Scalable models

Scalability study - API

This API facilitates the use of the gemseo.problems.scalable.data_driven.study package implementing classes to benchmark MDO formulations based on scalable disciplines.

ScalabilityStudy class implements the concept of scalability study:

  1. By instantiating a ScalabilityStudy, the user defines the MDO problem in terms of design parameters, objective function and constraints.

  2. For each discipline, the user adds a dataset stored in a Dataset and select a type of ScalableModel to build the ScalableDiscipline associated with this discipline.

  3. The user adds different optimization strategies, defined in terms of both optimization algorithms and MDO formulation.

  4. The user adds different scaling strategies, in terms of sizes of design parameters, coupling variables and equality and inequality constraints. The user can also define a scaling strategies according to particular parameters rather than groups of parameters.

  5. Lastly, the user executes the ScalabilityStudy and the results are written in several files and stored into directories in a hierarchical way, where names depend on both MDO formulation, scaling strategy and replications when it is necessary. Different kinds of files are stored: optimization graphs, dependency matrix plots and of course, scalability results by means of a dedicated class: ScalabilityResult.

gemseo.problems.scalable.data_driven.api.create_scalability_study(objective, design_variables, directory='study', prefix='', eq_constraints=None, ineq_constraints=None, maximize_objective=False, fill_factor=0.7, active_probability=0.1, feasibility_level=0.8, start_at_equilibrium=True, early_stopping=True, coupling_variables=None)[source]

This method creates a ScalabilityStudy. It requires two mandatory arguments:

  • the 'objective' name,

  • the list of 'design_variables' names.

Concerning output files, we can specify:

  • the directory which is 'study' by default,

  • the prefix of output file names (default: no prefix).

Regarding optimization parametrization, we can specify:

  • the list of equality constraints names (eq_constraints),

  • the list of inequality constraints names (ineq_constraints),

  • the choice of maximizing the objective function (maximize_objective).

By default, the objective function is minimized and the MDO problem is unconstrained.

Last but not least, with regard to the scalability methodology, we can overwrite:

  • the default fill factor of the input-output dependency matrix ineq_constraints,

  • the probability to set the inequality constraints as active at initial step of the optimization active_probability,

  • the offset of satisfaction for inequality constraints feasibility_level,

  • the use of a preliminary MDA to start at equilibrium start_at_equilibrium,

  • the post-processing of the optimization database to get results earlier than final step early_stopping.

Parameters:
  • objective (str) – name of the objective

  • design_variables (list(str)) – names of the design variables

  • directory (str) –

    working directory of the study. Default: ‘study’.

    By default it is set to “study”.

  • prefix (str) –

    prefix for the output filenames. Default: ‘’.

    By default it is set to “”.

  • eq_constraints (list(str)) – names of the equality constraints. Default: None.

  • ineq_constraints (list(str)) – names of the inequality constraints Default: None.

  • maximize_objective (bool) –

    maximizing objective. Default: False.

    By default it is set to False.

  • fill_factor (float) –

    default fill factor of the input-output dependency matrix. Default: 0.7.

    By default it is set to 0.7.

  • active_probability (float) –

    probability to set the inequality constraints as active at initial step of the optimization. Default: 0.1

    By default it is set to 0.1.

  • feasibility_level (float) –

    offset of satisfaction for inequality constraints. Default: 0.8.

    By default it is set to 0.8.

  • start_at_equilibrium (bool) –

    start at equilibrium using a preliminary MDA. Default: True.

    By default it is set to True.

  • early_stopping (bool) –

    post-process the optimization database to get results earlier than final step.

    By default it is set to True.

gemseo.problems.scalable.data_driven.api.plot_scalability_results(study_directory)[source]

This method plots the set of ScalabilityResult generated by a ScalabilityStudy and located in the directory created by this study.

Parameters:

study_directory (str) – directory of the scalability study.

Scalable MDO problem

This module implements the concept of scalable problem by means of the ScalableProblem class.

Given

  • a MDO scenario based on a set of sampled disciplines with a particular problem dimension,

  • a new problem dimension (= number of inputs and outputs),

a scalable problem:

  1. makes each discipline scalable based on the new problem dimension,

  2. creates the corresponding MDO scenario.

