gemseo / mda

Hide inherited members

newton module

A set of Newton algorithm variants for solving MDAs.

Root finding methods include:

Each of these methods is implemented by a class in this module. Both inherit from a common abstract cache.

class gemseo.mda.newton.MDANewtonRaphson(disciplines, max_mda_iter=10, relax_factor=0.99, name=None, grammar_type=GrammarType.JSON, linear_solver='DEFAULT', tolerance=1e-06, linear_solver_tolerance=1e-12, warm_start=False, use_lu_fact=False, coupling_structure=None, log_convergence=False, linear_solver_options=None, newton_linear_solver_name='DEFAULT', newton_linear_solver_options=None)[source]

Bases: MDARoot

Newton solver for MDA.

The Newton-Raphson method is parameterized by a relaxation factor \(\alpha \in (0, 1]\) to limit the length of the steps taken along the Newton direction. The new iterate is given by:

\[x_{k+1} = x_k - \alpha f'(x_k)^{-1} f(x_k)\]

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

Parameters:

  • disciplines (Sequence[MDODiscipline]) – The disciplines from which to compute the MDA.

  • max_mda_iter (int) –

    The maximum iterations number for the MDA algorithm.

    By default it is set to 10.

  • relax_factor (float) –

    The relaxation factor in the Newton step.

    By default it is set to 0.99.

  • name (str | None) – The name to be given to the MDA. If None, use the name of the class.

  • grammar_type (MDODiscipline.GrammarType) –

    The type of the input and output grammars.

    By default it is set to “JSONGrammar”.

  • linear_solver (str) –

    The name of the linear solver.

    By default it is set to “DEFAULT”.

  • tolerance (float) –

    The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

    By default it is set to 1e-06.

  • linear_solver_tolerance (float) –

    The tolerance of the linear solver in the adjoint equation.

    By default it is set to 1e-12.

  • warm_start (bool) –

    Whether the second iteration and ongoing start from the previous coupling solution.

    By default it is set to False.

  • use_lu_fact (bool) –

    Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

    By default it is set to False.

  • coupling_structure (MDOCouplingStructure | None) – The coupling structure to be used by the MDA. If None, it is created from disciplines.

  • log_convergence (bool) –

    Whether to log the MDA convergence, expressed in terms of normed residuals.

    By default it is set to False.

  • linear_solver_options (Mapping[str, Any]) – The options passed to the linear solver factory.

  • newton_linear_solver_name (str) –

    The description is missing.

    By default it is set to “DEFAULT”.

  • newton_linear_solver_options (Mapping[str, Any] | None) – The options for the Newton linear solver.

class ApproximationMode(value)

Bases: StrEnum

The approximation derivation modes.

COMPLEX_STEP = 'complex_step'

The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences'

The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class CacheType(value)

Bases: StrEnum

The name of the cache class.

HDF5 = 'HDF5Cache'
MEMORY_FULL = 'MemoryFullCache'
NONE = ''

No cache is used.

SIMPLE = 'SimpleCache'
class ExecutionStatus(value)

Bases: StrEnum

The execution statuses of a discipline.

DONE = 'DONE'
FAILED = 'FAILED'
LINEARIZE = 'LINEARIZE'
PENDING = 'PENDING'
RUNNING = 'RUNNING'
VIRTUAL = 'VIRTUAL'
class GrammarType(value)

Bases: StrEnum

The name of the grammar class.

JSON = 'JSONGrammar'
PYDANTIC = 'PydanticGrammar'
SIMPLE = 'SimpleGrammar'
class InitJacobianType(value)

Bases: StrEnum

The way to initialize Jacobian matrices.

DENSE = 'dense'

The Jacobian is initialized as a NumPy ndarray filled in with zeros.

EMPTY = 'empty'

The Jacobian is initialized as an empty NumPy ndarray.

SPARSE = 'sparse'

The Jacobian is initialized as a SciPy CSR array with zero elements.

class LinearizationMode(value)

Bases: StrEnum

An enumeration.

ADJOINT = 'adjoint'
AUTO = 'auto'
COMPLEX_STEP = 'complex_step'
DIRECT = 'direct'
FINITE_DIFFERENCES = 'finite_differences'
REVERSE = 'reverse'
class ReExecutionPolicy(value)

Bases: StrEnum

The re-execution policy of a discipline.

DONE = 'RE_EXEC_DONE'
NEVER = 'RE_EXEC_NEVER'
class ResidualScaling(value)

Bases: LowercaseStrEnum

The scaling method applied to MDA residuals for convergence monitoring.

INITIAL_RESIDUAL_COMPONENT = 'initial_residual_component'

The residual is scaled component-wise with the initial residual if not null, and not scaled otherwise. The MDA is considered converged when,

\[\max_i \left| \frac{(R_k)_i}{(R_0)_i} \right| \leq \text{tol}.\]
INITIAL_RESIDUAL_NORM = 'initial_residual_norm'

The residual is scaled by the norm of the initial residual if it is not null, and not scaled otherwise. The MDA is considered converged when,

\[\frac{ \|R_k\|_2 }{ \|R_0\|_2 } \leq \text{tol}.\]
INITIAL_SUBRESIDUAL_NORM = 'initial_subresidual_norm'

The residual is scaled by considering the convergence of each sub-residual individually. The MDA is considered converged when,

\[\max_i \left| \frac{\|r^i_k\|_2}{\|r^i_0\|_2} \right| \leq \text{tol}.\]
NO_SCALING = 'no_scaling'

The residual is not scaled and the MDA is considered converged when,

\[\|R_k\|_2 \leq \text{tol}.\]
N_COUPLING_VARIABLES = 'n_coupling_variables'

The residual is scaled by the number of coupling variables. The MDA is considered converged when,

\[\frac{ \|R_k\|_2 }{ \sqrt{n_\text{coupl.}} } \leq \text{tol}.\]
SCALED_INITIAL_RESIDUAL_COMPONENT = 'scaled_initial_residual_component'

The residual is not scaled and the MDA is considered converged when.

\[\frac{1}{\sqrt{n_\text{coupl.}}} \| R_k \div R_0 \|_2 \leq \text{tol}.\]
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.

