gemseo / mda

# jacobi module¶

A Jacobi algorithm for solving MDAs.

class gemseo.mda.jacobi.MDAJacobi(disciplines, max_mda_iter=10, name=None, n_processes=2, acceleration='m2d', tolerance=1e-06, linear_solver_tolerance=1e-12, use_threading=True, warm_start=False, use_lu_fact=False, grammar_type='JSONGrammar', coupling_structure=None, log_convergence=False, linear_solver='DEFAULT', linear_solver_options=None)[source]

Bases: MDA

Perform a MDA analysis using a Jacobi algorithm.

This algorithm is an iterative technique to solve the linear system:

$Ax = b$

by decomposing the matrix $$A$$ into the sum of a diagonal matrix $$D$$ and the reminder $$R$$.

The new iterate is given by:

$x_{k+1} = D^{-1}(b-Rx_k)$
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.

• 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.

• acceleration (str) –

The type of acceleration to be used to extrapolate the residuals and save CPU time by reusing the information from the last iterations, either None, "m2d", or "secant", "m2d" is faster but uses the 2 last iterations.

By default it is set to “m2d”.

• 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.

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 True.

• 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.

• grammar_type (str) –

The type of the input and output grammars, either MDODiscipline.JSON_GRAMMAR_TYPE or MDODiscipline.SIMPLE_GRAMMAR_TYPE.

By default it is set to “JSONGrammar”.

• 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.

classmethod activate_time_stamps()

Activate the time stamps.

For storing start and end times of execution and linearizations.

Return type:

None

Add inputs against which to differentiate the outputs.

This method updates MDODiscipline._differentiated_inputs with inputs.

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

This method updates MDODiscipline._differentiated_outputs with outputs.

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 a namespace prefix to an existing input grammar element.

The updated input grammar element name will be namespace + namespaces_separator + name.

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

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

Add a namespace prefix to an existing output grammar element.

The updated output grammar element name will be namespace + namespaces_separator + name.

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

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

Add an observer for the status.

Add an observer for the status to be notified when self changes of status.

Parameters:

obs (Any) – The observer to add.

Return type:

None

auto_get_grammar_file(is_input=True, name=None, comp_dir=None)

Use a naming convention to associate a grammar file to the discipline.

Search in the directory comp_dir for either an input grammar file named name + "_input.json" or an output grammar file named name + "_output.json".

Parameters:
• is_input (bool) –

Whether to search for an input or output grammar file.

By default it is set to True.

• name (str | None) – The name to be searched in the file names. If None, use the name of the discipline class.

• comp_dir (str | Path | None) – The directory in which to search the grammar file. If None, use the GRAMMAR_DIRECTORY if any, or the directory of the discipline class module.

Returns:

The grammar file path.

Return type:

str

check_input_data(input_data, raise_exception=True)

Check the input data validity.

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

• raise_exception (bool) –

Whether to raise on error.

By default it is set to True.

Return type:

None

check_jacobian(input_data=None, derr_approx='finite_differences', step=1e-07, threshold=1e-08, linearization_mode='auto', inputs=None, outputs=None, parallel=False, n_processes=2, use_threading=False, wait_time_between_fork=0, auto_set_step=False, plot_result=False, file_path='jacobian_errors.pdf', show=False, fig_size_x=10, fig_size_y=10, reference_jacobian_path=None, save_reference_jacobian=False, indices=None)

Check if the analytical Jacobian is correct with respect to a reference one.

If reference_jacobian_path is not None and save_reference_jacobian is True, compute the reference Jacobian with the approximation method and save it in reference_jacobian_path.

If reference_jacobian_path is not None and save_reference_jacobian is False, do not compute the reference Jacobian but read it from reference_jacobian_path.

If reference_jacobian_path is None, compute the reference Jacobian without saving it.

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

• derr_approx (str) –

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.

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 – The path of the reference Jacobian file.

• save_reference_jacobian

Whether to save the reference Jacobian.

By default it is set to False.

• indices – The indices of the inputs and outputs for the different sub-Jacobian matrices, formatted as {variable_name: variable_components} where variable_components can be either an integer, e.g. 2 a sequence of integers, e.g. [0, 3], a slice, e.g. slice(0,3), the ellipsis symbol () or None, which is the same as ellipsis. If a variable name is missing, consider all its components. If None, consider all the components of all the inputs and outputs.

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

static deserialize(file_path)

Deserialize a discipline from a file.

