Integrators

RK45Integrator

openscvx.integrators.solve_ivp_rk45(f: Callable[[jnp.ndarray, jnp.ndarray, Any], jnp.ndarray], tau_final: float, y_0: jnp.ndarray, args, tau_0: float = 0.0, num_substeps: int = 50, is_not_compiled: bool = False)

Solve an initial-value ODE problem using fixed-step RK45 integration.

Parameters:

Name	Type	Description	Default
f	Callable[[ndarray, ndarray, Any], ndarray]	ODE right-hand side; signature f(t, y, *args) -> dy/dt.	required
tau_final	float	Final integration time.	required
y_0	ndarray	Initial state at tau_0.	required
args	tuple	Extra arguments to pass to f.	required
tau_0	float	Initial time. Defaults to 0.0.	0.0
num_substeps	int	Number of output time points. Defaults to 50.	50
is_not_compiled	bool	If True, use Python loop instead of JAX lax.fori_loop. Defaults to False.	False

Returns:

Type	Description
	jnp.ndarray: Array of shape (num_substeps, state_dim) with solution at each time.

openscvx.integrators.rk45_step(f: Callable[[jnp.ndarray, jnp.ndarray, Any], jnp.ndarray], t: jnp.ndarray, y: jnp.ndarray, h: float, *args) -> jnp.ndarray

Perform a single RK45 (Runge-Kutta-Fehlberg) integration step.

This implements the classic Dorman-Prince coefficients for an explicit 4(5) method, returning the fourth-order estimate.

Parameters:

Name	Type	Description	Default
f	Callable[[ndarray, ndarray, Any], ndarray]	ODE right-hand side; signature f(t, y, *args) -> dy/dt.	required
t	ndarray	Current time.	required
y	ndarray	Current state vector.	required
h	float	Step size.	required
*args		Additional arguments passed to f.	()

Returns:

Type	Description
ndarray	jnp.ndarray: Next state estimate at t + h.

Diffrax Integrators

openscvx.integrators.solve_ivp_diffrax(f: Callable[[jnp.ndarray, jnp.ndarray, Any], jnp.ndarray], tau_final: float, y_0: jnp.ndarray, args, tau_0: float = 0.0, num_substeps: int = 50, solver_name: str = 'Dopri8', rtol: float = 0.001, atol: float = 1e-06, extra_kwargs=None)

Solve an initial-value ODE problem using a Diffrax adaptive solver.

Parameters:

Name	Type	Description	Default
f	Callable[[ndarray, ndarray, Any], ndarray]	ODE right-hand side; f(t, y, *args).	required
tau_final	float	Final integration time.	required
y_0	ndarray	Initial state at tau_0.	required
args	tuple	Extra arguments to pass to f in the solver term.	required
tau_0	float	Initial time. Defaults to 0.0.	0.0
num_substeps	int	Number of save points between tau_0 and tau_final. Defaults to 50.	50
solver_name	str	Key into SOLVER_MAP for the Diffrax solver class. Defaults to "Dopri8".	'Dopri8'
rtol	float	Relative tolerance for adaptive stepping. Defaults to 1e-3.	0.001
atol	float	Absolute tolerance for adaptive stepping. Defaults to 1e-6.	1e-06
extra_kwargs	dict	Additional keyword arguments forwarded to diffeqsolve.	None

Returns:

Type	Description
	jnp.ndarray: Solution states at the requested save points, shape (num_substeps, state_dim).

Raises:

Type	Description
ValueError	If solver_name is not in SOLVER_MAP.

openscvx.integrators.solve_ivp_diffrax_prop(f: Callable[[jnp.ndarray, jnp.ndarray, Any], jnp.ndarray], tau_final: float, y_0: jnp.ndarray, args, tau_0: float = 0.0, num_substeps: int = 50, solver_name: str = 'Dopri8', rtol: float = 0.001, atol: float = 1e-06, extra_kwargs=None, save_time: jnp.ndarray = None, mask: jnp.ndarray = None)

Solve an initial-value ODE problem using a Diffrax adaptive solver. This function is specifically designed for use in the context of trajectory optimization and handles the nonlinear single-shot propagation of state variables in undilated time.

Parameters:

Name	Type	Description	Default
f	Callable[[ndarray, ndarray, Any], ndarray]	ODE right-hand side; signature f(t, y, *args) -> dy/dt.	required
tau_final	float	Final integration time.	required
y_0	ndarray	Initial state at tau_0.	required
args	tuple	Extra arguments to pass to f in the solver term.	required
tau_0	float	Initial time. Defaults to 0.0.	0.0
num_substeps	int	Number of save points between tau_0 and tau_final. Defaults to 50.	50
solver_name	str	Key into SOLVER_MAP for the Diffrax solver class. Defaults to "Dopri8".	'Dopri8'
rtol	float	Relative tolerance for adaptive stepping. Defaults to 1e-3.	0.001
atol	float	Absolute tolerance for adaptive stepping. Defaults to 1e-6.	1e-06
extra_kwargs	dict	Additional keyword arguments forwarded to diffeqsolve.	None
save_time	ndarray	Time points at which to evaluate the solution. Must be provided for export compatibility.	None
mask	ndarray	Boolean mask for the save_time points.	None

Returns:

Type	Description
	jnp.ndarray: Solution states at the requested save points, shape (num_substeps, state_dim).

Raises: ValueError: If solver_name is not in SOLVER_MAP or if save_time is not provided.