If the discipline grammar type is MDODiscipline.GrammarType.JSON and an input is either a non-numeric array or not an array, it will be ignored. If an input is declared as an array but the type of its items is not defined, it is assumed as a numeric array.

If the discipline grammar type is MDODiscipline.GrammarType.SIMPLE and an input is not an array, it will be ignored. Keep in mind that in this case the array subtype is not checked.

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.

If the discipline grammar type is MDODiscipline.GrammarType.JSON and an output is either a non-numeric array or not an array, it will be ignored. If an output is declared as an array but the type of its items is not defined, it is assumed as a numeric array.

If the discipline grammar type is MDODiscipline.GrammarType.SIMPLE and an output is not an array, it will be ignored. Keep in mind that in this case the array subtype is not checked.

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.

Return type:

None

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.

Return type:

None

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:

Path

check_input_data(input_data, raise_exception=True)

Check the input data validity.

Parameters:

  • input_data (Mapping[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=ApproximationMode.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 (Mapping[str, ndarray] | None) – The input values. If None, use the default input values.

  • derr_approx (MDODiscipline.ApproximationMode) –

    The derivative approximation method.

    By default it is set to “finite_differences”.

  • step (float) –

    The step for finite differences or complex step differentiation methods.

    By default it is set to 1e-07.

  • threshold (float) –

    The acceptance threshold for the Jacobian error.

    By default it is set to 1e-08.

  • linearization_mode (str) –

    The mode of linearization, either “direct”, “adjoint” or “auto” switch depending on dimensions of inputs and outputs.

    By default it is set to “auto”.

  • inputs (Iterable[str] | None) – The names of the inputs with respect to which to differentiate. If None, use the inputs of the MDA.

  • outputs (Iterable[str] | None) – The outputs to differentiate. If None, use all the outputs of the MDA.

  • parallel (bool) –

    Whether to execute the MDA 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 (int) –

    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 comparing the exact and 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 (None | Path | str) – 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 passed Jacobian is correct.

Return type:

bool

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

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 supported yet.

Return type:

dict[str, Any]

execute_all_disciplines(input_local_data, update_local_data=True)

Execute all self.disciplines.

Parameters:

  • input_local_data (Mapping[str, ndarray]) – The input data of the disciplines.

  • update_local_data (bool) –

    Whether to update the local data from the disciplines.

    By default it is set to True.

Return type:

None

static from_pickle(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

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]

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 in the XDSM.

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:

LoopExecSequence

get_input_data(with_namespaces=True)

Return the local input data as a dictionary.

Parameters:

with_namespaces (bool) –

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 (bool) –

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.

Parameters:

with_namespaces (bool) –

By default it is set to True.

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 (bool) –

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 (bool) –

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]

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, compute_all_jacobians=False, execute=True)

Compute the Jacobians of some outputs with respect to some inputs.

Parameters:

  • input_data (Mapping[str, Any] | None) – The input data for which to compute the Jacobian. If None, use the MDODiscipline.default_inputs.

  • compute_all_jacobians (bool) –

    Whether to compute the Jacobians of all the output with respect to all the inputs. Otherwise, set the input variables against which to differentiate the output ones with add_differentiated_inputs() and set these output variables to differentiate with add_differentiated_outputs().

    By default it is set to False.

  • execute (bool) –

    Whether to start by executing the discipline with the input data for which to compute the Jacobian; this allows to ensure that the discipline was executed with the right input data; it can be almost free if the corresponding output data have been stored in the cache.

    By default it is set to True.

Returns:

The Jacobian of the discipline shaped as {output_name: {input_name: jacobian_array}} where jacobian_array[i, j] is the partial derivative of output_name[i] with respect to input_name[j].

Raises:

ValueError – When either the inputs for which to differentiate the outputs or the outputs to differentiate are missing.

Return type:

dict[str, dict[str, NDArray[float]]]

notify_status_observers()

Notify all status observers that the status has changed.

Return type:

None

plot_residual_history(show=False, save=True, n_iterations=None, logscale=None, filename=None, fig_size=None)

Generate a plot of the residual history.

The first iteration of each new execution is marked with a red dot.

Parameters:

  • show (bool) –

    Whether to display the plot on screen.

    By default it is set to False.

  • save (bool) –

    Whether to save the plot as a PDF file.

    By default it is set to True.

  • n_iterations (int | None) – The number of iterations on the x axis. If None, use all the iterations.

  • logscale (tuple[int, int] | None) – The limits of the y axis. If None, do not change the limits of the y axis.

  • filename (str | None) – The name of the file to save the figure. If None, use “{mda.name}_residual_history.pdf”.

  • fig_size (FigSizeType | None) – The width and height of the figure in inches, e.g. (w, h).

Returns:

The figure, to be customized if not closed.

