Source code for autolyap.algorithms.proximal_point

# SPDX-FileCopyrightText: 2025-2026 AutoLyap contributors
# SPDX-License-Identifier: GPL-3.0-only

import numpy as np
from typing import Tuple
from .algorithm import Algorithm



class ProximalPoint(Algorithm):
    r"""
    Proximal point method :cite:`Moreau1965`, :cite:`Martinet1970`, :cite:`Rockafellar1976PPA`.

    See :doc:`3. Algorithm representation </theory/algorithm_representation>`
    for mathematical notation and definitions.

    Notation-driven assumptions are declared by the user via
    :class:`~autolyap.problemclass.InclusionProblem`: when present, terms written with
    :math:`\nabla` use differentiable functions, terms written with
    :math:`\prox_{\gamma f}` use proper, lower semicontinuous, convex functions,
    and terms written with :math:`J_{\gamma G}` use maximally monotone operators.

    Standard form
    -------------


    For an initial point :math:`x^0 \in \calH` and step size
    :math:`\gamma \in \reals_{++}`,

    .. math::
        (\forall k \in \naturals)\quad
        x^{k+1} = \prox_{\gamma f}(x^k).

    Equivalently,

    .. math::
        (\forall k \in \naturals)\quad
        x^{k+1} = x^k - \gamma u^k, \qquad u^k \in \partial f(x^{k+1}).

    State-space representation
    --------------------------

    The update can be written in the algorithm representation with

    .. math::
        \bx^k = x^k, \qquad
        \bu^k = u^k, \qquad
        \by^k = x^{k+1}.

    Using the equivalent standard form,

    .. math::
        u^k \in \partial f(x^{k+1}).

    With this representation, the system matrices are

    .. math::
        \begin{aligned}
            A_k &= \begin{bmatrix} 1 \end{bmatrix}, & B_k &= \begin{bmatrix} -\gamma \end{bmatrix}, \\
            C_k &= \begin{bmatrix} 1 \end{bmatrix}, & D_k &= \begin{bmatrix} -\gamma \end{bmatrix}.
        \end{aligned}

    These are the system matrices returned by :meth:`~autolyap.algorithms.Algorithm.get_ABCD`.

    Structural parameters
    ---------------------

    .. math::
        n = 1,\quad m = 1,\quad (\bar{m}_i)_{i=1}^{m} = (1),\quad \bar{m} = 1.

    .. math::
        I_{\text{func}} = \{1\},\quad I_{\text{op}} = \varnothing.
    """
    def __init__(self, gamma: float) -> None:
        r"""
        Initialize the proximal point method.

        Structural inputs passed to :class:`~autolyap.algorithms.Algorithm` are

        .. math::
            n = 1,\quad m = 1,\quad (\bar m_i)_{i=1}^{m} = (1),\quad \bar m = 1,\quad
            I_{\mathrm{func}} = \{1\},\quad I_{\mathrm{op}} = \varnothing.
        """
        super().__init__(1, 1, [1], [1], [])
        self.gamma = gamma
    


    def set_gamma(self, gamma: float) -> None:
        r"""
        Set the step-size parameter :math:`\gamma`.

        Shared notation follows the class-level reference in
        :class:`~autolyap.algorithms.ProximalPoint`.

        **Parameters**

        - `gamma` (:class:`~typing.Union`\[:class:`int`, :class:`float`\]): The value corresponding to :math:`\gamma`.

        **Raises**

        - `ValueError`: If `gamma` is not a finite real number or if :math:`\gamma \le 0`.
        """
        gamma = self._validate_positive_finite_real(gamma, "gamma")
        self._set_dynamic_parameter("gamma", gamma)

    


    def get_ABCD(self, k: int) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
        A = np.array([[1]])
        B = np.array([[-self.gamma]])
        C = np.array([[1]])
        D = np.array([[-self.gamma]])
        return (A, B, C, D)