# Source code for gemseo.algos.sequence_transformer.acceleration.aitken

# 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 - initial API and implementation and/or initial
# documentation
# :author: Sebastien Bocquet, Alexandre Scotto Di Perrotolo
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""The Aitken's acceleration method."""
from __future__ import annotations
from typing import TYPE_CHECKING
from gemseo.algos.sequence_transformer.sequence_transformer import SequenceTransformer
if TYPE_CHECKING:
from typing import ClassVar
from numpy.typing import NDArray
[docs]class Aitken(SequenceTransformer):
"""The vector Δ²-Aitken acceleration method.
The method is introduced in: Isabelle Ramiere, Thomas Helfer, "Iterative residual-
based vector methods to accelerate fixed point iterations", Computers and
Mathematics with Applications, (2015) eq. (45).
"""
_MINIMUM_NUMBER_OF_ITERATES: ClassVar[int] = 1
_MINIMUM_NUMBER_OF_RESIDUALS: ClassVar[int] = 2
def _compute_transformed_iterate(self) -> NDArray:
dxn_1, dxn = self._residuals
gxn = self._iterates[-1]
d2xn = dxn - dxn_1
return gxn - (d2xn.T @ dxn) / (d2xn.T @ d2xn) * dxn