Return type:

Figure

remove_status_observer(obs)

Remove an observer for the status.

Parameters:

obs (Any) – The observer to remove.

Return type:

None

reset_disciplines_statuses()

Reset all the statuses of the disciplines.

Return type:

None

reset_statuses_for_run()

Set all the statuses to MDODiscipline.ExecutionStatus.PENDING.

Raises:

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

Return type:

None

set_cache_policy(cache_type=CacheType.SIMPLE, cache_tolerance=0.0, cache_hdf_file=None, cache_hdf_node_path=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 (CacheType) –

    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.CacheType.HDF5 policy is used.

  • cache_hdf_node_path (str | None) – The name of the HDF file node to store the discipline data, possibly passed as a path root_name/.../group_name/.../node_name. 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=ApproximationMode.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 (ApproximationMode) –

    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, compute_all_jacobians=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.

  • compute_all_jacobians (bool) –

    Whether to compute the Jacobians of all the output with respect to all the inputs. Otherwise, set the input variables against which to differentiate the output ones with add_differentiated_inputs() and set these output variables to differentiate with add_differentiated_outputs().

    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

to_pickle(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

GRAMMAR_DIRECTORY: ClassVar[str | None] = None

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

N_CPUS = 2
RESIDUALS_NORM: ClassVar[str] = 'MDA residuals norm'
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.

all_couplings: list[str]

The names of the coupling variables.

assembly: JacobianAssembly
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.

coupling_structure: MDOCouplingStructure

The coupling structure to be used by the MDA.

data_processor: DataProcessor

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

property default_inputs: Defaults

The default inputs.

property default_outputs: Defaults

The default outputs.

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: GrammarType

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.

The structure is {output: {input: matrix}}.

lin_cache_tol_fact: float

The tolerance factor to cache the Jacobian.

linear_solver: str

The name of the linear solver.

linear_solver_options: dict[str, Any]

The options of the linear solver.

linear_solver_tolerance: float

The tolerance of the linear solver in the adjoint equation.

property linearization_mode: LinearizationMode

The linearization mode among MDODiscipline.LinearizationMode.

Raises:

ValueError – When the linearization mode is unknown.

property local_data: DisciplineData

The current input and output data.

property log_convergence: bool

Whether to log the MDA convergence.

matrix_type: JacobianAssembly.JacobianType

The type of the matrix.

max_mda_iter: int

The maximum iterations number for the MDA algorithm.

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.

norm0: float | None

The reference residual, if any.

normed_residual: float

The normed residual.

output_grammar: BaseGrammar

The output grammar.

re_exec_policy: ReExecutionPolicy

The policy to re-execute the same discipline.

reset_history_each_run: bool

Whether to reset the history of MDA residuals before each run.

residual_history: list[float]

The history of MDA residuals.

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

Whether the run method shall solve the residuals.

scaling: ResidualScaling

The scaling method applied to MDA residuals for convergence monitoring.

property status: ExecutionStatus

The status of the discipline.

The status aims at monitoring the process and give the user a simplified view on the state (the process state = execution or linearize or done) of the disciplines. The core part of the execution is _run, the core part of linearize is _compute_jacobian or approximate jacobian computation.

strong_couplings: list[str]

The names of the strong coupling variables.

time_stamps = None
tolerance: float

The tolerance of the iterative direct coupling solver.

use_lu_fact: bool

Whether to store a LU factorization of the matrix.

virtual_execution: ClassVar[bool] = False

Whether to skip the _run() method during execution and return the default_outputs, whatever the inputs.

warm_start: bool

Whether the second iteration and ongoing start from the previous solution.

class gemseo.mda.newton.MDAQuasiNewton(disciplines, max_mda_iter=10, name=None, grammar_type=GrammarType.JSON, method='hybr', use_gradient=False, tolerance=1e-06, linear_solver_tolerance=1e-12, warm_start=False, use_lu_fact=False, coupling_structure=None, linear_solver='DEFAULT', linear_solver_options=None)[source]

Bases: MDARoot

Quasi-Newton solver for MDA.

Quasi-Newton methods include numerous variants ( Broyden, Levenberg-Marquardt, …). The name of the variant should be provided as a parameter method of the class.

The new iterate is given by:

\[\begin{split}x_{k+1} = x_k - \\rho_k B_k f(x_k)\end{split}\]

where \(\\rho_k\) is a coefficient chosen in order to minimize the convergence and \(B_k\) is an approximation of the inverse of the Jacobian \(Df(x_k)^{-1}\).

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

Parameters:

  • disciplines (Sequence[MDODiscipline]) – The disciplines from which to compute the MDA.

  • max_mda_iter (int) –

    The maximum iterations number for the MDA algorithm.

    By default it is set to 10.

  • name (str | None) – The name to be given to the MDA. If None, use the name of the class.

  • grammar_type (MDODiscipline.GrammarType) –

    The type of the input and output grammars.

    By default it is set to “JSONGrammar”.

  • method (str) –

    The name of the method in scipy root finding, among QUASI_NEWTON_METHODS.

    By default it is set to “hybr”.

  • use_gradient (bool) –

    Whether to use the analytic gradient of the discipline.

    By default it is set to False.

  • tolerance (float) –

    The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

    By default it is set to 1e-06.

  • linear_solver_tolerance (float) –

    The tolerance of the linear solver in the adjoint equation.

    By default it is set to 1e-12.

  • warm_start (bool) –

    Whether the second iteration and ongoing start from the previous coupling solution.

