Source code for qutip.solver.stochastic

__all__ = ["smesolve", "SMESolver", "ssesolve", "SSESolver"]

from .sode.ssystem import StochasticOpenSystem, StochasticClosedSystem
from .result import MultiTrajResult, Result, ExpectOp
from .multitraj import _MultiTrajRHS, MultiTrajSolver
from .. import Qobj, QobjEvo
from ..core.dimensions import Dimensions
import numpy as np
from functools import partial
from .solver_base import _solver_deprecation
from ._feedback import _QobjFeedback, _DataFeedback, _WienerFeedback


class StochasticTrajResult(Result):
    def _post_init(self, m_ops=(), dw_factor=(), heterodyne=False):
        super()._post_init()
        self.W = []
        self.m_ops = []
        self.m_expect = []
        self.dW_factor = dw_factor
        self.heterodyne = heterodyne
        for op in m_ops:
            f = self._e_op_func(op)
            self.W.append([0.0])
            self.m_expect.append([])
            self.m_ops.append(ExpectOp(op, f, self.m_expect[-1].append))
            self.add_processor(self.m_ops[-1]._store)

    def add(self, t, state, noise=None):
        super().add(t, state)
        if noise is not None and self.options["store_measurement"]:
            for i, dW in enumerate(noise):
                self.W[i].append(self.W[i][-1] + dW)

    @property
    def wiener_process(self):
        """
        Wiener processes for each stochastic collapse operators.

        The output shape is
            (len(sc_ops), len(tlist))
        for homodyne detection, and
            (len(sc_ops), 2, len(tlist))
        for heterodyne detection.
        """
        W = np.array(self.W)
        if self.heterodyne:
            W = W.reshape(-1, 2, W.shape[1])
        return W

    @property
    def dW(self):
        """
        Wiener increment for each stochastic collapse operators.

        The output shape is
            (len(sc_ops), len(tlist)-1)
        for homodyne detection, and
            (len(sc_ops), 2, len(tlist)-1)
        for heterodyne detection.
        """
        dw = np.diff(self.W, axis=1)
        if self.heterodyne:
            dw = dw.reshape(-1, 2, dw.shape[1])
        return dw

    @property
    def measurement(self):
        """
        Measurements for each stochastic collapse operators.

        The output shape is
            (len(sc_ops), len(tlist)-1)
        for homodyne detection, and
            (len(sc_ops), 2, len(tlist)-1)
        for heterodyne detection.
        """
        dts = np.diff(self.times)
        m_expect = np.array(self.m_expect)[:, 1:]
        noise = np.einsum(
            "i,ij,j->ij", self.dW_factor, np.diff(self.W, axis=1), (1 / dts)
        )
        if self.heterodyne:
            m_expect = m_expect.reshape(-1, 2, m_expect.shape[1])
            noise = noise.reshape(-1, 2, noise.shape[1])
        return m_expect + noise


class StochasticResult(MultiTrajResult):
    def _post_init(self):
        super()._post_init()

        store_measurement = self.options["store_measurement"]
        keep_runs = self.options["keep_runs_results"]

        if not keep_runs and store_measurement:
            self.add_processor(
                partial(self._reduce_attr, attr="wiener_process")
            )
            self._wiener_process = []
            self.add_processor(partial(self._reduce_attr, attr="dW"))
            self._dW = []

        if not keep_runs and store_measurement:
            self.add_processor(partial(self._reduce_attr, attr="measurement"))
            self._measurement = []

    def _reduce_attr(self, trajectory, attr):
        """
        Add a result attribute to a list when the trajectories are not stored.
        """
        getattr(self, "_" + attr).append(getattr(trajectory, attr))

    def _trajectories_attr(self, attr):
        """
        Get the result associated to the attr, whether the trajectories are
        saved or not.
        """
        if hasattr(self, "_" + attr):
            return getattr(self, "_" + attr)
        elif self.options["keep_runs_results"]:
            return np.array([
                getattr(traj, attr) for traj in self.trajectories
            ])
        return None

    @property
    def measurement(self):
        """
        Measurements for each trajectories and stochastic collapse operators.

        The output shape is
            (ntraj, len(sc_ops), len(tlist)-1)
        for homodyne detection, and
            (ntraj, len(sc_ops), 2, len(tlist)-1)
        for heterodyne detection.
        """
        return self._trajectories_attr("measurement")

    @property
    def dW(self):
        """
        Wiener increment for each trajectories and stochastic collapse
        operators.

