gemseo / problems / sellar

# sellar module¶

The disciplines for the MDO problem proposed by Sellar et al. in

Sellar, R., Batill, S., & Renaud, J. (1996). Response surface based, concurrent subspace optimization for multidisciplinary system design. In 34th aerospace sciences meeting and exhibit (p. 714).

The MDO problem is written as follows:

\begin{split}\begin{aligned} \text{minimize the objective function }&obj=x_{local}^2 + x_{shared,2} +y_1^2+e^{-y_2} \\ \text{with respect to the design variables }&x_{shared},\,x_{local} \\ \text{subject to the general constraints } & c_1 \leq 0\\ & c_2 \leq 0\\ \text{subject to the bound constraints } & -10 \leq x_{shared,1} \leq 10\\ & 0 \leq x_{shared,2} \leq 10\\ & 0 \leq x_{local} \leq 10. \end{aligned}\end{split}

where the coupling variables are

$\text{Discipline 1: } y_1 = \sqrt{x_{shared,1}^2 + x_{shared,2} + x_{local} - 0.2\,y_2},$

and

$\text{Discipline 2: }y_2 = |y_1| + x_{shared,1} + x_{shared,2}.$

and where the general constraints are

\begin{align}\begin{aligned}c_1 = 3.16 - y_1^2\\c_2 = y_2 - 24\end{aligned}\end{align}

This module implements three disciplines to compute the different coupling variables, constraints and objective:

Classes:

 Sellar1([residual_form]) The discipline to compute the coupling variable $$y_1$$. Sellar2([residual_form]) The discipline to compute the coupling variable $$y_2$$. The discipline to compute the objective and constraints of the Sellar problem.

Functions:

 get_inputs([names]) Generate an initial solution for the MDO problem.
class gemseo.problems.sellar.sellar.Sellar1(residual_form=False)[source]

The discipline to compute the coupling variable $$y_1$$.

input_grammar

The input grammar.

Type

AbstractGrammar

output_grammar

The output grammar.

Type

AbstractGrammar

grammar_type

The type of grammar to be used for inputs and outputs declaration.

Type

str

comp_dir

The path to the directory of the discipline module file if any.

Type

str

data_processor

A tool to pre- and post-process discipline data.

Type

DataProcessor

re_exec_policy

The policy to re-execute the same discipline.

Type

str

residual_variables

The output variables to be considered as residuals; they shall be equal to zero.

Type

List[str]

jac

The Jacobians of the outputs wrt inputs of the form {output: {input: matrix}}.

Type

Dict[str, Dict[str, ndarray]]

exec_for_lin

Whether the last execution was due to a linearization.

Type

bool

name

The name of the discipline.

Type

str

cache

The cache containing one or several executions of the discipline according to the cache policy.

Type

AbstractCache

local_data

The last input and output data.

Type

Dict[str, Any]

Initialize self. See help(type(self)) for accurate signature.

Parameters

residual_form (bool) –

If True, then only residuals are computed, not the coupling variables.

By default it is set to False.

Return type

None

Attributes:

 APPROX_MODES AVAILABLE_MODES COMPLEX_STEP FINITE_DIFFERENCES HDF5_CACHE JSON_GRAMMAR_TYPE MEMORY_FULL_CACHE N_CPUS RE_EXECUTE_DONE_POLICY RE_EXECUTE_NEVER_POLICY SIMPLE_CACHE SIMPLE_GRAMMAR_TYPE STATUS_DONE STATUS_FAILED STATUS_PENDING STATUS_RUNNING STATUS_VIRTUAL cache_tol The cache input tolerance. default_inputs The default inputs. exec_time The cumulated execution time of the discipline. grammar_type The grammar type. linearization_mode The linearization mode among LINEARIZE_MODE_LIST. n_calls The number of times the discipline was executed. n_calls_linearize The number of times the discipline was linearized. status The status of the discipline. time_stamps

Methods:

