective_statistic_name, n_samples, objective_statistic_parameters=None, maximize_objective=False, grammar_type=GrammarType.JSON, algo='OT_OPT_LHS', algo_options=None, seed=1, **options)[source]¶
Bases:
UMDOFormulation
Sampling-based robust MDO formulation.
- Parameters:
disciplines (Sequence[MDODiscipline]) – The disciplines.
objective_name (str) – The name(s) of the discipline output(s) used as objective. If multiple names are passed, the objective will be a vector.
design_space (DesignSpace) – The design space.
mdo_formulation (MDOFormulation) – The class name of the MDO formulation, e.g. “MDF”.
uncertain_space (ParameterSpace) – The uncertain variables with their probability distributions.
objective_statistic_name (str) – The name of the statistic to be applied to the objective.
n_samples (int) – The number of samples, i.e. the size of the DOE.
objective_statistic_parameters (Mapping[str, Any] | None) – The values of the parameters of the statistic to be applied to the objective, if any.
maximize_objective (bool) –
Whether to maximize the objective.
By default it is set to False.
grammar_type (MDODiscipline.GrammarType) –
The type of the input and output grammars.
By default it is set to “JSONGrammar”.
algo (str) –
The name of the DOE algorithm.
By default it is set to “OT_OPT_LHS”.
algo_options (Mapping[str, Any] | None) – The options of the DOE algorithm.
seed (int) –
The description is missing.
By default it is set to 1.
**options (Any) – The options of the formulation.
- add_constraint(output_name, statistic_name, constraint_type=ConstraintType.INEQ, constraint_name=None, value=None, positive=False, **statistic_parameters)¶
Add a user constraint.
A user constraint is a design constraint in addition to the formulation specific constraints such as the targets (a.k.a. consistency constraints) in IDF.
The strategy of repartition of constraints is defined in the formulation class.
- Parameters:
output_name (str | Sequence[str]) – The name of the output to be used as a constraint. For instance, if g_1 is given and constraint_type=”eq”, g_1=0 will be added as a constraint to the optimizer.
statistic_name (str) – The name of the statistic to be applied to the constraint.
constraint_type (str) –
The type of constraint, either “eq” for equality constraint or “ineq” for inequality constraint.
By default it is set to “ineq”.
constraint_name (str | None) – The name of the constraint to be stored, If
None
, the name is generated from the output name.value (float | None) – The value of activation of the constraint. If
None
, the value is equal to 0.positive (bool) –
Whether to consider an inequality constraint as positive.
By default it is set to False.
**statistic_parameters (Any) – The description is missing.
- Return type:
None
- add_observable(output_names, statistic_name, observable_name=None, discipline=None, **statistic_parameters)¶
Add an observable to the optimization problem.
The repartition strategy of the observable is defined in the formulation class.
- Parameters:
output_names (Sequence[str]) – The name(s) of the output(s) to observe.
statistic_name (str) – The name of the statistic to be applied to the observable.
observable_name (Sequence[str] | None) – The name of the observable.
discipline (MDODiscipline | None) – The discipline computing the observed outputs. If
None
, the discipline is detected from inner disciplines.**statistic_parameters (Any) – The description is missing.
- Return type:
None
- compute_samples(problem)[source]¶
Evaluate the functions of a problem with a DOE algorithm.
- Parameters:
problem (OptimizationProblem) – The problem.
- Return type:
None
- classmethod get_default_sub_option_values(**options)¶
Return the default values of the sub-options of the formulation.
When some options of the formulation depend on higher level options, the default values of these sub-options may be obtained here, mainly for use in the API.
- get_expected_dataflow()¶
Get the expected data exchange sequence.
This method is used for the XDSM representation and can be overloaded by subclasses.
- Returns:
The expected sequence of data exchange where the i-th item is described by the starting discipline, the ending discipline and the coupling variables.
- Return type:
list[tuple[gemseo.core.discipline.MDODiscipline, gemseo.core.discipline.MDODiscipline, list[str]]]
- get_expected_workflow()¶
Get the expected sequence of execution of the disciplines.
This method is used for the XDSM representation and can be overloaded by subclasses.
For instance:
[A, B] denotes the execution of A, then the execution of B
(A, B) denotes the concurrent execution of A and B
[A, (B, C), D] denotes the execution of A, then the concurrent execution of B and C, then the execution of D.
