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=GrammarType.JSON, coupling_structure=None, log_convergence=False, linear_solver='DEFAULT', linear_solver_options=None)[source]

Bases: MDA

Perform an 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:

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

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.

• 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.

• 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 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 (MDODiscipline.GrammarType) –

The type of the input and output grammars.

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.

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_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.

See also

MDOFormulation.get_expected_workflow

Returns:

The expected execution sequence.

Return type:

LoopExecSequence

M2D_ACCELERATION = 'm2d'
SECANT_ACCELERATION = 'secant'
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.

coupling_structure: MDOCouplingStructure

The coupling structure to be used by the MDA.

data_processor: DataProcessor

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

exec_for_lin: bool

Whether the last execution was due to a linearization.

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.

matrix_type: JacobianAssembly.JacobianType

The type of the matrix.

max_mda_iter: int

The maximum iterations number for the MDA algorithm.

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.

strong_couplings: list[str]

The names of the strong coupling variables.

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