content: """
  This module provides result classes for multi-trajectory solvers.
  Note that single trajectories are described by regular `Result` objects from the
  `qutip.solver.result` module.
  """
  # Required for Sphinx to follow autodoc_type_aliases
  from __future__ import annotations
  
  from typing import TypedDict
  from ..core.numpy_backend import np
  
  from copy import copy
  
  from .result import _BaseResult
  from ..core import qzero_like
  
  __all__ = [
      "MultiTrajResult",
      "McResult",
      "NmmcResult",
  ]
  
  
  class MultiTrajResultOptions(TypedDict):
      store_states: bool
      store_final_state: bool
      keep_runs_results: bool
  
  
  class MultiTrajResult(_BaseResult):
      """
      Base class for storing results for solver using multiple trajectories.
  
      Parameters
      ----------
      e_ops : :obj:`.Qobj`, :obj:`.QobjEvo`, function or list or dict of these
          The ``e_ops`` parameter defines the set of values to record at
          each time step ``t``. If an element is a :obj:`.Qobj` or
          :obj:`.QobjEvo` the value recorded is the expectation value of that
          operator given the state at ``t``. If the element is a function, ``f``,
          the value recorded is ``f(t, state)``.
  
          The values are recorded in the ``.expect`` attribute of this result
          object. ``.expect`` is a list, where each item contains the values
          of the corresponding ``e_op``.
  
          Function ``e_ops`` must return a number so the average can be computed.
  
      options : dict
          The options for this result class.
  
      solver : str or None
          The name of the solver generating these results.
  
      stats : dict or None
          The stats generated by the solver while producing these results. Note
          that the solver may update the stats directly while producing results.
  
      kw : dict
          Additional parameters specific to a result sub-class.
  
      Attributes
      ----------
      times : list
          A list of the times at which the expectation values and states were
          recorded.
  
      average_states : list of :obj:`.Qobj`
          The state at each time ``t`` (if the recording of the state was
          requested) averaged over all trajectories as a density matrix.
  
      runs_states : list of list of :obj:`.Qobj`
          The state for each trajectory and each time ``t`` (if the recording of
          the states and trajectories was requested)
  
      average_final_state : :obj:`.Qobj`:
          The final state (if the recording of the final state was requested)
          averaged over all trajectories as a density matrix.
  
      runs_final_states : list of :obj:`.Qobj`
          The final state for each trajectory (if the recording of the final
          state and trajectories was requested).
  
      average_expect : list of array of expectation values
          A list containing the values of each ``e_op`` averaged over each
          trajectories. The list is in the same order in which the ``e_ops`` were
          supplied and empty if no ``e_ops`` were given.
  
          Each element is itself an array and contains the values of the
          corresponding ``e_op``, with one value for each time in ``.times``.
  
      std_expect : list of array of expectation values
          A list containing the standard derivation of each ``e_op`` over each
          trajectories. The list is in the same order in which the ``e_ops`` were
          supplied and empty if no ``e_ops`` were given.
  
          Each element is itself an array and contains the values of the
          corresponding ``e_op``, with one value for each time in ``.times``.
  
      runs_expect : list of array of expectation values
          A list containing the values of each ``e_op`` for each trajectories.
          The list is in the same order in which the ``e_ops`` were
          supplied and empty if no ``e_ops`` were given. Only available if the
          storing of trajectories was requested.
  
          The order of the elements is ``runs_expect[e_ops][trajectory][time]``.
  
          Each element is itself an array and contains the values of the
          corresponding ``e_op``, with one value for each time in ``.times``.
  
      average_e_data : dict
          A dictionary containing the values of each ``e_op`` averaged over each
          trajectories. If the ``e_ops`` were supplied as a dictionary, the keys
          are the same as in that dictionary. Otherwise the keys are the index of
          the ``e_op`` in the ``.expect`` list.
  
          The lists of expectation values returned are the *same* lists as
          those returned by ``.expect``.
  
      std_e_data : dict
          A dictionary containing the standard derivation of each ``e_op`` over
          each trajectories. If the ``e_ops`` were supplied as a dictionary, the
          keys are the same as in that dictionary. Otherwise the keys are the
          index of the ``e_op`` in the ``.expect`` list.
  