        The output shape is
            (ntraj, len(sc_ops), len(tlist)-1)
        for homodyne detection, and
            (ntraj, len(sc_ops), 2, len(tlist)-1)
        for heterodyne detection.
        """
        return self._trajectories_attr("dW")

    @property
    def wiener_process(self):
        """
        Wiener processes for each trajectories and stochastic collapse
        operators.

        The output shape is
            (ntraj, len(sc_ops), len(tlist)-1)
        for homodyne detection, and
            (ntraj, len(sc_ops), 2, len(tlist)-1)
        for heterodyne detection.
        """
        return self._trajectories_attr("wiener_process")


class _StochasticRHS(_MultiTrajRHS):
    """
    In between object to store the stochastic system.

    It store the Hamiltonian (not Liouvillian when possible), and sc_ops.
    dims and flags are provided to be usable the the base ``Solver`` class.

    We don't want to use the cython rhs (``StochasticOpenSystem``, etc.) since
    the rouchon integrator need the part but does not use the usual drift and
    diffusion computation.
    """

    def __init__(self, issuper, H, sc_ops, c_ops, heterodyne):

        if not isinstance(H, (Qobj, QobjEvo)) or not H.isoper:
            raise TypeError("The Hamiltonian must be an operator")
        self.H = QobjEvo(H)

        if isinstance(sc_ops, (Qobj, QobjEvo)):
            sc_ops = [sc_ops]
        self.sc_ops = [QobjEvo(c_op) for c_op in sc_ops]

        if isinstance(c_ops, (Qobj, QobjEvo)):
            c_ops = [c_ops]
        self.c_ops = [QobjEvo(c_op) for c_op in c_ops]

        if any(not c_op.isoper for c_op in c_ops):
            raise TypeError("c_ops must be operators")

        if any(not c_op.isoper for c_op in sc_ops):
            raise TypeError("sc_ops must be operators")

        self.issuper = issuper
        self.heterodyne = heterodyne
        self._noise_key = None

        if heterodyne:
            sc_ops = []
            for c_op in self.sc_ops:
                sc_ops.append(c_op / np.sqrt(2))
                sc_ops.append(c_op * (-1j / np.sqrt(2)))
            self.sc_ops = sc_ops

        if self.issuper and not self.H.issuper:
            self.dims = [self.H.dims, self.H.dims]
            self._dims = Dimensions([self.H._dims, self.H._dims])
        else:
            self.dims = self.H.dims
            self._dims = self.H._dims

    def __call__(self, options):
        if self.issuper:
            return StochasticOpenSystem(
                self.H, self.sc_ops, self.c_ops, options.get("derr_dt", 1e-6)
            )
        else:
            return StochasticClosedSystem(self.H, self.sc_ops)

    def arguments(self, args):
        self.H.arguments(args)
        for c_op in self.c_ops:
            c_op.arguments(args)
        for sc_op in self.sc_ops:
            sc_op.arguments(args)

    def _register_feedback(self, val):
        self.H._register_feedback({"wiener_process": val}, "stochastic solver")
        for c_op in self.c_ops:
            c_op._register_feedback(
                {"WienerFeedback": val}, "stochastic solver"
            )
        for sc_op in self.sc_ops:
            sc_op._register_feedback(
                {"WienerFeedback": val}, "stochastic solver"
            )