 Activate the time stamps. add_differentiated_inputs([inputs]) Add inputs against which to differentiate the outputs. add_differentiated_outputs([outputs]) Add outputs to be differentiated. Add an observer for the status. auto_get_grammar_file([is_input, name, comp_dir]) Use a naming convention to associate a grammar file to a discipline. check_input_data(input_data[, raise_exception]) Check the input data validity. check_jacobian([input_data, derr_approx, ...]) Check if the analytical Jacobian is correct with respect to a reference one. check_output_data([raise_exception]) Check the output data validity. compute_r_1(x_local, x_shared, y_1, y_2) Evaluate the first coupling equation in residual form. compute_y_1(x_local, x_shared, y_2) Evaluate the first coupling equation in functional form. Deactivate the time stamps. deserialize(in_file) Deserialize a discipline from a file. execute([input_data]) Execute the discipline. Return the local input data as a list. Return the local output data as a list. Define the names of the attributes to be serialized. get_data_list_from_dict(keys, data_dict) Filter the dict from a list of keys or a single key. Return the expected data exchange sequence. Return the expected execution sequence. Return the local input data as a dictionary. Return the names of the input variables. Return the names of the input and output variables. Return the local output data as a large NumPy array. get_inputs_by_name(data_names) Return the local data associated with input variables. get_local_data_by_name(data_names) Return the local data of the discipline associated with variables names. Return the local output data as a dictionary. Return the names of the output variables. Return the local input data as a large NumPy array. get_outputs_by_name(data_names) Return the local data associated with output variables. Return the sub-disciplines if any. 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. Whether the discipline is a scenario. linearize([input_data, force_all, force_no_exec]) Execute the linearized version of the code. Notify all status observers that the status has changed. Remove an observer for the status. Set all the statuses to PENDING. serialize(out_file) Serialize the discipline and store it in a file. set_cache_policy([cache_type, ...]) Set the type of cache to use and the tolerance level. Set the sub-disciplines statuses. Set the Jacobian approximation method. set_optimal_fd_step([outputs, inputs, ...]) Compute the optimal finite-difference step. store_local_data(**kwargs) Store discipline data in local data.
APPROX_MODES = ['finite_differences', 'complex_step']
AVAILABLE_MODES = ('auto', 'direct', 'adjoint', 'reverse', 'finite_differences', 'complex_step')
COMPLEX_STEP = 'complex_step'
FINITE_DIFFERENCES = 'finite_differences'
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'
classmethod activate_time_stamps()

Activate the time stamps.

For storing start and end times of execution and linearizations.

Return type

None

Add inputs against which to differentiate the outputs.

This method updates _differentiated_inputs with inputs.

Parameters

inputs (Optional[Iterable[str]]) –

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

This method updates _differentiated_outputs with outputs.

Parameters

outputs (Optional[Iterable[str]]) –

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 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 a discipline.

This method searches in a directory for either an input grammar file named name + "_input.json" or an output grammar file namedname + “_output.json”.

Parameters
• is_input (bool) –

If True, autodetect the input grammar file; otherwise, autodetect the output grammar file.

By default it is set to True.

• name (Optional[str]) –

The name to be searched in the file names. If None, use the name name of the discipline.

By default it is set to None.

• comp_dir (Optional[Union[str, pathlib.Path]]) –

The directory in which to search the grammar file. If None, use comp_dir.

By default it is set to None.

Returns

The grammar file path.

Return type

pathlib.Path

property cache_tol

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).

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) –

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, figsize_x=10, figsize_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

The input data needed to execute the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

• derr_approx

The approximation method, either “complex_step” or “finite_differences”.

By default it is set to finite_differences.

• threshold

The acceptance threshold for the Jacobian error.

By default it is set to 1e-08.

• linearization_mode

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

The names of the inputs wrt which to differentiate the outputs.

By default it is set to None.

• outputs

The names of the outputs to be differentiated.

By default it is set to None.

• step

The differentiation step.

By default it is set to 1e-07.

• parallel

Whether to differentiate the discipline in parallel.

By default it is set to False.

• n_processes

The maximum number of processors on which to run.

By default it is set to 2.

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

The time waited between two forks of the process / thread.

By default it is set to 0.

• auto_set_step

Whether to compute the optimal step for a forward first order finite differences gradient approximation.

By default it is set to False.

• plot_result

Whether to plot the result of the validation (computed vs approximated Jacobians).

By default it is set to False.

• file_path

The path to the output file if plot_result is True.

By default it is set to jacobian_errors.pdf.

• show

Whether to open the figure.

By default it is set to False.

• figsize_x

The x-size of the figure in inches.

By default it is set to 10.

• figsize_y

The y-size of the figure in inches.

By default it is set to 10.

• reference_jacobian_path

The path of the reference Jacobian file.

By default it is set to None.

• save_reference_jacobian

Whether to save the reference Jacobian.

By default it is set to False.

• indices

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.

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

static compute_r_1(x_local, x_shared, y_1, y_2)[source]

Evaluate the first coupling equation in residual form.

Parameters
• x_local (numpy.ndarray) – The design variables local to the first discipline.

• x_shared (numpy.ndarray) – The shared design variables.

• y_1 (numpy.ndarray) – The coupling variable coming from the first discipline.

• y_2 (numpy.ndarray) – The coupling variable coming from the second discipline.

Returns

The value of the residues related to the first discipline.

Return type

float

static compute_y_1(x_local, x_shared, y_2)[source]

Evaluate the first coupling equation in functional form.

Parameters
• x_local (numpy.ndarray) – The design variables local to first discipline.

• x_shared (numpy.ndarray) – The shared design variables.

• y_2 (numpy.ndarray) – The coupling variable coming from the second discipline.

Returns

The value of the coupling variable $$y_1$$.

Return type

float

classmethod deactivate_time_stamps()

Deactivate the time stamps.

For storing start and end times of execution and linearizations.