    By default it is set to False.

  • use_lu_fact (bool) –

    Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

    By default it is set to False.

  • coupling_structure (MDOCouplingStructure | None) – The coupling structure to be used by the MDA. If None, it is created from disciplines.

  • linear_solver (str) –

    The name of the linear solver.

    By default it is set to “DEFAULT”.

  • linear_solver_options (Mapping[str, Any]) – The options passed to the linear solver factory.

Raises:

ValueError – If the method is not a valid quasi-Newton method.

class ApproximationMode(value)

Bases: StrEnum

The approximation derivation modes.

COMPLEX_STEP = 'complex_step'

The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences'

The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class CacheType(value)

Bases: StrEnum

The name of the cache class.

HDF5 = 'HDF5Cache'
MEMORY_FULL = 'MemoryFullCache'
NONE = ''

No cache is used.

SIMPLE = 'SimpleCache'
class ExecutionStatus(value)

Bases: StrEnum

The execution statuses of a discipline.

DONE = 'DONE'
FAILED = 'FAILED'
LINEARIZE = 'LINEARIZE'
PENDING = 'PENDING'
RUNNING = 'RUNNING'
VIRTUAL = 'VIRTUAL'
class GrammarType(value)

Bases: StrEnum

The name of the grammar class.

JSON = 'JSONGrammar'
PYDANTIC = 'PydanticGrammar'
SIMPLE = 'SimpleGrammar'
class InitJacobianType(value)

Bases: StrEnum

The way to initialize Jacobian matrices.

DENSE = 'dense'

The Jacobian is initialized as a NumPy ndarray filled in with zeros.

EMPTY = 'empty'

The Jacobian is initialized as an empty NumPy ndarray.

SPARSE = 'sparse'

The Jacobian is initialized as a SciPy CSR array with zero elements.

class LinearizationMode(value)

Bases: StrEnum

An enumeration.

ADJOINT = 'adjoint'
AUTO = 'auto'
COMPLEX_STEP = 'complex_step'
DIRECT = 'direct'
FINITE_DIFFERENCES = 'finite_differences'
REVERSE = 'reverse'
class ReExecutionPolicy(value)

Bases: StrEnum

The re-execution policy of a discipline.

DONE = 'RE_EXEC_DONE'
NEVER = 'RE_EXEC_NEVER'
class ResidualScaling(value)

Bases: LowercaseStrEnum

The scaling method applied to MDA residuals for convergence monitoring.

INITIAL_RESIDUAL_COMPONENT = 'initial_residual_component'

The residual is scaled component-wise with the initial residual if not null, and not scaled otherwise. The MDA is considered converged when,

\[\max_i \left| \frac{(R_k)_i}{(R_0)_i} \right| \leq \text{tol}.\]
INITIAL_RESIDUAL_NORM = 'initial_residual_norm'

The residual is scaled by the norm of the initial residual if it is not null, and not scaled otherwise. The MDA is considered converged when,

\[\frac{ \|R_k\|_2 }{ \|R_0\|_2 } \leq \text{tol}.\]
INITIAL_SUBRESIDUAL_NORM = 'initial_subresidual_norm'

The residual is scaled by considering the convergence of each sub-residual individually. The MDA is considered converged when,

\[\max_i \left| \frac{\|r^i_k\|_2}{\|r^i_0\|_2} \right| \leq \text{tol}.\]
NO_SCALING = 'no_scaling'

The residual is not scaled and the MDA is considered converged when,

\[\|R_k\|_2 \leq \text{tol}.\]
N_COUPLING_VARIABLES = 'n_coupling_variables'

The residual is scaled by the number of coupling variables. The MDA is considered converged when,

\[\frac{ \|R_k\|_2 }{ \sqrt{n_\text{coupl.}} } \leq \text{tol}.\]
SCALED_INITIAL_RESIDUAL_COMPONENT = 'scaled_initial_residual_component'

The residual is not scaled and the MDA is considered converged when.

\[\frac{1}{\sqrt{n_\text{coupl.}}} \| R_k \div R_0 \|_2 \leq \text{tol}.\]
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.

If the discipline grammar type is MDODiscipline.GrammarType.JSON and an input is either a non-numeric array or not an array, it will be ignored. If an input is declared as an array but the type of its items is not defined, it is assumed as a numeric array.

If the discipline grammar type is MDODiscipline.GrammarType.SIMPLE and an input is not an array, it will be ignored. Keep in mind that in this case the array subtype is not checked.

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.

If the discipline grammar type is MDODiscipline.GrammarType.JSON and an output is either a non-numeric array or not an array, it will be ignored. If an output is declared as an array but the type of its items is not defined, it is assumed as a numeric array.

If the discipline grammar type is MDODiscipline.GrammarType.SIMPLE and an output is not an array, it will be ignored. Keep in mind that in this case the array subtype is not checked.

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.

Return type:

None

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.

Return type:

None

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:

Path

check_input_data(input_data, raise_exception=True)

Check the input data validity.

Parameters:

  • input_data (Mapping[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=ApproximationMode.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 (Mapping[str, ndarray] | None) – The input values. If None, use the default input values.

  • derr_approx (MDODiscipline.ApproximationMode) –

    The derivative approximation method.

    By default it is set to “finite_differences”.

  • step (float) –

    The step for finite differences or complex step differentiation methods.

    By default it is set to 1e-07.

  • threshold (float) –

    The acceptance threshold for the Jacobian error.