          The lists of expectation values returned are the *same* lists as
          those returned by ``.expect``.
  
      runs_e_data : dict
          A dictionary containing the values of each ``e_op`` for each
          trajectories. If the ``e_ops`` were supplied as a dictionary, the keys
          are the same as in that dictionary. Otherwise the keys are the index of
          the ``e_op`` in the ``.expect`` list. Only available if the storing
          of trajectories was requested.
  
          The order of the elements is ``runs_expect[e_ops][trajectory][time]``.
  
          The lists of expectation values returned are the *same* lists as
          those returned by ``.expect``.
  
      runs_weights : list
          For each trajectory, the weight with which that trajectory enters
          averages.
  
      deterministic_weights : list
          For each deterministic trajectory, (when using improved_sampling)
          the weight with which that trajectory enters averages.
  
      solver : str or None
          The name of the solver generating these results.
  
      num_trajectories: int
          Number of trajectories computed.
  
      seeds: list of SeedSequence
          The seeds used to compute each trajectories.
  
      trajectories: list of Result
          If the option `keep_runs_results` is set, a list of all trajectories.
  
      deterministic_trajectories: list of Result
          A list of the no-jump trajectories if the option ``improved_sampling``
          is set.
  
      stats : dict or None
          The stats generated by the solver while producing these results.
  
      options : :obj:`~SolverResultsOptions`
          The options for this result class.
      """
  
      options: MultiTrajResultOptions
  
      def __init__(
          self, e_ops, options: MultiTrajResultOptions, *,
          solver=None, stats=None, **kw,
      ):
          super().__init__(options, solver=solver, stats=stats)
          self._raw_ops = self._e_ops_to_dict(e_ops)
  
          self.trajectories = []
          self.deterministic_trajectories = []
          self.num_trajectories = 0
          self.seeds = []
  
          self._average_e_data = {}
          self._std_e_data = {}
          if self.options["keep_runs_results"]:
              self.runs_e_data = {k: [] for k in self._raw_ops}
          else:
              self.runs_e_data = {}
  
          # Will be initialized at the first trajectory
          self.times = None
          self.e_ops = None
  
          # We separate all sums into terms of trajectories with specified
          # deterministic trajectories weight (_det) or without (_rel). They will
          # be initialized when the first trajectory of the respective type is
          # added.
          self._sum_rel = None
          self._sum_det = None
          # Needed for merging results
          self._trajectories_weight_info = []
          self._deterministic_weight_info = []
  
          self._post_init(**kw)
  
      @property
      def _store_average_density_matrices(self) -> bool:
          return (
              self.options["store_states"]
              or (self.options["store_states"] is None and self._raw_ops == {})
          ) and not self.options["keep_runs_results"]
  
      @property
      def _store_final_density_matrix(self) -> bool:
          return (
              self.options["store_final_state"]
              and not self._store_average_density_matrices
              and not self.options["keep_runs_results"]
          )
  
      def _add_first_traj(self, trajectory):
          """
          Read the first trajectory, intitializing needed data.
          """
          self.times = trajectory.times
          self.e_ops = trajectory.e_ops
  
      def _store_trajectory(self, trajectory, *, abs=None, rel=None):
          if abs is None:
              self.trajectories.append(trajectory)
  
      def _reduce_states(self, trajectory, *, abs=None, rel=None):
          if abs is not None:
              self._sum_det.reduce_states(trajectory, abs)
          else:
              self._sum_rel.reduce_states(trajectory, rel)
  
      def _reduce_final_state(self, trajectory, *, abs=None, rel=None):
          if abs is not None:
              self._sum_det.reduce_final_state(trajectory, abs)
          else:
              self._sum_rel.reduce_final_state(trajectory, rel)
  
      def _reduce_expect(self, trajectory, *, abs=None, rel=None):
          """
          Compute the average of the expectation values and store it in it's
          multiple formats.
          """
          if abs is not None:
              self._sum_det.reduce_expect(trajectory, abs)
          else:
              self._sum_rel.reduce_expect(trajectory, rel)
  
