"""Multiple shooting backend with block-structured Newton-Raphson.

This module provides a dedicated backend for multiple shooting differential
correction. Unlike single shooting, this backend operates on an augmented
parameter space containing all patch initial states and enforces continuity
constraints through the residual function.

The multiple shooting method divides a trajectory into N segments (patches)
and treats each patch's initial state as an independent variable. Continuity
constraints ensure the trajectory is continuous across patch boundaries.

See Also
--------
:class:`~hiten.algorithms.corrector.backends.newton._NewtonBackend`
    Single shooting Newton backend.
:class:`~hiten.algorithms.corrector.backends.base._CorrectorBackend`
    Base class for all correction backends.
"""

from typing import Tuple, Any, List

import numpy as np

from hiten.algorithms.corrector.backends.base import _CorrectorBackend
from hiten.algorithms.corrector.types import (
    CorrectorInput,
    CorrectorOutput,
    StepperFactory,
)


class _MultipleShootingBackend(_CorrectorBackend):
    def __init__(
        self,
        *,
        stepper_factory: StepperFactory | None = None,
    ) -> None:
        super().__init__(stepper_factory=stepper_factory)


    def run(
        self,
        *,
        request: CorrectorInput,
        stepper_factory: StepperFactory | None = None,
    ) -> CorrectorOutput:
        pass