    By default it is set to 1e-08.

  • linearization_mode (str) –

    The mode of linearization, either “direct”, “adjoint” or “auto” switch depending on dimensions of inputs and outputs.

    By default it is set to “auto”.

  • inputs (Iterable[str] | None) – The names of the inputs with respect to which to differentiate. If None, use the inputs of the MDA.

  • outputs (Iterable[str] | None) – The outputs to differentiate. If None, use all the outputs of the MDA.

  • parallel (bool) –

    Whether to execute the MDA 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 (int) –

    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 comparing the exact and 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 (None | Path | str) – 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 passed Jacobian is correct.

Return type:

bool

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

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 supported yet.

Return type:

dict[str, Any]

execute_all_disciplines(input_local_data, update_local_data=True)

Execute all self.disciplines.

Parameters:

  • input_local_data (Mapping[str, ndarray]) – The input data of the disciplines.

  • update_local_data (bool) –

    Whether to update the local data from the disciplines.

    By default it is set to True.

Return type:

None

static from_pickle(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

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]

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 in the XDSM.

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:

LoopExecSequence

get_input_data(with_namespaces=True)

Return the local input data as a dictionary.

Parameters:

with_namespaces (bool) –

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 (bool) –

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.

Parameters:

with_namespaces (bool) –

By default it is set to True.

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 (bool) –

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 (bool) –

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]

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, compute_all_jacobians=False, execute=True)

Compute the Jacobians of some outputs with respect to some inputs.

Parameters:

  • input_data (Mapping[str, Any] | None) – The input data for which to compute the Jacobian. If None, use the MDODiscipline.default_inputs.

  • compute_all_jacobians (bool) –

    Whether to compute the Jacobians of all the output with respect to all the inputs. Otherwise, set the input variables against which to differentiate the output ones with add_differentiated_inputs() and set these output variables to differentiate with add_differentiated_outputs().

    By default it is set to False.

  • execute (bool) –

    Whether to start by executing the discipline with the input data for which to compute the Jacobian; this allows to ensure that the discipline was executed with the right input data; it can be almost free if the corresponding output data have been stored in the cache.

    By default it is set to True.

Returns:

The Jacobian of the discipline shaped as {output_name: {input_name: jacobian_array}} where jacobian_array[i, j] is the partial derivative of output_name[i] with respect to input_name[j].

Raises:

ValueError – When either the inputs for which to differentiate the outputs or the outputs to differentiate are missing.

Return type:

dict[str, dict[str, NDArray[float]]]

notify_status_observers()

Notify all status observers that the status has changed.

Return type:

None

plot_residual_history(show=False, save=True, n_iterations=None, logscale=None, filename=None, fig_size=None)

Generate a plot of the residual history.

The first iteration of each new execution is marked with a red dot.

Parameters:

  • show (bool) –

    Whether to display the plot on screen.

    By default it is set to False.

  • save (bool) –

    Whether to save the plot as a PDF file.

    By default it is set to True.

  • n_iterations (int | None) – The number of iterations on the x axis. If None, use all the iterations.

  • logscale (tuple[int, int] | None) – The limits of the y axis. If None, do not change the limits of the y axis.

  • filename (str | None) – The name of the file to save the figure. If None, use “{mda.name}_residual_history.pdf”.

  • fig_size (FigSizeType | None) – The width and height of the figure in inches, e.g. (w, h).

Returns:

The figure, to be customized if not closed.

Return type:

Figure

remove_status_observer(obs)

Remove an observer for the status.

Parameters:

obs (Any) – The observer to remove.

Return type:

None

reset_disciplines_statuses()

Reset all the statuses of the disciplines.

Return type:

None

reset_statuses_for_run()

Set all the statuses to MDODiscipline.ExecutionStatus.PENDING.

Raises:

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

Return type:

None

set_cache_policy(cache_type=CacheType.SIMPLE, cache_tolerance=0.0, cache_hdf_file=None, cache_hdf_node_path=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 (CacheType) –

    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.CacheType.HDF5 policy is used.

  • cache_hdf_node_path (str | None) – The name of the HDF file node to store the discipline data, possibly passed as a path root_name/.../group_name/.../node_name. 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=ApproximationMode.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 (ApproximationMode) –

    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, compute_all_jacobians=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.

  • compute_all_jacobians (bool) –

    Whether to compute the Jacobians of all the output with respect to all the inputs. Otherwise, set the input variables against which to differentiate the output ones with add_differentiated_inputs() and set these output variables to differentiate with add_differentiated_outputs().

    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

to_pickle(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

ANDERSON = 'anderson'
BROYDEN1 = 'broyden1'
BROYDEN2 = 'broyden2'
DF_SANE = 'df-sane'
DIAG_BROYDEN = 'diagbroyden'
EXCITING_MIXING = 'excitingmixing'
GRAMMAR_DIRECTORY: ClassVar[str | None] = None

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

HYBRID = 'hybr'
KRYLOV = 'krylov'
LEVENBERG_MARQUARDT = 'lm'
LINEAR_MIXING = 'linearmixing'
N_CPUS = 2
QUASI_NEWTON_METHODS = ['hybr', 'lm', 'broyden1', 'broyden2', 'anderson', 'linearmixing', 'diagbroyden', 'excitingmixing', 'krylov', 'df-sane']
RESIDUALS_NORM: ClassVar[str] = 'MDA residuals norm'
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.

all_couplings: list[str]

The names of the coupling variables.

assembly: JacobianAssembly
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.

coupling_structure: MDOCouplingStructure

The coupling structure to be used by the MDA.

data_processor: DataProcessor

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

property default_inputs: Defaults

The default inputs.

property default_outputs: Defaults

The default outputs.

