Karana.Integrators ================== .. py:module:: Karana.Integrators .. autoapi-nested-parse:: Collection of classes to represent mathematical object used in Karana Dynamics simulations. Examples include unit quaternions, homogeneous transforms, and spatial vectors. Submodules ---------- .. toctree:: :maxdepth: 1 /generated/python_api/Karana/Integrators/Integrator_types/index Attributes ---------- .. autoapisummary:: Karana.Integrators.ArkExplicitIntegratorOptions Classes ------- .. autoapisummary:: Karana.Integrators.ArkExplicitIntegrator Karana.Integrators.ArkExplicitIntegratorVars Karana.Integrators.ArkImplicitIntegrator Karana.Integrators.ArkImplicitIntegratorOptions Karana.Integrators.ArkImplicitIntegratorVars Karana.Integrators.CVodeIntegrator Karana.Integrators.CVodeIntegratorOptions Karana.Integrators.CVodeIntegratorVars Karana.Integrators.EulerIntegrator Karana.Integrators.ExplicitVerletIntegrator Karana.Integrators.Integrator Karana.Integrators.IntegratorOptions Karana.Integrators.IntegratorType Karana.Integrators.PartitionedIntegrator Karana.Integrators.RK4Integrator Karana.Integrators.SundialsImplicitIntegrator Karana.Integrators.SundialsImplicitIntegratorOptions Karana.Integrators.SundialsImplicitIntegratorVars Karana.Integrators.SundialsIntegrator Karana.Integrators.SundialsIntegratorOptions Karana.Integrators.SundialsIntegratorVars Functions --------- .. autoapisummary:: Karana.Integrators.createIntegrator Karana.Integrators.strToIntegratorType Package Contents ---------------- .. py:class:: ArkExplicitIntegrator Bases: :py:obj:`SundialsIntegrator`, :py:obj:`Integrator` The multistep ArkODE explicit integrator from the SUNDIALS suite .. py:method:: getAdaptiveStepping() -> bool Report whether adaptive step-size control is enabled. :returns: True when ARKODE controls the step size adaptively. .. py:method:: getErrorContributions() -> Annotated[numpy.typing.NDArray[numpy.float64], [m, 1]] Get the error contribution for each state. :returns: A vector with the error contribution for each state. .. py:method:: getOptions() -> SundialsIntegratorOptions Get the options associated with the integrator. :returns: The options associated with the integrator. .. py:method:: getVars() -> ArkExplicitIntegratorVars .. py:method:: setAdaptiveStepping(use_adaptive_steps: bool) -> None Select adaptive or fixed-step integration. :param use_adaptive_steps: True for adaptive stepping; false for fixed stepping. .. py:method:: setFixedStepSize(fixed_step_size: SupportsFloat | SupportsIndex) -> None Set a fixed step size in fixed-step mode. Call setAdaptiveStepping(false) to enable fixed stepping. ARKODE may take a smaller final step only to reach the requested target time exactly. :param fixed_step_size: Positive fixed step size in seconds. .. py:data:: ArkExplicitIntegratorOptions .. py:class:: ArkExplicitIntegratorVars Bases: :py:obj:`SundialsIntegratorVars` The Vars for the ArkExplicitIntegrator class. .. py:class:: ArkImplicitIntegrator Bases: :py:obj:`SundialsImplicitIntegrator` The (implicit) Adaptive Runge-Kutta integrator from the SUNDIALS suite .. py:class:: PredictorMethod(*args, **kwds) Bases: :py:obj:`enum.Enum` Create a collection of name/value pairs. Example enumeration: >>> class Color(Enum): ... RED = 1 ... BLUE = 2 ... GREEN = 3 Access them by: - attribute access: >>> Color.RED - value lookup: >>> Color(1) - name lookup: >>> Color['RED'] Enumerations can be iterated over, and know how many members they have: >>> len(Color) 3 >>> list(Color) [, , ] Methods can be added to enumerations, and members can have their own attributes -- see the documentation for details. .. py:attribute:: CUTOFF_ORDER :type: ClassVar[ArkImplicitIntegrator] .. py:attribute:: MAXIMUM_ORDER :type: ClassVar[ArkImplicitIntegrator] .. py:attribute:: TRIVIAL :type: ClassVar[ArkImplicitIntegrator] .. py:attribute:: VARIABLE_ORDER :type: