# MDA algorithms¶

Warning

Some capabilities may require the installation of GEMSEO with all its features and some others may depend on plugins.

Note

All the features of the wrapped libraries may not be exposed through GEMSEO.

## MDAChain¶

Module: `gemseo.mda.mda_chain`

- Required parameters
**disciplines**:*Sequence[MDODiscipline]*The disciplines from which to compute the MDA.

- Optional parameters
**chain_linearize**:*bool, optional*Whether to linearize the chain of execution. Otherwise, linearize the overall MDA with base class method. This last option is preferred to minimize computations in adjoint mode, while in direct mode, linearizing the chain may be cheaper.

By default it is set to False.

**coupling_structure**:*MDOCouplingStructure | None, optional*The coupling structure to be used by the MDA. If

`None`

, it is created from disciplines.By default it is set to None.

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**initialize_defaults**:*bool, optional*Whether to create a

`MDOInitializationChain`

to compute the eventually missing`default_inputs`

at the first execution.By default it is set to False.

**inner_mda_name**:*str, optional*The class name of the inner-MDA.

By default it is set to MDAJacobi.

**linear_solver**:*str, optional*The name of the linear solver.

By default it is set to DEFAULT.

**linear_solver_options**:*Mapping[str, Any] | None, optional*The options passed to the linear solver factory.

By default it is set to None.

**linear_solver_tolerance**:*float, optional*The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.

**log_convergence**:*bool, optional*Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.

**max_mda_iter**:*int, optional*The maximum iterations number for the MDA algorithm.

By default it is set to 20.

**mdachain_parallel_options**:*Mapping[str, int | bool] | None, optional*The options of the MDOParallelChain instances, if any.

By default it is set to None.

**mdachain_parallelize_tasks**:*bool, optional*Whether to parallelize the parallel tasks, if any.

By default it is set to False.

**n_processes**:*int, optional*The maximum simultaneous number of threads if

`use_threading`

is set to True, otherwise processes, used to parallelize the execution.By default it is set to 2.

**name**:*str | None, optional*The name to be given to the MDA. If

`None`

, use the name of the class.By default it is set to None.

**sub_coupling_structures**:*Iterable[MDOCouplingStructure | None] | None, optional*The coupling structures to be used by the inner-MDAs. If

`None`

, they are created from the sub-disciplines.By default it is set to None.

**tolerance**:*float, optional*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.

**use_lu_fact**:*bool, optional*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.

****inner_mda_options**:*float | int | bool | str | None*The options of the inner-MDAs.

## MDAGSNewton¶

Module: `gemseo.mda.sequential_mda`

- Required parameters
**disciplines**:*Sequence[MDODiscipline]*The disciplines from which to compute the MDA.

- Optional parameters
**coupling_structure**:*MDOCouplingStructure | None, optional*The coupling structure to be used by the MDA. If

`None`

, it is created from disciplines.By default it is set to None.

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**linear_solver**:*str, optional*The name of the linear solver.

By default it is set to DEFAULT.

**linear_solver_options**:*Mapping[str, Any] | None, optional*The options passed to the linear solver factory.

By default it is set to None.

**linear_solver_tolerance**:*float, optional*The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.

**log_convergence**:*bool, optional*Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.

**max_mda_iter**:*int, optional*The maximum iterations number for the MDA algorithm.

By default it is set to 10.

**max_mda_iter_gs**:*int, optional*The maximum number of iterations of the Gauss-Seidel MDA.

By default it is set to 3.

**name**:*str | None, optional*The name to be given to the MDA. If

`None`

, use the name of the class.By default it is set to None.

**relax_factor**:*float, optional*The relaxation factor.

By default it is set to 0.99.

**tolerance**:*float, optional*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.

**use_lu_fact**:*bool, optional*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.

**warm_start**:*bool, optional*Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

****newton_mda_options**:*float | str | None*The options for the Newton MDA.

## MDAGaussSeidel¶

Module: `gemseo.mda.gauss_seidel`

- Required parameters
**disciplines**:*Sequence[MDODiscipline]*The disciplines from which to compute the MDA.