Return type

None

property default_inputs

The default inputs.

Raises

TypeError – When the default inputs are not passed as a dictionary.

static deserialize(in_file)

Deserialize a discipline from a file.

Parameters

in_file (Union[str, pathlib.Path]) – The path to the file containing the discipline.

Returns

The discipline instance.

Return type

gemseo.core.discipline.MDODiscipline

property exec_time

The cumulated execution time of the discipline.

Note

This property is multiprocessing safe.

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 in _default_inputs.

• Checks whether the last execution of the discipline was called with identical inputs, ie. cached in cache; if so, directly returns self.cache.get_output_cache(inputs).

• Caches the inputs.

• Checks the input data against input_grammar.

• If data_processor is not None, runs the preprocessor.

• Updates the status to RUNNING.

• Calls the _run() method, that shall be defined.

• If data_processor is not None, runs the postprocessor.

• Checks the output data.

• Caches the outputs.

• Updates the status to DONE or FAILED.

Parameters

input_data (Optional[Dict[str, Any]]) –

The input data needed to execute the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

Returns

The discipline local data after execution.

Return type

Dict[str, Any]

get_all_inputs()

Return the local input data as a list.

The order is given by 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 get_output_data_names().

Returns

The local output data.

Return type

List[Any]

get_attributes_to_serialize()[source]

Define the names of the attributes to be serialized.

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 (Union[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

Union[Any, Generator[Any]]

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.

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.

MDOFormulation.get_expected_workflow

Returns

The expected execution sequence.

Return type

SerialExecSequence

get_input_data()

Return the local input data as a dictionary.

Returns

The local input data.

Return type

Dict[str, Any]

get_input_data_names()

Return the names of the input variables.

Returns

The names of the input variables.

Return type

List[str]

get_input_output_data_names()

Return the names of the input and output variables.

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 get_all_outputs().

Returns

The local output data.

Return type

numpy.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 not a discipline input name.

Return type

Generator[Any]

get_output_data()

Return the local output data as a dictionary.

Returns

The local output data.

Return type

Dict[str, Any]

get_output_data_names()

Return the names of the output variables.

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 get_all_inputs().

Returns

The local input data.

Return type

numpy.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()

Return the sub-disciplines if any.

Returns

The sub-disciplines.

Return type
property grammar_type

The grammar type.

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

property linearization_mode

The linearization mode among LINEARIZE_MODE_LIST.

Raises

ValueError – When the linearization mode is unknown.

linearize(input_data=None, force_all=False, force_no_exec=False)

Execute the linearized version of the code.

Parameters
• input_data (Optional[Dict[str, Any]]) –

The input data needed to linearize the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

• force_all (bool) –

If False, _differentiated_inputs and differentiated_output 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, numpy.ndarray]]

property n_calls

The number of times the discipline was executed.

Note

This property is multiprocessing safe.

property n_calls_linearize

The number of times the discipline was linearized.

Note

This property is multiprocessing safe.

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 PENDING.

Raises

ValueError – When the discipline cannot be run because of its status.

Return type

None

serialize(out_file)

Serialize the discipline and store it in a file.

Parameters

out_file (Union[str, pathlib.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 (Optional[Union[str, pathlib.Path]]) –

The path to the HDF file to store the data; this argument is mandatory when the HDF5Cache policy is used.

By default it is set to None.

• cache_hdf_node_name (Optional[str]) –

The name of the HDF file node to store the discipline data. If None, 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 the Jacobian approximation method.

Sets the linearization mode to approx_method, sets the parameters of the approximation for further use when calling 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 number of processors on which to run.

By default it is set to 1.

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 (roundoff when doing f(x+step)-f(x))

are approximately equal.

Warning

This calls the discipline execution twice per input variables.

https://en.wikipedia.org/wiki/Numerical_differentiation and “Numerical Algorithms and Digital Representation”, Knut Morken , Chapter 11, “Numerical Differenciation”

Parameters
• inputs

The inputs wrt which the outputs are linearized. If None, use the _differentiated_inputs.

By default it is set to None.

• outputs

The outputs to be linearized. If None, use the _differentiated_outputs.

By default it is set to None.

• force_all

Whether to consider all the inputs and outputs of the discipline;

By default it is set to False.

• print_errors

Whether to display the estimated errors.

By default it is set to False.

• numerical_error

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.

property status

The status of the discipline.

store_local_data(**kwargs)

Store discipline data in local data.

Parameters
Return type

None

time_stamps = None
class gemseo.problems.sellar.sellar.Sellar2(residual_form=False)[source]

The discipline to compute the coupling variable $$y_2$$.

input_grammar

The input grammar.

Type

AbstractGrammar

output_grammar

The output grammar.

Type

AbstractGrammar

grammar_type

The type of grammar to be used for inputs and outputs declaration.

Type

str

comp_dir

The path to the directory of the discipline module file if any.

Type

str

data_processor

A tool to pre- and post-process discipline data.