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: GrammarType

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.

The structure is {output: {input: matrix}}.

lin_cache_tol_fact: float

The tolerance factor to cache the Jacobian.

linear_solver: str

The name of the linear solver.

linear_solver_options: dict[str, Any]

The options of the linear solver.

linear_solver_tolerance: float

The tolerance of the linear solver in the adjoint equation.

property linearization_mode: LinearizationMode

The linearization mode among MDODiscipline.LinearizationMode.

Raises:

ValueError – When the linearization mode is unknown.

property local_data: DisciplineData

The current input and output data.

property log_convergence: bool

Whether to log the MDA convergence.

matrix_type: JacobianAssembly.JacobianType

The type of the matrix.

max_mda_iter: int

The maximum iterations number for the MDA algorithm.

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.

norm0: float | None

The reference residual, if any.

normed_residual: float

The normed residual.

output_grammar: BaseGrammar

The output grammar.

re_exec_policy: ReExecutionPolicy

The policy to re-execute the same discipline.

reset_history_each_run: bool

Whether to reset the history of MDA residuals before each run.

residual_history: list[float]

The history of MDA residuals.

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

Whether the run method shall solve the residuals.

scaling: ResidualScaling

The scaling method applied to MDA residuals for convergence monitoring.

property status: ExecutionStatus

The status of the discipline.

The status aims at monitoring the process and give the user a simplified view on the state (the process state = execution or linearize or done) of the disciplines. The core part of the execution is _run, the core part of linearize is _compute_jacobian or approximate jacobian computation.

strong_couplings: list[str]

The names of the strong coupling variables.

time_stamps = None
tolerance: float

The tolerance of the iterative direct coupling solver.

use_lu_fact: bool

Whether to store a LU factorization of the matrix.

virtual_execution: ClassVar[bool] = False

Whether to skip the _run() method during execution and return the default_outputs, whatever the inputs.

warm_start: bool

Whether the second iteration and ongoing start from the previous solution.

class gemseo.mda.newton.MDARoot(disciplines, max_mda_iter=10, name=None, grammar_type=GrammarType.JSON, tolerance=1e-06, linear_solver_tolerance=1e-12, warm_start=False, use_lu_fact=False, coupling_structure=None, log_convergence=False, linear_solver='DEFAULT', linear_solver_options=None)[source]

Bases: MDA

Abstract class implementing MDAs based on (Quasi-)Newton methods.

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

Parameters:

  • disciplines (Sequence[MDODiscipline]) – The disciplines from which to compute the MDA.

  • max_mda_iter (int) –

    The maximum iterations number for the MDA algorithm.

    By default it is set to 10.

  • name (str | None) – The name to be given to the MDA. If None, use the name of the class.

  • grammar_type (MDODiscipline.GrammarType) –

    The type of the input and output grammars.

    By default it is set to “JSONGrammar”.

  • tolerance (float) –

    The tolerance of the iterative direct coupling solver; the norm of the current residuals divided by initial residuals norm shall be lower than the tolerance to stop iterating.

    By default it is set to 1e-06.

  • linear_solver_tolerance (float) –

    The tolerance of the linear solver in the adjoint equation.

    By default it is set to 1e-12.

  • warm_start (bool) –

    Whether the second iteration and ongoing start from the previous coupling solution.

    By default it is set to False.

  • use_lu_fact (bool) –

    Whether to store a LU factorization of the matrix when using adjoint/forward differentiation. to solve faster multiple RHS problem.

    By default it is set to False.

  • coupling_structure (MDOCouplingStructure | None) – The coupling structure to be used by the MDA. If None, it is created from disciplines.

  • log_convergence (bool) –

    Whether to log the MDA convergence, expressed in terms of normed residuals.

    By default it is set to False.

  • linear_solver (str) –

    The name of the linear solver.

    By default it is set to “DEFAULT”.

  • linear_solver_options (Mapping[str, Any]) – The options passed to the linear solver factory.

class ApproximationMode(value)

Bases: StrEnum

The approximation derivation modes.

COMPLEX_STEP = 'complex_step'

The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences'

The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class CacheType(value)

Bases: StrEnum

The name of the cache class.

HDF5 = 'HDF5Cache'
MEMORY_FULL = 'MemoryFullCache'
NONE = ''

No cache is used.

SIMPLE = 'SimpleCache'
class ExecutionStatus(value)

Bases: StrEnum

The execution statuses of a discipline.

DONE = 'DONE'
FAILED = 'FAILED'
LINEARIZE = 'LINEARIZE'
PENDING = 'PENDING'
RUNNING = 'RUNNING'
VIRTUAL = 'VIRTUAL'
class GrammarType(value)

Bases: StrEnum

The name of the grammar class.

JSON = 'JSONGrammar'
PYDANTIC = 'PydanticGrammar'
SIMPLE = 'SimpleGrammar'
class InitJacobianType(value)

Bases: StrEnum

The way to initialize Jacobian matrices.

DENSE = 'dense'

The Jacobian is initialized as a NumPy ndarray filled in with zeros.

EMPTY = 'empty'

The Jacobian is initialized as an empty NumPy ndarray.

SPARSE = 'sparse'

The Jacobian is initialized as a SciPy CSR array with zero elements.

class LinearizationMode(value)

Bases: StrEnum

An enumeration.