[docs]def smesolve( H, rho0, tlist, c_ops=(), sc_ops=(), heterodyne=False, *, e_ops=(), args={}, ntraj=500, options=None, seeds=None, target_tol=None, timeout=None, **kwargs ): """ Solve stochastic master 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. rho0 : :class:`.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), optional Deterministic collapse operator which will contribute with a standard Lindblad type of dissipation. sc_ops : list of (:obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format) List of stochastic collapse operators. 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:`.expect` for more detail of operator expectation. args : dict, optional Dictionary of parameters for time-dependent Hamiltonians and collapse operators. ntraj : int, default: 500 Number of trajectories to compute. heterodyne : bool, default: False Whether to use heterodyne or homodyne detection. seeds : int, SeedSequence, list, optional Seed for the random number generator. It can be a single seed used to spawn seeds for each trajectory or a list of seeds, one for each trajectory. Seeds are saved in the result and they can be reused with:: seeds=prev_result.seeds When using a parallel map, the trajectories can be re-ordered. target_tol : {float, tuple, list}, optional Target tolerance of the evolution. The evolution will compute trajectories until the error on the expectation values is lower than this tolerance. The maximum number of trajectories employed is given by ``ntraj``. The error is computed using jackknife resampling. ``target_tol`` can be an absolute tolerance or 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. timeout : float, optional Maximum time for the evolution in second. When reached, no more trajectories will be computed. Overwrite the option of the same name. 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. - | store_measurement: bool | Whether to store the measurement and wiener process for each trajectories. - | keep_runs_results : bool | Whether to store results from all trajectories or just store the averages. - | normalize_output : bool | Normalize output state to hide ODE numerical errors. - | 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 | Which stochastic differential equation integration method to use. Main ones are {"euler", "rouchon", "platen", "taylor1.5_imp"} - | map : str {"serial", "parallel", "loky", "mpi"} | How to run the trajectories. "parallel" uses the multiprocessing module to run in parallel while "loky" and "mpi" use the "loky" and "mpi4py" modules to do so. - | num_cpus : NoneType, int | Number of cpus to use when running in parallel. ``None`` detect the number of available cpus. - | dt : float | The finite steps lenght for the Stochastic integration method. Default change depending on the integrator. Additional options are listed under `options <./classes.html#qutip.solver.stochastic.SMESolver.options>`__. More options may be available depending on the selected differential equation integration method, see `SIntegrator <./classes.html#classes-sode>`_. Returns ------- output: :class:`.Result` An instance of the class :class:`.Result`. """ options = _solver_deprecation(kwargs, options, "stoc") H = QobjEvo(H, args=args, tlist=tlist) c_ops = [QobjEvo(c_op, args=args, tlist=tlist) for c_op in c_ops] sc_ops = [QobjEvo(c_op, args=args, tlist=tlist) for c_op in sc_ops] sol = SMESolver( H, sc_ops, c_ops=c_ops, options=options, heterodyne=heterodyne ) return sol.run( rho0, tlist, ntraj, e_ops=e_ops, seeds=seeds, target_tol=target_tol, timeout=timeout, )
[docs]def ssesolve( H, psi0, tlist, sc_ops=(), heterodyne=False, *, e_ops=(), args={}, ntraj=500, options=None, seeds=None, target_tol=None, timeout=None, **kwargs ): """ Solve stochastic Schrodinger 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`. sc_ops : list of (:obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format) List of stochastic collapse operators. 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:`expect` for more detail of operator expectation. args : dict, optional Dictionary of parameters for time-dependent Hamiltonians and collapse operators. ntraj : int, default: 500 Number of trajectories to compute. heterodyne : bool, default: False Whether to use heterodyne or homodyne detection. seeds : int, SeedSequence, list, optional Seed for the random number generator. It can be a single seed used to spawn seeds for each trajectory or a list of seeds, one for each trajectory. Seeds are saved in the result and they can be reused with:: seeds=prev_result.seeds target_tol : {float, tuple, list}, optional Target tolerance of the evolution. The evolution will compute trajectories until the error on the expectation values is lower than this tolerance. The maximum number of trajectories employed is given by ``ntraj``. The error is computed using jackknife resampling. ``target_tol`` can be an absolute tolerance or 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. timeout : float, optional Maximum time for the evolution in second. When reached, no more trajectories will be computed. Overwrite the option of the same name. 