rosenbrock module¶
The Rosenbrock analytic problem¶
- class gemseo.problems.analytical.rosenbrock.RosenMF(dimension=2)[source]¶
Bases:
gemseo.core.discipline.MDODiscipline
RosenMF, a multi-fidelity Rosenbrock
MDODiscipline
, returns the value:\[\mathrm{fidelity} * \mathrm{Rosenbrock}(x)\]where both \(\mathrm{fidelity}\) and \(x\) are provided as input data.
- Parameters
dimension (int) –
The dimension of the design space.
By default it is set to 2.
- Return type
None
- classmethod activate_time_stamps()¶
Activate the time stamps.
For storing start and end times of execution and linearizations.
- Return type
None
- add_differentiated_inputs(inputs=None)¶
Add inputs against which to differentiate the outputs.
This method updates
MDODiscipline._differentiated_inputs
withinputs
.- Parameters
inputs (Iterable[str] | None) –
The input variables against which to differentiate the outputs. If None, all the inputs of the discipline are used.
By default it is set to None.
- Raises
ValueError – When the inputs wrt which differentiate the discipline are not inputs of the latter.
- Return type
None
- add_differentiated_outputs(outputs=None)¶
Add outputs to be differentiated.
This method updates
MDODiscipline._differentiated_outputs
withoutputs
.- Parameters
outputs (Iterable[str] | None) –
The output variables to be differentiated. If None, all the outputs of the discipline are used.
By default it is set to None.
- Raises
ValueError – When the outputs to differentiate are not discipline outputs.
- Return type
None
- add_namespace_to_input(name, namespace)¶
Add a namespace prefix to an existing input grammar element.
The updated input grammar element name will be
namespace``+:data:`~gemseo.core.namespaces.namespace_separator`+``name
.
- add_namespace_to_output(name, namespace)¶
Add a namespace prefix to an existing output grammar element.
The updated output grammar element name will be
namespace``+:data:`~gemseo.core.namespaces.namespace_separator`+``name
.
- add_status_observer(obs)¶
Add an observer for the status.
Add an observer for the status to be notified when self changes of status.
- Parameters
obs (Any) – The observer to add.
- Return type
None
- auto_get_grammar_file(is_input=True, name=None, comp_dir=None)¶
Use a naming convention to associate a grammar file to the discipline.
Search in the directory
comp_dir
for either an input grammar file namedname + "_input.json"
or an output grammar file namedname + "_output.json"
.- Parameters
is_input (bool) –
Whether to search for an input or output grammar file.
By default it is set to True.
name (str | None) –
The name to be searched in the file names. If
None
, use the name of the discipline class.By default it is set to None.
comp_dir (str | Path | None) –
The directory in which to search the grammar file. If None, use the
GRAMMAR_DIRECTORY
if any, or the directory of the discipline class module.By default it is set to None.
- Returns
The grammar file path.
- Return type
- check_input_data(input_data, raise_exception=True)¶
Check the input data validity.
- check_jacobian(input_data=None, derr_approx='finite_differences', step=1e-07, threshold=1e-08, linearization_mode='auto', inputs=None, outputs=None, parallel=False, n_processes=2, use_threading=False, wait_time_between_fork=0, auto_set_step=False, plot_result=False, file_path='jacobian_errors.pdf', show=False, fig_size_x=10, fig_size_y=10, reference_jacobian_path=None, save_reference_jacobian=False, indices=None)¶
Check if the analytical Jacobian is correct with respect to a reference one.
If reference_jacobian_path is not None and save_reference_jacobian is True, compute the reference Jacobian with the approximation method and save it in reference_jacobian_path.
If reference_jacobian_path is not None and save_reference_jacobian is False, do not compute the reference Jacobian but read it from reference_jacobian_path.
If reference_jacobian_path is None, compute the reference Jacobian without saving it.
- Parameters
input_data (dict[str, ndarray] | None) –
The input data needed to execute the discipline according to the discipline input grammar. If None, use the
MDODiscipline.default_inputs
.By default it is set to None.
derr_approx (str) –
The approximation method, either “complex_step” or “finite_differences”.
By default it is set to finite_differences.
threshold (float) –
The acceptance threshold for the Jacobian error.
By default it is set to 1e-08.
linearization_mode (str) –
the mode of linearization: direct, adjoint or automated switch depending on dimensions of inputs and outputs (Default value = ‘auto’)
By default it is set to auto.
inputs (Iterable[str] | None) –
The names of the inputs wrt which to differentiate the outputs.
By default it is set to None.
outputs (Iterable[str] | None) –
The names of the outputs to be differentiated.
By default it is set to None.
step (float) –
The differentiation step.
By default it is set to 1e-07.
parallel (bool) –
Whether to differentiate the discipline in parallel.
