gemseo / mda

mda module¶

Base class for all Multi-disciplinary Design Analyses (MDA).

class gemseo.mda.mda.MDA(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, acceleration_method=AccelerationMethod.NONE, over_relaxation_factor=1.0)[source]

Bases: MDODiscipline

An MDA analysis.

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] | None) – The options passed to the linear solver factory.
acceleration_method (AccelerationMethod) –
The acceleration method to be used to improve the convergence rate of the fixed point iteration method.

By default it is set to “NoTransformation”.
over_relaxation_factor (float) –
The over-relaxation factor.

By default it is set to 1.0.

class ResidualScaling(value)[source]

Bases: LowercaseStrEnum

The scaling method applied to MDA residuals for convergence monitoring.

INITIAL_RESIDUAL_COMPONENT = 'initial_residual_component'

k`-th residual is scaled component-wise. Each component is scaled by the corresponding component of the initial residual (if not null, else it is not scaled). The MDA is considered converged when each component satisfies,

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

Type:: The
Type:: math

INITIAL_RESIDUAL_NORM = 'initial_residual_norm'

k`-th residual vector is scaled by the Euclidean norm of the initial residual (if not null, else it is not scaled). The MDA is considered converged when its Euclidean norm satisfies,

\[\frac{ \|R_k\|_2 }{ \|R_0\|_2 } \leq \text{tol}.\]

Type:: The
Type:: math

INITIAL_SUBRESIDUAL_NORM = 'initial_subresidual_norm'

k`-th residual vector is scaled discipline-wise. The sub-residual associated wich each discipline is scaled by the Euclidean norm of the initial sub-residual (if not null, else it is not scaled). The MDA is considered converged when the Euclidean norm of each sub-residual satisfies,

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

Type:: The
Type:: math

NO_SCALING = 'no_scaling': The residual vector is not scaled. The MDA is considered converged when its Euclidean norm satisfies,

\[\|R_k\|_2 \leq \text{tol}.\]

N_COUPLING_VARIABLES = 'n_coupling_variables'

k`-th residual vector is scaled using the number of coupling variables. The MDA is considered converged when its Euclidean norm satisfies, .. math:

\frac{ \|R_k\|_2 }{ \sqrt{n_\text{coupl.}} } \leq \text{tol}.

Type:: The
Type:: math

SCALED_INITIAL_RESIDUAL_COMPONENT = 'scaled_initial_residual_component'

k`-th residual vector is scaled component-wise and by the number coupling variables. If \(\div\) denotes the component-wise division between two vectors, then the MDA is considered converged when the residual vector satisfies,

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

Type:: The
Type:: math

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)[source]

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

execute(input_data=None)[source]

Execute the discipline.

This method executes the discipline:

Adds the default inputs to the input_data if some inputs are not defined in input_data but exist in MDODiscipline.default_inputs.
Checks whether the last execution of the discipline was called with identical inputs, i.e. cached in MDODiscipline.cache; if so, directly returns self.cache.get_output_cache(inputs).
Caches the inputs.
Checks the input data against MDODiscipline.input_grammar.
If MDODiscipline.data_processor is not None, runs the preprocessor.
Updates the status to MDODiscipline.ExecutionStatus.RUNNING.
Calls the MDODiscipline._run() method, that shall be defined.
If MDODiscipline.data_processor is not None, runs the postprocessor.
Checks the output data.
Caches the outputs.
Updates the status to MDODiscipline.ExecutionStatus.DONE or MDODiscipline.ExecutionStatus.FAILED.
Updates summed execution time.

Parameters:: input_data (Mapping[str, Any] | None) – The input data needed to execute the discipline according to the discipline input grammar. If None, use the MDODiscipline.default_inputs.
Returns:: The discipline local data after execution.
Return type:: DisciplineData

get_expected_dataflow()[source]

Return the expected data exchange sequence.

This method is used for the XDSM representation.

The default expected data exchange sequence is an empty list.

Examples using MDA¶

MDAChain with independent parallel MDAs