ADJOINT = 'adjoint'
AUTO = 'auto'
COMPLEX_STEP = 'complex_step'
DIRECT = 'direct'
FINITE_DIFFERENCES = 'finite_differences'
REVERSE = 'reverse'
class ReExecutionPolicy(value)

Bases: StrEnum

The re-execution policy of a discipline.

DONE = 'RE_EXEC_DONE'
NEVER = 'RE_EXEC_NEVER'
class ResidualScaling(value)

Bases: LowercaseStrEnum

The scaling method applied to MDA residuals for convergence monitoring.

INITIAL_RESIDUAL_COMPONENT = 'initial_residual_component'

The residual is scaled component-wise with the initial residual if not null, and not scaled otherwise. The MDA is considered converged when,

\[\max_i \left| \frac{(R_k)_i}{(R_0)_i} \right| \leq \text{tol}.\]
INITIAL_RESIDUAL_NORM = 'initial_residual_norm'

The residual is scaled by the norm of the initial residual if it is not null, and not scaled otherwise. The MDA is considered converged when,

\[\frac{ \|R_k\|_2 }{ \|R_0\|_2 } \leq \text{tol}.\]
INITIAL_SUBRESIDUAL_NORM = 'initial_subresidual_norm'

The residual is scaled by considering the convergence of each sub-residual individually. The MDA is considered converged when,

\[\max_i \left| \frac{\|r^i_k\|_2}{\|r^i_0\|_2} \right| \leq \text{tol}.\]
NO_SCALING = 'no_scaling'

The residual is not scaled and the MDA is considered converged when,

\[\|R_k\|_2 \leq \text{tol}.\]
N_COUPLING_VARIABLES = 'n_coupling_variables'

The residual is scaled by the number of coupling variables. The MDA is considered converged when,

\[\frac{ \|R_k\|_2 }{ \sqrt{n_\text{coupl.}} } \leq \text{tol}.\]
SCALED_INITIAL_RESIDUAL_COMPONENT = 'scaled_initial_residual_component'

The residual is not scaled and the MDA is considered converged when.

\[\frac{1}{\sqrt{n_\text{coupl.}}} \| R_k \div R_0 \|_2 \leq \text{tol}.\]
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.

If the discipline grammar type is MDODiscipline.GrammarType.JSON and an input is either a non-numeric array or not an array, it will be ignored. If an input is declared as an array but the type of its items is not defined, it is assumed as a numeric array.

If the discipline grammar type is MDODiscipline.GrammarType.SIMPLE and an input is not an array, it will be ignored. Keep in mind that in this case the array subtype is not checked.

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.

If the discipline grammar type is MDODiscipline.GrammarType.JSON and an output is either a non-numeric array or not an array, it will be ignored. If an output is declared as an array but the type of its items is not defined, it is assumed as a numeric array.

If the discipline grammar type is MDODiscipline.GrammarType.SIMPLE and an output is not an array, it will be ignored. Keep in mind that in this case the array subtype is not checked.

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.

Return type:

None

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.

Return type:

None

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:

Path

check_input_data(input_data, raise_exception=True)

Check the input data validity.

Parameters:

  • input_data (Mapping[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=ApproximationMode.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 (Mapping[str, ndarray] | None) – The input values. If None, use the default input values.

  • derr_approx (MDODiscipline.ApproximationMode) –

    The derivative approximation method.

    By default it is set to “finite_differences”.

  • step (float) –

    The step for finite differences or complex step differentiation methods.

    By default it is set to 1e-07.

  • threshold (float) –

    The acceptance threshold for the Jacobian error.

    By default it is set to 1e-08.

  • linearization_mode (str) –

    The mode of linearization, either “direct”, “adjoint” or “auto” switch depending on dimensions of inputs and outputs.

    By default it is set to “auto”.

  • inputs (Iterable[str] | None) – The names of the inputs with respect to which to differentiate. If None, use the inputs of the MDA.

  • outputs (Iterable[str] | None) – The outputs to differentiate. If None, use all the outputs of the MDA.

  • parallel (bool) –

    Whether to execute the MDA 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 (int) –

    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 comparing the exact and 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 (None | Path | str) – 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 passed Jacobian is correct.

Return type:

bool

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

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 supported yet.

Return type:

dict[str, Any]

execute_all_disciplines(input_local_data, update_local_data=True)[source]

Execute all self.disciplines.

Parameters:

  • input_local_data (Mapping[str, ndarray]) – The input data of the disciplines.

  • update_local_data (bool) –

    Whether to update the local data from the disciplines.

    By default it is set to True.

Return type:

None

static from_pickle(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

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]

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 in the XDSM.

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:

LoopExecSequence

get_input_data(with_namespaces=True)

Return the local input data as a dictionary.

Parameters:

with_namespaces (bool) –

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 (bool) –

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.

Parameters:

with_namespaces (bool) –

By default it is set to True.

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 (bool) –

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 (bool) –

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]

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, compute_all_jacobians=False, execute=True)

Compute the Jacobians of some outputs with respect to some inputs.

Parameters:

  • input_data (Mapping[str, Any] | None) – The input data for which to compute the Jacobian. If None, use the MDODiscipline.default_inputs.

  • compute_all_jacobians (bool) –

    Whether to compute the Jacobians of all the output with respect to all the inputs. Otherwise, set the input variables against which to differentiate the output ones with add_differentiated_inputs() and set these output variables to differentiate with add_differentiated_outputs().