By default it is set to False.
n_processes (int) –
The maximum simultaneous number of threads, if
use_threading
is True, or processes otherwise, used to parallelize the execution.By default it is set to 2.
use_threading (bool) –
Whether to use threads instead of processes to parallelize the execution; multiprocessing will copy (serialize) all the disciplines, while threading will share all the memory This is important to note if you want to execute the same discipline multiple times, you shall use multiprocessing.
By default it is set to False.
wait_time_between_fork (float) –
The time waited between two forks of the process / thread.
By default it is set to 0.
auto_set_step (bool) –
Whether to compute the optimal step for a forward first order finite differences gradient approximation.
By default it is set to False.
plot_result (bool) –
Whether to plot the result of the validation (computed vs approximated Jacobians).
By default it is set to False.
file_path (str | Path) –
The path to the output file if
plot_result
isTrue
.By default it is set to jacobian_errors.pdf.
show (bool) –
Whether to open the figure.
By default it is set to False.
fig_size_x (float) –
The x-size of the figure in inches.
By default it is set to 10.
fig_size_y (float) –
The y-size of the figure in inches.
By default it is set to 10.
reference_jacobian_path (str | Path | None) –
The path of the reference Jacobian file.
By default it is set to None.
save_reference_jacobian (bool) –
Whether to save the reference Jacobian.
By default it is set to False.
indices (Iterable[int] | None) –
The indices of the inputs and outputs for the different sub-Jacobian matrices, formatted as
{variable_name: variable_components}
wherevariable_components
can be either an integer, e.g. 2 a sequence of integers, e.g. [0, 3], a slice, e.g. slice(0,3), the ellipsis symbol (…) or None, which is the same as ellipsis. If a variable name is missing, consider all its components. If None, consider all the components of all theinputs
andoutputs
.By default it is set to None.
- Returns
Whether the analytical Jacobian is correct with respect to the reference one.
- check_output_data(raise_exception=True)¶
Check the output data validity.
- Parameters
raise_exception (bool) –
Whether to raise an exception when the data is invalid.
By default it is set to True.
- Return type
None
- classmethod deactivate_time_stamps()¶
Deactivate the time stamps.
For storing start and end times of execution and linearizations.
- Return type
None
- static deserialize(file_path)¶
Deserialize a discipline from a file.
- Parameters
file_path (str | Path) – The path to the file containing the discipline.
- Returns
The discipline instance.
- Return type
- execute(input_data=None)¶
Execute the discipline.
This method executes the discipline:
Adds the default inputs to the
input_data
if some inputs are not defined in input_data but exist inMDODiscipline.default_inputs
.Checks whether the last execution of the discipline was called with identical inputs, i.e. cached in
MDODiscipline.cache
; if so, directly returnsself.cache.get_output_cache(inputs)
.Caches the inputs.
Checks the input data against
MDODiscipline.input_grammar
.If
MDODiscipline.data_processor
is not None, runs the preprocessor.Updates the status to
MDODiscipline.STATUS_RUNNING
.Calls the
MDODiscipline._run()
method, that shall be defined.If
MDODiscipline.data_processor
is not None, runs the postprocessor.Checks the output data.
Caches the outputs.
Updates the status to
MDODiscipline.STATUS_DONE
orMDODiscipline.STATUS_FAILED
.Updates summed execution time.
- Parameters
input_data (Mapping[str, Any] | None) –
The input data needed to execute the discipline according to the discipline input grammar. If None, use the
MDODiscipline.default_inputs
.By default it is set to None.
- Returns
The discipline local data after execution.
- Raises
RuntimeError – When residual_variables are declared but self.run_solves_residuals is False. This is not suported yet.
- Return type
- get_all_inputs()¶
Return the local input data as a list.
The order is given by
MDODiscipline.get_input_data_names()
.
- get_all_outputs()¶
Return the local output data as a list.
The order is given by
MDODiscipline.get_output_data_names()
.
- get_attributes_to_serialize()¶
Define the names of the attributes to be serialized.
Shall be overloaded by disciplines
- static get_data_list_from_dict(keys, data_dict)¶
Filter the dict from a list of keys or a single key.
If keys is a string, then the method return the value associated to the key. If keys is a list of strings, then the method returns a generator of value corresponding to the keys which can be iterated.
- get_disciplines_in_dataflow_chain()¶
Return the disciplines that must be shown as blocks within the XDSM representation of a chain.
By default, only the discipline itself is shown. This function can be differently implemented for any type of inherited discipline.
- Returns
The disciplines shown in the XDSM chain.
- Return type
- get_expected_dataflow()¶
Return the expected data exchange sequence.
This method is used for the XDSM representation.
The default expected data exchange sequence is an empty list.
See also
MDOFormulation.get_expected_dataflow
- Returns
The data exchange arcs.
- Return type
list[tuple[gemseo.core.discipline.MDODiscipline, gemseo.core.discipline.MDODiscipline, list[str]]]
- get_expected_workflow()¶
Return the expected execution sequence.
This method is used for the XDSM representation.
The default expected execution sequence is the execution of the discipline itself.