- Optional parameters
**acceleration_method**:*AccelerationMethod, optional*The acceleration method to be used to improve the convergence rate of the fixed point iteration method.

By default it is set to NoTransformation.

**coupling_structure**:*MDOCouplingStructure | None, optional*The coupling structure to be used by the MDA. If

`None`

, it is created from disciplines.By default it is set to None.

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**linear_solver**:*str, optional*The name of the linear solver.

By default it is set to DEFAULT.

**linear_solver_options**:*Mapping[str, Any] | None, optional*The options passed to the linear solver factory.

By default it is set to None.

**linear_solver_tolerance**:*float, optional*The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.

**log_convergence**:*bool, optional*Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.

**max_mda_iter**:*int, optional*The maximum iterations number for the MDA algorithm.

By default it is set to 10.

**name**:*str | None, optional*The name to be given to the MDA. If

`None`

, use the name of the class.By default it is set to None.

**over_relax_factor**:*float | None, optional*Deprecated, please consider using

`MDA.over_relaxation_factor`

instead. The relaxation coefficient, used to make the method more robust, if`0<over_relax_factor<1`

or faster if`1<over_relax_factor<=2`

. If`over_relax_factor =1.`

, it is deactivated.By default it is set to None.

**over_relaxation_factor**:*float, optional*The over-relaxation factor.

By default it is set to 1.0.

**tolerance**:*float, optional*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.

**use_lu_fact**:*bool, optional*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.

**warm_start**:*bool, optional*Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

## MDAJacobi¶

Module: `gemseo.mda.jacobi`

- Required parameters
**acceleration**:*str*Deprecated, please consider using the

`MDA.acceleration_method`

instead. 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.**disciplines**:*Sequence[MDODiscipline]*The disciplines from which to compute the MDA.

- Optional parameters
**acceleration_method**:*AccelerationMethod, optional*The acceleration method to be used to improve the convergence rate of the fixed point iteration method.

By default it is set to Alternate2Delta.

**coupling_structure**:*MDOCouplingStructure | None, optional*The coupling structure to be used by the MDA. If

`None`

, it is created from disciplines.By default it is set to None.

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**linear_solver**:*str, optional*The name of the linear solver.

By default it is set to DEFAULT.

**linear_solver_options**:*Mapping[str, Any] | None, optional*The options passed to the linear solver factory.

By default it is set to None.

**linear_solver_tolerance**:*float, optional*The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.

**log_convergence**:*bool, optional*Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.

**max_mda_iter**:*int, optional*The maximum iterations number for the MDA algorithm.

By default it is set to 10.

**n_processes**:*int, optional*The maximum simultaneous number of threads if

`use_threading`

is set to True, otherwise processes, used to parallelize the execution.By default it is set to 2.

**name**:*str | None, optional*The name to be given to the MDA. If

`None`

, use the name of the class.By default it is set to None.

**over_relaxation_factor**:*float, optional*The over-relaxation factor.

By default it is set to 1.0.

**tolerance**:*float, optional*By default it is set to 1e-06.

**use_lu_fact**:*bool, optional*By default it is set to False.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the execution. Processes will copy (serialize) all the disciplines, while threads will share all the memory. If one wants to execute the same discipline multiple times then multiprocessing should be prefered.

By default it is set to True.

**warm_start**:*bool, optional*Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

## MDANewtonRaphson¶

Module: `gemseo.mda.newton_raphson`

- Required parameters
**disciplines**:*Sequence[MDODiscipline]*The disciplines from which to compute the MDA.

- Optional parameters
**acceleration_method**:*AccelerationMethod, optional*The acceleration method to be used to improve the convergence rate of the fixed point iteration method.

By default it is set to NoTransformation.

**coupling_structure**:*MDOCouplingStructure | None, optional*The coupling structure to be used by the MDA. If

`None`

, it is created from disciplines.By default it is set to None.

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**linear_solver**:*str, optional*The name of the linear solver.

By default it is set to DEFAULT.

**linear_solver_options**:*Mapping[str, Any] | None, optional*The options passed to the linear solver factory.

By default it is set to None.