              if self.runs_e_data:
                  for k in self._raw_ops:
                      self.runs_e_data[k].append(trajectory.e_data[k])
  
      def _create_e_data(self):
          for i, k in enumerate(self._raw_ops):
              avg = 0
              avg2 = 0
              if self._sum_det:
                  avg += self._sum_det.sum_expect[i]
                  avg2 += self._sum_det.sum2_expect[i]
              if self._sum_rel:
                  avg += (
                      self._sum_rel.sum_expect[i] / self.num_trajectories
                  )
                  avg2 += (
                      self._sum_rel.sum2_expect[i] / self.num_trajectories
                  )
  
              self._average_e_data[k] = list(avg)
              # mean(expect**2) - mean(expect)**2 can something be very small
              # negative (-1e-15) which raise an error for float sqrt.
              self._std_e_data[k] = list(np.sqrt(np.abs(avg2 - np.abs(avg**2))))
  
      def _increment_traj(self, trajectory, *, abs=None, rel=None):
          if self.num_trajectories == 0 and not self._deterministic_weight_info:
              self._add_first_traj(trajectory)
  
          if abs is not None:
              if self._sum_det is None:
                  self._sum_det = _TrajectorySum(
                      trajectory,
                      self._store_average_density_matrices,
                      self._store_final_density_matrix)
          else:
              self.num_trajectories += 1
              if self._sum_rel is None:
                  self._sum_rel = _TrajectorySum(
                      trajectory,
                      self._store_average_density_matrices,
                      self._store_final_density_matrix)
  
      def _no_end(self):
          """
          Remaining number of trajectories needed to finish cannot be determined
          by this object.
          """
          return np.inf
  
      def _fixed_end(self):
          """
          Finish at a known number of trajectories.
          """
          ntraj_left = self._target_ntraj - self.num_trajectories
          if ntraj_left == 0:
              self.stats["end_condition"] = "ntraj reached"
          return ntraj_left
  
      def _average_computer(self):
          avg = np.array(self._sum_rel.sum_expect) / self.num_trajectories
          avg2 = np.array(self._sum_rel.sum2_expect) / self.num_trajectories
          return avg, avg2
  
      def _target_tolerance_end(self):
          """
          Compute the error on the expectation values using jackknife resampling.
          Return the approximate number of trajectories needed to have this
          error within the tolerance fot all e_ops and times.
          """
          if self.num_trajectories >= self._target_ntraj:
              # First make sure that "ntraj" setting is always respected
              self.stats["end_condition"] = "ntraj reached"
              return 0
  
          if self.num_trajectories <= 1:
              return np.inf
          avg, avg2 = self._average_computer()
          target = np.array(
              [
                  atol + rtol * mean
                  for mean, (atol, rtol) in zip(avg, self._target_tols)
              ]
          )
  
          one = np.array(1)
          if sum(self._deterministic_weight_info):
              # We do not include deterministic traj. in this calculation.
              # When there is a deterministic trajectory, the weights don't add
              # up to one. We have to consider that as follows:
              # err = (std * <w>**2 / (N-1)) ** 0.5
              # avg = <x * w>
              # avg2 = <x**2 * w>
              # std * <w>**2 = (<x**2> - <x>**2) * <w>**2
              #              = avg2 * <w> - avg**2
              # and "<w>" is one minus the sum of all deterministic trajectories
              # weights
              one = one - sum(self._deterministic_weight_info)
  
          std = avg2 * one - abs(avg)**2
          target_ntraj = np.max(std / target**2) + 1
          self._estimated_ntraj = min(target_ntraj - self.num_trajectories,
                                      self._target_ntraj - self.num_trajectories)
          if self._estimated_ntraj <= 0:
              self.stats["end_condition"] = "target tolerance reached"
          return self._estimated_ntraj
  
      def _post_init(self):
          self._target_ntraj = None
          self._target_tols = None
          self._early_finish_check = self._no_end
  
          self.add_processor(self._increment_traj)
          store_trajectory = self.options["keep_runs_results"]
          if store_trajectory:
              self.add_processor(self._store_trajectory)
          if self._store_average_density_matrices:
              self.add_processor(self._reduce_states)
          if self._store_final_density_matrix:
              self.add_processor(self._reduce_final_state)
          if self._raw_ops:
              self.add_processor(self._reduce_expect)
          # self.add_processor(self._store_weight_info)
  
          self.stats["end_condition"] = "unknown"
  
      def add_deterministic(self, trajectory, weight):
          """
          Add a trajectory that was not randomly generated.
          The weight provided here is the exact weight that will be used for this
          trajectory in all averages.
  