    By default it is set to False.

  • execute (bool) –

    Whether to start by executing the discipline with the input data for which to compute the Jacobian; this allows to ensure that the discipline was executed with the right input data; it can be almost free if the corresponding output data have been stored in the cache.

    By default it is set to True.

Returns:

The Jacobian of the discipline shaped as {output_name: {input_name: jacobian_array}} where jacobian_array[i, j] is the partial derivative of output_name[i] with respect to input_name[j].

Raises:

ValueError – When either the inputs for which to differentiate the outputs or the outputs to differentiate are missing.

Return type:

dict[str, dict[str, NDArray[float]]]

notify_status_observers()

Notify all status observers that the status has changed.

Return type:

None

plot_residual_history(show=False, save=True, n_iterations=None, logscale=None, filename=None, fig_size=None)

Generate a plot of the residual history.

The first iteration of each new execution is marked with a red dot.

Parameters:

  • show (bool) –

    Whether to display the plot on screen.

    By default it is set to False.

  • save (bool) –

    Whether to save the plot as a PDF file.

    By default it is set to True.

  • n_iterations (int | None) – The number of iterations on the x axis. If None, use all the iterations.

  • logscale (tuple[int, int] | None) – The limits of the y axis. If None, do not change the limits of the y axis.

  • filename (str | None) – The name of the file to save the figure. If None, use “{mda.name}_residual_history.pdf”.

  • fig_size (FigSizeType | None) – The width and height of the figure in inches, e.g. (w, h).

Returns:

The figure, to be customized if not closed.

Return type:

Figure

remove_status_observer(obs)

Remove an observer for the status.

Parameters:

obs (Any) – The observer to remove.

Return type:

None

reset_disciplines_statuses()

Reset all the statuses of the disciplines.

Return type:

None

reset_statuses_for_run()

Set all the statuses to MDODiscipline.ExecutionStatus.PENDING.

Raises:

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

Return type:

None

set_cache_policy(cache_type=CacheType.SIMPLE, cache_tolerance=0.0, cache_hdf_file=None, cache_hdf_node_path=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 (CacheType) –

    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.CacheType.HDF5 policy is used.

  • cache_hdf_node_path (str | None) – The name of the HDF file node to store the discipline data, possibly passed as a path root_name/.../group_name/.../node_name. 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=ApproximationMode.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 (ApproximationMode) –

    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, compute_all_jacobians=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.

  • compute_all_jacobians (bool) –

    Whether to compute the Jacobians of all the output with respect to all the inputs. Otherwise, set the input variables against which to differentiate the output ones with add_differentiated_inputs() and set these output variables to differentiate with add_differentiated_outputs().

    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

to_pickle(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

GRAMMAR_DIRECTORY: ClassVar[str | None] = None

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

N_CPUS = 2
RESIDUALS_NORM: ClassVar[str] = 'MDA residuals norm'
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.

all_couplings: list[str]

The names of the coupling variables.

assembly: JacobianAssembly
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.

coupling_structure: MDOCouplingStructure

The coupling structure to be used by the MDA.

data_processor: DataProcessor

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

property default_inputs: Defaults

The default inputs.

property default_outputs: Defaults

The default outputs.

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: GrammarType

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.

The structure is {output: {input: matrix}}.

lin_cache_tol_fact: float

The tolerance factor to cache the Jacobian.

linear_solver: str

The name of the linear solver.

linear_solver_options: dict[str, Any]

The options of the linear solver.

linear_solver_tolerance: float

The tolerance of the linear solver in the adjoint equation.

property linearization_mode: LinearizationMode

The linearization mode among MDODiscipline.LinearizationMode.

Raises:

ValueError – When the linearization mode is unknown.

property local_data: DisciplineData

The current input and output data.

property log_convergence: bool

Whether to log the MDA convergence.

matrix_type: JacobianAssembly.JacobianType

The type of the matrix.

max_mda_iter: int

The maximum iterations number for the MDA algorithm.

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.

norm0: float | None

The reference residual, if any.

normed_residual: float

The normed residual.

output_grammar: BaseGrammar

The output grammar.

re_exec_policy: ReExecutionPolicy

The policy to re-execute the same discipline.

reset_history_each_run: bool

Whether to reset the history of MDA residuals before each run.

residual_history: list[float]

The history of MDA residuals.

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

Whether the run method shall solve the residuals.

scaling: ResidualScaling

The scaling method applied to MDA residuals for convergence monitoring.

property status: ExecutionStatus

The status of the discipline.

The status aims at monitoring the process and give the user a simplified view on the state (the process state = execution or linearize or done) of the disciplines. The core part of the execution is _run, the core part of linearize is _compute_jacobian or approximate jacobian computation.

strong_couplings: list[str]

The names of the strong coupling variables.

time_stamps = None
tolerance: float

The tolerance of the iterative direct coupling solver.

use_lu_fact: bool

Whether to store a LU factorization of the matrix.

virtual_execution: ClassVar[bool] = False

Whether to skip the _run() method during execution and return the default_outputs, whatever the inputs.

warm_start: bool

Whether the second iteration and ongoing start from the previous solution.

Examples using MDANewtonRaphson

Hybrid Jacobi/Newton MDA

Hybrid Jacobi/Newton MDA

Newton-Raphson MDA

Newton-Raphson MDA

Examples using MDAQuasiNewton

Quasi-Newton MDA

Quasi-Newton MDA