Source code for gemseo.algos.sequence_transformer.acceleration.secant

# 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.
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# 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.
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# 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 secant 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 Secant(SequenceTransformer):
"""The secant 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] = 2
_MINIMUM_NUMBER_OF_RESIDUALS: ClassVar[int] = 2

def _compute_transformed_iterate(self) -> NDArray:
dxn_1, dxn = self._residuals
gxn_1, gxn = self._iterates

d2xn = dxn - dxn_1
dgxn = gxn - gxn_1

return gxn - (d2xn.T @ dxn) / (d2xn.T @ d2xn) * dgxn