          Parameters
          ----------
          trajectory : :class:`Result`
              The result of the simulation of the deterministic trajectory
  
          weight : float
              Number (usually between 0 and 1), exact weight of this trajectory
          """
          for op in self._state_processors:
              op(trajectory, abs=weight)
  
          self._deterministic_weight_info.append(weight)
          self.deterministic_trajectories.append(trajectory)
  
      def add(self, trajectory_info):
          """
          Add a trajectory to the evolution.
  
          Trajectories can be saved or average canbe extracted depending on the
          options ``keep_runs_results``.
  
          Parameters
          ----------
          trajectory_info : tuple of seed and trajectory
              - seed: int, SeedSequence
                Seed used to generate the trajectory.
              - trajectory : :class:`Result`
                Run result for one evolution over the times.
              - *weight: float, optional
                Relative weight of the trajectory.
  
          Returns
          -------
          remaing_traj : number
              Return the number of trajectories still needed to reach the target
              tolerance. If no tolerance is provided, return infinity.
          """
          seed, trajectory, *weight = trajectory_info
          weight = weight[0] if weight else 1
  
          self.seeds.append(seed)
          self._trajectories_weight_info.append(weight)
  
          for op in self._state_processors:
              op(trajectory, rel=weight)
  
          return self._early_finish_check()
  
      def add_end_condition(self, ntraj, target_tol=None):
          """
          Set the condition to stop the computing trajectories when the certain
          condition are fullfilled.
          Supported end condition for multi trajectories computation are:
  
          - Reaching a number of trajectories.
          - Error bar on the expectation values reach smaller than a given
            tolerance.
  
          Parameters
          ----------
          ntraj : int
              Number of trajectories expected.
  
          target_tol : float, array_like, [optional]
              Target tolerance of the evolution. The evolution will compute
              trajectories until the error on the expectation values is lower
              than this tolerance. The error is computed using jackknife
              resampling. ``target_tol`` can be an absolute tolerance, a pair of
              absolute and relative tolerance, in that order. Lastly, it can be a
              list of pairs of (atol, rtol) for each e_ops.
  
              Error estimation is done with jackknife resampling.
          """
          self._target_ntraj = ntraj
          self.stats["end_condition"] = "timeout"
  
          if target_tol is None:
              self._early_finish_check = self._fixed_end
              return
  
          num_e_ops = len(self._raw_ops)
  
          if not num_e_ops:
              raise ValueError("Cannot target a tolerance without e_ops")
  
          self._estimated_ntraj = ntraj
  
          targets = np.array(target_tol)
          if targets.ndim == 0:
              self._target_tols = np.array([(target_tol, 0.0)] * num_e_ops)
          elif targets.shape == (2,):
              self._target_tols = np.ones((num_e_ops, 2)) * targets
          elif targets.shape == (num_e_ops, 2):
              self._target_tols = targets
          else:
              raise ValueError(
                  "target_tol must be a number, a pair of (atol, "
                  "rtol) or a list of (atol, rtol) for each e_ops"
              )
  
          self._early_finish_check = self._target_tolerance_end
  
      @property
      def runs_states(self):
          """
          States of every runs as ``states[run][t]``.
          """
          if self.trajectories and self.trajectories[0].states:
              return [traj.states for traj in self.trajectories]
          else:
              return None
  