See also
MDOFormulation.get_expected_workflow
- Returns
The expected execution sequence.
- Return type
- get_input_data(with_namespaces=True)¶
Return the local input data as a dictionary.
- get_input_data_names(with_namespaces=True)¶
Return the names of the input variables.
- get_input_output_data_names(with_namespaces=True)¶
Return the names of the input and output variables.
- Args:
- with_namespaces: Whether to keep the namespace prefix of the
output names, if any.
- get_inputs_asarray()¶
Return the local output data as a large NumPy array.
The order is the one of
MDODiscipline.get_all_outputs()
.- Returns
The local output data.
- Return type
- get_inputs_by_name(data_names)¶
Return the local data associated with input variables.
- Parameters
data_names (Iterable[str]) – The names of the input variables.
- Returns
The local data for the given input variables.
- Raises
ValueError – When a variable is not an input of the discipline.
- Return type
- get_local_data_by_name(data_names)¶
Return the local data of the discipline associated with variables names.
- Parameters
data_names (Iterable[str]) – The names of the variables.
- Returns
The local data associated with the variables names.
- Raises
ValueError – When a name is not a discipline input name.
- Return type
Generator[Any]
- get_output_data(with_namespaces=True)¶
Return the local output data as a dictionary.
- get_output_data_names(with_namespaces=True)¶
Return the names of the output variables.
- get_outputs_asarray()¶
Return the local input data as a large NumPy array.
The order is the one of
MDODiscipline.get_all_inputs()
.- Returns
The local input data.
- Return type
- get_outputs_by_name(data_names)¶
Return the local data associated with output variables.
- Parameters
data_names (Iterable[str]) – The names of the output variables.
- Returns
The local data for the given output variables.
- Raises
ValueError – When a variable is not an output of the discipline.
- Return type
- get_sub_disciplines()¶
Return the sub-disciplines if any.
- Returns
The sub-disciplines.
- Return type
- is_all_inputs_existing(data_names)¶
Test if several variables are discipline inputs.
- is_all_outputs_existing(data_names)¶
Test if several variables are discipline outputs.
- is_input_existing(data_name)¶
Test if a variable is a discipline input.
- is_output_existing(data_name)¶
Test if a variable is a discipline output.
- linearize(input_data=None, force_all=False, force_no_exec=False)¶
Execute the linearized version of the code.
- Parameters
input_data (dict[str, Any] | None) –
The input data needed to linearize the discipline according to the discipline input grammar. If None, use the
MDODiscipline.default_inputs
.By default it is set to None.
force_all (bool) –
If False,
MDODiscipline._differentiated_inputs
andMDODiscipline._differentiated_outputs
are used to filter the differentiated variables. otherwise, all outputs are differentiated wrt all inputs.By default it is set to False.
force_no_exec (bool) –
If True, the discipline is not re-executed, cache is loaded anyway.
By default it is set to False.
- Returns
The Jacobian of the discipline.
- Return type
- notify_status_observers()¶
Notify all status observers that the status has changed.
- Return type
None
- remove_status_observer(obs)¶
Remove an observer for the status.
- Parameters
obs (Any) – The observer to remove.
- Return type
None
- reset_statuses_for_run()¶
Set all the statuses to
MDODiscipline.STATUS_PENDING
.- Raises
ValueError – When the discipline cannot be run because of its status.
- Return type
None
- serialize(file_path)¶
Serialize the discipline and store it in a file.
- Parameters
file_path (str | Path) – The path to the file to store the discipline.
- Return type
None
- set_cache_policy(cache_type='SimpleCache', cache_tolerance=0.0, cache_hdf_file=None, cache_hdf_node_name=None, is_memory_shared=True)¶
Set the type of cache to use and the tolerance level.
This method defines when the output data have to be cached according to the distance between the corresponding input data and the input data already cached for which output data are also cached.
The cache can be either a
SimpleCache
recording the last execution or a cache storing all executions, e.g.MemoryFullCache
andHDF5Cache
. Caching data can be either in-memory, e.g.SimpleCache
andMemoryFullCache
, or on the disk, e.g.HDF5Cache
.The attribute
CacheFactory.caches
provides the available caches types.- Parameters
cache_type (str) –
The type of cache.
By default it is set to SimpleCache.
cache_tolerance (float) –
The maximum relative norm of the difference between two input arrays to consider that two input arrays are equal.
By default it is set to 0.0.
cache_hdf_file (str | Path | None) –
The path to the HDF file to store the data; this argument is mandatory when the
MDODiscipline.HDF5_CACHE
policy is used.By default it is set to None.
cache_hdf_node_name (str | None) –
The name of the HDF file node to store the discipline data. If None,
MDODiscipline.name
is used.By default it is set to None.
is_memory_shared (bool) –
Whether to store the data with a shared memory dictionary, which makes the cache compatible with multiprocessing.
By default it is set to True.
- Return type
None
- set_disciplines_statuses(status)¶
Set the sub-disciplines statuses.