Then, this MDO scenario can be executed and post-processed.

We can repeat this tasks for different sizes of variables and compare the scalability, which is the dependence of the scenario results on the problem dimension.

class gemseo.problems.scalable.data_driven.problem.ScalableProblem(datasets, design_variables, objective_function, eq_constraints=None, ineq_constraints=None, maximize_objective=False, sizes=None, **parameters)[source]

Scalable problem.

Constructor.

Parameters:
  • datasets (list(Dataset)) – disciplinary datasets.

  • design_variables (list(str)) – list of design variable names

  • objective_function (str) – objective function

  • eq_constraints (list(str)) – equality constraints. Default: None.

  • eq_constraints – inequality constraints. Default: None.

  • maximize_objective (bool) –

    maximize objective. Default: False.

    By default it is set to False.

  • sizes (dict) – sizes of input and output variables. If None, use the original sizes. Default: None.

  • parameters – optional parameters for the scalable model.

create_scenario(formulation='DisciplinaryOpt', scenario_type='MDO', start_at_equilibrium=False, active_probability=0.1, feasibility_level=0.5, **options)[source]

Create a Scenario from the scalable disciplines.

Parameters:
  • formulation (str) –

    The MDO formulation to use for the scenario.

    By default it is set to “DisciplinaryOpt”.

  • scenario_type (str) –

    The type of scenario, either MDO or DOE.

    By default it is set to “MDO”.

  • start_at_equilibrium (bool) –

    Whether to start at equilibrium using a preliminary MDA.

    By default it is set to False.

  • active_probability (float) –

    The probability to set the inequality constraints as active at the initial step of the optimization.

    By default it is set to 0.1.

  • feasibility_level (float) –

    The offset of satisfaction for inequality constraints.

    By default it is set to 0.5.

  • **options – The formulation options.

Returns:

The Scenario from the scalable disciplines.

Return type:

Scenario

exec_time(do_sum=True)[source]

Get total execution time per discipline.

Parameters:

do_sum (bool) –

sum over disciplines (default: True)

By default it is set to True.

Returns:

execution time

Return type:

list(float) or float

plot_1d_interpolations(save=True, show=False, step=0.01, varnames=None, directory='.', png=False)[source]

Plot 1d interpolations.

Parameters:
  • save (bool) –

    save plot. Default: True.

    By default it is set to True.

  • show (bool) –

    show plot. Default: False.

    By default it is set to False.

  • step (bool) –

    Step to evaluate the 1d interpolation function Default: 0.01.

    By default it is set to 0.01.

  • varnames (list(str)) – names of the variable to plot; if None, all variables are plotted. Default: None.

  • directory (str) –

    directory path. Default: ‘.’.

    By default it is set to “.”.

  • png (bool) –

    if True, the file format is PNG. Otherwise, use PDF. Default: False.

    By default it is set to False.

plot_coupling_graph()[source]

Plot a coupling graph.

plot_dependencies(save=True, show=False, directory='.')[source]

Plot dependency matrices.

Parameters:
  • save (bool) –

    save plot (default: True)

    By default it is set to True.

  • show (bool) –

    show plot (default: False)

    By default it is set to False.

  • directory (str) –

    directory path (default: ‘.’)

    By default it is set to “.”.

plot_n2_chart(save=True, show=False)[source]

Plot a N2 chart.

Parameters:
  • save (bool) –

    save plot. Default: True.

    By default it is set to True.

  • show (bool) –

    show plot. Default: False.

    By default it is set to False.

property is_feasible

Get the feasibility property of the scenario.

property n_calls

Get number of disciplinary calls per discipline.

Returns:

number of disciplinary calls per discipline

Return type:

list(int) or int

property n_calls_linearize

Get number of disciplinary calls per discipline.

Returns:

number of disciplinary calls per discipline

Return type:

list(int) or int

property n_calls_linearize_top_level

Get number of top level disciplinary calls per discipline.

Returns:

number of top level disciplinary calls per discipline

Return type:

list(int) or int

property n_calls_top_level

Get number of top level disciplinary calls per discipline.