ClassVar[ArkImplicitIntegrator] .. py:method:: getAdaptiveStepping() -> bool Return whether adaptive stepping is enabled. .. py:method:: getErrorContributions() -> Annotated[numpy.typing.NDArray[numpy.float64], [m, 1]] Get the error contribution for each state. :returns: A vector with the error contribution for each state. .. py:method:: getOptions() -> ArkImplicitIntegratorOptions Get the options associated with the integrator. :returns: The options associated with the integrator. .. py:method:: getVars() -> ArkImplicitIntegratorVars .. py:method:: setAdaptiveStepping(use_adaptive_steps: bool) -> None Enable or disable adaptive stepping. .. py:method:: setFixedStepSize(fixed_step_size: SupportsFloat | SupportsIndex) -> None Set the fixed step size in seconds. .. py:class:: ArkImplicitIntegratorOptions Bases: :py:obj:`SundialsImplicitIntegratorOptions` Options specific to the implicit ARKODE integrator. .. py:property:: predictor_method :type: ArkImplicitIntegrator Implicit-stage predictor used by ARK implicit. .. py:class:: ArkImplicitIntegratorVars Bases: :py:obj:`SundialsImplicitIntegratorVars` The Vars for the ArkImplicitIntegrator class. .. py:class:: CVodeIntegrator Bases: :py:obj:`SundialsImplicitIntegrator` The multistep CVode integrator from the SUNDIALS suite .. py:method:: estimateDynamicsJacobian() -> Annotated[numpy.typing.NDArray[numpy.float64], [m, n]] Estimate the current RHS Jacobian; columns identify perturbed state indices. This explicit diagnostic performs extra RHS calls and restores the base state. .. py:method:: getDetectStalls() -> bool Return whether automatic stall monitoring and tracing are enabled. .. py:method:: getErrorContributions() -> Annotated[numpy.typing.NDArray[numpy.float64], [m, 1]] Get the error contribution for each state. :returns: A vector with the error contribution for each state. .. py:method:: getLastAdvanceErrorTestFailures() -> int Return error-test failures in the most recent monitored CVODE advance. .. py:method:: getLastAdvanceRhsEvals() -> int Return RHS evaluations in the most recent monitored CVODE advance. .. py:method:: getLastAdvanceSteps() -> int Return accepted steps in the most recent monitored CVODE advance. .. py:method:: getOptions() -> CVodeIntegratorOptions Get the options associated with the integrator. :returns: The options associated with the integrator. .. py:method:: getStallCount() -> int Return the number of flagged advances since the last hard reset. .. py:method:: getStallLogFile() -> str Return the configured stall log filename, or empty when disabled. .. py:method:: getVars() -> CVodeIntegratorVars .. py:method:: setDetectStalls(enabled: bool) -> None Toggle automatic stall monitoring and its timestamped trace file. .. py:method:: setEtaFixedStepBounds(eta_min_fx: SupportsFloat | SupportsIndex, eta_max_fx: SupportsFloat | SupportsIndex) -> None Experimental: retain step size for proposed ratios strictly between the bounds. :param lower: Finite lower bound in [0, 1]; raising it permits more decreases. :param upper: Finite upper bound >= 1 and > lower; raising it suppresses more increases. .. seealso:: https://sundials.readthedocs.io/en/latest/cvode/Usage/index.html#c .CVodeSetEtaFixedStepBounds .. py:method:: setMaxOrder(order: SupportsInt | SupportsIndex) -> None Set the maximum multistep order; zero restores the method default. Lowering below active history restarts that history at the current state/time, preserving cumulative work counters. Invalid values leave options unchanged. :param order: Zero, or 1..12 for Adams / 1..5 for BDF. .. py:method:: setStabilityLimitDetection(enabled: bool) -> None Experimental: toggle BDF stability-limit detection. May reset or reduce num_stab_lim_order_reductions. :param enabled: True only for BDF; false is supported for every CVODE preset. .. seealso:: https://sundials.readthedocs.io/en/latest/cvode/Usage/index.html#c .CVodeSetStabLimDet .. py:property:: detect_stalls :type: bool Enable automatic CVODE stall detection and timestamped HDF5 tracing. .. py:property:: stall_log_file :type: str Automatically generated HDF5 stall-trace filename, or empty while disabled. .. py:class:: CVodeIntegratorOptions Bases: :py:obj:`SundialsImplicitIntegratorOptions` CVODE multistep controls shared by its Adams and BDF presets. .. py:property:: eta_max_fx :type: float upper bound of the step-size ratio deadband after successful integration steps. .. seealso:: https://sundials.readthedocs.io/en/latest/cvode/Usage/index.html#c .CVodeSetEtaFixedStepBounds :type: Experimental .. py:property:: eta_min_fx :type: float lower bound of the step-size ratio deadband after successful integration steps. .. seealso:: https://sundials.readthedocs.io/en/latest/cvode/Usage/index.html#c .CVodeSetEtaFixedStepBounds :type: Experimental .. py:property:: max_order :type: int Maximum integration order; 0 uses the default (Adams 12, BDF 5). .. seealso:: https://sundials.readthedocs.io/en/latest/cvode/Usage/index.html#c .CVodeSetMaxOrd .. py:property:: stability_limit_detection :type: bool reduce BDF order when a stability limit is detected (BDF only). Toggling may reset or reduce num_stab_lim_order_reductions. .. seealso:: https://sundials.readthedocs.io/en/latest/cvode/Usage/index.html#c .CVodeSetStabLimDet :type: Experimental .. py:class:: CVodeIntegratorVars Bases: :py:obj:`SundialsImplicitIntegratorVars` The Vars for the CVodeIntegrator class. .. py:property:: curr_gamma :type: Karana.Core._KCore_pybind11_Py._VarDouble Current CVODE gamma coefficient in I - gamma J. Returns -1.0 (unavailable) before the first accepted step after initialization or reset. .. py:property:: curr_order :type: Karana.Core._KCore_pybind11_Py._VarInt Order selected for the next CVODE step; zero immediately after initialization/reset. .. py:property:: last_advance_error_test_failures :type: Karana.Core._KCore_pybind11_Py._VarLong Error-test failures in the last monitored advance; -1 while monitoring is inactive. .. py:property:: last_advance_rhs_evals :type: Karana.Core._KCore_pybind11_Py._VarLong RHS evaluations in the last monitored advance; -1 while monitoring is inactive. .. py:property:: last_advance_steps :type: Karana.Core._KCore_pybind11_Py._VarLong Accepted steps in the last monitored advance; -1 while monitoring is inactive. .. py:property:: last_order :type: Karana.Core._KCore_pybind11_Py._VarInt Integration method order used during last step .. py:property:: num_quasi_full_refreshes :type: Karana.Core._KCore_pybind11_Py._VarLong Complete finite-difference refreshes performed by quasi-Newton; -1 when not selected. .. py:property:: num_quasi_partial_refreshes :type: Karana.Core._KCore_pybind11_Py._VarLong Motion-ranked partial refreshes performed by quasi-Newton; -1 when not selected. .. py:property:: num_quasi_probes :type: Karana.Core._KCore_pybind11_Py._VarLong Fixed-time secant probes performed by quasi-Newton; -1 when not selected. .. py:property:: num_quasi_refreshed_columns :type: Karana.Core._KCore_pybind11_Py._VarLong Finite-difference columns refreshed by quasi-Newton; -1 when not selected. .. py:property:: num_quasi_rhs_evals :type: Karana.Core._KCore_pybind11_Py._VarLong Extra RHS evaluations performed by quasi-Newton; -1 when not selected. .. py:property:: num_stab_lim_order_reductions :type: Karana.Core._KCore_pybind11_Py._VarLong BDF stability-limit order reductions; -1 when detection is disabled. Toggling detection may reset or reduce this count. .. py:property:: stall_count :type: Karana.Core._KCore_pybind11_Py._VarLong Detected stall advances since hard reset; -1 while monitoring is inactive. .. py:class:: EulerIntegrator Bases: :py:obj:`Integrator` The fixed-step Euler one step integrator. .. py:class:: ExplicitVerletIntegrator Bases: :py:obj:`PartitionedIntegrator` Explicit kick-drift-kick Verlet for separable Q/U equations. This implementation