# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# 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
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# 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: Charlie Vanaret, Francois Gallard
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""A set of quasi Newton algorithm variants for solving MDAs.
`quasi-Newton methods <https://en.wikipedia.org/wiki/Quasi-Newton_method>`__
"""
from __future__ import annotations
import logging
from typing import TYPE_CHECKING
from typing import Callable
from typing import ClassVar
from numpy import array
from numpy import ndarray
from scipy.optimize import root
from gemseo.core.discipline import MDODiscipline
from gemseo.mda.base_mda_root import BaseMDARoot
if TYPE_CHECKING:
from collections.abc import Mapping
from collections.abc import Sequence
from typing import Any
from gemseo.core.coupling_structure import MDOCouplingStructure
from gemseo.core.discipline_data import DisciplineData
LOGGER = logging.getLogger(__name__)
[docs]
class MDAQuasiNewton(BaseMDARoot):
r"""Quasi-Newton solver for MDA.
`Quasi-Newton methods <https://en.wikipedia.org/wiki/Quasi-Newton_method>`__
include numerous variants (
`Broyden <https://en.wikipedia.org/wiki/Broyden%27s_method>`__,
`Levenberg-Marquardt <https://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm>`
__, ...).
The name of the variant should be provided via the :code:`method` parameter of the
class.
The new iterate is given by:
.. math::
x_{k+1} = x_k - \\rho_k B_k f(x_k)
where :math:`\\rho_k` is a coefficient chosen in order to minimize the convergence
and :math:`B_k` is an approximation of :math:`Df(x_k)^{-1}`, the inverse of the
Jacobian of :math:`f` at :math:`x_k`.
"""
# Available quasi-Newton methods
HYBRID = "hybr"
LEVENBERG_MARQUARDT = "lm"
BROYDEN1 = "broyden1"
BROYDEN2 = "broyden2"
ANDERSON = "anderson"
LINEAR_MIXING = "linearmixing"
DIAG_BROYDEN = "diagbroyden"
EXCITING_MIXING = "excitingmixing"
KRYLOV = "krylov"
DF_SANE = "df-sane"
# TODO: API: use enums.
QUASI_NEWTON_METHODS: ClassVar[list[str]] = [
HYBRID,
LEVENBERG_MARQUARDT,
BROYDEN1,
BROYDEN2,
ANDERSON,
LINEAR_MIXING,
DIAG_BROYDEN,
EXCITING_MIXING,
KRYLOV,
DF_SANE,
]
__current_couplings: ndarray
"""The current values of the coupling variables."""
def __init__(
self,
disciplines: Sequence[MDODiscipline],
max_mda_iter: int = 10,
name: str | None = None,
grammar_type: MDODiscipline.GrammarType = MDODiscipline.GrammarType.JSON,
method: str = HYBRID,
use_gradient: bool = False,
tolerance: float = 1e-6,
linear_solver_tolerance: float = 1e-12,
warm_start: bool = False,
use_lu_fact: bool = False,
coupling_structure: MDOCouplingStructure | None = None,
linear_solver: str = "DEFAULT",
linear_solver_options: Mapping[str, Any] | None = None,
) -> None:
"""
Args:
method: The name of the method in scipy root finding, among
:attr:`.QUASI_NEWTON_METHODS`.
use_gradient: Whether to use the analytic gradient of the discipline.
Raises:
ValueError: If the method is not a valid quasi-Newton method.
""" # noqa:D205 D212 D415
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,
linear_solver=linear_solver,
linear_solver_options=linear_solver_options,
coupling_structure=coupling_structure,
)
if method not in self.QUASI_NEWTON_METHODS:
msg = f"Method '{method}' is not a valid quasi-Newton method."
raise ValueError(msg)
self.method = method
if self.method not in self._methods_with_callback():
del self.output_grammar[self.RESIDUALS_NORM]
self.use_gradient = use_gradient
# TODO: API: prepend verb.
def _solver_options(self) -> dict[str, float | int]:
"""Determine options for the solver, based on the resolution method."""