To be implemented in subclasses.
- Parameters
status (str) – The status.
- Return type
None
- set_jacobian_approximation(jac_approx_type='finite_differences', jax_approx_step=1e-07, jac_approx_n_processes=1, jac_approx_use_threading=False, jac_approx_wait_time=0)¶
Set the Jacobian approximation method.
Sets the linearization mode to approx_method, sets the parameters of the approximation for further use when calling
MDODiscipline.linearize()
.- Parameters
jac_approx_type (str) –
The approximation method, either “complex_step” or “finite_differences”.
By default it is set to finite_differences.
jax_approx_step (float) –
The differentiation step.
By default it is set to 1e-07.
jac_approx_n_processes (int) –
The maximum simultaneous number of threads, if
jac_approx_use_threading
is True, or processes otherwise, used to parallelize the execution.By default it is set to 1.
jac_approx_use_threading (bool) –
Whether to use threads instead of processes to parallelize the execution; multiprocessing will copy (serialize) all the disciplines, while threading will share all the memory This is important to note if you want to execute the same discipline multiple times, you shall use multiprocessing.
By default it is set to False.
jac_approx_wait_time (float) –
The time waited between two forks of the process / thread.
By default it is set to 0.
- Return type
None
- set_optimal_fd_step(outputs=None, inputs=None, force_all=False, print_errors=False, numerical_error=2.220446049250313e-16)¶
Compute the optimal finite-difference step.
Compute the optimal step for a forward first order finite differences gradient approximation. Requires a first evaluation of the perturbed functions values. The optimal step is reached when the truncation error (cut in the Taylor development), and the numerical cancellation errors (round-off when doing f(x+step)-f(x)) are approximately equal.
Warning
This calls the discipline execution twice per input variables.
See also
https://en.wikipedia.org/wiki/Numerical_differentiation and “Numerical Algorithms and Digital Representation”, Knut Morken , Chapter 11, “Numerical Differentiation”
- Parameters
inputs (Iterable[str] | None) –
The inputs wrt which the outputs are linearized. If None, use the
MDODiscipline._differentiated_inputs
.By default it is set to None.
outputs (Iterable[str] | None) –
The outputs to be linearized. If None, use the
MDODiscipline._differentiated_outputs
.By default it is set to None.
force_all (bool) –
Whether to consider all the inputs and outputs of the discipline;
By default it is set to False.
print_errors (bool) –
Whether to display the estimated errors.
By default it is set to False.
numerical_error (float) –
The numerical error associated to the calculation of f. By default, this is the machine epsilon (appx 1e-16), but can be higher when the calculation of f requires a numerical resolution.
By default it is set to 2.220446049250313e-16.
- Returns
The estimated errors of truncation and cancellation error.
- Raises
ValueError – When the Jacobian approximation method has not been set.
- store_local_data(**kwargs)¶
Store discipline data in local data.
- Parameters
**kwargs (Any) – The data to be stored in
MDODiscipline.local_data
.- Return type
None
- APPROX_MODES = ['finite_differences', 'complex_step']¶
- AVAILABLE_MODES = ('auto', 'direct', 'adjoint', 'reverse', 'finite_differences', 'complex_step')¶
- AVAILABLE_STATUSES = ['DONE', 'FAILED', 'PENDING', 'RUNNING', 'VIRTUAL']¶
- COMPLEX_STEP = 'complex_step'¶
- FINITE_DIFFERENCES = 'finite_differences'¶
- GRAMMAR_DIRECTORY: ClassVar[str | None] = None¶
The directory in which to search for the grammar files if not the class one.
- HDF5_CACHE = 'HDF5Cache'¶
- JSON_GRAMMAR_TYPE = 'JSONGrammar'¶
- MEMORY_FULL_CACHE = 'MemoryFullCache'¶
- N_CPUS = 2¶
- RE_EXECUTE_DONE_POLICY = 'RE_EXEC_DONE'¶
- RE_EXECUTE_NEVER_POLICY = 'RE_EXEC_NEVER'¶
- SIMPLE_CACHE = 'SimpleCache'¶
- SIMPLE_GRAMMAR_TYPE = 'SimpleGrammar'¶
- STATUS_DONE = 'DONE'¶
- STATUS_FAILED = 'FAILED'¶
- STATUS_PENDING = 'PENDING'¶
- STATUS_RUNNING = 'RUNNING'¶
- STATUS_VIRTUAL = 'VIRTUAL'¶
- activate_counters: ClassVar[bool] = True¶
Whether to activate the counters (execution time, calls and linearizations).
- activate_input_data_check: ClassVar[bool] = True¶
Whether to check the input data respect the input grammar.
- activate_output_data_check: ClassVar[bool] = True¶
Whether to check the output data respect the output grammar.
- cache: AbstractCache¶
The cache containing one or several executions of the discipline according to the cache policy.
- property cache_tol: float¶
The cache input tolerance.
