# Source code for qutip.solver.mesolve

    """
    This module provides solvers for the Lindblad master equation and von Neumann
    equation.
    """

    # Required for Sphinx to follow autodoc_type_aliases
    from __future__ import annotations

    __all__ = ['mesolve', 'MESolver']

    from numpy.typing import ArrayLike
    from typing import Any, Callable
    from time import time
    from .. import (Qobj, QobjEvo, liouvillian, lindblad_dissipator)
    from ..typing import EopsLike, QobjEvoLike
    from ..core import data as _data
    from .solver_base import Solver, _solver_deprecation, _kwargs_migration
    from .sesolve import sesolve, SESolver
    from ._feedback import _QobjFeedback, _DataFeedback
    from . import Result

    def mesolve(
        H: QobjEvoLike,
        rho0: Qobj,
        tlist: ArrayLike,
        c_ops: Qobj | QobjEvo | list[QobjEvoLike] = None,
        _e_ops = None,
        _args = None,
        _options = None,
        *,
        e_ops: EopsLike | list[EopsLike] | dict[Any, EopsLike] = None,
        args: dict[str, Any] = None,
        options: dict[str, Any] = None,
        **kwargs
    ) -> Result:
        """
        Master equation evolution of a density matrix for a given Hamiltonian and
        set of collapse operators, or a Liouvillian.

        Evolve the state vector or density matrix (``rho0``) using a given
        Hamiltonian or Liouvillian (``H``) and an optional set of collapse operators
        (``c_ops``), by integrating the set of ordinary differential equations
        that define the system. In the absence of collapse operators the system is
        evolved according to the unitary evolution of the Hamiltonian.

        The output is either the state vector 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.

        If either ``H`` or the Qobj elements in ``c_ops`` are superoperators, they
        will be treated as direct contributions to the total system Liouvillian.
        This allows the solution of master equations that are not in standard
        Lindblad form.

        **Time-dependent operators**

        For time-dependent problems, ``H`` and ``c_ops`` can be a :obj:`.QobjEvo`
        or object that can be interpreted as :obj:`.QobjEvo` such as a list of
        (Qobj, Coefficient) pairs or a function.

        **Additional options**

        Additional options to mesolve can be set via the ``options`` argument. Many
        ODE integration options can be set this way, and the ``store_states`` and
        ``store_final_state`` options can be used to store states even though
        expectation values are requested via the ``e_ops`` argument.

        Notes
        -----
        When no collapse operator are given and the `H` is not a superoperator,
        it will defer to :func:`sesolve`.

        Parameters
        ----------

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

        rho0 : :obj:`.Qobj`
            initial density matrix or state vector (ket).

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

        c_ops : list of (:obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format)
            Single collapse operator, or list of collapse operators, or a list
            of Liouvillian superoperators. None is equivalent to an empty list.

        e_ops : :obj:`.Qobj`, callable, list or dict, optional
            Single operator, or list or dict of operators, for which to evaluate
            expectation values. Operator can be Qobj, QobjEvo or callables with the
            signature `f(t: float, state: Qobj) -> Any`.

        args : dict, optional
            dictionary of parameters for time-dependent Hamiltonians and
            collapse operators.

        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`.
            - | method : str ["adams", "bdf", "lsoda", "dop853", "vern9", etc.]
              | Which differential equation integration method to use.
            - | atol, rtol : float
              | Absolute and relative tolerance of the ODE integrator.
            - | nsteps : int
              | Maximum number of (internally defined) steps allowed in one ``tlist``
                step.
            - | max_step : float
              | Maximum lenght of one internal step. When using pulses, it should be
                less than half the width of the thinnest pulse.

            Other options could be supported depending on the integration method,
            see `Integrator <./classes.html#classes-ode>`_.