options = {}
if self.method in {
self.BROYDEN1,
self.BROYDEN2,
self.ANDERSON,
self.LINEAR_MIXING,
self.DIAG_BROYDEN,
self.EXCITING_MIXING,
self.KRYLOV,
}:
options["ftol"] = self.tolerance
options["maxiter"] = self.max_mda_iter
elif self.method == self.LEVENBERG_MARQUARDT:
options["xtol"] = self.tolerance
options["maxiter"] = self.max_mda_iter
elif self.method == self.DF_SANE:
options["fatol"] = self.tolerance
options["maxfev"] = self.max_mda_iter
elif self.method == self.HYBRID:
options["xtol"] = self.tolerance
options["maxfev"] = self.max_mda_iter
return options
# TODO: API: prepend verb.
def _methods_with_callback(self) -> list[str]:
"""Determine whether resolution method accepts a callback function.
Returns:
The names of the methods with callback.
"""
return [self.BROYDEN1, self.BROYDEN2]
def __get_jacobian_computer(self) -> Callable[[ndarray], ndarray] | None:
"""Return the function to compute the jacobian.
Returns:
The callable to compute the jacobian.
"""
if not self.use_gradient:
return None
self.assembly.set_newton_differentiated_ios(self._resolved_variable_names)
def compute_jacobian(
x_vect: ndarray,
) -> ndarray:
"""Linearize all residuals.
Args:
x_vect: The value of the design variables.
Returns:
The linearized residuals.
"""
self._update_local_data(x_vect)
self.reset_disciplines_statuses()
for discipline in self.disciplines:
discipline.linearize(self._local_data)
self.assembly.compute_sizes(
self._resolved_variable_names,
self._resolved_variable_names,
self._resolved_variable_names,
)
return (
self.assembly.assemble_jacobian(
self._resolved_variable_names,
self._resolved_variable_names,
is_residual=True,
)
.toarray()
.real
)
return compute_jacobian
def __get_residual_history_callback(self) -> Callable[[ndarray, Any], None] | None:
"""Return the callback used to store the residual history."""
if self.method not in self._methods_with_callback():
return None
def callback(
new_couplings: ndarray,
_,
) -> None:
"""Store the current residual in the history.
Args:
new_couplings: The new coupling variables.
_: ignored
"""
self._compute_residual()
self.__current_couplings = new_couplings
return callback
def __compute_residuals(
self,
x_vect: ndarray,
) -> ndarray:
"""Evaluate all residuals, possibly in parallel.
Args:
x_vect: The value of the design variables.
Returns:
The residuals.
"""
self.current_iter += 1
# Work on a temporary copy so _update_local_data can be called.
local_data_copy = self._local_data.copy()
self._update_local_data(x_vect)
input_data = self._local_data
self._local_data = local_data_copy
self.reset_disciplines_statuses()
self.execute_all_disciplines(input_data)
self._update_residuals(input_data)
return self.assembly.residuals(input_data, self._resolved_variable_names).real
def _run(self) -> DisciplineData:
super()._run()
self.reset_disciplines_statuses()
self.execute_all_disciplines(self._local_data)
if not self.strong_couplings:
msg = (
"MDAQuasiNewton found no strong couplings. Executed all"
"disciplines once."
)
LOGGER.warning(msg)
self._local_data[self.RESIDUALS_NORM] = array([0.0])
return self._local_data
self.current_iter = 0
if self.reset_history_each_run:
self.residual_history = []
# initial solution
self.__current_couplings = self.get_current_resolved_variables_vector().real
# solve the system
y_opt = root(
self.__compute_residuals,
x0=self.__current_couplings,
method=self.method,
jac=self.__get_jacobian_computer(),
callback=self.__get_residual_history_callback(),
tol=self.tolerance,
options=self._solver_options(),
)
self._warn_convergence_criteria()
self._update_local_data(y_opt.x)
if self.method in self._methods_with_callback():
self._local_data[self.RESIDUALS_NORM] = array([self.normed_residual])
return self._local_data