Returns:

number of top level disciplinary calls per discipline

Return type:

list(int) or int

property status

Get the status of the scenario.

Scalable discipline

The discipline implements the concept of scalable discipline. This is a particular discipline built from an input-output learning dataset associated with a function and generalizing its behavior to a new user-defined problem dimension, that is to say new user-defined input and output dimensions.

Alone or in interaction with other objects of the same type, a scalable discipline can be used to compare the efficiency of an algorithm applying to disciplines with respect to the problem dimension, e.g. optimization algorithm, surrogate model, MDO formulation, MDA, …

The ScalableDiscipline class implements this concept. It inherits from the MDODiscipline class in such a way that it can easily be used in a Scenario. It is composed of a ScalableModel.

The user only needs to provide:

  • the name of a class overloading ScalableModel,

  • a dataset as an Dataset

  • variables sizes as a dictionary whose keys are the names of inputs and outputs and values are their new sizes. If a variable is missing, its original size is considered.

The ScalableModel parameters can also be filled in, otherwise the model uses default values.

class gemseo.problems.scalable.data_driven.discipline.ScalableDiscipline(name, data, sizes=None, **parameters)[source]

Scalable discipline.

Constructor.

Parameters:
  • name (str) – scalable model class name.

  • data (Dataset) – learning dataset.

  • sizes (dict) – sizes of input and output variables. If None, use the original sizes. Default: None.

  • parameters – model parameters

  • name – The name of the discipline. If None, use the class name.

  • input_grammar_file – The input grammar file path. If None and auto_detect_grammar_files=True, look for "ClassName_input.json" in the GRAMMAR_DIRECTORY if any or in the directory of the discipline class module. If None and auto_detect_grammar_files=False, do not initialize the input grammar from a schema file.

  • output_grammar_file – The output grammar file path. If None and auto_detect_grammar_files=True, look for "ClassName_output.json" in the GRAMMAR_DIRECTORY if any or in the directory of the discipline class module. If None and auto_detect_grammar_files=False, do not initialize the output grammar from a schema file.

  • auto_detect_grammar_files – Whether to look for "ClassName_{input,output}.json" in the GRAMMAR_DIRECTORY if any or in the directory of the discipline class module when {input,output}_grammar_file is None.

  • grammar_type – The type of grammar to define the input and output variables, e.g. MDODiscipline.JSON_GRAMMAR_TYPE or MDODiscipline.SIMPLE_GRAMMAR_TYPE.

  • cache_type – The type of policy to cache the discipline evaluations, e.g. MDODiscipline.SIMPLE_CACHE to cache the last one, MDODiscipline.HDF5_CACHE to cache them in an HDF file, or MDODiscipline.MEMORY_FULL_CACHE to cache them in memory. If None or if activate_cache is True, do not cache the discipline evaluations.

  • cache_file_path – The HDF file path when grammar_type is MDODiscipline.HDF5_CACHE.

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 the inputs against which to differentiate the outputs.

Parameters:

inputs (Iterable[str] | None) – The input variables against which to differentiate the outputs. If None, all the inputs of the discipline are used.

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 the outputs to be differentiated.

Parameters:

outputs (Iterable[str] | None) – The output variables to be differentiated. If None, all the outputs of the discipline are used.

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 + namespaces_separator + name.

Parameters:
  • name (str) – The element name to rename.

  • namespace (str) – The name of the namespace.

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 + namespaces_separator + name.

Parameters:
  • name (str) – The element name to rename.

  • namespace (str) – The name of the namespace.

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 named name + "_input.json" or an output grammar file named name + "_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.

  • 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.

Returns:

The grammar file path.

Return type:

str

check_input_data(input_data, raise_exception=True)

Check the input data validity.

Parameters:
  • input_data (dict[str, Any]) – The input data needed to execute the discipline according to the discipline input grammar.

  • raise_exception (bool) –

    Whether to raise on error.

    By default it is set to True.

Return type:

None

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.

  • 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.

  • outputs (Iterable[str] | None) – The names of the outputs to be differentiated.

  • 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 is True.

    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.

  • 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} where variable_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 the inputs and outputs.

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:

MDODiscipline

execute(input_data=None)

Execute the discipline.

This method executes the discipline:

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.