**linear_solver_tolerance**:*float, optional*The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.

**log_convergence**:*bool, optional*Whether to log the MDA convergence, expressed in terms of normed residuals.

By default it is set to False.

**max_mda_iter**:*int, optional*The maximum iterations number for the MDA algorithm.

By default it is set to 10.

**n_processes**:*int, optional*The maximum simultaneous number of threads if

`use_threading`

is set to True, otherwise processes, used to parallelize the execution.By default it is set to 2.

**name**:*str | None, optional*The name to be given to the MDA. If

`None`

, use the name of the class.By default it is set to None.

**newton_linear_solver_name**:*str, optional*The name of the linear solver for the Newton method.

By default it is set to DEFAULT.

**newton_linear_solver_options**:*Mapping[str, Any] | None, optional*The options for the Newton linear solver.

By default it is set to None.

**over_relaxation_factor**:*float, optional*The over-relaxation factor.

By default it is set to 0.99.

**parallel**:*bool, optional*Whether to execute and linearize the disciplines in parallel.

By default it is set to False.

**relax_factor**:*float | None, optional*The relaxation factor.

By default it is set to None.

**tolerance**:*float, optional*By default it is set to 1e-06.

**use_lu_fact**:*bool, optional*By default it is set to False.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the execution. Processes will copy (serialize) all the disciplines, while threads will share all the memory. If one wants to execute the same discipline multiple times then multiprocessing should be preferred.

By default it is set to True.

**warm_start**:*bool, optional*Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

## MDAQuasiNewton¶

Module: `gemseo.mda.quasi_newton`

- Required parameters
**disciplines**:*Sequence[MDODiscipline]*The disciplines from which to compute the MDA.

- Optional parameters
**coupling_structure**:*MDOCouplingStructure | None, optional*The coupling structure to be used by the MDA. If

`None`

, it is created from disciplines.By default it is set to None.

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**linear_solver**:*str, optional*The name of the linear solver.

By default it is set to DEFAULT.

**linear_solver_options**:*Mapping[str, Any] | None, optional*The options passed to the linear solver factory.

By default it is set to None.

**linear_solver_tolerance**:*float, optional*The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.

**max_mda_iter**:*int, optional*The maximum iterations number for the MDA algorithm.

By default it is set to 10.

**method**:*str, optional*The name of the method in scipy root finding, among

`QUASI_NEWTON_METHODS`

.By default it is set to hybr.

**name**:*str | None, optional*The name to be given to the MDA. If

`None`

, use the name of the class.By default it is set to None.

**tolerance**:*float, optional*By default it is set to 1e-06.

**use_gradient**:*bool, optional*Whether to use the analytic gradient of the discipline.

By default it is set to False.

**use_lu_fact**:*bool, optional*By default it is set to False.

**warm_start**:*bool, optional*Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.

## MDASequential¶

Module: `gemseo.mda.sequential_mda`

- Required parameters
**disciplines**:*Sequence[MDODiscipline]*The disciplines from which to compute the MDA.

**mda_sequence**:*Sequence[MDA]*The sequence of MDAs.

- Optional parameters
**coupling_structure**:*MDOCouplingStructure | None, optional*The coupling structure to be used by the MDA. If

`None`

, it is created from disciplines.By default it is set to None.

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**linear_solver**:*str, optional*The name of the linear solver.

By default it is set to DEFAULT.

**linear_solver_options**:*Mapping[str, Any] | None, optional*The options passed to the linear solver factory.

By default it is set to None.

**linear_solver_tolerance**:*float, optional*The tolerance of the linear solver in the adjoint equation.

By default it is set to 1e-12.

**max_mda_iter**:*int, optional*The maximum iterations number for the MDA algorithm.

By default it is set to 10.

**name**:*str | None, optional*The name to be given to the MDA. If

`None`

, use the name of the class.By default it is set to None.

**tolerance**:*float, optional*By default it is set to 1e-06.

**use_lu_fact**:*bool, optional*By default it is set to False.

**warm_start**:*bool, optional*Whether the second iteration and ongoing start from the previous coupling solution.

By default it is set to False.