Type

DataProcessor

re_exec_policy

The policy to re-execute the same discipline.

Type

str

residual_variables

The output variables to be considered as residuals; they shall be equal to zero.

Type

List[str]

jac

The Jacobians of the outputs wrt inputs of the form {output: {input: matrix}}.

Type

Dict[str, Dict[str, ndarray]]

exec_for_lin

Whether the last execution was due to a linearization.

Type

bool

name

The name of the discipline.

Type

str

cache

The cache containing one or several executions of the discipline according to the cache policy.

Type

AbstractCache

local_data

The last input and output data.

Type

Dict[str, Any]

Initialize self. See help(type(self)) for accurate signature.

Parameters

residual_form (bool) –

If True, then only residuals are computed, not the coupling variables.

By default it is set to False.

Return type

None

Attributes:

 APPROX_MODES AVAILABLE_MODES COMPLEX_STEP FINITE_DIFFERENCES HDF5_CACHE JSON_GRAMMAR_TYPE MEMORY_FULL_CACHE N_CPUS RE_EXECUTE_DONE_POLICY RE_EXECUTE_NEVER_POLICY SIMPLE_CACHE SIMPLE_GRAMMAR_TYPE STATUS_DONE STATUS_FAILED STATUS_PENDING STATUS_RUNNING STATUS_VIRTUAL cache_tol The cache input tolerance. default_inputs The default inputs. exec_time The cumulated execution time of the discipline. grammar_type The grammar type. linearization_mode The linearization mode among LINEARIZE_MODE_LIST. n_calls The number of times the discipline was executed. n_calls_linearize The number of times the discipline was linearized. status The status of the discipline. time_stamps

Methods:

 Activate the time stamps. add_differentiated_inputs([inputs]) Add inputs against which to differentiate the outputs. add_differentiated_outputs([outputs]) Add outputs to be differentiated. Add an observer for the status. auto_get_grammar_file([is_input, name, comp_dir]) Use a naming convention to associate a grammar file to a discipline. check_input_data(input_data[, raise_exception]) Check the input data validity. check_jacobian([input_data, derr_approx, ...]) Check if the analytical Jacobian is correct with respect to a reference one. check_output_data([raise_exception]) Check the output data validity. compute_r_2(x_shared, y_1, y_2) Evaluate the second coupling equation in residual form. compute_y_2(x_shared, y_1) Evaluate the second coupling equation in functional form. Deactivate the time stamps. deserialize(in_file) Deserialize a discipline from a file. execute([input_data]) Execute the discipline. Return the local input data as a list. Return the local output data as a list. Define the names of the attributes to be serialized. get_data_list_from_dict(keys, data_dict) Filter the dict from a list of keys or a single key. Return the expected data exchange sequence. Return the expected execution sequence. Return the local input data as a dictionary. Return the names of the input variables. Return the names of the input and output variables. Return the local output data as a large NumPy array. get_inputs_by_name(data_names) Return the local data associated with input variables. get_local_data_by_name(data_names) Return the local data of the discipline associated with variables names. Return the local output data as a dictionary. Return the names of the output variables. Return the local input data as a large NumPy array. get_outputs_by_name(data_names) Return the local data associated with output variables. Return the sub-disciplines if any. 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. Whether the discipline is a scenario. linearize([input_data, force_all, force_no_exec]) Execute the linearized version of the code. Notify all status observers that the status has changed. Remove an observer for the status. Set all the statuses to PENDING. serialize(out_file) Serialize the discipline and store it in a file. set_cache_policy([cache_type, ...]) Set the type of cache to use and the tolerance level. Set the sub-disciplines statuses. Set the Jacobian approximation method. set_optimal_fd_step([outputs, inputs, ...]) Compute the optimal finite-difference step. store_local_data(**kwargs) Store discipline data in local data.
APPROX_MODES = ['finite_differences', 'complex_step']
AVAILABLE_MODES = ('auto', 'direct', 'adjoint', 'reverse', 'finite_differences', 'complex_step')
COMPLEX_STEP = 'complex_step'
FINITE_DIFFERENCES = 'finite_differences'
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'
classmethod activate_time_stamps()

Activate the time stamps.

For storing start and end times of execution and linearizations.

Return type

None

Add inputs against which to differentiate the outputs.

This method updates _differentiated_inputs with inputs.

Parameters

inputs (Optional[Iterable[str]]) –

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

This method updates _differentiated_outputs with outputs.

Parameters

outputs (Optional[Iterable[str]]) –

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 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 a discipline.

This method searches in a directory for either an input grammar file named name + "_input.json" or an output grammar file namedname + “_output.json”.

Parameters
• is_input (bool) –

If True, autodetect the input grammar file; otherwise, autodetect the output grammar file.

By default it is set to True.

• name (Optional[str]) –

The name to be searched in the file names. If None, use the name name of the discipline.

By default it is set to None.