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:

dict[str, Any]

get_all_inputs()

Return the local input data as a list.

The order is given by MDODiscipline.get_input_data_names().

Returns:

The local input data.

Return type:

list[Any]

get_all_outputs()

Return the local output data as a list.

The order is given by MDODiscipline.get_output_data_names().

Returns:

The local output data.

Return type:

list[Any]

get_attributes_to_serialize()

Define the names of the attributes to be serialized.

Shall be overloaded by disciplines

Returns:

The names of the attributes to be serialized.

Return type:

list[str]

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.

Parameters:
  • keys (str | Iterable) – One or several names.

  • data_dict (dict[str, Any]) – The mapping from which to get the data.

Returns:

Either a data or a generator of data.

Return type:

Any | Generator[Any]

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:

list[gemseo.core.discipline.MDODiscipline]

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:

SerialExecSequence

get_input_data(with_namespaces=True)

Return the local input data as a dictionary.

Parameters:

with_namespaces

Whether to keep the namespace prefix of the input names, if any.

By default it is set to True.

Returns:

The local input data.

Return type:

dict[str, Any]

get_input_data_names(with_namespaces=True)

Return the names of the input variables.

Parameters:

with_namespaces

Whether to keep the namespace prefix of the input names, if any.

By default it is set to True.

Returns:

The names of the input variables.

Return type:

list[str]

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.

Returns:

The name of the input and output variables.

Return type:

list[str]

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:

ndarray

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:

list[Any]

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.

Parameters:

with_namespaces

Whether to keep the namespace prefix of the output names, if any.

By default it is set to True.

Returns:

The local output data.

Return type:

dict[str, Any]

get_output_data_names(with_namespaces=True)

Return the names of the output variables.

Parameters:

with_namespaces

Whether to keep the namespace prefix of the output names, if any.

By default it is set to True.

Returns:

The names of the output variables.

Return type:

list[str]

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:

ndarray

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:

list[Any]

get_sub_disciplines(recursive=False)

Determine the sub-disciplines.

This method lists the sub-disciplines’ disciplines. It will list up to one level of disciplines contained inside another one unless the recursive argument is set to True.

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. If False, 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:

list[gemseo.core.discipline.MDODiscipline]

initialize_grammars(data)[source]

Initialize input and output grammars from data names.

Parameters:

data (Dataset) – learning dataset.

is_all_inputs_existing(data_names)

Test if several variables are discipline inputs.

Parameters:

data_names (Iterable[str]) – The names of the variables.

Returns:

Whether all the variables are discipline inputs.

Return type:

bool

is_all_outputs_existing(data_names)

Test if several variables are discipline outputs.

Parameters:

data_names (Iterable[str]) – The names of the variables.

Returns:

Whether all the variables are discipline outputs.

Return type:

bool

is_input_existing(data_name)

Test if a variable is a discipline input.

Parameters:

data_name (str) – The name of the variable.

Returns:

Whether the variable is a discipline input.

Return type:

bool

is_output_existing(data_name)

Test if a variable is a discipline output.

Parameters:

data_name (str) – The name of the variable.

Returns:

Whether the variable is a discipline output.

Return type:

bool

static is_scenario()

Whether the discipline is a scenario.

Return type:

bool

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.

  • force_all (bool) –

    If False, MDODiscipline._differentiated_inputs and MDODiscipline._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:

dict[str, dict[str, ndarray]]

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 and HDF5Cache. Caching data can be either in-memory, e.g. SimpleCache and MemoryFullCache, 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.

  • cache_hdf_node_name (str | None) – The name of the HDF file node to store the discipline data. If None, MDODiscipline.name is used.

  • 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.

  • outputs (Iterable[str] | None) – The outputs to be linearized. If None, use the MDODiscipline._differentiated_outputs.

  • 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

GRAMMAR_DIRECTORY: ClassVar[str | None] = None

The directory in which to search for the grammar files if not the class one.

activate_cache: bool = True

Whether to cache the discipline evaluations by default.

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 | None

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 calling self.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 disciplines: list[gemseo.core.discipline.MDODiscipline]

The sub-disciplines, if any.

exec_for_lin: bool

Whether the last execution was due to a linearization.

