Source code for pyproximal.projection.L0

import warnings

import numpy as np
from pylops.utils.typing import NDArray


class L0BallProj:
    r""":math:`L_0` ball projection.

    Parameters
    ----------
    radius : :obj:`int`
        Radius

    Notes
    -----
    Given an L0 ball defined as:

    .. math::

        L0_{r} = \{ \mathbf{x}: ||\mathbf{x}||_0 \leq r \}

    its orthogonal projection is computed by finding the :math:`r` highest
    largest entries of :math:`\mathbf{x}` (in absolute value), keeping those
    and zero-ing all the other entries.
    Note that this is the proximal operator of the corresponding
    indicator function :math:`\mathcal{I}_{L0_{r}}`.

    """

    def __init__(self, radius: int) -> None:
        self.radius = int(radius)

    def __call__(self, x: NDArray) -> NDArray:
        xshape = x.shape
        xf = x.copy().flatten()
        xf[np.argsort(np.abs(xf))[: -self.radius]] = 0
        return xf.reshape(xshape)


class L10BallProj:
    r""":math:`L_{1,0}` ball projection.

    Parameters
    ----------
    radius : :obj:`int`
        Radius

    Notes
    -----
    Given an :math:`L_{1,0}` ball defined as:

    .. math::

        L_{1,0}^{r} =
        \{ \mathbf{x}: \text{count}([||\mathbf{x}_1||_1,
        ||\mathbf{x}_2||_1, ..., ||\mathbf{x}_1||_1] \ne 0) \leq r \}

    its orthogonal projection is computed by finding the :math:`r` highest
    largest entries of a vector obtained by applying the :math:`L_1` norm to each
    column of a matrix :math:`\mathbf{x}` (in absolute value), keeping those
    and zero-ing all the other entries.
    Note that this is the proximal operator of the corresponding
    indicator function :math:`\mathcal{I}_{L_{1,0}^{r}}`.

    """

    def __init__(self, radius: int) -> None:
        self.radius = int(radius)

    def __call__(self, x: NDArray) -> NDArray:
        xc = x.copy()
        xf = np.linalg.norm(x, axis=0, ord=1)
        xc[:, np.argsort(np.abs(xf))[: -self.radius]] = 0
        return xc


class L01BallProj(L10BallProj):
    def __init__(self, radius: int) -> None:
        warnings.warn(
            "The L01BallProj class has been renamed L10BallProj due "
            "to a mistake in the original choice of the name. As such "
            "L01BallProj will be deprecated in v1.0.0.",
            FutureWarning,
        )
        super().__init__(radius)