• comp_dir (Optional[Union[str, pathlib.Path]]) –

The directory in which to search the grammar file. If None, use comp_dir.

By default it is set to None.

Returns

The grammar file path.

Return type

pathlib.Path

property cache_tol

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).

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) –

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, figsize_x=10, figsize_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

The input data needed to execute the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

• derr_approx

The approximation method, either “complex_step” or “finite_differences”.

By default it is set to finite_differences.

• threshold

The acceptance threshold for the Jacobian error.

By default it is set to 1e-08.

• linearization_mode

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

The names of the inputs wrt which to differentiate the outputs.

By default it is set to None.

• outputs

The names of the outputs to be differentiated.

By default it is set to None.

• step

The differentiation step.

By default it is set to 1e-07.

• parallel

Whether to differentiate the discipline in parallel.

By default it is set to False.

• n_processes

The maximum number of processors on which to run.

By default it is set to 2.

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

The time waited between two forks of the process / thread.

By default it is set to 0.

• auto_set_step

Whether to compute the optimal step for a forward first order finite differences gradient approximation.

By default it is set to False.

• plot_result

Whether to plot the result of the validation (computed vs approximated Jacobians).

By default it is set to False.

• file_path

The path to the output file if plot_result is True.

By default it is set to jacobian_errors.pdf.

• show

Whether to open the figure.

By default it is set to False.

• figsize_x

The x-size of the figure in inches.

By default it is set to 10.

• figsize_y

The y-size of the figure in inches.

By default it is set to 10.

• reference_jacobian_path

The path of the reference Jacobian file.

By default it is set to None.

• save_reference_jacobian

Whether to save the reference Jacobian.

By default it is set to False.

• indices

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.

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

static compute_r_2(x_shared, y_1, y_2)[source]

Evaluate the second coupling equation in residual form.

Parameters
• x_shared (numpy.ndarray) – The shared design variables.

• y_1 (numpy.ndarray) – The coupling variable coming from the first discipline.

• y_2 (numpy.ndarray) – The coupling variable coming from the second discipline.

Returns

The value of the residues related to the second discipline.

Return type

float

static compute_y_2(x_shared, y_1)[source]

Evaluate the second coupling equation in functional form.

Parameters
• x_shared (numpy.ndarray) – The shared design variables.

• y_1 (numpy.ndarray) – The coupling variable coming from the first discipline.

Returns

The value of the coupling variable $$y_2$$.

Return type

float

classmethod deactivate_time_stamps()

Deactivate the time stamps.

For storing start and end times of execution and linearizations.

Return type

None

property default_inputs

The default inputs.

Raises

TypeError – When the default inputs are not passed as a dictionary.

static deserialize(in_file)

Deserialize a discipline from a file.

Parameters

in_file (Union[str, pathlib.Path]) – The path to the file containing the discipline.

Returns

The discipline instance.

Return type

gemseo.core.discipline.MDODiscipline

property exec_time

The cumulated execution time of the discipline.

Note

This property is multiprocessing safe.

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 in _default_inputs.

• Checks whether the last execution of the discipline was called with identical inputs, ie. cached in cache; if so, directly returns self.cache.get_output_cache(inputs).

• Caches the inputs.

• Checks the input data against input_grammar.

• If data_processor is not None, runs the preprocessor.

• Updates the status to RUNNING.

• Calls the _run() method, that shall be defined.

• If data_processor is not None, runs the postprocessor.

• Checks the output data.

• Caches the outputs.

• Updates the status to DONE or FAILED.

Parameters

input_data (Optional[Dict[str, Any]]) –

The input data needed to execute the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

Returns

The discipline local data after execution.

Return type

Dict[str, Any]

get_all_inputs()

Return the local input data as a list.

The order is given by 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 get_output_data_names().

Returns

The local output data.

Return type

List[Any]

get_attributes_to_serialize()[source]

Define the names of the attributes to be serialized.

Returns

The names of the attributes to be serialized.

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 (Union[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

Union[Any, Generator[Any]]

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.

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.

MDOFormulation.get_expected_workflow

Returns

The expected execution sequence.

Return type

SerialExecSequence

get_input_data()

Return the local input data as a dictionary.

Returns

The local input data.

Return type

Dict[str, Any]

get_input_data_names()

Return the names of the input variables.

Returns

The names of the input variables.

Return type

List[str]

get_input_output_data_names()

Return the names of the input and output variables.

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 get_all_outputs().

Returns

The local output data.

Return type

numpy.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 not a discipline input name.

Return type

Generator[Any]

get_output_data()

Return the local output data as a dictionary.

Returns

The local output data.

Return type

Dict[str, Any]

get_output_data_names()

Return the names of the output variables.

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 get_all_inputs().

Returns

The local input data.

Return type

numpy.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()

Return the sub-disciplines if any.

Returns

The sub-disciplines.

Return type
property grammar_type

The grammar type.

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

property linearization_mode

The linearization mode among LINEARIZE_MODE_LIST.