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: 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: 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.

name: str

The name of the discipline.

output_grammar: BaseGrammar

The output grammar.

re_exec_policy: str

The policy to re-execute the same discipline.

residual_variables: Mapping[str, str]

The output variables mapping to their inputs, to be considered as residuals; they shall be equal to zero.

run_solves_residuals: bool

If True, the run method shall solve the residuals.

property status: str

The status of the discipline.

Scalable model factory

This module contains the ScalableModelFactory which is a factory to create a ScalableModel from its class name by means of the ScalableModelFactory.create() method. It is also possible to get a list of available scalable models (see ScalableModelFactory.scalable_models method) and to check is a type of scalable model is available (see ScalableModelFactory.is_available() method)

class gemseo.problems.scalable.data_driven.factory.ScalableModelFactory[source]

This factory instantiates a class:.ScalableModel from its class name.

The class can be internal to GEMSEO or located in an external module whose path is provided to the constructor.

Initializes the factory: scans the directories to search for subclasses of ScalableModel.

Searches in “GEMSEO_PATH” and gemseo.caches

create(model_name, data, sizes=None, **parameters)[source]

Create a scalable model.

Parameters:
  • model_name (str) – name of the scalable model (its class name)

  • data (Dataset) – learning dataset.

  • sizes (dict) – sizes of input and output variables. If None, use the original sizes. Default: None.

  • parameters – model parameters

Returns:

model_name scalable model

is_available(model_name)[source]

Checks the availability of a scalable model.

Parameters:

model_name (str) – model_name of the scalable model.

Returns:

True if the scalable model is available.

Return type:

bool

property scalable_models

Lists the available classes for scalable models.

Returns:

the list of classes names.

Return type:

list(str)

Scalable model

This module implements the abstract concept of scalable model which is used by scalable disciplines. A scalable model is built from an input-output learning dataset associated with a function and generalizing its behavior to a new user-defined problem dimension, that is to say new user-defined input and output dimensions.

The concept of scalable model is implemented through ScalableModel, an abstract class which is instantiated from:

  • data provided as a Dataset

  • variables sizes provided as a dictionary whose keys are the names of inputs and outputs and values are their new sizes. If a variable is missing, its original size is considered.

Scalable model parameters can also be filled in. Otherwise, the model uses default values.

See also

The ScalableDiagonalModel class overloads ScalableModel.

class gemseo.problems.scalable.data_driven.model.ScalableModel(data, sizes=None, **parameters)[source]

Scalable model.

Constructor.

Parameters:
  • data (Dataset) – learning dataset.

  • sizes (dict) – sizes of input and output variables. If None, use the original sizes. Default: None.

  • parameters – model parameters

build_model()[source]

Build model with original sizes for input and output variables.

compute_bounds()[source]

Compute lower and upper bounds of both input and output variables.

Returns:

lower bounds, upper bounds.

Return type:

dict, dict

normalize_data()[source]

Normalize dataset from lower and upper bounds.

scalable_derivatives(input_value=None)[source]

Evaluate the scalable derivatives.

Parameters:

input_value (dict) – input values. If None, use default inputs. Default: None

Returns:

evaluation of the scalable derivatives.

Return type:

dict

scalable_function(input_value=None)[source]

Evaluate the scalable function.

Parameters:

input_value (dict) – input values. If None, use default inputs. Default: None.

Returns:

evaluation of the scalable function.

Return type:

dict

property inputs_names

Inputs names.

Returns:

names of the inputs.

Return type:

list(str)

property original_sizes

Original sizes of variables.

Returns:

original sizes of variables.

Return type:

dict

property outputs_names

Outputs names.

Returns:

names of the outputs.

Return type:

list(str)

Scalable diagonal model

This module implements the concept of scalable diagonal model, which is a particular scalable model built from an input-output dataset relying on a diagonal design of experiments (DOE) where inputs vary proportionally from their lower bounds to their upper bounds, following the diagonal of the input space.

So for every output, the dataset catches its evolution with respect to this proportion, which makes it a mono dimensional behavior. Then, for a new user-defined problem dimension, the scalable model extrapolates this mono dimensional behavior to the different input directions.