Parameters:

file_path (str | Path) – The path to the file containing the discipline.

Returns:

The discipline instance.

Return type:

MDODiscipline

execute(input_data=None)

Execute the discipline.

This method executes the discipline:

Parameters:

input_data (Mapping[str, Any] | None) – The input data needed to execute the discipline according to the discipline input grammar. If None, use the MDODiscipline.default_inputs.

Returns:

The discipline local data after execution.

Raises:

RuntimeError – When residual_variables are declared but self.run_solves_residuals is False. This is not suported yet.

Return type:

dict[str, Any]

execute_all_disciplines(input_local_data)[source]

Execute all the disciplines.

Parameters:

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

Return type:

None

get_all_inputs()

Return the local input data as a list.

The order is given by MDODiscipline.get_input_data_names().

Returns:

The local input data.

Return type:

list[Any]

get_all_outputs()

Return the local output data as a list.

The order is given by MDODiscipline.get_output_data_names().

Returns:

The local output data.

Return type:

list[Any]

get_attributes_to_serialize()

Define the names of the attributes to be serialized.

Returns:

The names of the attributes to be serialized.

Return type:

list[str]

static get_data_list_from_dict(keys, data_dict)

Filter the dict from a list of keys or a single key.

If keys is a string, then the method return the value associated to the key. If keys is a list of strings, then the method returns a generator of value corresponding to the keys which can be iterated.

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

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

Returns:

Either a data or a generator of data.

Return type:

Any | Generator[Any]

get_disciplines_in_dataflow_chain()

Return the disciplines that must be shown as blocks within the XDSM representation of a chain.

By default, only the discipline itself is shown. This function can be differently implemented for any type of inherited discipline.

Returns:

The disciplines shown in the XDSM chain.

Return type:
get_expected_dataflow()

Return the expected data exchange sequence.

This method is used for the XDSM representation.

The default expected data exchange sequence is an empty list.

MDOFormulation.get_expected_dataflow

Returns:

The data exchange arcs.

Return type:
get_expected_workflow()[source]

Return the expected execution sequence.

This method is used for the XDSM representation.

The default expected execution sequence is the execution of the discipline itself.

MDOFormulation.get_expected_workflow

Returns:

The expected execution sequence.

Return type:

LoopExecSequence

get_input_data(with_namespaces=True)

Return the local input data as a dictionary.

Parameters:

with_namespaces

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

By default it is set to True.

Returns:

The local input data.

Return type:

dict[str, Any]

get_input_data_names(with_namespaces=True)

Return the names of the input variables.

Parameters:

with_namespaces

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

By default it is set to True.

Returns:

The names of the input variables.

Return type:

list[str]

get_input_output_data_names(with_namespaces=True)

Return the names of the input and output variables.

Args:
with_namespaces: Whether to keep the namespace prefix of the

output names, if any.

Returns:

The name of the input and output variables.

Return type:

list[str]

get_inputs_asarray()

Return the local output data as a large NumPy array.

The order is the one of MDODiscipline.get_all_outputs().

Returns:

The local output data.

Return type:

ndarray

get_inputs_by_name(data_names)

Return the local data associated with input variables.

Parameters:

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

Returns:

The local data for the given input variables.

Raises:

ValueError – When a variable is not an input of the discipline.

Return type:

list[Any]

get_local_data_by_name(data_names)

Return the local data of the discipline associated with variables names.

Parameters:

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

Returns:

The local data associated with the variables names.

Raises:

ValueError – When a name is not a discipline input name.

Return type:

Generator[Any]

get_output_data(with_namespaces=True)

Return the local output data as a dictionary.

Parameters:

with_namespaces

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

By default it is set to True.

Returns:

The local output data.

Return type:

dict[str, Any]

get_output_data_names(with_namespaces=True)

Return the names of the output variables.

Parameters:

with_namespaces

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

By default it is set to True.

Returns:

The names of the output variables.

Return type:

list[str]

get_outputs_asarray()

Return the local input data as a large NumPy array.

The order is the one of MDODiscipline.get_all_inputs().

Returns:

The local input data.

Return type:

ndarray

get_outputs_by_name(data_names)

Return the local data associated with output variables.

Parameters:

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

Returns:

The local data for the given output variables.

Raises:

ValueError – When a variable is not an output of the discipline.

Return type:

list[Any]

get_sub_disciplines()

Return the sub-disciplines if any.