        Returns
        -------
        result: :obj:`.Result`

            An instance of the class :obj:`.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")
        options = _solver_deprecation(kwargs, options)
        H = QobjEvo(H, args=args, tlist=tlist)

        c_ops = c_ops if c_ops is not None else []
        if not isinstance(c_ops, (list, tuple)):
            c_ops = [c_ops]
        c_ops = [QobjEvo(c_op, args=args, tlist=tlist) for c_op in c_ops]

        use_mesolve = len(c_ops) > 0 or (not rho0.isket) or H.issuper

        if not use_mesolve:
            return sesolve(H, rho0, tlist, e_ops=e_ops, args=args,
                           options=options)

        solver = MESolver(H, c_ops, options=options)

        return solver.run(rho0, tlist, e_ops=e_ops)

    class MESolver(SESolver):
        """
        Master equation evolution of a density matrix for a given Hamiltonian and
        set of collapse operators, or a Liouvillian.

        Evolve the density matrix (`rho0`) using a given
        Hamiltonian or Liouvillian (`H`) and an optional set of collapse operators
        (`c_ops`), by integrating the set of ordinary differential equations
        that define the system.

        If either `H` or the Qobj elements in `c_ops` are superoperators, they
        will be treated as direct contributions to the total system Liouvillian.
        This allows the solution of master equations that are not in standard
        Lindblad form.

        Parameters
        ----------
        H : :obj:`.Qobj`, :obj:`.QobjEvo`
            Possibly time-dependent system Liouvillian or Hamiltonian as a Qobj or
            QobjEvo. List of [:obj:`.Qobj`, :obj:`.Coefficient`] or callable that
            can be made into :obj:`.QobjEvo` are also accepted.

        c_ops : list of :obj:`.Qobj`, :obj:`.QobjEvo`
            Single collapse operator, or list of collapse operators, or a list
            of Liouvillian superoperators. None is equivalent to an empty list.

        options : dict, optional
            Options for the solver, see :obj:`MESolver.options` and
            `Integrator <./classes.html#classes-ode>`_ for a list of all options.

        Attributes
        ----------
        stats: dict
            Diverse diagnostic statistics of the evolution.
        """
        name = "mesolve"
        _avail_integrators: dict[str, object] = {}
        solver_options = {
            "progress_bar": "",
            "progress_kwargs": {"chunk_size":10},
            "store_final_state": False,
            "store_states": None,
            "normalize_output": True,
            'method': 'adams',
        }

        def __init__(
            self,
            H: Qobj | QobjEvo,
            c_ops: Qobj | QobjEvo | list[Qobj | QobjEvo] = None,
            *,
            options: dict = None,
        ):
            _time_start = time()

            if not isinstance(H, (Qobj, QobjEvo)):
                raise TypeError("The Hamiltonian must be a Qobj or QobjEvo")
            c_ops = c_ops or []
            c_ops = [c_ops] if isinstance(c_ops, (Qobj, QobjEvo)) else c_ops
            for c_op in c_ops:
                if not isinstance(c_op, (Qobj, QobjEvo)):
                    raise TypeError("All `c_ops` must be a Qobj or QobjEvo")

            self._num_collapse = len(c_ops)

            rhs = H if H.issuper else liouvillian(H)
            rhs += sum(c_op if c_op.issuper else lindblad_dissipator(c_op)
                       for c_op in c_ops)

            Solver.__init__(self, rhs, options=options)

        def _initialize_stats(self):
            stats = super()._initialize_stats()
            stats.update({
                "solver": "Master Equation Evolution",
                "num_collapse": self._num_collapse,
            })
            return stats

        @classmethod
        def StateFeedback(
            cls,
            default: Qobj | _data.Data = None,
            raw_data: bool = False,
            prop: bool = False
        ):
            """
            State of the evolution to be used in a time-dependent operator.

            When used as an args:

                ``QobjEvo([op, func], args={"state": MESolver.StateFeedback()})``

            The ``func`` will receive the density matrix as ``state`` during the
            evolution.

            Parameters
            ----------
            default : Qobj or qutip.core.data.Data, default : None
                Initial value to be used at setup of the system.

            prop : bool, default : False
                Set to True when computing propagators.
                The default with take the shape of the propagator instead of a
                state.

            raw_data : bool, default : False
                If True, the raw matrix will be passed instead of a Qobj.
                For density matrices, the matrices can be column stacked or square
                depending on the integration method.
            """
            if raw_data:
                return _DataFeedback(default, open=True, prop=prop)
            return _QobjFeedback(default, open=True, prop=prop)