      @property
      def average_states(self):
          """
          States averages as density matrices.
          """
  
          trajectory_states_available = (self.trajectories and
                                         self.trajectories[0].states)
          need_to_reduce_states = False
          if self._sum_det and not self._sum_det.sum_states:
              if not trajectory_states_available:
                  return None
              self._sum_det._initialize_sum_states(self.trajectories[0])
              need_to_reduce_states = True
          if self._sum_rel and not self._sum_rel.sum_states:
              if not trajectory_states_available:
                  return None
              self._sum_rel._initialize_sum_states(self.trajectories[0])
              need_to_reduce_states = True
          if need_to_reduce_states:
              for trajectory, weight in zip(
                  self.deterministic_trajectories,
                  self._deterministic_weight_info
              ):
                  self._reduce_states(trajectory, abs=weight)
              for trajectory, weight in zip(
                  self.trajectories,
                  self._trajectories_weight_info
              ):
                  self._reduce_states(trajectory, rel=weight)
  
          if self._sum_det and self._sum_rel:
              return [a + r / self.num_trajectories for a, r in zip(
                  self._sum_det.sum_states, self._sum_rel.sum_states)
              ]
          if self._sum_rel:
              return [r / self.num_trajectories
                      for r in self._sum_rel.sum_states]
          return self._sum_det.sum_states
  
      @property
      def states(self):
          """
          Runs final states if available, average otherwise.
          """
          return self.runs_states or self.average_states
  
      @property
      def runs_final_states(self):
          """
          Last states of each trajectories.
          """
          if self.trajectories and self.trajectories[0].final_state:
              return [traj.final_state for traj in self.trajectories]
          else:
              return None
  
      @property
      def average_final_state(self):
          """
          Last states of each trajectories averaged into a density matrix.
          """
          trajectory_states_available = (self.trajectories and
                                         self.trajectories[0].final_state)
          states = self.average_states
          need_to_reduce_states = False
          if self._sum_det and not self._sum_det.sum_final_state:
              if not (trajectory_states_available or states):
                  return None
              need_to_reduce_states = True
  
          if self._sum_rel and not self._sum_rel.sum_final_state:
              if not (trajectory_states_available or states):
                  return None
              need_to_reduce_states = True
  
          if need_to_reduce_states and states:
              return states[-1]
          elif need_to_reduce_states:
              if self._sum_det:
                  self._sum_det._initialize_sum_finalstate(self.trajectories[0])
              if self._sum_rel:
                  self._sum_rel._initialize_sum_finalstate(self.trajectories[0])
              for trajectory, weight in zip(
                  self.deterministic_trajectories,
                  self._deterministic_weight_info
              ):
                  self._reduce_final_state(trajectory, abs=weight)
              for trajectory, weight in zip(
                  self.trajectories,
                  self._trajectories_weight_info
              ):
                  self._reduce_final_state(trajectory, rel=weight)
  
          if self._sum_det and self._sum_rel:
              return (self._sum_det.sum_final_state +
                      self._sum_rel.sum_final_state / self.num_trajectories)
          if self._sum_rel:
              return self._sum_rel.sum_final_state / self.num_trajectories
          return self._sum_det.sum_final_state
  
      @property
      def final_state(self):
          """
          Runs final states if available, average otherwise.
          """
          return self.runs_final_states or self.average_final_state
  
      @property
      def average_e_data(self):
          if not self._average_e_data:
              self._create_e_data()
          return self._average_e_data
  
      @property
      def std_e_data(self):
          if not self._std_e_data:
              self._create_e_data()
          return self._std_e_data
  
      @property
      def average_expect(self):
          return [np.array(val) for val in self.average_e_data.values()]
  
      @property
      def std_expect(self):
          return [np.array(val) for val in self.std_e_data.values()]
  
      @property
      def runs_expect(self):
          return [np.array(val) for val in self.runs_e_data.values()]
  
      @property
      def expect(self):
          return [np.array(val) for val in self.e_data.values()]
  
      @property
      def e_data(self):
          return self.runs_e_data or self.average_e_data
  
      @property
      def deterministic_weights(self):
          return self._deterministic_weight_info.copy()
  
      @property
      def runs_weights(self):
          return [
              w / self.num_trajectories
              for w in self._trajectories_weight_info
          ]
  
      def steady_state(self, N=0):
          """
          Average the states of the last ``N`` times of every runs as a density
          matrix. Should converge to the steady state in the right circumstances.
  
