Source code for gemseo.algos.sequence_transformer.sequence_transformer

# 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 - initial API and implementation and/or initial
#                           documentation
#        :author: Charlie Vanaret, Benoit Pauwels, Francois Gallard
"""Sequence transformer methods."""

from __future__ import annotations

from abc import abstractmethod
from collections import deque
from typing import TYPE_CHECKING

from gemseo.utils.metaclasses import ABCGoogleDocstringInheritanceMeta

    from typing import ClassVar

    from numpy.typing import NDArray

[docs] class SequenceTransformer(metaclass=ABCGoogleDocstringInheritanceMeta): r"""A vector sequence transformer for fixed-point iteration method. For any function :math:`G : \mathbb{R}^n \rightarrow \mathbb{R}^n`, the fixed point iteration method computes the sequence :math:`x_{n+1} = G(x_n)`, whih is exepcted to converge towards a fixed point of :math:`G`. A sequence transformer is a function :math:`f : \mathbb{R}^n \rightarrow \mathbb{R}^n` so that the new iterate is instead computed as .. math:: x_{n+1}' = f(G, x_n, \dots, x_{n-k}, G(x_n)), for a given :math:`k \geq 0`. The transformed sequence is expected to exhibit faster convergence and/or better numerical stability. """ _MINIMUM_NUMBER_OF_ITERATES: ClassVar[int] """The minimum number of :math:`G(x_i)` required to compute the transformation.""" _MINIMUM_NUMBER_OF_RESIDUALS: ClassVar[int] """The minimum number of residuals :math:`G(x_i) - x_i` required to compute the transformation.""" _iterates: deque """The previously computed iterates :math:`G(x_i)`.""" _residuals: deque """The previously computed residuals :math:`G(x_i) - x_i`.""" def __init__(self) -> None: # noqa:D107 # Instantiate double-ended queues to store the relevant quantities self._iterates = deque(maxlen=self._MINIMUM_NUMBER_OF_ITERATES) self._residuals = deque(maxlen=self._MINIMUM_NUMBER_OF_RESIDUALS)
[docs] def clear(self) -> None: """Clear the iterates.""" self._iterates.clear() self._residuals.clear()
[docs] def compute_transformed_iterate( self, iterate: NDArray, residual: NDArray, ) -> NDArray: """Compute the next transformed iterate. Args: iterate: The iterate :math:`G(x_n)`. residual: The associated residual :math:`G(x_n) - x_n`. Returns: The next transformed iterate :math:`x_{n+1}`. """ # Store iterates and residuals self._iterates.append(iterate.copy()) self._residuals.append(residual.copy()) # Compute the transformed iterate only if sufficient material at hand if ( len(self._iterates) >= self._MINIMUM_NUMBER_OF_ITERATES and len(self._residuals) >= self._MINIMUM_NUMBER_OF_RESIDUALS ): return self._compute_transformed_iterate() return iterate
@abstractmethod def _compute_transformed_iterate(self) -> NDArray: """Compute the next transformed iterate."""