This is the tolerance for equality of the inputs in the cache. If norm(stored_input_data-input_data) <= cache_tol * norm(stored_input_data), the cached data for
stored_input_data
is returned when callingself.execute(input_data)
.- Raises
ValueError – When the discipline does not have a cache.
- data_processor: DataProcessor¶
A tool to pre- and post-process discipline data.
- property default_inputs: dict[str, Any]¶
The default inputs.
- Raises
TypeError – When the default inputs are not passed as a dictionary.
- property exec_time: float | None¶
The cumulated execution time of the discipline.
This property is multiprocessing safe.
- Raises
RuntimeError – When the discipline counters are disabled.
- property grammar_type: gemseo.core.grammars.base_grammar.BaseGrammar¶
The type of grammar to be used for inputs and outputs declaration.
- input_grammar: BaseGrammar¶
The input grammar.
- jac: dict[str, dict[str, ndarray]]¶
The Jacobians of the outputs wrt inputs of the form
{output: {input: matrix}}
.
- property linearization_mode: str¶
The linearization mode among
MDODiscipline.AVAILABLE_MODES
.- Raises
ValueError – When the linearization mode is unknown.
- property local_data: gemseo.core.discipline_data.DisciplineData¶
The current input and output data.
- property n_calls: int | None¶
The number of times the discipline was executed.
This property is multiprocessing safe.
- Raises
RuntimeError – When the discipline counters are disabled.
- property n_calls_linearize: int | None¶
The number of times the discipline was linearized.
This property is multiprocessing safe.
- Raises
RuntimeError – When the discipline counters are disabled.
- output_grammar: BaseGrammar¶
The output grammar.
- residual_variables: Mapping[str, str]¶
The output variables mapping to their inputs, to be considered as residuals; they shall be equal to zero.
- time_stamps = None¶
- class gemseo.problems.analytical.rosenbrock.Rosenbrock(n_x=2, l_b=- 2.0, u_b=2.0, scalar_var=False, initial_guess=None)[source]¶
Bases:
gemseo.algos.opt_problem.OptimizationProblem
Rosenbrock
OptimizationProblem
uses the Rosenbrock objective function\[f(x) = \sum_{i=2}^{n_x} 100(x_{i} - x_{i-1}^2)^2 + (1 - x_{i-1})^2\]with the default
DesignSpace
\([-0.2,0.2]^{n_x}\).- Parameters
n_x (int) –
The dimension of the design space.
By default it is set to 2.
l_b (float) –
The lower bound (common value to all variables).
By default it is set to -2.0.
u_b (float) –
The upper bound (common value to all variables).
By default it is set to 2.0.
scalar_var (bool) –
If
True
, the design space will contain only scalar variables (as many as the problem dimension); ifFalse
, the design space will contain a single multidimensional variable (whose size equals the problem dimension).By default it is set to False.
initial_guess (ndarray | None) –
The initial guess for optimal solution.
By default it is set to None.
- Return type
None
- add_callback(callback_func, each_new_iter=True, each_store=False)¶
Add a callback function after each store operation or new iteration.
- Parameters
callback_func (Callable) – A function to be called after some event.
each_new_iter (bool) –
If True, then callback at every iteration.
By default it is set to True.
each_store (bool) –
If True, then callback at every call to
Database.store()
.By default it is set to False.
- Return type
None
- add_constraint(cstr_func, value=None, cstr_type=None, positive=False)¶
Add a constraint (equality and inequality) to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
cstr_type (str | None) –
The type of the constraint. Either equality or inequality.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Raises
TypeError – When the constraint of a linear optimization problem is not an
MDOLinearFunction
.ValueError – When the type of the constraint is missing.
- Return type
None
- add_eq_constraint(cstr_func, value=None)¶
Add an equality constraint to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
- Return type
None
- add_ineq_constraint(cstr_func, value=None, positive=False)¶
Add an inequality constraint to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Return type
None
- add_observable(obs_func, new_iter=True)¶
Add a function to be observed.
When the
OptimizationProblem
is executed, the observables are called following this sequence:The optimization algorithm calls the objective function with a normalized
x_vect
.The
OptimizationProblem.preprocess_functions()
wraps the function as aNormDBFunction
, which unnormalizes thex_vect
before evaluation.The unnormalized
x_vect
and the result of the evaluation are stored in theOptimizationProblem.database
.The previous step triggers the
OptimizationProblem.new_iter_listeners
, which calls the observables with the unnormalizedx_vect
.The observables themselves are wrapped as a
NormDBFunction
byOptimizationProblem.preprocess_functions()
, but in this case the input is always expected as unnormalized to avoid an additional normalizing-unnormalizing step.Finally, the output is stored in the
OptimizationProblem.database
.
- Parameters
obs_func (gemseo.core.mdofunctions.mdo_function.MDOFunction) – An observable to be observed.
new_iter (bool) –
If True, then the observable will be called at each new iterate.
By default it is set to True.