assumes that the first `num_q_states` are Q and the rest U coordinates. Each advanceTo call takes one step of size h using the full-state callback: \f[ U_{1/2}=U_n+\frac h2 g(t_n,Q_n),\qquad Q_{n+1}=Q_n+h f(U_{1/2}),\qquad U_{n+1}=U_{1/2}+\frac h2 g(t_{n+1},Q_{n+1}). \f] Second-order accuracy requires separable dynamics: Qdot = f(U) and Udot = g(t, Q). If the dynamics are not separable this method falls back to first order, in which case using Euler or RK4 is more appropriate. Unequal sizes, such as one Q state and two U states, still give second-order accuracy for the smooth separable equations above. Symplecticity is a separate property: standard Hamiltonian position-momentum pairs require equal Q and U counts and equations from a separable Hamiltonian. A full three- dimensional state cannot be symplectic. If an extra state is constant or redundant, a reduced even-dimensional system may still be symplectic; this depends on the equations and how the reduced state is defined. .. py:class:: Integrator Bases: :py:obj:`Karana.Core.BaseWithVars` Base class for numerical integrators .. py:method:: create() -> None :staticmethod: .. py:method:: advanceTo(to_t: SupportsFloat | SupportsIndex | numpy.timedelta64) -> numpy.timedelta64 Method to advance the system state to a specified time :param to_t: the desired end time :returns: the actual end time .. py:method:: derivFunction() -> collections.abc.Callable[[SupportsFloat | SupportsIndex | numpy.timedelta64, Annotated[numpy.typing.ArrayLike, numpy.float64, [m, 1]], Annotated[numpy.typing.ArrayLike, numpy.float64, [m, 1]]], bool] Return the derivative function :returns: the derivative function .. py:method:: getIntegratorType() -> IntegratorType Get the IntegratorType for this integrator. :returns: The IntegratorType for this integrator. .. py:method:: getOptions() -> IntegratorOptions Get the options associated with the integrator. :returns: The options associated with the integrator. .. py:method:: getTime() -> numpy.timedelta64 Return the current integrator time :returns: the integrator state time .. py:method:: getX() -> Annotated[numpy.typing.NDArray[numpy.float64], [m, 1]] Return the current integrator state :returns: the integrator state vector .. py:method:: hardReset(num_states: SupportsInt | SupportsIndex, num_q_states: SupportsInt | SupportsIndex) -> None Replace the state size and Q partition count :param num_states: the new state size :param num_q_states: Number of leading Q states; zero means no partition is specified. .. py:method:: nQ() -> int Return the number of leading Q states, or zero for an unspecified partition. :returns: The Q partition size supplied at construction or hard reset. .. py:method:: nStates() -> int Return the state size :returns: the integrator state size .. py:method:: setVerboseTracing(verbose: bool) -> None Tell the integrator to be very verbose; mostly used for debugging numerics in a brute-force approach. :param verbose: .. py:method:: softReset(new_t: SupportsFloat | SupportsIndex | numpy.timedelta64, new_x: Annotated[numpy.typing.ArrayLike, numpy.float64, [m, 1]]) -> None Reset the cached time and state and to the new values going forward :param new_t: the new time :param new_x: the new state .. py:method:: updateJacobian(arg0: Annotated[numpy.typing.ArrayLike, numpy.float64, [m, n]]) -> None Update the stored Jacobian matrix with the provided one This is currently an experimental feature - and not all integrators support the use of Jacobians. :param mat: the new Jacobian matrix .. py:class:: IntegratorOptions A struct with integrator options. This struct can be sub-classed by specialized classes to add custom options. .. py:class:: IntegratorType(*args, **kwds) Bases: :py:obj:`enum.Enum` Enum of integrator types. .. py:attribute:: ARKEXPLICIT :type: ClassVar[IntegratorType] .. py:attribute:: ARKEXPLICIT_CASH :type: ClassVar[IntegratorType] .. py:attribute:: ARKEXPLICIT_DOPRI :type: ClassVar[IntegratorType] .. py:attribute:: ARKEXPLICIT_FEHLBERG78 :type: ClassVar[IntegratorType] .. py:attribute:: ARKEXPLICIT_HUEN_EULER :type: ClassVar[IntegratorType] .. py:attribute:: ARKIMPLICIT :type: ClassVar[IntegratorType] .. py:attribute:: ARKIMPLICIT_DIRK23 :type: ClassVar[IntegratorType] .. py:attribute:: ARKIMPLICIT_ESDIRK45 :type: ClassVar[IntegratorType] .. py:attribute:: ARKIMPLICIT_SDIRK12 :type: ClassVar[IntegratorType] .. py:attribute:: ARKIMPLICIT_SDIRK34 :type: ClassVar[IntegratorType] .. py:attribute:: CVODE :type: ClassVar[IntegratorType] .. py:attribute:: CVODE_NEWTON :type: ClassVar[IntegratorType] .. py:attribute:: CVODE_NEWTON_QUASI_NEWTON :type: ClassVar[IntegratorType] .. py:attribute:: CVODE_STIFF :type: ClassVar[IntegratorType] .. py:attribute:: CVODE_STIFF_JFNK :type: ClassVar[IntegratorType] .. py:attribute:: CVODE_STIFF_QUASI_NEWTON :type: ClassVar[IntegratorType] .. py:attribute:: EULER :type: ClassVar[IntegratorType] .. py:attribute:: EXPLICIT_VERLET :type: ClassVar[IntegratorType] .. py:attribute:: IDA :type: ClassVar[IntegratorType] .. py:attribute:: NO_OP :type: ClassVar[IntegratorType] .. py:attribute:: RK4 :type: ClassVar[IntegratorType] .. py:method:: to_yaml(representer, node) :classmethod: Class method used to represent IntegratorType in a yaml file. .. py:method:: from_yaml(_, node) -> Self :classmethod: Construct a IntegratorType from yaml file data. .. py:method:: to_json(o: IntegratorType) -> dict[str, Any] :staticmethod: Class method used to represent IntegratorType in a json file. .. py:method:: from_json(d: dict[str, Any]) -> Self :classmethod: Construct a IntegratorType from json file data. .. py:class:: PartitionedIntegrator Bases: :py:obj:`Integrator` Abstract integrator for states packed as [Q, U]. This class provides validation checks used by child classes. .. py:class:: RK4Integrator Bases: :py:obj:`Integrator` Fixed-step Runge-Kutta 4th order integrator .. py:class:: SundialsImplicitIntegrator Bases: :py:obj:`SundialsIntegrator` Abstract base class for implicit Sundials integrators (CVode/ARKStep). This class manages linear and nonlinear solvers specifically, and adds options and vars relating to implicit integration. .. py:method:: getOptions() -> SundialsImplicitIntegratorOptions Get the options associated with the integrator. :returns: The options associated with the integrator. .. py:method:: setAndersonDamping(damping: SupportsFloat | SupportsIndex) -> None Set the Anderson damping factor to use for nonlinear solves; must be in (0, 1] and smaller means stronger damping. :param damping: Damping factor; pass a value of 1 for no damping. .. py:method:: setAndersonLength(length: SupportsInt | SupportsIndex) -> None Set the subspace size to use for Anderson acceleration. :param length: Damping factor; pass a value of 0 for no damping. .. py:method:: setJacobianEvalFrequency(frequency: SupportsInt | SupportsIndex) -> None Set the number of integration steps between Jacobian evaluations. :param frequency: Evaluation frequency; zero selects the SUNDIALS default. .. py:method:: setLinearSetupFrequency(frequency: SupportsInt | SupportsIndex) -> None Set the number of integration steps between linear-solver setups. :param frequency: Setup frequency; zero selects the SUNDIALS default. .. py:method:: setMaxNLIters(iters: SupportsInt | SupportsIndex) -> None Set the maximum nonlinear iterations. :param iters: Max iters to take before trying a smaller timestep. .. py:class:: SundialsImplicitIntegratorOptions Bases: :py:obj:`SundialsIntegratorOptions` Struct with options for this integrator .. py:property:: anderson_damping :type: float Anderson damping in (0, 1] used for implicit integrators with fixed- point solves. This is used to potentially speed up internal iterations by reusing past iterates (within the same time step). A value of 1 indicates no damping, and smaller values