The concept of scalable diagonal model is implemented through the ScalableDiagonalModel class which is composed of a ScalableDiagonalApproximation. With regard to the diagonal DOE, GEMSEO proposes the DiagonalDOE class.

class gemseo.problems.scalable.data_driven.diagonal.ScalableDiagonalApproximation(sizes, output_dependency, io_dependency, seed=0)[source]

Methodology that captures the trends of a physical problem, and extends it into a problem that has scalable input and outputs dimensions The original and the resulting scalable problem have the same interface:

all inputs and outputs have the same names; only their dimensions vary.

Constructor:

Parameters:
  • sizes (dict) – sizes of both input and output variables.

  • output_dependency (dict) – dependency between old and new outputs.

  • io_dependency (dict) – dependency between new inputs and new outputs.

build_scalable_function(function_name, dataset, input_names, degree=3)[source]

Build interpolation from a 1D input and output function. Add the model to the local dictionary.

Parameters:
  • function_name (str) – name of the output function

  • dataset (Dataset) – the input-output dataset

  • input_names (list(str)) – names of the input variables

  • degree (int) –

    degree of interpolation (Default value = 3)

    By default it is set to 3.

get_scalable_derivative(output_function)[source]

Retrieve the (scalable) gradient of the scalable function generated from the original discipline.

Parameters:

output_function (str) – name of the output function

get_scalable_function(output_function)[source]

Retrieve the scalable function generated from the original discipline.

Parameters:

output_function (str) – name of the output function

static scale_samples(samples)[source]

Scale samples of array into [0, 1]

Parameters:

samples (list(ndarray)) – samples of multivariate array

Returns:

samples of multivariate array

Return type:

ndarray

class gemseo.problems.scalable.data_driven.diagonal.ScalableDiagonalModel(data, sizes=None, fill_factor=-1, comp_dep=None, inpt_dep=None, force_input_dependency=False, allow_unused_inputs=True, seed=1, group_dep=None)[source]

Scalable diagonal model.

Constructor.

Parameters:
  • data (Dataset) – learning dataset.

  • sizes (dict) – sizes of input and output variables. If None, use the original sizes. Default: None.

  • fill_factor

    degree of sparsity of the dependency matrix. Default: -1.

    By default it is set to -1.

  • comp_dep – matrix that establishes the selection of a single original component for each scalable component

  • inpt_dep – dependency matrix that establishes the dependency of outputs wrt inputs

  • force_input_dependency (bool) –

    for any output, force dependency with at least on input.

    By default it is set to False.

  • allow_unused_inputs (bool) –

    possibility to have an input with no dependence with any output

    By default it is set to True.

  • seed (int) –

    seed

    By default it is set to 1.

  • group_dep (dict(list(str))) – dependency between inputs and outputs

build_model()[source]

Build model with original sizes for input and output variables.

Returns:

scalable approximation.

Return type:

ScalableDiagonalApproximation

compute_bounds()

Compute lower and upper bounds of both input and output variables.

Returns:

lower bounds, upper bounds.

Return type:

dict, dict

generate_random_dependency()[source]

Generates a random dependency structure for use in scalable discipline.

Returns:

output component dependency and input-output dependency

Return type:

dict(int), dict(dict(ndarray))

normalize_data()

Normalize dataset from lower and upper bounds.

plot_1d_interpolations(save=False, show=False, step=0.01, varnames=None, directory='.', png=False)[source]

Plot the scaled 1D interpolations, a.k.a. the basis functions.

A basis function is a mono dimensional function interpolating the samples of a given output component over the input sampling line \(t\in[0,1]\mapsto \\underline{x}+t(\overline{x}-\\underline{x})\).

There are as many basis functions as there are output components from the discipline. Thus, for a discipline with a single output in dimension 1, there is 1 basis function. For a discipline with a single output in dimension 2, there are 2 basis functions. For a discipline with an output in dimension 2 and an output in dimension 13, there are 15 basis functions. And so on. This method allows to plot the basis functions associated with all outputs or only part of them, either on screen (show=True), in a file (save=True) or both. We can also specify the discretization step whose default value is 0.01.