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. - | store_measurement: bool Whether to store the measurement and wiener process, or brownian noise for each trajectories. - | keep_runs_results : bool | Whether to store results from all trajectories or just store the averages. - | normalize_output : bool | Normalize output state to hide ODE numerical errors. - | 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 | Which stochastic differential equation integration method to use. Main ones are {"euler", "rouchon", "platen", "taylor1.5_imp"} - | map : str {"serial", "parallel", "loky", "mpi"} | How to run the trajectories. "parallel" uses the multiprocessing module to run in parallel while "loky" and "mpi" use the "loky" and "mpi4py" modules to do so. - | num_cpus : NoneType, int | Number of cpus to use when running in parallel. ``None`` detect the number of available cpus. - | dt : float | The finite steps lenght for the Stochastic integration method. Default change depending on the integrator. Additional options are listed under `options <./classes.html#qutip.solver.stochastic.SSESolver.options>`__. More options may be available depending on the selected differential equation integration method, see `SIntegrator <./classes.html#classes-sode>`_. Returns ------- output: :class:`.Result` An instance of the class :class:`.Result`. """ options = _solver_deprecation(kwargs, options, "stoc") H = QobjEvo(H, args=args, tlist=tlist) sc_ops = [QobjEvo(c_op, args=args, tlist=tlist) for c_op in sc_ops] sol = SSESolver(H, sc_ops, options=options, heterodyne=heterodyne) return sol.run( psi0, tlist, ntraj, e_ops=e_ops, seeds=seeds, target_tol=target_tol, timeout=timeout, )
class StochasticSolver(MultiTrajSolver): """ Generic stochastic solver. """ name = "StochasticSolver" _resultclass = StochasticResult _avail_integrators = {} _open = None solver_options = { "progress_bar": "text", "progress_kwargs": {"chunk_size": 10}, "store_final_state": False, "store_states": None, "keep_runs_results": False, "normalize_output": False, "map": "serial", "mpi_options": {}, "num_cpus": None, "bitgenerator": None, "method": "platen", "store_measurement": False, } def _trajectory_resultclass(self, e_ops, options): return StochasticTrajResult( e_ops, options, m_ops=self.m_ops, dw_factor=self.dW_factors, heterodyne=self.heterodyne, ) def __init__(self, H, sc_ops, heterodyne, *, c_ops=(), options=None): self._heterodyne = heterodyne if self.name == "ssesolve" and c_ops: raise ValueError("c_ops are not supported by ssesolve.") rhs = _StochasticRHS(self._open, H, sc_ops, c_ops, heterodyne) super().__init__(rhs, options=options) if heterodyne: self._m_ops = [] for op in sc_ops: self._m_ops += [op + op.dag(), -1j * (op - op.dag())] self._dW_factors = np.ones(len(sc_ops) * 2) * 2**0.5 else: self._m_ops = [op + op.dag() for op in sc_ops] self._dW_factors = np.ones(len(sc_ops)) @property def heterodyne(self): return self._heterodyne @property def m_ops(self): return self._m_ops @m_ops.setter def m_ops(self, new_m_ops): """ Measurements operators. Default are: m_ops = sc_ops + sc_ops.dag() for homodyne detection, and m_ops = sc_ops + sc_ops.dag(), -1j*(sc_ops - sc_ops.dag()) for heterodyne detection. Measurements opput is computed as: expect(m_ops_i, state(t)) + dW_i / dt * dW_factors Where ``dW`` follows a gaussian distribution with norm 0 and derivation of ``dt**0.5``. ``dt`` is the time difference between step in the ``tlist``. ``m_ops`` can be overwritten, but the number of operators must be constant. """ if len(new_m_ops) != len(self.m_ops): if self.heterodyne: raise ValueError( f"2 `m_ops` per `sc_ops`, {len(self.rhs.sc_ops)} operators" " are expected for heterodyne measurement." ) else: raise ValueError( f"{len(self.rhs.sc_ops)} measurements " "operators are expected." ) if not all( isinstance(op, Qobj) and op.dims == self.rhs.sc_ops[0].dims for op in new_m_ops ): raise ValueError( "m_ops must be Qobj with the same dimensions" " as the Hamiltonian" ) self._m_ops = new_m_ops @property def dW_factors(self): return self._dW_factors @dW_factors.setter def dW_factors(self, new_dW_factors): """ Scaling of the noise on the measurements. Default are ``1`` for homodyne and ``sqrt(1/2)`` for heterodyne. ``dW_factors`` must be a list of the same length as ``m_ops``. """ if len(new_dW_factors) != len(self._dW_factors): if self.heterodyne: raise ValueError( f"2 `dW_factors` per `sc_ops`, {len(self.rhs.sc_ops)} " "values are expected for heterodyne measurement." ) else: raise ValueError( f"{len(self.rhs.sc_ops)} dW_factors are expected." ) self._dW_factors = new_dW_factors def _integrate_one_traj(self, seed, tlist, result): for t, state, noise in self._integrator.run(tlist): result.add(t, self._restore_state(state, copy=False), noise) return seed, result @classmethod def avail_integrators(cls): if cls is StochasticSolver: return cls._avail_integrators.copy() return { **StochasticSolver.avail_integrators(), **cls._avail_integrators, } @property def options(self): """ Options for stochastic solver: store_final_state: bool, default: False