imply a "stronger" damping. .. py:property:: anderson_length :type: int Number of past iterates to consider with Anderson acceleration. .. py:property:: jacobian_eval_frequency :type: int Number of integration steps between implicit Jacobian evaluations. This option applies to CVODE Newton and ARKODE implicit solvers. A value of zero selects the backend's SUNDIALS default. .. py:property:: linear_setup_frequency :type: int Number of integration steps between implicit linear-solver setups. This option applies to CVODE Newton and ARKODE implicit solvers. A value of zero selects the backend's SUNDIALS default. .. py:property:: max_nl_iters :type: int Maximum number of nonlinear iterations before we try a smaller step size .. py:property:: use_jacobian :type: bool the application must keep the stored Jacobian current with updateJacobian(); kdFlex does not compute or refresh it automatically. :type: Experimental .. py:class:: SundialsImplicitIntegratorVars Bases: :py:obj:`SundialsIntegratorVars` The Vars for the SundialsImplicitIntegrator class. .. py:property:: num_jac_evals :type: Karana.Core._KCore_pybind11_Py._VarLong Number of calls made to the linear solver interface's Jacobian function. .. note:: Returns -1 when no linear solver is attached. .. note:: Before SUNDIALS 7.6, the stale native value is ignored after a soft reset until the next successful advance. .. py:property:: num_lin_conv_fails :type: Karana.Core._KCore_pybind11_Py._VarLong Number of linear solver convergence failures. .. note:: Returns -1 when no linear solver is attached. .. note:: Before SUNDIALS 7.6, the stale native value is ignored after a soft reset until the next successful advance. .. py:property:: num_lin_iters :type: Karana.Core._KCore_pybind11_Py._VarLong Number of linear iterations. .. note:: Returns -1 when no linear solver is attached. .. note:: Before SUNDIALS 7.6, the stale native value is ignored after a soft reset until the next successful advance. .. py:property:: num_lin_rhs_evals :type: Karana.Core._KCore_pybind11_Py._VarLong Number of RHS/derivative calls used to estimate Jacobians. .. note:: Returns -1 when no linear solver is attached. .. note:: Before SUNDIALS 7.6, the stale native value is ignored after a soft reset until the next successful advance. .. py:property:: num_lin_solver_setups :type: Karana.Core._KCore_pybind11_Py._VarLong Number of times the linear solver setup routine was called. .. note:: Returns -1 when no linear solver is attached. .. py:property:: num_nonlin_conv_fails :type: Karana.Core._KCore_pybind11_Py._VarLong Number of nonlinear solver convergence failures. .. note:: In SUNDIALS 6.2 and newer this counts every failed nonlinear solve, not only rejected timesteps. ARKODE accumulates it for the nonlinear solver object's lifetime, so soft resets do not reset or cache the native counter. .. py:property:: num_nonlin_iters :type: Karana.Core._KCore_pybind11_Py._VarLong Cumulative number of nonlinear iterations. .. note:: ARKODE reports this value for the lifetime of its nonlinear solver object, so soft resets do not reset or cache the native counter. .. py:property:: num_step_solve_fails :type: Karana.Core._KCore_pybind11_Py._VarLong Number of rejected timesteps due to nonlinear solve failure. .. note:: This statistic is distinct from nonlinear convergence failures in SUNDIALS 6.2 and newer. Starting with SUNDIALS 7.6, CVODE excludes inequality-constraint failures. .. py:class:: SundialsIntegrator Bases: :py:obj:`Integrator` Abstract base class for Sundials-related integrators. This class helps manage shared memory, options, and vars. It defines several pure virtual methods for the subclass to override and satisfies all virtual functions of an Integrator. .. py:method:: getOptions() -> SundialsIntegratorOptions Get the options associated with the integrator. :returns: The options associated with the integrator. .. py:method:: setAtol(atol: SupportsFloat | SupportsIndex) -> None Set the scalar absolute tolerance used for controlling error vs runtime. :param atol: The scalar atol to use for all state variables. .. py:method:: setRtol(rtol: SupportsFloat | SupportsIndex) -> None Set the relative tolerance used for controlling error vs runtime. :param rtol: The rtol to use for all state variables. .. py:method:: setVectorAtol(atol_vec: Annotated[numpy.typing.ArrayLike, numpy.float64, [m, 1]] | None) -> None Set the vector absolute tolerance used for controlling error vs runtime, or a null value to fall back to scalar atol. :param atol_vec: The optional vector atol to use; must have same length as state vector or be null. .. py:class:: SundialsIntegratorOptions Bases: :py:obj:`IntegratorOptions` Struct with options for this integrator .. py:property:: atol :type: float The desired absolute tolerance used to control the integrator error .. py:property:: atol_vec :type: Annotated[numpy.typing.NDArray[numpy.float64], [m, 1]] | None The desired absolute tolerance vector used to control the integrator error. This can be used rather than a scalar tolerance to set different values for different states. .. py:property:: max_num_steps :type: int The maximum number of steps the solver can take before throwing a too much work error. .. py:property:: min_step_size :type: float Minimum acceptable step size before we error out. .. py:property:: rtol :type: float The desired relative tolerance used to control the integrator error .. py:class:: SundialsIntegratorVars Bases: :py:obj:`Karana.Core.BaseVars` The Vars for the SundialsIntegrator class. .. py:property:: curr_step :type: Karana.Core._KCore_pybind11_Py._VarDouble Current step size to try on next advance call .. py:property:: last_step :type: Karana.Core._KCore_pybind11_Py._VarDouble Last successful step size .. py:property:: num_err_test_fails :type: Karana.Core._KCore_pybind11_Py._VarLong Cumulative number of error test failures due to too large of step size .. py:property:: num_q_states :type: Karana.Core._KCore_pybind11_Py._VarSizeT Current number of leading Q states; zero means unspecified. .. py:property:: num_rhs_evals :type: Karana.Core._KCore_pybind11_Py._VarLong Cumulative number of RHS calls taken by the solver .. py:property:: num_states :type: Karana.Core._KCore_pybind11_Py._VarSizeT Current total state-vector size, updated after hard reset. .. py:property:: num_steps :type: Karana.Core._KCore_pybind11_Py._VarLong Cumulative number of internal steps taken by the solver .. py:function:: createIntegrator(integrator_type: IntegratorType, num_states: SupportsInt | SupportsIndex, num_q_states: SupportsInt | SupportsIndex, deriv_fn: collections.abc.Callable, options: IntegratorOptions = None) -> Integrator createIntegrator(integrator_type: IntegratorType, num_states: SupportsInt | SupportsIndex, num_q_states: SupportsInt | SupportsIndex, num_algebraic: SupportsInt | SupportsIndex, residuals_fn: collections.abc.Callable[[SupportsFloat | SupportsIndex | numpy.timedelta64, Annotated[numpy.typing.ArrayLike, numpy.float64, [m, 1]], Annotated[numpy.typing.ArrayLike, numpy.float64, [m, 1]], Annotated[numpy.typing.ArrayLike, numpy.float64, [m, 1]]], None], options: IntegratorOptions = None) -> Integrator Factory method for creating DAE Integrator instances :param integrator_type: the type of integrator to create :param num_states: the length of the states vector (continuous+algebraic) :param num_q_states: Number of leading Q states; zero means no partition is specified. :param num_algebraic: the number of algebraic values :param residuals_fn: the residuals function :param options: options for the integrator :returns: a new DAE Integrator instance .. py:function:: strToIntegratorType(arg0: str) -> IntegratorType Convert string to IntegratorType enum. :param str: The name of the integrator type. :returns: The IntegratorType associated with the string.