Parameters:
  • save (bool) –

    if True, export the plot as a PDF file (Default value = False)

    By default it is set to False.

  • show (bool) –

    if True, display the plot (Default value = False)

    By default it is set to False.

  • step (bool) –

    Step to evaluate the 1d interpolation function (Default value = 0.01)

    By default it is set to 0.01.

  • varnames (list(str)) – names of the variable to plot; if None, all variables are plotted (Default value = None)

  • directory (str) –

    directory path. Default: ‘.’.

    By default it is set to “.”.

  • png (bool) –

    if True, the file format is PNG. Otherwise, use PDF. Default: False.

    By default it is set to False.

plot_dependency(add_levels=True, save=True, show=False, directory='.', png=False)[source]

This method plots the dependency matrix of a discipline in the form of a chessboard, where rows represent inputs, columns represent output and gray scale represent the dependency level between inputs and outputs.

Parameters:
  • add_levels (bool) –

    add values of dependency levels in percentage. Default: True.

    By default it is set to True.

  • save (bool) –

    if True, export the plot into a file. Default: True.

    By default it is set to True.

  • show (bool) –

    if True, display the plot. Default: False.

    By default it is set to False.

  • directory (str) –

    directory path. Default: ‘.’.

    By default it is set to “.”.

  • png (bool) –

    if True, the file format is PNG. Otherwise, use PDF. Default: False.

    By default it is set to False.

scalable_derivatives(input_value=None)[source]

Evaluate the scalable derivatives.

Parameters:

input_value (dict) – input values. If None, use default inputs.

Returns:

evaluation of the scalable derivatives.

Return type:

dict

scalable_function(input_value=None)[source]

Evaluate the scalable functions.

Parameters:

input_value (dict) – input values. If None, use default inputs.

Returns:

evaluation of the scalable functions.

Return type:

dict

property inputs_names

Inputs names.

Returns:

names of the inputs.

Return type:

list(str)

property original_sizes

Original sizes of variables.

Returns:

original sizes of variables.

Return type:

dict

property outputs_names

Outputs names.

Returns:

names of the outputs.

Return type:

list(str)

gemseo.problems.scalable.data_driven.diagonal.choice(a, size=None, replace=True, p=None)

Generates a random sample from a given 1-D array

New in version 1.7.0.

Note

New code should use the choice method of a default_rng() instance instead; please see the Quick Start.

Parameters:
  • a (1-D array-like or int) – If an ndarray, a random sample is generated from its elements. If an int, the random sample is generated as if it were np.arange(a)

  • size (int or tuple of ints, optional) – Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned.

  • replace (boolean, optional) – Whether the sample is with or without replacement. Default is True, meaning that a value of a can be selected multiple times.

  • p (1-D array-like, optional) – The probabilities associated with each entry in a. If not given, the sample assumes a uniform distribution over all entries in a.

Returns:

samples – The generated random samples

Return type:

single item or ndarray

Raises:

ValueError – If a is an int and less than zero, if a or p are not 1-dimensional, if a is an array-like of size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size

See also

randint, shuffle, permutation

random.Generator.choice

which should be used in new code

Notes

Setting user-specified probabilities through p uses a more general but less efficient sampler than the default. The general sampler produces a different sample than the optimized sampler even if each element of p is 1 / len(a).

Sampling random rows from a 2-D array is not possible with this function, but is possible with Generator.choice through its axis keyword.

Examples

Generate a uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3)
array([0, 3, 4]) # random
>>> #This is equivalent to np.random.randint(0,5,3)

Generate a non-uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0])
array([3, 3, 0]) # random

Generate a uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False)
array([3,1,0]) # random
>>> #This is equivalent to np.random.permutation(np.arange(5))[:3]

Generate a non-uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0])
array([2, 3, 0]) # random

Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance:

>>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher']
>>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])
array(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], # random
      dtype='<U11')
gemseo.problems.scalable.data_driven.diagonal.npseed()

seed(self, seed=None)

Reseed a legacy MT19937 BitGenerator

Notes

This is a convenience, legacy function.

The best practice is to not reseed a BitGenerator, rather to recreate a new one. This method is here for legacy reasons. This example demonstrates best practice.

