Source code for gemseo.mda.gauss_seidel

# Copyright 2021 IRT Saint Exupéry,
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# Lesser General Public License for more details.
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
# Contributors:
#    INITIAL AUTHORS - API and implementation and/or documentation
#        :author: Francois Gallard
"""A Gauss Seidel algorithm for solving MDAs."""
from __future__ import annotations

from typing import TYPE_CHECKING

from gemseo.algos.sequence_transformer.acceleration import AccelerationMethod
from gemseo.core.discipline import MDODiscipline
from gemseo.mda.mda import MDA
from gemseo.utils.data_conversion import split_array_to_dict_of_arrays

    from typing import Any
    from typing import Mapping
    from typing import Sequence
    from numpy.typing import NDArray
    from gemseo.core.coupling_structure import MDOCouplingStructure

[docs]class MDAGaussSeidel(MDA): r"""Perform an MDA using the Gauss-Seidel algorithm. This algorithm is a fixed point iteration method to solve systems of non-linear equations of the form, .. math:: \left\{ \begin{matrix} F_1(x_1, x_2, \dots, x_n) = 0 \\ F_2(x_1, x_2, \dots, x_n) = 0 \\ \vdots \\ F_n(x_1, x_2, \dots, x_n) = 0 \end{matrix} \right. Beginning with :math:`x_1^{(0)}, \dots, x_n^{(0)}`, the iterates are obtained by performing **sequentially** the following :math:`n` steps. **Step 1:** knowing :math:`x_2^{(i)}, \dots, x_n^{(i)}`, compute :math:`x_1^{(i+1)}` by solving, .. math:: r_1\left( x_1^{(i+1)} \right) = F_1(x_1^{(i+1)}, x_2^{(i)}, \dots, x_n^{(i)}) = 0. **Step** :math:`k \leq n`: knowing :math:`x_1^{(i+1)}, \dots, x_{k-1}^{(i+1)}` on one hand, and :math:`x_{k+1}^{(i)}, \dots, x_n^{(i)}` on the other hand, compute :math:`x_1^{(i+1)}` by solving, .. math:: r_k\left( x_k^{(i+1)} \right) = F_1(x_1^{(i+1)}, \dots, x_{k-1}^{(i+1)}, x_k^{(i+1)}, x_{k+1}^{(i)}, \dots, x_n^{(i)}) = 0. These :math:`n` steps account for one iteration of the Gauss-Seidel method. """ def __init__( # noqa: D107 self, disciplines: Sequence[MDODiscipline], name: str | None = None, max_mda_iter: int = 10, grammar_type: MDODiscipline.GrammarType = MDODiscipline.GrammarType.JSON, tolerance: float = 1e-6, linear_solver_tolerance: float = 1e-12, warm_start: bool = False, use_lu_fact: bool = False, over_relax_factor: float | None = None, # TODO: API: Remove the argument. coupling_structure: MDOCouplingStructure | None = None, log_convergence: bool = False, linear_solver: str = "DEFAULT", linear_solver_options: Mapping[str, Any] | None = None, acceleration_method: AccelerationMethod = AccelerationMethod.NONE, over_relaxation_factor: float = 1.0, ) -> None: """ Args: over_relax_factor: Deprecated, please consider using :attr:`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. """ # noqa:D205 D212 D415 # TODO: API: Remove the old name and attributes for over-relaxation factor. if over_relax_factor is not None: over_relaxation_factor = over_relax_factor super().__init__( disciplines, max_mda_iter=max_mda_iter, name=name, grammar_type=grammar_type, tolerance=tolerance, linear_solver_tolerance=linear_solver_tolerance, warm_start=warm_start, use_lu_fact=use_lu_fact, coupling_structure=coupling_structure, log_convergence=log_convergence, linear_solver=linear_solver, linear_solver_options=linear_solver_options, acceleration_method=acceleration_method, over_relaxation_factor=over_relaxation_factor, ) self._compute_input_couplings() self._resolved_coupling_names = self.strong_couplings # TODO: API: Remove the property and its setter. @property def over_relax_factor(self) -> float: """The over-relaxation factor.""" return self.over_relaxation_factor @over_relax_factor.setter def over_relax_factor(self, over_relaxation_factor: float) -> None: self.over_relaxation_factor = over_relaxation_factor def _initialize_grammars(self) -> None: """Define the input and output grammars from the disciplines' ones.""" self.input_grammar.clear() self.output_grammar.clear() for discipline in self.disciplines: self.input_grammar.update( discipline.input_grammar, exclude_names=self.output_grammar.keys() ) self.output_grammar.update(discipline.output_grammar) self._add_residuals_norm_to_output_grammar() def __execute_all_disciplines(self) -> None: """Execute all the disciplines in sequence.""" for discipline in self.disciplines: discipline.execute(self.local_data) self.local_data.update(discipline.get_output_data()) def __compute_initial_coupling_vector(self) -> NDArray: """Compute the initial coupling vector. Returns: The vector filled in with the initial coupling values. """ self.__execute_all_disciplines() self._compute_coupling_sizes() return self._current_working_couplings() def _run(self) -> None: if self.warm_start: self._couplings_warm_start() current_couplings = self.__compute_initial_coupling_vector() self._sequence_transformer.clear() # Perform fixed point iterations while True: self.__execute_all_disciplines() new_couplings = self._sequence_transformer.compute_transformed_iterate( current_couplings, self._current_working_couplings() ) self.local_data.update( split_array_to_dict_of_arrays( new_couplings, self._coupling_sizes, self.strong_couplings ) ) self._compute_residual( current_couplings, new_couplings, log_normed_residual=self._log_convergence, ) if self._stop_criterion_is_reached: break current_couplings = new_couplings