# Source code for qutip.solver.krylovsolve

    # Required for Sphinx to follow autodoc_type_aliases
    from __future__ import annotations

    __all__ = ['krylovsolve']

    from .. import QobjEvo, Qobj
    from .sesolve import SESolver
    from .result import Result
    from .solver_base import _kwargs_migration
    from numpy.typing import ArrayLike
    from typing import Any, Callable

    def krylovsolve(
        H: Qobj,
        psi0: Qobj,
        tlist: ArrayLike,
        krylov_dim: int,
        _e_ops = None,
        _args = None,
        _options = None,
        *,
        e_ops: dict[Any, Qobj | QobjEvo | Callable[[float, Qobj], Any]] = None,
        args: dict[str, Any] = None,
        options: dict[str, Any] = None,
    ) -> Result:
        """
        Schrodinger equation evolution of a state vector for time independent
        Hamiltonians using Krylov method.

        Evolve the state vector ("psi0") finding an approximation for the time
        evolution operator of Hamiltonian ("H") by obtaining the projection of
        the time evolution operator on a set of small dimensional Krylov
        subspaces (m << dim(H)).

        The output is either the state vector or unitary matrix at arbitrary points
        in time (`tlist`), or the expectation values of the supplied operators
        (`e_ops`). If e_ops is a callback function, it is invoked for each
        time in `tlist` with time and the state as arguments, and the function
        does not use any return values. e_ops cannot be used in conjunction
        with solving the Schrodinger operator equation

        Parameters
        ----------
        H : :obj:`.Qobj`, :obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format.
            System Hamiltonian as a Qobj or QobjEvo for time-dependent
            Hamiltonians. List of [:obj:`.Qobj`, :obj:`.Coefficient`] or callable
            that can be made into :obj:`.QobjEvo` are also accepted.

        psi0 : :class:`.Qobj`
            Initial state vector (ket)

        tlist : *list* / *array*
            list of times for :math:`t`.

        krylov_dim: int
            Dimension of Krylov approximation subspaces used for the time
            evolution approximation.

        e_ops : :class:`.Qobj`, callable, or list, optional
            Single operator or list of operators for which to evaluate
            expectation values or callable or list of callable.
            Callable signature must be, `f(t: float, state: Qobj)`.
            See :func:`~qutip.core.expect.expect` for more detail of operator
            expectation.

        args : dict, optional
            dictionary of parameters for time-dependent Hamiltonians

        options : dict, optional
            Dictionary of options for the solver.

            - | store_final_state : bool
              | Whether or not to store the final state of the evolution in the
                result class.
            - | store_states : bool, None
              | Whether or not to store the state vectors or density matrices.
                On `None` the states will be saved if no expectation operators are
                given.
            - | normalize_output : bool
              | Normalize output state to hide ODE numerical errors. Only normalize
                the state if the initial state is already normalized.
            - | progress_bar : str {'text', 'enhanced', 'tqdm', ''}
              | How to present the solver progress.
                'tqdm' uses the python module of the same name and raise an error
                if not installed. Empty string or False will disable the bar.
            - | progress_kwargs : dict
              | kwargs to pass to the progress_bar. Qutip's bars use `chunk_size`.
            - | atol: float
              | Absolute tolerance of the ODE integrator.
            - | nsteps : int
              | Maximum number of (internally defined) steps allowed in one
                ``tlist`` step.
            - | min_step, max_step : float
              | Miniumum and maximum lenght of one internal step.
            - | always_compute_step: bool
              | If True, the step lenght is computed each time a new Krylov
                subspace is computed. Otherwise it is computed only once when
                creating the integrator.
            - | sub_system_tol: float
              | Tolerance to detect an happy breakdown. An happy breakdown happens
                when the initial ket is in a subspace of the Hamiltonian smaller
                than ``krylov_dim``.

        Returns
        -------
        result: :class:`.Result`

            An instance of the class :class:`.Result`, which contains
            a *list of array* ``result.expect`` of expectation values for the times
            specified by ``tlist``, and/or a *list* ``result.states`` of state
            vectors or density matrices corresponding to the times in ``tlist`` [if
            ``e_ops`` is an empty list of ``store_states=True`` in options].
        """
        e_ops = _kwargs_migration(_e_ops, e_ops, "e_ops")
        args = _kwargs_migration(_args, args, "args")
        options = _kwargs_migration(_options, options, "options")
        H = QobjEvo(H, args=args, tlist=tlist)
        options = options or {}
        options["method"] = "krylov"
        options["krylov_dim"] = krylov_dim
        solver = SESolver(H, options=options)
        return solver.run(psi0, tlist, e_ops=e_ops)