          Parameters
          ----------
          N : int [optional]
              Number of states from the end of ``tlist`` to average. Per default
              all states will be averaged.
          """
          N = int(N) or len(self.times)
          N = len(self.times) if N > len(self.times) else N
          states = self.average_states
          if states is not None:
              return sum(states[-N:]) / N
          else:
              return None
  
      def __repr__(self):
          lines = [
              f"<{self.__class__.__name__}",
              f"  Solver: {self.solver}",
          ]
          if self.stats:
              lines.append("  Solver stats:")
              lines.extend(f"    {k}: {v!r}" for k, v in self.stats.items())
          if self.times:
              lines.append(
                  f"  Time interval: [{self.times[0]}, {self.times[-1]}]"
                  f" ({len(self.times)} steps)"
              )
          lines.append(f"  Number of e_ops: {len(self.e_data)}")
          if self.states:
              lines.append("  States saved.")
          elif self.final_state is not None:
              lines.append("  Final state saved.")
          else:
              lines.append("  State not saved.")
          lines.append(f"  Number of trajectories: {self.num_trajectories}")
          if self.trajectories:
              lines.append("  Trajectories saved.")
          else:
              lines.append("  Trajectories not saved.")
          lines.append(">")
          return "\n".join(lines)
  
      def merge(self, other, p=None):
          r"""
          Merges two multi-trajectory results.
  
          If this result represent an ensemble :math:`\rho`, and `other`
          represents an ensemble :math:`\rho'`, then the merged result
          represents the ensemble
  
          .. math::
              \rho_{\mathrm{merge}} = p \rho + (1 - p) \rho'
  
          where p is a parameter between 0 and 1. Its default value is
          :math:`p_{\textrm{def}} = N / (N + N')`, N and N' being the number of
          trajectories in the two result objects.
  
          Parameters
          ----------
          other : MultiTrajResult
              The multi-trajectory result to merge with this one
          p : float [optional]
              The relative weight of this result in the combination. By default,
              will be chosen such that all trajectories contribute equally
              to the merged result.
          """
          if not isinstance(other, MultiTrajResult):
              return NotImplemented
          if self._raw_ops != other._raw_ops:
              raise ValueError("Shared `e_ops` is required to merge results")
          if self.times != other.times:
              raise ValueError("Shared `times` are is required to merge results")
  
          new = self.__class__(
              self._raw_ops, self.options, solver=self.solver, stats=self.stats
          )
          new.times = self.times
          new.e_ops = self.e_ops
  
          if bool(self.trajectories) != bool(other.trajectories):
              # ensure the states are reduced.
              if self.trajectories:
                  self.average_states
                  self.average_final_state
              else:
                  other.average_states
                  other.average_final_state
  
          new.num_trajectories = self.num_trajectories + other.num_trajectories
          new.seeds = self.seeds + other.seeds
  
          p_equal = self.num_trajectories / new.num_trajectories
          if p is None:
              p = self.num_trajectories / new.num_trajectories
  
          new._deterministic_weight_info = [
              w * p for w in self._deterministic_weight_info
          ] + [
              w * (1 - p) for w in other._deterministic_weight_info
          ]
          new._trajectories_weight_info = [
              w * p / p_equal for w in self._trajectories_weight_info
          ] + [
              w * (1 - p) / (1 - p_equal)
              for w in other._trajectories_weight_info
          ]
  
          if self.trajectories and other.trajectories:
              new.deterministic_trajectories = (
                  self.deterministic_trajectories
                  + other.deterministic_trajectories
              )
              new.trajectories = self.trajectories + other.trajectories
          else:
              new.trajectories = []
              new.options["keep_runs_results"] = False
              new.runs_e_data = {}
  
          self_states = self.options["store_states"]
          self_fstate = self.options["store_final_state"]
          other_states = other.options["store_states"]
          other_fstate = other.options["store_final_state"]
  