Returns:

The sub-disciplines.

Return type:
is_all_inputs_existing(data_names)

Test if several variables are discipline inputs.

Parameters:

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

Returns:

Whether all the variables are discipline inputs.

Return type:

bool

is_all_outputs_existing(data_names)

Test if several variables are discipline outputs.

Parameters:

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

Returns:

Whether all the variables are discipline outputs.

Return type:

bool

is_input_existing(data_name)

Test if a variable is a discipline input.

Parameters:

data_name (str) – The name of the variable.

Returns:

Whether the variable is a discipline input.

Return type:

bool

is_output_existing(data_name)

Test if a variable is a discipline output.

Parameters:

data_name (str) – The name of the variable.

Returns:

Whether the variable is a discipline output.

Return type:

bool

static is_scenario()

Whether the discipline is a scenario.

Return type:

bool

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

Execute the linearized version of the code.

Parameters:
• input_data (dict[str, Any] | None) – The input data needed to linearize the discipline according to the discipline input grammar. If None, use the MDODiscipline.default_inputs.

• force_all (bool) –

If False, MDODiscipline._differentiated_inputs and MDODiscipline._differentiated_outputs are used to filter the differentiated variables. otherwise, all outputs are differentiated wrt all inputs.

By default it is set to False.

• force_no_exec (bool) –

If True, the discipline is not re-executed, cache is loaded anyway.

By default it is set to False.

Returns:

The Jacobian of the discipline.

Return type:

dict[str, dict[str, ndarray]]

notify_status_observers()

Notify all status observers that the status has changed.

Return type:

None

plot_residual_history(show=False, save=True, n_iterations=None, logscale=None, filename=None, fig_size=(50.0, 10.0))

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 (tuple[float, float]) –

The width and height of the figure in inches, e.g. (w, h).

By default it is set to (50.0, 10.0).

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.STATUS_PENDING.

Raises:

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

Return type:

None

serialize(file_path)

Serialize the discipline and store it in a file.

Parameters:

file_path (str | Path) – The path to the file to store the discipline.

Return type:

None

set_cache_policy(cache_type='SimpleCache', cache_tolerance=0.0, cache_hdf_file=None, cache_hdf_node_name=None, is_memory_shared=True)

Set the type of cache to use and the tolerance level.

This method defines when the output data have to be cached according to the distance between the corresponding input data and the input data already cached for which output data are also cached.

The cache can be either a SimpleCache recording the last execution or a cache storing all executions, e.g. MemoryFullCache and HDF5Cache. Caching data can be either in-memory, e.g. SimpleCache and MemoryFullCache, or on the disk, e.g. HDF5Cache.

The attribute CacheFactory.caches provides the available caches types.

Parameters:
• cache_type (str) –

The type of cache.

By default it is set to “SimpleCache”.

• cache_tolerance (float) –

The maximum relative norm of the difference between two input arrays to consider that two input arrays are equal.

By default it is set to 0.0.

• cache_hdf_file (str | Path | None) – The path to the HDF file to store the data; this argument is mandatory when the MDODiscipline.HDF5_CACHE policy is used.

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

• is_memory_shared (bool) –

Whether to store the data with a shared memory dictionary, which makes the cache compatible with multiprocessing.

By default it is set to True.

Return type:

None

set_disciplines_statuses(status)

Set the sub-disciplines statuses.

To be implemented in subclasses.

Parameters:

status (str) – The status.

Return type:

None

Set the Jacobian approximation method.

Sets the linearization mode to approx_method, sets the parameters of the approximation for further use when calling MDODiscipline.linearize().

Parameters:
• jac_approx_type (str) –

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

By default it is set to “finite_differences”.

• jax_approx_step (float) –

The differentiation step.

By default it is set to 1e-07.

• jac_approx_n_processes (int) –

The maximum simultaneous number of threads, if jac_approx_use_threading is True, or processes otherwise, used to parallelize the execution.

By default it is set to 1.

Whether to use threads instead of processes to parallelize the execution; multiprocessing will copy (serialize) all the disciplines, while threading will share all the memory This is important to note if you want to execute the same discipline multiple times, you shall use multiprocessing.

By default it is set to False.

• jac_approx_wait_time (float) –

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

By default it is set to 0.

Return type:

None

set_optimal_fd_step(outputs=None, inputs=None, force_all=False, print_errors=False, numerical_error=2.220446049250313e-16)

Compute the optimal finite-difference step.