- Returns:
A sequence of elements which are either an
ExecutionSequence
or a tuple ofExecutionSequence
for concurrent execution.- Return type:
list[gemseo.core.execution_sequence.ExecutionSequence, tuple[gemseo.core.execution_sequence.ExecutionSequence]]
- get_optim_variable_names()¶
Get the optimization unknown names to be provided to the optimizer.
This is different from the design variable names provided by the user, since it depends on the formulation, and can include target values for coupling for instance in IDF.
- get_sub_disciplines(recursive=False)¶
Accessor to the sub-disciplines.
This method lists the sub scenarios’ disciplines. It will list up to one level of disciplines contained inside another one unless the
recursive
argument is set toTrue
.- Parameters:
recursive (bool) –
If
True
, the method will look inside any discipline that has other disciplines inside until it reaches a discipline without sub-disciplines, in this case the return value will not include any discipline that has sub-disciplines. IfFalse
, the method will list up to one level of disciplines contained inside another one, in this case the return value may include disciplines that contain sub-disciplines.By default it is set to False.
- Returns:
The sub-disciplines.
- Return type:
- classmethod get_sub_options_grammar(**options)¶
Get the sub-options grammar.
When some options of the formulation depend on higher level options, the schema of the sub-options may be obtained here, mainly for use in the API.
- Parameters:
**options (str) – The options required to deduce the sub-options grammar.
- Returns:
Either
None
or the sub-options grammar.- Return type:
- get_sub_scenarios()¶
List the disciplines that are actually scenarios.
- get_top_level_disc()¶
Return the disciplines which inputs are required to run the scenario.
A formulation seeks to compute the objective and constraints from the input variables. It structures the optimization problem into multiple levels of disciplines. The disciplines directly depending on these inputs are called top level disciplines.
By default, this method returns all disciplines. This method can be overloaded by subclasses.
- Returns:
The top level disciplines.
- Return type:
- get_x_mask_x_swap_order(masking_data_names, all_data_names=None)¶
Mask a vector from a subset of names, with respect to a set of names.
This method eventually swaps the order of the values if the order of the data names is inconsistent between these sets.
- Parameters:
- Returns:
The masked version of the input vector.
- Raises:
IndexError – when the sizes of variables are inconsistent.
ValueError – when the names of variables are inconsistent.
- Return type:
ndarray
- get_x_names_of_disc(discipline)¶
Get the design variables names of a given discipline.
- Parameters:
discipline (MDODiscipline) – The discipline.
- Returns:
The names of the design variables.
- Return type:
- mask_x_swap_order(masking_data_names, x_vect, all_data_names=None)¶
Mask a vector from a subset of names, with respect to a set of names.
This method eventually swaps the order of the values if the order of the data names is inconsistent between these sets.
- Parameters:
- Returns:
The masked version of the input vector.
- Raises:
IndexError – when the sizes of variables are inconsistent.
- Return type:
ndarray
- unmask_x_swap_order(masking_data_names, x_masked, all_data_names=None, x_full=None)¶
Unmask a vector from a subset of names, with respect to a set of names.
This method eventually swaps the order of the values if the order of the data names is inconsistent between these sets.
- Parameters:
masking_data_names (Iterable[str]) – The names of the kept data.
x_masked (ndarray) – The boolean vector to unmask.
all_data_names (Iterable[str] | None) – The set of all names. If
None
, use the design variables stored in the design space.x_full (ndarray) – The default values for the full vector. If
None
, use the zero vector.
- Returns:
The vector related to the input mask.
- Raises:
IndexError – when the sizes of variables are inconsistent.
- Return type:
ndarray
- update_top_level_disciplines(design_values)¶
Update the default input values of the top-level disciplines.
- property available_statistics: list[str]¶
The names of the statistics to quantify the output uncertainties.
- property design_space: DesignSpace¶
The design space on which the formulation is applied.
- property disciplines: list[gemseo.core.discipline.MDODiscipline]¶
The disciplines of the MDO process.
- property mdo_formulation: MDOFormulation¶
The MDO formulation.
- opt_problem: OptimizationProblem¶
The optimization problem generated by the formulation from the disciplines.
- property uncertain_space: ParameterSpace¶
The uncertain variable space.