>>> from numpy.random import MT19937
>>> from numpy.random import RandomState, SeedSequence
>>> rs = RandomState(MT19937(SeedSequence(123456789)))
# Later, you want to restart the stream
>>> rs = RandomState(MT19937(SeedSequence(987654321)))
gemseo.problems.scalable.data_driven.diagonal.rand(d0, d1, ..., dn)

Random values in a given shape.

Note

This is a convenience function for users porting code from Matlab, and wraps random_sample. That function takes a tuple to specify the size of the output, which is consistent with other NumPy functions like numpy.zeros and numpy.ones.

Create an array of the given shape and populate it with random samples from a uniform distribution over [0, 1).

Parameters:
  • d0 (int, optional) – The dimensions of the returned array, must be non-negative. If no argument is given a single Python float is returned.

  • d1 (int, optional) – The dimensions of the returned array, must be non-negative. If no argument is given a single Python float is returned.

  • ... (int, optional) – The dimensions of the returned array, must be non-negative. If no argument is given a single Python float is returned.

  • dn (int, optional) – The dimensions of the returned array, must be non-negative. If no argument is given a single Python float is returned.

Returns:

out – Random values.

Return type:

ndarray, shape (d0, d1, ..., dn)

See also

random

Examples

>>> np.random.rand(3,2)
array([[ 0.14022471,  0.96360618],  #random
       [ 0.37601032,  0.25528411],  #random
       [ 0.49313049,  0.94909878]]) #random
gemseo.problems.scalable.data_driven.diagonal.randint(low, high=None, size=None, dtype=int)

Return random integers from low (inclusive) to high (exclusive).

Return random integers from the “discrete uniform” distribution of the specified dtype in the “half-open” interval [low, high). If high is None (the default), then results are from [0, low).

Note

New code should use the integers method of a default_rng() instance instead; please see the Quick Start.

Parameters:
  • low (int or array-like of ints) – Lowest (signed) integers to be drawn from the distribution (unless high=None, in which case this parameter is one above the highest such integer).

  • high (int or array-like of ints, optional) – If provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if high=None). If array-like, must contain integer values

  • size (int or tuple of ints, optional) – Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned.

  • dtype (dtype, optional) –

    Desired dtype of the result. Byteorder must be native. The default value is int.

    New in version 1.11.0.

Returns:

outsize-shaped array of random integers from the appropriate distribution, or a single such random int if size not provided.

Return type:

int or ndarray of ints

See also

random_integers

similar to randint, only for the closed interval [low, high], and 1 is the lowest value if high is omitted.

random.Generator.integers

which should be used for new code.

Examples

>>> np.random.randint(2, size=10)
array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) # random
>>> np.random.randint(1, size=10)
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

Generate a 2 x 4 array of ints between 0 and 4, inclusive:

>>> np.random.randint(5, size=(2, 4))
array([[4, 0, 2, 1], # random
       [3, 2, 2, 0]])

Generate a 1 x 3 array with 3 different upper bounds

>>> np.random.randint(1, [3, 5, 10])
array([2, 2, 9]) # random

Generate a 1 by 3 array with 3 different lower bounds

>>> np.random.randint([1, 5, 7], 10)
array([9, 8, 7]) # random

Generate a 2 by 4 array using broadcasting with dtype of uint8

>>> np.random.randint([1, 3, 5, 7], [[10], [20]], dtype=np.uint8)
array([[ 8,  6,  9,  7], # random
       [ 1, 16,  9, 12]], dtype=uint8)

MDODiscipline <|-- ScalableDiscipline
ScalableDiscipline *-- ScalableModel
ScalableModel <|-- ScalableDiagonalModel
ScalableDiagonalModel *-- ScalableApproximation

class ScalableDiscipline {
 +scalable_model
 +initialize_grammars()
     #compute_jacobian()
     #run()
     #set_default_inputs()
}

class ScalableModel {
 +cache
 +lower_bounds
 +upper_bounds
 +model
 +name
 +parameters
 +sizes
 +build_model()
 +compute_bounds()
 +inputs_names()
 +outputs_names()
 +original_sizes()
 +scalable_function()
 +scalable_derivatives()
 #set_sizes()
}