Raises

ValueError – When the linearization mode is unknown.

linearize(input_data=None, force_all=False, force_no_exec=False)

Execute the linearized version of the code.

Parameters
• input_data (Optional[Dict[str, Any]]) –

The input data needed to linearize the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

• force_all (bool) –

If False, _differentiated_inputs and differentiated_output 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, numpy.ndarray]]

property n_calls

The number of times the discipline was executed.

Note

This property is multiprocessing safe.

property n_calls_linearize

The number of times the discipline was linearized.

Note

This property is multiprocessing safe.

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 PENDING.

Raises

ValueError – When the discipline cannot be run because of its status.

Return type

None

serialize(out_file)

Serialize the discipline and store it in a file.

Parameters

out_file (Union[str, pathlib.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 (Optional[Union[str, pathlib.Path]]) –

The path to the HDF file to store the data; this argument is mandatory when the HDF5Cache policy is used.

By default it is set to None.

• cache_hdf_node_name (Optional[str]) –

The name of the HDF file node to store the discipline data. If None, 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 the Jacobian approximation method.

Sets the linearization mode to approx_method, sets the parameters of the approximation for further use when calling 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 number of processors on which to run.

By default it is set to 1.

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 (roundoff when doing f(x+step)-f(x))

are approximately equal.

Warning

This calls the discipline execution twice per input variables.

https://en.wikipedia.org/wiki/Numerical_differentiation and “Numerical Algorithms and Digital Representation”, Knut Morken , Chapter 11, “Numerical Differenciation”

Parameters
• inputs

The inputs wrt which the outputs are linearized. If None, use the _differentiated_inputs.

By default it is set to None.

• outputs

The outputs to be linearized. If None, use the _differentiated_outputs.

By default it is set to None.

• force_all

Whether to consider all the inputs and outputs of the discipline;

By default it is set to False.

• print_errors

Whether to display the estimated errors.

By default it is set to False.

• numerical_error

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.

property status

The status of the discipline.

store_local_data(**kwargs)

Store discipline data in local data.

Parameters
Return type

None

time_stamps = None
class gemseo.problems.sellar.sellar.SellarSystem[source]

The discipline to compute the objective and constraints of the Sellar problem.

Return type

None

input_grammar

The input grammar.

Type

AbstractGrammar

output_grammar

The output grammar.

Type

AbstractGrammar

grammar_type

The type of grammar to be used for inputs and outputs declaration.

Type

str

comp_dir

The path to the directory of the discipline module file if any.

Type

str

data_processor

A tool to pre- and post-process discipline data.

Type

DataProcessor

re_exec_policy

The policy to re-execute the same discipline.

Type

str

residual_variables

The output variables to be considered as residuals; they shall be equal to zero.

Type

List[str]

jac

The Jacobians of the outputs wrt inputs of the form {output: {input: matrix}}.

Type

Dict[str, Dict[str, ndarray]]

exec_for_lin

Whether the last execution was due to a linearization.

Type

bool

name

The name of the discipline.

Type

str

cache

The cache containing one or several executions of the discipline according to the cache policy.

Type

AbstractCache

local_data

The last input and output data.

Type

Dict[str, Any]

Attributes:

 APPROX_MODES AVAILABLE_MODES COMPLEX_STEP FINITE_DIFFERENCES HDF5_CACHE JSON_GRAMMAR_TYPE MEMORY_FULL_CACHE N_CPUS RE_EXECUTE_DONE_POLICY RE_EXECUTE_NEVER_POLICY SIMPLE_CACHE SIMPLE_GRAMMAR_TYPE STATUS_DONE STATUS_FAILED STATUS_PENDING STATUS_RUNNING STATUS_VIRTUAL cache_tol The cache input tolerance. default_inputs The default inputs. exec_time The cumulated execution time of the discipline. grammar_type The grammar type. linearization_mode The linearization mode among LINEARIZE_MODE_LIST. n_calls The number of times the discipline was executed. n_calls_linearize The number of times the discipline was linearized. status The status of the discipline. time_stamps

Methods:

 Activate the time stamps. add_differentiated_inputs([inputs]) Add inputs against which to differentiate the outputs. add_differentiated_outputs([outputs]) Add outputs to be differentiated. Add an observer for the status. auto_get_grammar_file([is_input, name, comp_dir]) Use a naming convention to associate a grammar file to a discipline. check_input_data(input_data[, raise_exception]) Check the input data validity. check_jacobian([input_data, derr_approx, ...]) Check if the analytical Jacobian is correct with respect to a reference one. check_output_data([raise_exception]) Check the output data validity. Evaluate the constraint $$c_1$$. Evaluate the constraint $$c_2$$. compute_obj(x_local, x_shared, y_1, y_2) Evaluate the objective $$obj$$. Deactivate the time stamps. deserialize(in_file) Deserialize a discipline from a file. execute([input_data]) Execute the discipline. Return the local input data as a list. Return the local output data as a list. Define the names of the attributes to be serialized. get_data_list_from_dict(keys, data_dict) Filter the dict from a list of keys or a single key. Return the expected data exchange sequence. Return the expected execution sequence. Return the local input data as a dictionary. Return the names of the input variables. Return the names of the input and output variables. Return the local output data as a large NumPy array. get_inputs_by_name(data_names) Return the local data associated with input variables. get_local_data_by_name(data_names) Return the local data of the discipline associated with variables names. Return the local output data as a dictionary. Return the names of the output variables. Return the local input data as a large NumPy array. get_outputs_by_name(data_names) Return the local data associated with output variables. Return the sub-disciplines if any. 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. Whether the discipline is a scenario. linearize([input_data, force_all, force_no_exec]) Execute the linearized version of the code. Notify all status observers that the status has changed. Remove an observer for the status. Set all the statuses to PENDING. serialize(out_file) Serialize the discipline and store it in a file. set_cache_policy([cache_type, ...]) Set the type of cache to use and the tolerance level. Set the sub-disciplines statuses. Set the Jacobian approximation method. set_optimal_fd_step([outputs, inputs, ...]) Compute the optimal finite-difference step. store_local_data(**kwargs) Store discipline data in local data.
APPROX_MODES = ['finite_differences', 'complex_step']
AVAILABLE_MODES = ('auto', 'direct', 'adjoint', 'reverse', 'finite_differences', 'complex_step')
COMPLEX_STEP = 'complex_step'
FINITE_DIFFERENCES = 'finite_differences'
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'
classmethod activate_time_stamps()

Activate the time stamps.

For storing start and end times of execution and linearizations.

Return type

None

Add inputs against which to differentiate the outputs.

This method updates _differentiated_inputs with inputs.

Parameters

inputs (Optional[Iterable[str]]) –

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

This method updates _differentiated_outputs with outputs.

Parameters

outputs (Optional[Iterable[str]]) –

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 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 a discipline.

This method searches in a directory for either an input grammar file named name + "_input.json" or an output grammar file namedname + “_output.json”.

Parameters
• is_input (bool) –

If True, autodetect the input grammar file; otherwise, autodetect the output grammar file.

By default it is set to True.

• name (Optional[str]) –

The name to be searched in the file names. If None, use the name name of the discipline.

By default it is set to None.

• comp_dir (Optional[Union[str, pathlib.Path]]) –

The directory in which to search the grammar file. If None, use comp_dir.

By default it is set to None.

Returns

The grammar file path.

Return type

pathlib.Path

property cache_tol

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).

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) –

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, figsize_x=10, figsize_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

The input data needed to execute the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

• derr_approx

The approximation method, either “complex_step” or “finite_differences”.

By default it is set to finite_differences.

• threshold

The acceptance threshold for the Jacobian error.

By default it is set to 1e-08.

• linearization_mode

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

The names of the inputs wrt which to differentiate the outputs.

By default it is set to None.

• outputs

The names of the outputs to be differentiated.

By default it is set to None.

• step

The differentiation step.

By default it is set to 1e-07.

• parallel

Whether to differentiate the discipline in parallel.

By default it is set to False.

• n_processes

The maximum number of processors on which to run.

By default it is set to 2.

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

The time waited between two forks of the process / thread.

By default it is set to 0.

• auto_set_step

Whether to compute the optimal step for a forward first order finite differences gradient approximation.

By default it is set to False.

• plot_result

Whether to plot the result of the validation (computed vs approximated Jacobians).

By default it is set to False.

• file_path

The path to the output file if plot_result is True.

By default it is set to jacobian_errors.pdf.

• show

Whether to open the figure.

By default it is set to False.

• figsize_x

The x-size of the figure in inches.

By default it is set to 10.

• figsize_y

The y-size of the figure in inches.

By default it is set to 10.

• reference_jacobian_path

The path of the reference Jacobian file.

By default it is set to None.

• save_reference_jacobian

Whether to save the reference Jacobian.

By default it is set to False.

• indices

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.

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

static compute_c_1(y_1)[source]

Evaluate the constraint $$c_1$$.

Parameters

y_1 (numpy.ndarray) – The coupling variable coming from the first discipline.

Returns

The value of the constraint $$c_1$$.

Return type

float

static compute_c_2(y_2)[source]

Evaluate the constraint $$c_2$$.

Parameters

y_2 (numpy.ndarray) – The coupling variable coming from the second discipline.

Returns

The value of the constraint $$c_2$$.

Return type

float

static compute_obj(x_local, x_shared, y_1, y_2)[source]

Evaluate the objective $$obj$$.

Parameters
• x_local (numpy.ndarray) – The design variables local to the first discipline.

• x_shared (numpy.ndarray) – The shared design variables.

• y_1 (numpy.ndarray) – The coupling variable coming from the first discipline.