- Return type
None
- aggregate_constraint(constr_id, method='max', groups=None, **options)¶
Aggregates a constraint to generate a reduced dimension constraint.
- Parameters
constr_id (int) – The index of the constraint in
constraints
.method (str | Callable[[Callable], Callable]) –
The aggregation method, e.g.
"max"
,"KS"
or"IKS"
.By default it is set to max.
groups (tuple[ndarray] | None) –
The groups for which to produce an output. If
None
, a single output constraint is produced.By default it is set to None.
**options (Any) – The options of the aggregation method.
- Raises
ValueError – When the given is index is greater or equal than the number of constraints or when the method is aggregation unknown.
- change_objective_sign()¶
Change the objective function sign in order to minimize its opposite.
The
OptimizationProblem
expresses any optimization problem as a minimization problem. Then, an objective function originally expressed as a performance function to maximize must be converted into a cost function to minimize, by means of this method.- Return type
None
- check()¶
Check if the optimization problem is ready for run.
- Raises
ValueError – If the objective function is missing.
- Return type
None
- static check_format(input_function)¶
Check that a function is an instance of
MDOFunction
.- Parameters
input_function (Any) – The function to be tested.
- Raises
TypeError – If the function is not a
MDOFunction
.- Return type
None
- clear_listeners()¶
Clear all the listeners.
- Return type
None
- evaluate_functions(x_vect=None, eval_jac=False, eval_obj=True, eval_observables=False, normalize=True, no_db_no_norm=False)¶
Compute the functions of interest, and possibly their derivatives.
These functions of interest are the constraints, and possibly the objective.
Some optimization libraries require the number of constraints as an input parameter which is unknown by the formulation or the scenario. Evaluation of initial point allows to get this mandatory information. This is also used for design of experiments to evaluate samples.
- Parameters
x_vect (ndarray) –
The input vector at which the functions must be evaluated; if None, the initial point x_0 is used.
By default it is set to None.
eval_jac (bool) –
Whether to compute the Jacobian matrices of the functions of interest.
By default it is set to False.
eval_obj (bool) –
Whether to consider the objective function as a function of interest.
By default it is set to True.
normalize (bool) –
Whether to consider the input vector
x_vect
normalized.By default it is set to True.
no_db_no_norm (bool) –
If True, then do not use the pre-processed functions, so we have no database, nor normalization.
By default it is set to False.
eval_observables (bool) –
By default it is set to False.
- Returns
The output values of the functions of interest, as well as their Jacobian matrices if
eval_jac
isTrue
.- Return type
- execute_observables_callback(last_x)¶
The callback function to be passed to the database.
Call all the observables with the last design variables values as argument.
- Parameters
last_x (numpy.ndarray) – The design variables values from the last evaluation.
- Return type
None
- export_hdf(file_path, append=False)¶
Export the optimization problem to an HDF file.
- export_to_dataset(name=None, by_group=True, categorize=True, opt_naming=True, export_gradients=False, input_values=None)¶
Export the database of the optimization problem to a
Dataset
.The variables can be classified into groups:
Dataset.DESIGN_GROUP
orDataset.INPUT_GROUP
for the design variables andDataset.FUNCTION_GROUP
orDataset.OUTPUT_GROUP
for the functions (objective, constraints and observables).- Parameters
name (str | None) –
The name to be given to the dataset. If
None
, use the name of theOptimizationProblem.database
.By default it is set to None.
by_group (bool) –
Whether to store the data by group in
Dataset.data
, in the sense of one unique NumPy array per group. Ifcategorize
isFalse
, there is a unique group:Dataset.PARAMETER_GROUP`
. Ifcategorize
isTrue
, the groups can be eitherDataset.DESIGN_GROUP
andDataset.FUNCTION_GROUP
ifopt_naming
isTrue
, orDataset.INPUT_GROUP
andDataset.OUTPUT_GROUP
. Ifby_group
isFalse
, store the data by variable names.By default it is set to True.
categorize (bool) –
Whether to distinguish between the different groups of variables. Otherwise, group all the variables in
Dataset.PARAMETER_GROUP`
.By default it is set to True.
opt_naming (bool) –
Whether to use
Dataset.DESIGN_GROUP
andDataset.FUNCTION_GROUP
as groups. Otherwise, useDataset.INPUT_GROUP
andDataset.OUTPUT_GROUP
.By default it is set to True.
export_gradients (bool) –
Whether to export the gradients of the functions (objective function, constraints and observables) if the latter are available in the database of the optimization problem.
By default it is set to False.
input_values (Iterable[ndarray] | None) –
The input values to be considered. If
None
, consider all the input values of the database.By default it is set to None.
- Returns
A dataset built from the database of the optimization problem.
- Return type
- get_active_ineq_constraints(x_vect, tol=1e-06)¶
For each constraint, indicate if its different components are active.
- Parameters
x_vect (numpy.ndarray) – The vector of design variables.
tol (float) –
The tolerance for deciding whether a constraint is active.
By default it is set to 1e-06.
