DIRKStep

DIRKStep provides a diagonally implicit Runge–Kutta integrator that solves stage systems with the cached Newton–Krylov helpers supplied by cubie.integrators.matrix_free_solvers. The factory consumes DIRKTableau instances, exposing L-stable SDIRK and ESDIRK schemes for stiff problems while preserving adaptive error control through embedded weights.

class cubie.integrators.algorithms.DIRKStep(precision: type[float16] | type[float32] | type[float64] | dtype[float16] | dtype[float32] | dtype[float64], n: int, evaluate_f: Callable | None = None, evaluate_observables: Callable | None = None, evaluate_driver_at_t: Callable | None = None, get_solver_helper_fn: Callable | None = None, tableau: DIRKTableau = DIRKTableau(a=((0.16666666666666666, 0.0, 0.0), (0.6666666666666666, 0.16666666666666666, 0.0), (0.16666666666666666, 0.6666666666666666, 0.16666666666666666)), b=(0.16666666666666666, 0.6666666666666666, 0.16666666666666666), c=(0.0, 0.5, 1.0), order=4, b_hat=None), n_drivers: int = 0, **kwargs)[source]

Bases: ODEImplicitStep

Diagonally implicit Runge–Kutta step with an embedded error estimate.

__init__(precision: type[float16] | type[float32] | type[float64] | dtype[float16] | dtype[float32] | dtype[float64], n: int, evaluate_f: Callable | None = None, evaluate_observables: Callable | None = None, evaluate_driver_at_t: Callable | None = None, get_solver_helper_fn: Callable | None = None, tableau: DIRKTableau = DIRKTableau(a=((0.16666666666666666, 0.0, 0.0), (0.6666666666666666, 0.16666666666666666, 0.0), (0.16666666666666666, 0.6666666666666666, 0.16666666666666666)), b=(0.16666666666666666, 0.6666666666666666, 0.16666666666666666), c=(0.0, 0.5, 1.0), order=4, b_hat=None), n_drivers: int = 0, **kwargs) → None[source]

Initialise the DIRK step configuration.

This constructor creates a DIRK step object and automatically selects appropriate default step controller settings based on whether the tableau has an embedded error estimate. Tableaus with error estimates default to adaptive stepping (PI controller), while errorless tableaus default to fixed stepping.

Parameters:

  • precision – Floating-point precision for CUDA computations.

  • n – Number of state variables in the ODE system.

  • evaluate_f – Device function for evaluating f(t, y) right-hand side.

  • evaluate_observables – Device function computing system observables.

  • evaluate_driver_at_t – Optional device function evaluating drivers at arbitrary times.

  • get_solver_helper_fn – Factory function returning solver helper for Jacobian operations.

  • tableau – DIRK tableau describing the coefficients. Defaults to DEFAULT_DIRK_TABLEAU.

  • n_drivers – Number of driver variables in the system.

  • **kwargs – Optional parameters passed to config classes. See DIRKStepConfig, ImplicitStepConfig, and solver config classes for available parameters. None values are ignored.

Notes

The step controller defaults are selected dynamically:

  • If tableau.has_error_estimate is True: Uses DIRK_ADAPTIVE_DEFAULTS (PI controller)

  • If tableau.has_error_estimate is False: Uses DIRK_FIXED_DEFAULTS (fixed-step controller)

This automatic selection prevents incompatible configurations where an adaptive controller is paired with an errorless tableau.

build_implicit_helpers() → None[source]

Construct the nonlinear solver chain used by implicit methods.

build_step(evaluate_f: Callable, evaluate_observables: Callable, evaluate_driver_at_t: Callable | None, solver_function: Callable, numba_precision: type, n: int, n_drivers: int) → StepCache[source]

Compile the DIRK device step.

property is_adaptive: bool

Return True because an embedded error estimate is produced.

property is_implicit: bool

Return True because the method solves nonlinear systems.

property is_multistage: bool

Return True as the method has multiple stages.

property order: int

Return the classical order of accuracy.

register_buffers() → None[source]

Register buffers according to locations in compile settings.

property threads_per_step: int

Return the number of CUDA threads that advance one state.

class cubie.integrators.algorithms.generic_dirk.DIRKStepConfig(precision: type[float16] | type[float32] | type[float64] | dtype[float16] | dtype[float32] | dtype[float64], n: int = 1, n_drivers: int = 0, evaluate_f: Callable | None = None, evaluate_observables: Callable | None = None, evaluate_driver_at_t: Callable | None = None, get_solver_helper_fn: Callable | None = None, beta: float = 1.0, gamma: float = 1.0, M: ndarray | MutableDenseMatrix = Matrix([[1]]), preconditioner_order: int = 2, solver_function=None, tableau: DIRKTableau = DIRKTableau(a=((0.16666666666666666, 0.0, 0.0), (0.6666666666666666, 0.16666666666666666, 0.0), (0.16666666666666666, 0.6666666666666666, 0.16666666666666666)), b=(0.16666666666666666, 0.6666666666666666, 0.16666666666666666), c=(0.0, 0.5, 1.0), order=4, b_hat=None), stage_increment_location: str = 'local', stage_base_location: str = 'local', accumulator_location: str = 'local', stage_rhs_location: str = 'local')[source]

Bases: ImplicitStepConfig

Configuration describing the DIRK integrator.

accumulator_location: str
stage_base_location: str
stage_increment_location: str
stage_rhs_location: str
tableau: DIRKTableau