Whether or not to store the final state of the evolution in the result class. store_states: None, bool, default: 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. store_measurement: bool, default: False Whether to store the measurement for each trajectories. Storing measurements will also store the wiener process, or brownian noise for each trajectories. progress_bar: str {'text', 'enhanced', 'tqdm', ''}, default: "text" 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, default: {"chunk_size":10} Arguments to pass to the progress_bar. Qutip's bars use ``chunk_size``. keep_runs_results: bool, default: False Whether to store results from all trajectories or just store the averages. normalize_output: bool Normalize output state to hide ODE numerical errors. method: str, default: "platen" Which differential equation integration method to use. map: str {"serial", "parallel", "loky", "mpi"}, default: "serial" How to run the trajectories. "parallel" uses the multiprocessing module to run in parallel while "loky" and "mpi" use the "loky" and "mpi4py" modules to do so. mpi_options: dict, default: {} Only applies if map is "mpi". This dictionary will be passed as keyword arguments to the `mpi4py.futures.MPIPoolExecutor` constructor. Note that the `max_workers` argument is provided separately through the `num_cpus` option. num_cpus: None, int, default: None Number of cpus to use when running in parallel. ``None`` detect the number of available cpus. bitgenerator: {None, "MT19937", "PCG64DXSM", ...}, default: None Which of numpy.random's bitgenerator to use. With ``None``, your numpy version's default is used. """ return self._options @options.setter def options(self, new_options): MultiTrajSolver.options.fset(self, new_options) @classmethod def WienerFeedback(cls, default=None): """ Wiener function of the trajectory argument for time dependent systems. When used as an args: ``QobjEvo([op, func], args={"W": SMESolver.WienerFeedback()})`` The ``func`` will receive a function as ``W`` that return an array of wiener processes values at ``t``. The wiener process for the i-th sc_ops is the i-th element for homodyne detection and the (2i, 2i+1) pairs of process in heterodyne detection. The process is a step function with step of length ``options["dt"]``. .. note:: WienerFeedback can't be added to a running solver when updating arguments between steps: ``solver.step(..., args={})``. Parameters ---------- default : callable, optional Default function used outside the solver. When not passed, a function returning ``np.array([0])`` is used. """ return _WienerFeedback(default) @classmethod def StateFeedback(cls, default=None, raw_data=False): """ State of the evolution to be used in a time-dependent operator. When used as an args: ``QobjEvo([op, func], args={"state": SMESolver.StateFeedback()})`` The ``func`` will receive the density matrix as ``state`` during the evolution. .. note:: Not supported by the ``rouchon`` mehtod. Parameters ---------- default : Qobj or qutip.core.data.Data, default : None Initial value to be used at setup of the system. 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=cls._open) return _QobjFeedback(default, open=cls._open)
[docs]class SMESolver(StochasticSolver): r""" Stochastic Master Equation Solver. 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. sc_ops : list of (:obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format) List of stochastic collapse operators. heterodyne : bool, default: False Whether to use heterodyne or homodyne detection. options : dict, optional Options for the solver, see :obj:`SMESolver.options` and `SIntegrator <./classes.html#classes-sode>`_ for a list of all options. """ name = "smesolve" _avail_integrators = {} _open = True solver_options = { "progress_bar": "text", "progress_kwargs": {"chunk_size": 10}, "store_final_state": False, "store_states": None, "keep_runs_results": False, "normalize_output": False, "map": "serial", "mpi_options": {}, "num_cpus": None, "bitgenerator": None, "method": "platen", "store_measurement": False, }
[docs]class SSESolver(StochasticSolver): r""" Stochastic Schrodinger Equation Solver. 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. c_ops : list of (:obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format) Deterministic collapse operator which will contribute with a standard Lindblad type of dissipation. sc_ops : list of (:obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format) List of stochastic collapse operators. heterodyne : bool, default: False Whether to use heterodyne or homodyne detection. options : dict, optional Options for the solver, see :obj:`SSESolver.options` and `SIntegrator <./classes.html#classes-sode>`_ for a list of all options. """ name = "ssesolve" _avail_integrators = {} _open = False solver_options = { "progress_bar": "text", "progress_kwargs": {"chunk_size": 10}, "store_final_state": False, "store_states": None, "keep_runs_results": False, "normalize_output": False, "map": "serial", "mpi_options": {}, "num_cpus": None, "bitgenerator": None, "method": "platen", "store_measurement": False, }