- Returns
For each constraint, a boolean indicator of activation of its different components.
- Return type
dict[gemseo.core.mdofunctions.mdo_function.MDOFunction, numpy.ndarray]
- get_all_functions()¶
Retrieve all the functions of the optimization problem.
These functions are the constraints, the objective function and the observables.
- Returns
All the functions of the optimization problem.
- Return type
- get_all_functions_names()¶
Retrieve the names of all the function of the optimization problem.
These functions are the constraints, the objective function and the observables.
- get_best_infeasible_point()¶
Retrieve the best infeasible point within a given tolerance.
- Returns
The best infeasible point expressed as the design variables values, the objective function value, the feasibility of the point and the functions values.
- Return type
Tuple[Optional[numpy.ndarray], Optional[numpy.ndarray], bool, Dict[str, numpy.ndarray]]
- get_constraints_names()¶
Retrieve the names of the constraints.
- get_constraints_number()¶
Retrieve the number of constraints.
- Returns
The number of constraints.
- Return type
- get_data_by_names(names, as_dict=True, filter_non_feasible=False)¶
Return the data for specific names of variables.
- Parameters
- Returns
The data related to the variables.
- Return type
- get_design_variable_names()¶
Retrieve the names of the design variables.
- get_dimension()¶
Retrieve the total number of design variables.
- Returns
The dimension of the design space.
- Return type
- get_eq_constraints()¶
Retrieve all the equality constraints.
- Returns
The equality constraints.
- Return type
- get_eq_constraints_number()¶
Retrieve the number of equality constraints.
- Returns
The number of equality constraints.
- Return type
- get_eq_cstr_total_dim()¶
Retrieve the total dimension of the equality constraints.
This dimension is the sum of all the outputs dimensions of all the equality constraints.
- Returns
The total dimension of the equality constraints.
- Return type
- get_feasible_points()¶
Retrieve the feasible points within a given tolerance.
This tolerance is defined by
OptimizationProblem.eq_tolerance
for equality constraints andOptimizationProblem.ineq_tolerance
for inequality ones.
- get_function_dimension(name)¶
Return the dimension of a function of the problem (e.g. a constraint).
- Parameters
name (str) – The name of the function.
- Returns
The dimension of the function.
- Raises
ValueError – If the function name is unknown to the problem.
RuntimeError – If the function dimension is not unavailable.
- Return type
- get_function_names(names)¶
Return the names of the functions stored in the database.
- get_functions_dimensions(names=None)¶
Return the dimensions of the outputs of the problem functions.
- Parameters
names (Iterable[str] | None) –
The names of the functions. If None, then the objective and all the constraints are considered.
By default it is set to None.
- Returns
The dimensions of the outputs of the problem functions. The dictionary keys are the functions names and the values are the functions dimensions.
- Return type
- get_ineq_constraints()¶
Retrieve all the inequality constraints.
- Returns
The inequality constraints.
- Return type
- get_ineq_constraints_number()¶
Retrieve the number of inequality constraints.
- Returns
The number of inequality constraints.
- Return type
- get_ineq_cstr_total_dim()¶
Retrieve the total dimension of the inequality constraints.
This dimension is the sum of all the outputs dimensions of all the inequality constraints.
- Returns
The total dimension of the inequality constraints.
- Return type
- get_nonproc_constraints()¶
Retrieve the non-processed constraints.
- Returns
The non-processed constraints.
- Return type
- get_nonproc_objective()¶
Retrieve the non-processed objective function.
- get_number_of_unsatisfied_constraints(design_variables)¶
Return the number of scalar constraints not satisfied by design variables.
- Parameters
design_variables (numpy.ndarray) – The design variables.
- Returns
The number of unsatisfied scalar constraints.
- Return type
- get_objective_name(standardize=True)¶
Retrieve the name of the objective function.
- get_observable(name)¶
Retrieve an observable from its name.
- Parameters
name (str) – The name of the observable.
- Returns
The observable.
- Raises
ValueError – If the observable cannot be found.
- Return type
- get_optimum()¶
Return the optimum solution within a given feasibility tolerances.
- Returns
The optimum result, defined by:
the value of the objective function,
the value of the design variables,
the indicator of feasibility of the optimal solution,
the value of the constraints,
the value of the gradients of the constraints.
- Return type
Tuple[numpy.ndarray, numpy.ndarray, bool, Dict[str, numpy.ndarray], Dict[str, numpy.ndarray]]
- get_scalar_constraints_names()¶
Return the names of the scalar constraints.
- get_solution()[source]¶
Return the theoretical optimal value.
- Returns
The design variables and the objective at optimum.
- Return type
- get_violation_criteria(x_vect)¶
Compute a violation measure associated to an iteration.
For each constraint, when it is violated, add the absolute distance to zero, in L2 norm.
If 0, all constraints are satisfied
- Parameters
x_vect (numpy.ndarray) – The vector of the design variables values.
- Returns
The feasibility of the point and the violation measure.