          new.options["store_states"] = self_states and other_states
  
          new.options["store_final_state"] = (
              (self_fstate or self_states) and (other_fstate or other_states)
          )
  
          new._sum_det = _TrajectorySum.merge(
              self._sum_det, p, other._sum_det, 1 - p)
          new._sum_rel = _TrajectorySum.merge(
              self._sum_rel, p / p_equal,
              other._sum_rel, (1 - p) / (1 - p_equal))
  
          if self.runs_e_data and other.runs_e_data:
              for k in self._raw_ops:
                  new.runs_e_data[k] = self.runs_e_data[k] + other.runs_e_data[k]
  
          new.stats["run time"] += other.stats["run time"]
          new.stats["end_condition"] = "Merged results"
  
          return new
  
      def __add__(self, other):
          return self.merge(other, p=None)
  
  
  class _TrajectorySum:
      """
      Keeps running sums of expectation values, and (if requested) states and
      final states, over a set of trajectories as they are added one-by-one.
      This is used in the `MultiTrajResult` class, which needs to keep track of
      several sums of this type.
  
      Parameters
      ----------
      example_trajectory : :obj:`.Result`
          An example trajectory with expectation values and states of the same
          shape like for the trajectories that will be added later. The data is
          only used for initializing arrays in the correct shape and otherwise
          ignored.
  
      store_states : bool
          Whether the states of the trajectories will be summed.
  
      store_final_state : bool
          Whether the final states of the trajectories will be summed.
      """
      def __init__(self, example_trajectory, store_states, store_final_state):
          if example_trajectory.states and store_states:
              self._initialize_sum_states(example_trajectory)
          else:
              self.sum_states = None
  
          if example_trajectory.final_state and store_final_state:
              self._initialize_sum_finalstate(example_trajectory)
          else:
              self.sum_final_state = None
  
          self.sum_expect = [
              np.zeros_like(expect) for expect in example_trajectory.expect
          ]
          self.sum2_expect = [
              np.zeros_like(expect) for expect in example_trajectory.expect
          ]
  
      def _initialize_sum_states(self, example_trajectory):
          self.sum_states = [
              qzero_like(_to_dm(state)) for state in example_trajectory.states]
  
      def _initialize_sum_finalstate(self, example_trajectory):
          self.sum_final_state = qzero_like(
              _to_dm(example_trajectory.final_state)
          )
  
      def reduce_states(self, trajectory, weight=1., td_weight=None):
          """
          Adds the states stored in the given trajectory to the running sum
          `sum_states`. Takes account of the trajectory's total weight if
          present.
          """
          if td_weight is not None:
              self.sum_states = [
                  accu + weight * weight_t * _to_dm(state)
                  for accu, state, weight_t in zip(
                      self.sum_states, trajectory.states, td_weight
                  )
              ]
          else:
              self.sum_states = [
                  accu + weight * _to_dm(state)
                  for accu, state in zip(self.sum_states, trajectory.states)
              ]
  
      def reduce_final_state(self, trajectory, weight=1.):
          """
          Adds the final state stored in the given trajectory to the running sum
          `sum_final_state`. Takes account of the trajectory's total weight if
          present.
          """
          self.sum_final_state += weight * _to_dm(trajectory.final_state)
  
      def reduce_expect(self, trajectory, weight=1.):
          """
          Adds the expectation values, and their squares, that are stored in the
          given trajectory to the running sums `sum_expect` and `sum2_expect`.
          Takes account of the trajectory's total weight if present.
          """
          for i, expect_traj in enumerate(trajectory.expect):
              self.sum_expect[i] += weight * expect_traj
              self.sum2_expect[i] += weight * expect_traj**2
  
      @staticmethod
      def merge(sum1, weight1, sum2, weight2):
          """
          Merges the sums of expectation values, states and final states with
          the given weights, i.e., `result = weight1 * sum1 + weight2 * sum2`.
          """
          if sum1 is None and sum2 is None:
              return None
          if sum1 is None:
              return _TrajectorySum.merge(sum2, weight2, sum1, weight1)
  
          new = copy(sum1)
  
          if sum2 is None:
              if sum1.sum_states:
  