Compute the optimal step for a forward first order finite differences gradient approximation. Requires a first evaluation of the perturbed functions values. The optimal step is reached when the truncation error (cut in the Taylor development), and the numerical cancellation errors (round-off when doing f(x+step)-f(x)) are approximately equal.

Warning

This calls the discipline execution twice per input variables.

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

Parameters:
• inputs (Iterable[str] | None) – The inputs wrt which the outputs are linearized. If None, use the MDODiscipline._differentiated_inputs.

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

• force_all (bool) –

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

By default it is set to False.

• print_errors (bool) –

Whether to display the estimated errors.

By default it is set to False.

• numerical_error (float) –

The numerical error associated to the calculation of f. By default, this is the machine epsilon (appx 1e-16), but can be higher when the calculation of f requires a numerical resolution.

By default it is set to 2.220446049250313e-16.

Returns:

The estimated errors of truncation and cancellation error.

Raises:

ValueError – When the Jacobian approximation method has not been set.

set_residuals_scaling_options(scale_residuals_with_coupling_size=False, scale_residuals_with_first_norm=True)

Set the options for the residuals scaling.

Parameters:
• scale_residuals_with_coupling_size (bool) –

Whether to activate the scaling of the MDA residuals by the number of coupling variables. This divides the residuals obtained by the norm of the difference between iterates by the square root of the coupling vector size.

By default it is set to False.

• scale_residuals_with_first_norm (bool) –

Whether to scale the residuals by the first residual norm, except if :attr:.norm0 is set by the user. If :attr:.norm0 is set to a value, it deactivates the residuals scaling by the design variables size.

By default it is set to True.

Return type:

None

store_local_data(**kwargs)

Store discipline data in local data.

Parameters:

**kwargs (Any) – The data to be stored in MDODiscipline.local_data.

Return type:

None

APPROX_MODES = ['finite_differences', 'complex_step']
AVAILABLE_MODES = ('auto', 'direct', 'adjoint', 'reverse', 'finite_differences', 'complex_step')
AVAILABLE_STATUSES = ['DONE', 'FAILED', 'PENDING', 'RUNNING', 'VIRTUAL']
COMPLEX_STEP = 'complex_step'
FINITE_DIFFERENCES = 'finite_differences'
GRAMMAR_DIRECTORY: ClassVar[str | None] = None

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

HDF5_CACHE = 'HDF5Cache'
JSON_GRAMMAR_TYPE = 'JSONGrammar'
M2D_ACCELERATION = 'm2d'
MEMORY_FULL_CACHE = 'MemoryFullCache'
N_CPUS = 2
RESIDUALS_NORM: ClassVar[str] = 'MDA residuals norm'
RE_EXECUTE_DONE_POLICY = 'RE_EXEC_DONE'
RE_EXECUTE_NEVER_POLICY = 'RE_EXEC_NEVER'
SECANT_ACCELERATION = 'secant'
SIMPLE_CACHE = 'SimpleCache'
SIMPLE_GRAMMAR_TYPE = 'SimpleGrammar'
STATUS_DONE = 'DONE'
STATUS_FAILED = 'FAILED'
STATUS_PENDING = 'PENDING'
STATUS_RUNNING = 'RUNNING'
STATUS_VIRTUAL = 'VIRTUAL'
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

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: dict[str, Any]

The default inputs.

Raises:

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

disciplines: Sequence[MDODiscipline]

The disciplines from which to compute the MDA.

exec_for_lin: bool

Whether the last execution was due to a linearization.

property exec_time: float | None

The cumulated execution time of the discipline.

This property is multiprocessing safe.

Raises:

RuntimeError – When the discipline counters are disabled.

property grammar_type: BaseGrammar

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

input_grammar: BaseGrammar

The input grammar.

jac: dict[str, dict[str, ndarray]]

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

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: str

The linearization mode among MDODiscipline.AVAILABLE_MODES.

Raises:

ValueError – When the linearization mode is unknown.

property local_data: DisciplineData

The current input and output data.

property log_convergence: bool

Whether to log the MDA convergence.

matrix_type: str

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: str

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

If True, the run method shall solve the residuals.

property status: str

The status of the discipline.

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.

warm_start: bool

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

## Examples using MDAJacobi¶

Hybrid Jacobi/Newton MDA

Hybrid Jacobi/Newton MDA

Jacobi MDA

Jacobi MDA