content: """
  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)
  