• y_2 (numpy.ndarray) – The coupling variable coming from the second discipline.

Returns

The value of the objective $$obj$$.

Return type

float

classmethod deactivate_time_stamps()

Deactivate the time stamps.

For storing start and end times of execution and linearizations.

Return type

None

property default_inputs

The default inputs.

Raises

TypeError – When the default inputs are not passed as a dictionary.

static deserialize(in_file)

Deserialize a discipline from a file.

Parameters

in_file (Union[str, pathlib.Path]) – The path to the file containing the discipline.

Returns

The discipline instance.

Return type

gemseo.core.discipline.MDODiscipline

property exec_time

The cumulated execution time of the discipline.

Note

This property is multiprocessing safe.

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 in _default_inputs.

• Checks whether the last execution of the discipline was called with identical inputs, ie. cached in cache; if so, directly returns self.cache.get_output_cache(inputs).

• Caches the inputs.

• Checks the input data against input_grammar.

• If data_processor is not None, runs the preprocessor.

• Updates the status to RUNNING.

• Calls the _run() method, that shall be defined.

• If data_processor is not None, runs the postprocessor.

• Checks the output data.

• Caches the outputs.

• Updates the status to DONE or FAILED.

Parameters

input_data (Optional[Dict[str, Any]]) –

The input data needed to execute the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

Returns

The discipline local data after execution.

Return type

Dict[str, Any]

get_all_inputs()

Return the local input data as a list.

The order is given by 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 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.

Returns

The names of the attributes to be serialized.

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 (Union[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

Union[Any, Generator[Any]]

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.

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.

MDOFormulation.get_expected_workflow

Returns

The expected execution sequence.

Return type

SerialExecSequence

get_input_data()

Return the local input data as a dictionary.

Returns

The local input data.

Return type

Dict[str, Any]

get_input_data_names()

Return the names of the input variables.

Returns

The names of the input variables.

Return type

List[str]

get_input_output_data_names()

Return the names of the input and output variables.

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 get_all_outputs().

Returns

The local output data.

Return type

numpy.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 not a discipline input name.

Return type

Generator[Any]

get_output_data()

Return the local output data as a dictionary.

Returns

The local output data.

Return type

Dict[str, Any]

get_output_data_names()

Return the names of the output variables.

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 get_all_inputs().

Returns

The local input data.

Return type

numpy.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()

Return the sub-disciplines if any.

Returns

The sub-disciplines.

Return type
property grammar_type

The grammar type.

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

property linearization_mode

The linearization mode among LINEARIZE_MODE_LIST.

Raises

ValueError – When the linearization mode is unknown.

linearize(input_data=None, force_all=False, force_no_exec=False)

Execute the linearized version of the code.

Parameters
• input_data (Optional[Dict[str, Any]]) –

The input data needed to linearize the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

• force_all (bool) –

If False, _differentiated_inputs and differentiated_output 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, numpy.ndarray]]

property n_calls

The number of times the discipline was executed.

Note

This property is multiprocessing safe.

property n_calls_linearize

The number of times the discipline was linearized.

Note

This property is multiprocessing safe.

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 PENDING.

Raises

ValueError – When the discipline cannot be run because of its status.

Return type

None

serialize(out_file)

Serialize the discipline and store it in a file.

Parameters

out_file (Union[str, pathlib.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 (Optional[Union[str, pathlib.Path]]) –

The path to the HDF file to store the data; this argument is mandatory when the HDF5Cache policy is used.

By default it is set to None.

• cache_hdf_node_name (Optional[str]) –

The name of the HDF file node to store the discipline data. If None, 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 the Jacobian approximation method.

Sets the linearization mode to approx_method, sets the parameters of the approximation for further use when calling 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 number of processors on which to run.

By default it is set to 1.

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 (roundoff when doing f(x+step)-f(x))

are approximately equal.

Warning

This calls the discipline execution twice per input variables.

https://en.wikipedia.org/wiki/Numerical_differentiation and “Numerical Algorithms and Digital Representation”, Knut Morken , Chapter 11, “Numerical Differenciation”

Parameters
• inputs

The inputs wrt which the outputs are linearized. If None, use the _differentiated_inputs.

By default it is set to None.

• outputs

The outputs to be linearized. If None, use the _differentiated_outputs.

By default it is set to None.

• force_all

Whether to consider all the inputs and outputs of the discipline;

By default it is set to False.

• print_errors

Whether to display the estimated errors.

By default it is set to False.

• numerical_error

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.

property status

The status of the discipline.

store_local_data(**kwargs)

Store discipline data in local data.

Parameters
Return type

None

time_stamps = None
gemseo.problems.sellar.sellar.get_inputs(names=None)[source]

Generate an initial solution for the MDO problem.

Parameters

names (Optional[Iterable[str]]) –

The names of the discipline inputs.

By default it is set to None.

Returns

The default values of the discipline inputs.

Return type

Dict[str, numpy.ndarray]