- Return type
- get_x0_normalized(cast_to_real=False)¶
Return the current values of the design variables after normalization.
- Parameters
cast_to_real (bool) –
Whether to cast the return value to real.
By default it is set to False.
- Returns
The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.
- Return type
- has_constraints()¶
Check if the problem has equality or inequality constraints.
- Returns
True if the problem has equality or inequality constraints.
- has_eq_constraints()¶
Check if the problem has equality constraints.
- Returns
True if the problem has equality constraints.
- Return type
- has_ineq_constraints()¶
Check if the problem has inequality constraints.
- Returns
True if the problem has inequality constraints.
- Return type
- has_nonlinear_constraints()¶
Check if the problem has non-linear constraints.
- Returns
True if the problem has equality or inequality constraints.
- Return type
- classmethod import_hdf(file_path, x_tolerance=0.0)¶
Import an optimization history from an HDF file.
- Parameters
- Returns
The read optimization problem.
- Return type
- is_max_iter_reached()¶
Check if the maximum amount of iterations has been reached.
- Returns
Whether the maximum amount of iterations has been reached.
- Return type
- is_point_feasible(out_val, constraints=None)¶
Check if a point is feasible.
Note
If the value of a constraint is absent from this point, then this constraint will be considered satisfied.
- Parameters
out_val (dict[str, ndarray]) – The values of the objective function, and eventually constraints.
constraints (Iterable[MDOFunction] | None) –
The constraints whose values are to be tested. If None, then take all constraints of the problem.
By default it is set to None.
- Returns
The feasibility of the point.
- Return type
- preprocess_functions(is_function_input_normalized=True, use_database=True, round_ints=True, eval_obs_jac=False)¶
Pre-process all the functions and eventually the gradient.
Required to wrap the objective function and constraints with the database and eventually the gradients by complex step or finite differences.
- Parameters
is_function_input_normalized (bool) –
Whether to consider the function input as normalized and unnormalize it before the evaluation takes place.
By default it is set to True.
use_database (bool) –
Whether to wrap the functions in the database.
By default it is set to True.
round_ints (bool) –
Whether to round the integer variables.
By default it is set to True.
eval_obs_jac (bool) –
Whether to evaluate the Jacobian of the observables.
By default it is set to False.
- Return type
None
- static repr_constraint(func, ctype, value=None, positive=False)¶
Express a constraint as a string expression.
- Parameters
func (MDOFunction) – The constraint function.
ctype (str) – The type of the constraint. Either equality or inequality.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Returns
A string representation of the constraint.
- Return type
- reset(database=True, current_iter=True, design_space=True, function_calls=True, preprocessing=True)¶
Partially or fully reset the optimization problem.
- Parameters
database (bool) –
Whether to clear the database.
By default it is set to True.
current_iter (bool) –
Whether to reset the current iteration
OptimizationProblem.current_iter
.By default it is set to True.
design_space (bool) –
Whether to reset the current point of the
OptimizationProblem.design_space
to its initial value (possibly none).By default it is set to True.
function_calls (bool) –
Whether to reset the number of calls of the functions.
By default it is set to True.
preprocessing (bool) –
Whether to turn the pre-processing of functions to False.
By default it is set to True.
- Return type
None
- DIFFERENTIATION_METHODS: ClassVar[str] = ['user', 'complex_step', 'finite_differences', 'no_derivatives']¶
- OPTIM_DESCRIPTION: ClassVar[str] = ['minimize_objective', 'fd_step', 'differentiation_method', 'pb_type', 'ineq_tolerance', 'eq_tolerance']¶
- activate_bound_check: ClassVar[bool] = True¶
Whether to check if a point is in the design space before calling functions.
- constraint_names: dict[str, list[str]]¶
The standardized constraint names bound to the original ones.
- constraints: list[MDOFunction]¶
The constraints.
- design_space: DesignSpace¶
The design space on which the optimization problem is solved.
- new_iter_observables: list[MDOFunction]¶
The observables to be called at each new iterate.
- nonproc_constraints: list[MDOFunction]¶
The non-processed constraints.
- nonproc_new_iter_observables: list[MDOFunction]¶
The non-processed observables to be called at each new iterate.
- nonproc_objective: MDOFunction¶
The non-processed objective function.
- nonproc_observables: list[MDOFunction]¶
The non-processed observables.
- property objective: gemseo.core.mdofunctions.mdo_function.MDOFunction¶
The objective function.
- observables: list[MDOFunction]¶
The observables.
- property parallel_differentiation_options: bool¶
The options to approximate the derivatives in parallel.
- solution: OptimizationResult¶
The solution of the optimization problem.
- use_standardized_objective: bool¶
Whether to use standardized objective for logging and post-processing.
The standardized objective corresponds to the original one expressed as a cost function to minimize. A
DriverLib
works with this standardized objective and theDatabase
stores its values. However, for convenience, it may be more relevant to log the expression and the values of the original objective.